Zeiltheorie inleiding Hier wil ik de betere theorieën achter het zeilen

Transcription

http://zeilplan.net/leren/theorie/inleiding.htm
Zeiltheorie
inleiding
De foute vleugeltheorie
de meest gebruikte vleugeltheorie en
waarom hij fout is.
Werking van de zeilen
Hier wil ik de betere theorieën achter het zeilen promoten.
Klik hier rechts op een link om meer over dat onderwerp te
weten te komen.
Uitleg over de werking van het
vleugelprofiel van de zeilen.
Proefjes
Enkele proefjes om de theorie te te
verduidelijken.
Deze informatie is ontstaan doordat er in de loop der tijd nogal
wat onzin theorieën zijn ontstaan waar je ook nog eens niks aan Koppels en Krachten
Ook dit 'lastige' onderwerp nog maar
hebt. Daar wil ik verandering in brengen.
even uitgediept.
Foute theorieën zijn zo wijdverbreid dat ze zelf op scholen en
zeilscholen worden onderwezen, waardoor theorie niet meer
toepasbaar is.
Ik hoop dat jij wat hebt aan de inhoud van deze site, en jij
beter zult weten na dit te hebben gelzezen!
Groet van Pim Geurts.
Het onderwaterschip
De Kiel en het roer.
Weerstand
uitleg van hoe de scheepsweerstand
werkt.
Stabiliteit
Waarom blijft een boot overeind?
trim
De basis van de boottrim.
Veelgestelde vragen
Enkele veelgestelde vragen en hun
antwoord.
Links
Links naar de bronnen en
achtergronden van deze theorie.
http://zeilplan.net/leren/theorie/inleiding.htm24-1-2004 17:22:16
http://zeilplan.net/leren/theorie/tekst.php?tekst=foutetheorie.txt
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Hoe werkt een vleugel niet.
Voorbeeld van de meest gehoorde foute theorie:
Kijk zo ziet een vleugel eruit:
Zoals je ziet is de bovenkant rond en de onderkant vlak.
Om langs de bovenkant te gaan moet je een grotere afstand afleggen dan langs de onderkant.
Als er lucht langs de vleugel gaat zal dit zich splitsen in lucht die boven langs gaat en lucht die onderlangs
gaat.
De lucht die bovenlangs gaat zal tegelijkertijd aankomen bij de achterkant als de lucht die onderlangs
gaat, Dat kan niet anders, anders zou er een gat in de lucht ontstaan, en dat kan dus niet.
De lucht die bovenlangs gaat zal dus in dezelfde tijd een grotere afstand afleggen, en zal dus
sneller moeten gaan.
Bernoulli zei dat snellere lucht een lagere druk heeft. Dit kan ik bewijzen met het volgende “trucje”.
Als ik bovenlangs een blaadje blaas gaat de lucht daar sneller, en krijg je daar dus een lagere druk en
wordt het blaadje omhoog gezogen.
Dus, omdat de lucht bovenlangs de vleugel een langere weg moet afleggen zal de lucht daar
sneller gaan, en dus een lagere druk hebben, en zo de vleugel als het ware “omhoogzuigen”
http://zeilplan.net/leren/theorie/tekst.php?tekst=foutetheorie.txt (1 of 7)24-1-2004 17:22:52
Een zeil werkt eigenlijk net zo. Een zeil is weliswaar even lang aan loef als aan lij, maar omdat
het bolling heeft is de binnenbocht toch korter dan de buitenbocht, waardoor de lucht aan lij sneller zal
gaan, en het zeil dus als het ware naar lij wordt getrokken.
Wat heb je hier nu aan om te weten: hoe meer bolling hoe meer power (want meer weglengteverschil) en
de zeilkracht werkt haaks op je zeil.
"
Dit verhaal heb ik verschillende malen gehoord, en ook enkele malen zelf verteld als zeilinstructeur.
Zelfs toen ik in mijn studie mijn eerste lessen stromingsleer over vleugels kreeg heb ik gedacht dat dit
verhaal klopte, en gebruikte het naast andere theorieën.
Pas vrij laat ben ik echt gaan nadenken en kwam erachter dat de theorie van geen kanten klopte.
Vanaf nu noem ik deze theorie de “gelijk aankomen” theorie.
Enkele kleine experimenten om te laten zien dat “gelijk aankomen theorie” gewoon niet klopt:
Super vleugel
Volgens de “gelijk aankomen” theorie zou deze vleugel zeer goed moeten werken, want er is een groot
weglengteverschil Tocht wordt dit type vleugel niet gebruikt omdat hij niet zo goed werkt.
Vliegtuig ondersteboven
Veel kleine vliegtuigen kunnen prima ondersteboven vliegen.
Vroeger dacht ik altijd dat men dan als het ware de bolling omdraaide door die platen aan het eind
van de vleugel de andere kant op te zetten. Toen ik zag dat die platen nooit groot genoeg waren om dat
te kunnen doen, en zag dat men dat ook gewoon niet deed snapte ik niks meer van de “gelijk aankomen”
theorie
zo dus
en niet zo
Vlakke plaat geeft ook lift
Een rechte plaat geeft ook lift, als hij onder een hoek met de luchtstroom wordt geplaatst. Dit kun je al
zien als je met een vel papier door de lucht beweegt. Vaak krijgt dat stuk papier dan ook nog eens een
bolling de verkeerde kant op, en wil toch omhoog.
Een niet aangetrokken doorgelat zeil geeft geen liftkracht.
Als je een doorgelat zeil niet aantrekt geeft het geen lift
Toch is er dan nog steeds hetzelfde weglengte verschil, dus je zou nog steeds dezelfde liftkracht
verwachten.
Ook het kracht verschil tussen een iets te slap aangetrokken grootzeil en een normaal aangetrokken zeil
zou er niet moeten zijn aangezien de weglengte verschillen hetzelfde blijven.
Lucht komt niet tegelijk aan bij de achterkant van het zeil.
Op een gegeven moment stond ik te roken op het voordek en zag dat mijn rookpuf absoluut niet
gelijk aankwam bij de achterrand van het zeil. Ook niet met de fok ingerold.
Toen ben ik gaan spelen met touwtjes in mijn zeil (telltales).
Bij sommige zeilstanden stonden de telltales aan loef slap naar beneden, en aan lij netjes naar
achter. Aan loef was er dus bijna geen snelheid, terwijl je zou verwachten dat er maar een redelijk klein
verschil zou zijn tussen loef en lij, aangezien de weglengte toch ook niet zo heel
veel verschilt.
Daar heb ik geen foto’s van. Wel van dit vleugelprofiel met pufjes rook in de stroming. De
wokjes rook zitten aan de voorkant gelijk, aan de achterkant duidelijk niet meer.
Als je het weglengte verschil uitrekent is de lift veel minder als gemeten.
Ergens kwam ik dit soort plaatje tegen van een vleugelprofiel met de bijbehorende lift coëfficiënt (Cm) en
natuurlijk drag (Cd)
Ik ging het weglengteverschil opmeten bij een hoek van 0, daarmee kan je het snelheidsverschil bepalen,
en daarmee de liftkracht.
Ik kwam uit op een liftwaarde die 5 tot 50 keer zo laag als hier werd opgegeven.
Afhankelijk van hoe ik het weglengteverschil precies meette.
Toch vreemd?? of niet?
Onder blaadje blazen
Een heel simpele test om te laten zien dat “als de lucht sneller gaat is daar een lagere druk en
wordt de vleugel daar naartoe gezogen” niet waar is vond ik de test dat als je onder een blaadje
doorblaast het blaadje juist omhoog gaat, dus juist van de snelbewegende lucht af.
Een kleine variatie hierop:
Als je het blaadje eerst opgerold hebt zodat het uiteinde omhoog gaat door de bolling en je er dan
voverheen blaast, gaat het wel naar beneden.
--Plaatje blazen over blaadje wat omhoogkrultOpvallend niet?
Ik hoop dat ik met bovenstaand verhaal duidelijk heb gemaakt dat de “gelijk aankomen theorie”
de werkelijkheid wel erg slecht beschrijft. Eigenlijk gewoon fout is.
Vergeet deze foute theorie alsjeblieft.
In het Werking van de zeilen geef ik een beter werkbare theorie, die ook vrij makkelijk is:
“een zeil buigt de wind af, daar is een kracht voor nodig is, en die kracht is nou je zeilkracht.”
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Werking van de Zeilen
De betere vleugeltheorie
Een vleugel buigt lucht naar beneden af. Als de vleugel de wind naar beneden duwt, duwt de vleugel zich juist omhoog. Dit is
nu de kracht “liftkracht” genoemd die het vliegtuig omhoog duwt.
Een vleugel staat onder een kleine hoek. Dit betekent dat de luchtdeeltjes onderlangs als het ware tegen de onderkant van de
vleugel botsen en naar beneden ketsen.
De lucht aan de bovenkant wordt ook omgebogen.
Dit gebeurt doordat constant aan de bovenkant als het ware een “gat” wordt gegraven, wat natuurlijk lucht aanzuigt, en dus de
lucht naar de onderliggende vleugel zuigt:
Natuurlijk botsen in de praktijk de luchtdeeltjes niet alleen tegen de vleugel, maar ook tegen elkaar. Het gat wordt natuurlijk
continu gegraven, en continu aangevuld, waardoor het er meer uit komt te zien als:
Een zeil werkt net zo:
●
●
1 Een zeil buigt de wind om. Hiervoor is een kracht nodig. Dit is nou je zeilkracht.
Hoe meer je dus ombuigt hoe groter de kracht.
2 Aan loef buigt je zeil de wind af door een soort van botsing, de wind wordt als het ware gewoon de bocht omgeduwd.
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●
3 Aan lij wordt de wind omgebogen doordat de wind als het ware het gat wat je zeil “graaft” in de lucht graaft word
ingezogen
.
Nu meer in detail met de stoere temen erbij (voor de iets verder gevorderde)
1 Een zeil buigt de wind om. Hiervoor is een kracht nodig geweest. Volgens Newton heeft elke
kracht een tegengestelde reactiekracht. Deze tegengestelde reactiekracht is nu de zeilkracht.
2 Het zeil buigt de wind aan loef door verdringing. De lucht kan niet rechtdoor doordat het zeil in
de weg zit. Lucht iets verder van het zeil kan ook niet rechtdoor doordat de lucht die gehinderd was door het zeil in de weg zat.
Lucht die nog verder van het zeil zit wordt ook afgebogen, omdat de lucht die gehinderd was door
de lucht die gehinderd was door het zeil in de weg zit. Lucht die nog verder van het zeil zit wordt ook zo beïnvloed. Natuurlijk is
het wel zo dat hoe
verder van het zeil je komt hoe minder de invloed wordt. De lucht stroomt als het ware steeds meer om de lucht heen die
beïnvloed wordt door het zeil.
3 Het zeil buigt de wind aan lij af door het Coanda effect:
Coanda kwam erachter dat een stroming een flink eind een gebogen oppervlak blijft volgen, mits
het niet te sterk is gebogen. Hoe dit kwam wist hij nog niet helemaal. Nu weten wij dat dit met de grenslaag en viscositeit
heeft te maken:
In het rechterplaatje zie je de start situatie.
Uit het gestippelde gebied wordt de lucht meegesleurd door wrijving tussen de snelle lucht en de
stilstaande lucht. Wrijving van lucht onderling noemen we viscositeit.
De gestippelde lucht gaat daar dus weg.
Dat zou dus betekenen dat daar een grote onderdruk heerst
De lucht uit de snelle stroom wil dat gat weer opvullen, waardoor de stroming wordt omgebogen.
Sommige mensen zeggen dat ook de lucht aan de bovenkant wordt meegesleurd. Dat klopt ook,
maar deze lucht wordt makkelijker aangevuld uit de gewone buitenlucht, er is namelijk meer buitenlucht omheen.
Dit is nou de reden dat de lucht om het profiel heen stroomt.
Waarom laat de stroming dan toch wel eens los?
Dit komt door wrijving van de lucht langs het oppervlak.
De lucht vlakbij het gebogen oppervlak wordt door wrijving afgeremd. Wordt deze afgeremde
lucht teveel dan komt het gestippelde gebied gewoon vol te staan met deze bijna stilstaande lucht en gaat de hoofdstroom net
zo lief rechtdoor.
Dit rechtdoor gaan of eigenlijk het niet meer volgen van de ronding noemen we "loslaten van de
stroming" en bij een zeil of vleugel "overtrokken" Het luchtlaagje wat afgeremd wordt door de wrijving noemen we "grenslaag"
Hoe verder je langs je profiel komt hoe meer grenslaag er is, omdat er meer lucht is afgeremd
door de wrijving. Daaruit volgt dat aan het begin van je profiel een grotere bolling kunt hebben dan aan het eind
van je profiel.
Stroming blijft dus aanliggen door de wrijving lucht-lucht, en laat los door de wrijving wandlucht.
Lucht aan lij gaat sneller dan aan loef
(voor ver gevorderden)
Bernoulli wist van de wet van behoud van energie. Hij zei eigenlijk dat als lucht versneld zonder energie uitwisseling met buiten
er meer bewegingsenergie inzat. Die energie moet ergens vandaan komen. Volgens Bernoulli komt die energie bijvoorbeeld
van druk energie. Uitwisseling
van energie met buiten moet je zien als een pomp of wrijving.
Anders gezegd; als er geen wrijving is, is de energie in een luchtstroom op verschillende punten gelijk. Energie in een
luchtstroom bestaat uit snelheidsenergie en druk energie:
Voorbeeld: lucht door een wrijvingsloze pijp:
Hier komt de veelgehoorde uitspraak “hoe sneller de lucht hoe lager de druk” vandaan. Die
uitspraak is eigenlijk wat uit zijn verband getrokken, omdat het eigenlijk om snelheidsverandering gaat, en er niks wordt
gezegd over wrijving.
Vier voorbeelden van stom toepassen van “hoe sneller de lucht hoe lager de druk”:
●
●
●
●
1 Een auto rijdt met 180 km/u op de snelweg. De lucht in de auto beweegt dus ook met een
snelheid van 180 km/u De druk in de auto moet dus erg laag zijn.
2 Ik heb een afgesloten vat met lucht. Daarin zit een roerder. Als ik de roerder aanzet wordt de lucht in het vat heel hard
rondgedraaid. Het vat moet dan sterk zijn anders klapt het in elkaar door de onderdruk in het vat.
3 Een gesloten romp moet altijd een beluchtinggaatje hebben. Anders klapt de romp in elkaar als je hard vaart door de
onderdruk in de romp.
4 Als je over een velletje papier blaast gaat de lucht omhoog doordat de snelheid boven het papier hoger is, en daar dus
een lagere druk is.
Even een uitleg waarom 4 fout is:
De wrijving mag je natuurlijk niet verwaarlozen!
Even onder het blaadje blazen en je weet zeker dat het onzin is. Het blaadje gaat dan namelijk omhoog.
Deze theorie toegepast op een zeil:
De lucht wordt omgebogen door het zeil, dus is er een kracht.
Deze zeilkracht wordt op je zeil overgebracht als een druk. Een overdruk aan loefzijde en een onderdruk aan lijzijde.
Overdruk betekent een lagere snelheid, en een lagere druk een hogere snelheid. De lucht zal dus sneller gaan aan lij en
langzamer aan loef.
Aan de reefknuttels kun je zien dat de lucht aan lij veel sneller gaat.
Wat heb je er aan te weten dat de lucht aan lijzijde sneller gaat:
-Je stroming aan lijzijde is belangrijker voor je totale kracht dan de kracht aan loefzijde, want aan lijzijde gaat de lucht sneller,
en geeft dus meer kracht als je hem ombuigt. (Het kost meer kracht om hard door een bocht te fietsen als zachtjes door een
bocht te fietsen)
Als je stroming dus loslaat aan lij van je zeil (en deze lucht dus niet meer ombuigt) heb je al snel beduidend minder kracht.
Hoe groot is je onderdruk aan lij nu in verhouding tot je druk aan loef? , dat hangt dus af van je zeilkracht!!. Bij een goed zeil
als je netjes zeilt kan hier best een factor 4 inzitten.
Tipwervels (leklucht) is verlies.
(voor ver gevorderden)
Er lekt lucht van de hoge druk aan loef naar de lage druk aan lij onder de giek door. (en ook over
de gaffel) Dit is een ombuiging de verkeerde kant op.
Je buigt de totale lucht dus minder af, met als gevolg dus minder kracht.
Hoe minder dit lekken onder je giek door hoe beter.
Bij vliegtuigvleugels gebeurt dit zelfde effect om de uiteinden van de vleugels, de vleugel tips genoemd
Vandaar dat dit effect meestal tipwervel wordt genoemd.
Wat heb je hieraan om te weten: Een hoog zeil met een korte giek (=hoge aspect ratio) het
efficiëntst qua voortstuwing is, omdat deze relatief de minste "tips" en dus tipwervel heeft. Deze tipwervels zijn ook de reden
dat bij wedstrijdschepen men graag de fok over het dek laat
schuiven, dan gaat er daar geen lucht van loef naar lij, en heb je aan de onderkant van je zeil dus geen tipwervel.
Van deze theorie komt de uitspraak "een gaffelgetuigd schip kan minder hoog aan de wind kan
varen dan een torengetuigd schip" vandaan. De meeste gaffelgetuigde schepen hebben namelijk een lagere hoogte/lengte
verhouding van de zeilen dan torengetuigde schepen.
Helaas zijn er zat uitzonderingen, waardoor deze uitspraak vrij dom is.
Toepassen van deze theorie.
Uitgangspunt van de theorie is dat als je zoveel mogelijk kracht naar voren wil hebben,je zoveel mogelijk lucht naar achter
afbuigt.
Als je dit voor elkaar krijgt ben je dus goed bezig:
Let wel dat je hier niet dit van maakt:
Nu buig je de lucht gedeeltelijk af naar loef, en wordt je zeilkracht teveel naar lij gericht, en dus niet naar voren.
Ook moet je opletten dat er niet dit gebeurt:
In het voorste gedeelte van je zeil moet de lucht heel scherp de bocht om, Dit kan wel eens een te scherpe bocht zijn, zodat
dat niet lukt. Dan laat de stroming los. Dit noemt men ook wel een overtrokken vleugel.
Als je je zeil boller maakt voorin moet de lucht minder scherp de bocht om.
Ook moet je natuurlijk niet je zeil te los hebben, dan valt de lucht in het voorlijk aan de verkeerde kant in. Dan gebruik je
voorste gedeelte van je zeil niet. Dit noemt men ook wel killen.
Uit dit bovenste verhaal kun je afleiden dat je met een vlakker zeil hoger kunt varen, alhoewel je de lucht dan minder afbuigt
en dus minder zeilkracht hebt.
Zou je het zeil verder aantrekken dan buig je ook lucht af naar loef, als je hoger gaat varen begint het zeil te killen.
Hierboven keken we alleen naar de bolling in langsrichting,
Het zeil heeft echter ook een kleine bolling in de hoogterichting:
Het zeil waait aan de bovenkant iets meer uit dan aan de onderkant.
Dit noemt men twist:
Een beetje twist is gunstig, aangezien hoe hoger je komt hoe harder de wind, en dus hoe ruimer de wind inkomt.
Interessant is ook dat je met de combinatie twist en helling in de boot je zeil veel vlakker kunt krijgen, althans zo ziet de wind
dat. Kijk maar eens in onderstaand plaatje. De blauwe lijn is de bolling zoals de wind erlangs gaat
Bij het rechter bootje wordt de wind maar een klein beetje van richting veranderd.
Zonder twist verandert de bolling zoals de wind die ziet nauwelijks. Zie de bootjes hieronder
Aangezien je met een vlakker zeil hoger kunt varen volgt hieruit dat je met wat helling in de boot ook hoger kunt varen. (Maar
helaas wat minder snel).
Bij relatief ruwe zeilen kan het ook gebeuren dat de stroming gewoon loslaat doordat er
vteveel bolling is. De lucht moet dan halverwege je zeil te scherp de bocht om. Dit gebeurt typisch als je ruwe zeilen hebt,
want dan krijg je meer grenslaag die als het ware in het gat aan lij blijft hangen. Dit is al beschreven in het Coanda verhaal
Heel leuk dit verhaal, maar hoe kun je zien hoe de stroming om je zeil verloopt?
Bijvoorbeeld met telltales. Meer hierover in trim
Ik zou je aanraden om voordat je daaraan begint eerst Koppels en Krachten
Door te lezen.
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Enkel huis tuin en keuken proefjes
Het befaamde over een blaadje heen blazen.
Het befaamde over een blaadje heenblazen om aan te tonen dat bij een hoge snelheid er
lage druk is.
Die redenering klopt in zoverre dat de druk daar lager is als de overdruk in je mond.
Hoe zit het dan wel:
Volgens het Coanda effect wordt de lucht afgebogen. Hiervoor is een kracht nodig. De
reactiekracht op het blaadje duwt het blaadje omhoog.
nu echter het volgende experiment:
http://zeilplan.net/leren/theorie/tekst.php?tekst=proefjes.txt (1 of 10)24-1-2004 17:26:44
Geef je het blaadje een ronding de andere kant op, dan wordt de lucht juist in de andere
kant afgebogen en duwt de reactiekracht het blaadje naar beneden.
Supervleugel??.
Het volgende gedachte proefje gebruik ik om mensen aan het denken te zetten over de
kansloze theorie: "de weg boven de vleugel is veel langer dan onder de vleugel en dus gaat
de lucht boven de vleugel sneller en krijg je lift"
Welke heeft het grootste lengteverschil tussen boven en onderkant?
Welke vleugel werkt het best?
Waarom wordt het onderste type nooit gebruikt?
Vleugel levert ook lift terwijl hij recht staat?
Veel mensen zeggen: Ja, maar een vleugel profiel levert ook lift als hij recht staat!.
Dit recht staan is een vorm van optisch bedrog.
Hierinder een vleugel welke volgens die mensen "recht staat".
Dit vleugelprofiel levert inderdaad liftkracht terwijl hij recht lijkt te staan.
Eigenlijk staat hij niet recht!
Stel je voor ik neem dit vleugelprofiel:
En verdraai dat een beetje:
Om het nog echter te laten lijken verander ik een heel klein beetje aan de voorkant:
Dit is hetzelfde als het eerste plaatje!.
De Kaars achter de fles uitblazen.
Dit is een experimentje om te laten zien dat er bij een dikkere grenslaag sneller loslating is.
Neem een 1,5 L petfles en plaats er direct een brandend kaarsje achter (liefst volle petfles
om te voorkomen dat hij in brand vliegt)). Blaas je nu recht tegenover het kaarsje tegen de
fles dan zal de stroming om de fles heengaan en het kaarsje uiblazen:
Door het coanda effect bleef de stroming de fles volgen en blies je dus het kaarsje uit.
Als je nu de fles heel ruw maakt rem je de stroming dicht bij de fles af, krijg je dus een veel
dikkere grenslaag en zal de stroming loslaten. Dit ruwen kun je bijvoorbeeld doen door er
een verfrommeld keukenpapiertje omheen te plakken. Dan is het moeilijker om het kaarsje
uit te blazen. (let wel op dat keukenpapier niet in de fik vliegt).
Dit effect is nog duidelijker als je een nog dikkere cilinder weet te vinden, (zoals een
bloempot) en minder duidelijk als je een kleinere cilinder neemt (een bierflesje).
Dit is effect is de hoofdreden dat men bij vliegtuigen zo bang is voor ijsafzetting op de
vleugels. Het ruwe ijs zorgt ervoor dat de stroming loslaat, de vleugel dus eigenlijk
overtrokken raakt, en het vliegtuig naar beneden valt. (Andere reden is dat het ijs ook wel
wat weegt).
Waarom blijft een ballon boven een stofzuiger hangen.
(als de stofzuiger omhoog blaast)
(of waarom je een pingpongbal omhoog kunt houden met een haardroger)
Pingpongbal in lucht (foto gekopieerd van http://www.nal.go.jp/eng/newsletter/98autumn/
m106.htm)
Vaak is de redenering dat de lucht daar sneller gaat en er daar dus een lagere druk is
volgens bernouilli. (Die redenering klopt in zoverre dat de druk daar lager is als de overdruk
in je mond.)
Hoe zit dat dan wel:
Als de ballon half in de hoofdstroom zit wordt de hoofdstroom afgebogen naar de zijkant,
met als gevolg dat de ballon terug de hoofdstroom ingaat.
Doe je ditzelfde met een prop papier dan werkt het niet. Dit komt omdat het oppervlak te
grof is en de stroming loslaat.
De pingpongbal welke je niet uit de trechter kunt blazen
Neem een pingpongbal en een trechter. Als je nu hard door de trechter blaast komt de
pinpongbal niet uit de trechter (je kunt ook een trechter uit papier vouwen).
Hoe komt dit nou weer?
De lucht wil de trechter volgen, de lucht wordt dus afgebogen naar de zijkant.
Het balletje buigt deze lucht weer terug, waardoor de reactiekracht de bal in de trechter
trekt (en het balletje iets uit elkaar trekt)
Een druppel is niet druppelvormig
Een druppel is niet druppelvormig als hij valt. Een druppel plat af:
Een druppel wil als er geen zwaartekracht enz is door de oppervlaktespanning rond worden.
Laten we deze ronde druppel vallen dan zien we het bovenstaande krachtenspel doordat de
lucht om de druppel heengaat. De boven en onderkant worden dus naar binnen geduwd, en
de zijkanten naar buiten gedrukt.
Iets soortgelijks zie je bij luchtbellen. Deze platten ook af. Omdat deze langzamer gaan kun
je dat wel duidelijker zien.
en ruw katoenen zeil wat luchtdoorlatend is minder goed werkt als een mooi vlak luchtdicht
plastic zeil
Dit komt namelijk omdat een katoenen zeil veel meer grenslaag maakt omdat de lucht
vlakbij je zeil meer wordt afgeremd en er lucht door je zeil gaat. De stroming zal dan dus
eerder loslaten volgens het coanda effect.
O ja, veel mensen denken dat een grenslaag heel erg dun is. Dit valt wel mee. bij een
binnenvaart schip is hij achter bij het schip al gauw 200mm dik. (afhankelijk van snelheid)
Bij je polyvalk is hij nog enkele centimeters. In de friese wateren kun je dit best
waarnemen. Ga is over de rand hangen en je zult zien dat bij het achterschip het water
inderdaad enigzins wordt meegesleurd.
Kun je meteen zien hoe een grenslaag er uitziet en hoe deze groeit, hoef ik dat niet te
tekenen
Lucht is als ik het goed heb begrepen wat lichter en wat visceuzer, maar het principe is
hetzelfde, alleen is de grenslaag bij lucht niet zo snel groeiend als in water.
Toch is de grenslaag achter op je zeil al gauw enkele mm dik, je kunt dit zien met behulp
van wat sigarattenrook (let op dat je het zeil niet in de fik steekt.
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http://zeilplan.net/leren/theorie/tekst.php?tekst=MenF.txt
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Dit hoofdstuk heb ik toegevoegd omdat blijkt dat hier mensen toch teveel op vastlopen.
Mijns inzien kom dit doordat veel mensen allerlei krachten gaan lopen optellen aftrekken ontbinden erbij halen, en ook nog
eens allerlei snelheden en koppels en momenten met pijlen aangeven, en nog met een aantal draaipunten werken.
Daarom wil ik laten zien dat als je het simpel houdt het wel begrijpelijk is en je er wel wat aan hebt.
Daarnaast heb ik al heel wat foute dingen hierover in zeilboeken gezien, vandaar dat ik toch nog iets hier op in ga, omdat dit
bij de basis van theorie hoort.
Krachten
Een kracht is de neiging tot verplaatsing. (dat is heel wat anders dan de snelheid of de richting van bewegen.)
Je kunt kracht leveren door te trekken of te duwen.
Verspeiden we een kracht over een oppervlak dan noemen we dit druk (of onderdruk)
Een kracht heeft een richting. Die geef ik aan met een pijl.
Volgens Newton heeft elke kracht een even grote reactiekracht
Vrij vertaald zei Newton actiekracht=reactiekracht.
Voorbeeld: als ik een tafel verschuif dan heb ik daar een kracht voor nodig die even groot is als de wrijving van de tafel over
de vloer.
Ander voorbeeld: als ik een bal wegtrap is mijn trapkracht even groot als de kracht nodig om de bal te versnellen. (de
versnellingskracht.
De kunst van deze manier van krachten bekijken is het simpel houden:
Er zijn namelijk nog meer krachten in het spel, zoals de vertragingskracht die de bal levert door de wrijving, de zwaarte
kracht, de kracht op de bal door de hogere druk die er inzit, De kracht op het stiksel door de druk in de bal, de kracht op de
buitenkant van de bal door de gewone luchtdruk, de kracht op de bal door de draaing van de aarde, de horizontaal
ontbonden kracht van de torsie in de vezels van het stiksel etc.
Ga je die allemaal er ook bij halen, vervolgens rekenen en dan de bal trappen dan is de kans groot dat je ergens een foutje
hebt gemaakt hebt en hem in het verkeerde doel trapt.
Daarom worden meestal niet alle krachten getekend, dat doe ik zelf ook niet.
Bij het voorbeeld verderop van de tafels teken ik ook niet de reactiekracht, maar je moet wel beseffen dat die er is.
Je kunt krachten bij elkaar optellen, maar dat lang niet altijd zo simpel voor degene zonder VWO 6 natuurkunde.
Gebruik je boerenverstand:
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Trek je met zijn tweeen zachtjes aan een touw aan een tafel, dat is hetzelfde als in je eentje hard trekken.
Als je als je tegenover elkaar zit allebij even hard tegen een tafel duwt is dat hetzelfde als dat er niemand duwt.
Duw je allebij een tafel schuin naar voren, elk aan een kant, dan gaat de tafel toch rechtdoor.
trek je allebij aan een hoekpunt van de tafel de tafel rechtdoor dan is dat hetzelfde als een persoon die hard in het
midden trekt.
Anders gezegd:
Krachten in dezelfde richting kun je simpel bij elkaar optellen
Krachten in precies de tegenovergestellde richting kun je van elkaar aftrekken.
De uitkomst van twee krachten welke onder een hoek ten opzichte van elkaar staan ligt hier tussenin.
Twee krachten in dezezelfde richting maar een stuk uitelkaar kun je vervangen door een grote kracht daar tussenin
Maar let op, een kracht zegt lang niet altijd wat over de richting en snelheid van bewegen:
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duw je tegen een stevige muur, dan is er een kracht welke niet tot beweging leidt.
duw je schuin van achter tegen een kleein wagentje, dan gaat het toch rechtuit.
Duw je heel erg hard tegen een grote vvrachtwagen, dan gaat hij misschien langzaam vooruit -wil je met een slee hard
blijven gaan dan moet je hard blijven trekken.
Koppels
Een koppel is de neiging om te draaien.
Dit kan natuurlijk linksom en rechtsom, maar je kunt het natuurlijk ook oploeven en afvallen noemen.
Liggen de actie en reactie kracht in elkaars verlengde dan is het koppel 0.
Liggen ze echter iets naast elkaar dan is er een koppel.
hoe groter de kracht en hoe verder ze uit elkaar liggen hoe groter het koppel.
Anders gezegd: koppel = kracht X afstand.
De afstand is de afstand tussen de werklijnen van de krachten. Laat je dus niet verlijden om de uiteinden van de krachten
met elkaar te verbinden.
Nu gaan we dit toepassen op een zeilboot.
de truuk als je sturen met de zeilen wil laten zien is:
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teken altijd de kracht loodrecht op heet zeil ca. 1/3 van de voorkant van de mast.
als je twee zeilen hebt neem deze bij elkaar.
teken altijd de kracht op het onderwaterschip vanuit je kiel.
Op bovenstaand plaatje van een zeilschip wat halve wind vaart zie je een klein koppel linksom, in dit geval oploevend.
Het bootje vaart bijna helemaal rechtdoor ondanks dat de krachten schuin lopen.
Dit komt natuurlijk omdat door het zwaard welke bij een lage zijwaartse snelheid al een grote kracht levert, en in voorwaarte
richting lang niet zoveel weerstand heeft.
Sturen met de zeilen
Teken ik een bootje met alleen een grootzeil nu:
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met een te los zeil (alleen achterlijkk van het zeil vangt nog wind, zeilkracht wordt minder en schuift naar achterlijk)
-met het zeil goed.
te strak zeil (achterlijk buigt de winnd niet meer goed om door loslaatwervels, zeilkracht schuift naar voren
dan zie je het volgende.
En dit klopt ook met de praktijk bij dit soort boten (wel flink overdrijven en boot rechthouden, en mast niet buigen)
Nu getekend bij verschillende koersen met de juiste zeilstand:
Ze ziet dat het bootje aan de wind neutraal is en voor de wind graag wil oploeven.
Ook dat klopt weer met de praktijk
Vuistregel bij deze boot is dus: hoe verder het zeil naar binnen hoe minder loefgierig. (bij constante helling en masbuiging
Nu gaan we kijken wat een fok doet.
zie de tekening hieronder van een boot met alleen een fok.
Eigenlijk zie je dat de fok een afvallende werking heeft, alleen voor de wind als je de fok heel los hebt is er een klein
oploevend koppel
Opvallend is dat je voor de wind vaak toch een afvallende werking hebt omdat men zelden de fok echt ver uitvierd.
De vuistregel "hoe strakker de fok hoe lijgieriger de boot wordt" klopt dus.
Het is zelfs zo dat deze de fok vuistregel "hoe strakker het grootzeil hoe minder loefgierig de boot" tot onzin verklaard.
Als we namelijk het grootzeil loslaten wordt de zeilkracht van het grootzeil minder, en het grootzeil levert maar een klein
oploevend koppel, terwijl de fok een flink afvallend koppel heeft.
Anders gezegd, als we het grootzeil loslaten blijft de werking van de fok over.
Sommige mensen denken om deze reden dat een boot met een genua of een heel grote fok, lijgieriger wordt.
meestal is het omgekeerde waar omdat het achterse gedeelte van de fok eigenlijk een oploevende werking heeft.
Maak je dat groter dan wordt de boot dus loefgieriger.
Met een flinke genua kun je over het algemeen best halve wind varen zonder dat het roer trekt.
Sturen met de helling van het schip
Hieronder zie je een bovenaanzicht van een schip wat halve wind over stuurboord vaart.
Links hang zij naar loef, rechts hangt zij steeds meer naar lij.
De zeilstand blijft gelijk.
Duidelijk is te zien dat de boot die naar loef hangt een afvallend koppel heeft, en de rechter boot een sterk oploevend koppel
heeft Dit komt doordat het zeilpunt als het ware steeds verder naar buiten wordt gebracht.
Veel meer is hier niet aan uit te leggen.
Nog even een misvatting uit de weg ruimen die in veel zeiboeken staat:
-Als het zeilpunt in de lengterichting gelijk staat met het lateraalpunt dan is de boot niet loef of lijgierigDIT IS KANSLOOS FOUT.
Zie het plaatje hieronder:
Het zeilpunt en het lateraal punt vallen duidelijk niet samen in het zijaanzicht.
Toch zie je duidelijk in het bovenaanzicht dat de boot neutraal vaart.
Gebruik dus geen zijaanzichten om de sturende werking uit te leggen.
De conclusie die zeilboeken aan hun foute uitspraak hangen: -Als je het zeilpunt naar achter verschuifd door bijvoorbeel de
mast naar achter te zetten word de boot loefgierigeris wel juist (met uitzondering van pal voor de wind met je zeil haaks op de boot)
Dat teken ik niet want dat kun je ook wel zelf uitvogelen.
Remmende werking van sturen met het roer
In andere hoofdstukken vergelijk ik enkele malen met "de remmende werking van het roer"
Hoe zit dat dan:
Stuur je niet dan heb je ook geen stuurkracht.
Stuur je dan buigt het roer het water af en krijg je dus een roerkracht.
Heb je een kleine roeruitslag dan is deze roerkracht bijna helemaal dwars gericht, zodat de kont van het schip die kant
opgaat en je waarschijnlijk gaat draaien.
Heb je een grote roeruitslag dan is deze roerkracht voor een gedeelte tegen de vaarrichting in.
Heb je het roer helemaal dwars gezet dan is deze roerkracht volledig tegen de vaarrichting in.
De natuurkundingen onder u mogen natuurlijk best de krachten gaan ontbinden, maar het principe blijft hetzelfde.
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Terug naar index
Het Onderwaterschip
Hoe werkt je kiel
Een kiel werkt volgens hetzelfde principe als een zeil en vleugel, alleen nu in het water.
Je anti-verlijerende kracht is de liftkracht van je kiel.
Als je normaal aan de wind vaart is je drifthoek al gauw enkele graden, je kiel wordt dus
scheef door het water getrokken met die drifthoek.
De kiel levert dan evenveel kracht als de zijwaartse component van je zeilkracht.
Vaar je langzamer dan moet je nog steeds dezelfde zijwaartse component van je zeilkracht
opheffen met je kiel.
Je kiel gaat dan minder water veel ombuigen om toch die zijwaartse component van je
zeilkracht op te heffen.
Dat kan hij alleen voor elkaar krijgen door schuiner door het water te gaan.
Vaar je echt heel langzaam dan raakt je kiel overtrokken,(=de stroming laat los)en kan hij
kan die kracht helemaal niet leveren, en je begint nog veel meer te verlijeren.
(Bij vliegtuigen is dit "overtrokken" raken heel dramatisch, een overtrokken vliegtuigvleugel
valt als het ware uit de lucht. Bij een "overtrokken" kiel begint gewoon de boot veel meer te
verlijeren.
Vandaar dat je bij aanspringen als je weinig wilt verlijeren je je druk rustig dient op te
bouwen met je snelheid of even iets lager moet varen om de zeilkracht even wat meer in de
vaarrichting te kunnen richten.
Natuurlijk is ook de vorm van je kiel en de ruwheid van je kiel (grenslaagbeinvloeding)erg
van belang om loslating van de stroming te vookomen.
Wat gebeurt er als een kiel overtrokken is?
Als de kiel inderdaad overtrokken is en alleen als een weerstandsprofiel zijwaarts door het
water gesleurd wordt is de kiel niet bijzonder efficient meer.
De romp van een polyvalk en vele andere boten heeft achter bijna rechte zijkanten, terwijl
ze voor nog onder een redelijke hoek staan.
De achterkant van het schip is daardoor moeilijker dwars door het water te sleuren als de in
zijwaartse richting meer gestroomlijnde voorkant.
De achterkant houd zich nog enigszins "vast" in het water.
Dat betekent dus dat de boot dan van de wind afdraait.
Ga je dan tegensturen en laat je je zeil strak in het midden staan, dan wordt het verlijeren
alleen maar erger.
Voeg je daar een klapperende fok, een smalle drukke brug met een leuk terras aan toe, dan
snap je meteen waarom dat terras zo goed loopt.
Laat je roer dus enigzins gaan en zet je zeil in de juiste stand (losser dus) zodat de
zeilkracht meer naar voren wordt gericht, je weer snelheid vooruit krijgt, het ernstig
verlijeren ophoud, en stuur dan pas weer rustig op en trek het zeil aan.
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Roer
Als je roerblad overtrokken raakt (zoals bij grote roeruitslagen) geeft het minder roerkracht.
Dit effect kun je nog bijtellen bij het effect dat je roerkracht bij grote uitslagen voor een
groot gedeelte remmende kracht geeft, ipv sturende kracht.
Geef dus niet te veel roer.
Overigens moet je niet vergeten dat als je hard aan het draaien bent het water niet recht
meer onder je kont naar achter gaat, waardoor je weer meer roer mag geven.
Ook opvallend is dat een profielroer beter werkt als een rechte plaat.
Dit komt natuurlijk doordat de stroming aan de onderdruk kant van het roer minder snel
loslaat, er kan dus meer water worden omgebogen.
Wel heeft een profielroer als nadeel dat hij in een keer overtrokken raakt.
Het uit het roer lopen is daardoor een vrij abrupt proces.
Een vlakke plaat levert weliswaar minder roerkracht, maar raakt gelijdelijk overtrokken,
omdat eigenlijk vanaf kleine hoeken de stroming aan lij loslaat. Je voelt uit het roer lopen
dus beter aankomen bij een vlakke plaat.
Je kunt dit verschil duidelijk merken als je met een nieuwe Hoora boot met profielroer en
een oude polyvalk bij harde wind naast elkaar vaart en ze in een windvlaag allebij uit het
roer lopen.
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http://zeilplan.net/leren/theorie/tekst.php?tekst=weerstand.txt
Terug naar index
Weerstand
Weerstand van een schip is globaal te verdelen in 5 zaken:
wrijvingsweerstand
drukweerstand
golfmakende weerstand
weerstand door drift
Wrijvingsweerstand.
Dit is de kracht door wrijving van het water langs de romp.
Deze weerstand is afhankelijk van de grote van het oppervlak, de ruwheid van het oppervlak, en de vorm van de grenslaag en
natuurlijk de snelheid.
Door deze weerstand ontstaat de grenslaag. Het is dus eigenlijk de kracht welke nodig is om water vlak langs een oppervlakte mee
te sleuren.
Het is vrij makkelijk voor te stellen hoe de wandruwheid hier invloed op heeft.
Hoe ruwer de wand hoe meer water wordt meegesleurd.
Ook de invloed van de grote van oppervlak is makkelijk te voorspellen: Hoe groter het oppervlak hoe groter de wrijvingsweerstand.
De vorm van de grenslaag is wat complexer. Globaal zijn er twee type grenslagen, de laminaire en de turbulente grenslaag.
Een laminaire grenslaag is een mooie, vloeiend verlopende grenslaag:
plaatje. Deze grenslaag geeft maar weinig wrijving. Hij is echter vrij makkelijk te verstoren zodat hij overgaat naar de turbulente
stroming.
Een turbulente grenslaag is veel "woester". De snelheidsverdeling is niet zo geleidelijk en niet constant. De snelheidsverdeling is
globaal veel anders. Vlak bij het oppervlakte is de snelheid heel laag, waarna er een vrij dik gebied is waarin de grenslaag bijna de
omringende snelheid heeft.
De turbulente grenslaag heeft een grote weerstand in verhouding tot een laminaire grenslaag.
Een turbulente grenslaag heeft vergeleken met een laminaire grenslaag maar voor een heel klein gedeelte een lage snelheid, en
voor een groot gedeelte een snelheid welke net iets langzamer gaat als het ongestoorde water.
Wat je typisch ziet is dat aan de voorkant van het schip de grenslaag laminair is, en verder naar achter omslaat in een turbulente
grenslaag. Hoe ruwer je romp en hoe harder je vaart hoe eerder de grenslaag omslaat.
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Dikte van de grenslaag is wel sterk overdreven voor deze lengte.
Als je een mooie schone romp hebt en het waait eigenlijk nauwelijks en het water is als een spiegel dan kan de grenslaag helemaal
laminair zijn.
Ben je vet in planee met een aangegroeide romp en zijn er veel golven dan is de grenslaag bijna meteen turbulent.
Natuurlijk wordt de grenslaag naar achter ook steeds dikker, Je remt tenslotte steeds meer water af.
Bij een zeilboot kun je deze weerstand dus verminderen door een hele mooie vlakke en schone romp te kiezen, zo min mogelijk
oppervlak in het water te hebben, en niet te stampen omdat dan de grenslaag omslaat van laminair naar turbulent (zeker niet bij
weinig wind).
Er zijn ook nog wat andere trucjes om de wrijvingsweerstand/grenslaag te beïnvloeden, maar deze gaan wat ver voor bij een
zeilboot in mijn ogen.
Dit zijn:
-Afzuigen van de grenslaag. Je boort een boel kleine gaatjes in het oppervlak, en daar zuig je aan. Dan zuig je de grenslaag weg,
Als gevolg heb je dus bijna geen grenslaag en dus bijna geen wrijvingweerstand.
-Aanblazen van de grenslaag. Je boort een boel gaatjes in de richting schuin naar achter en laat daar het met hoge snelheid
uitkomen. Je versnelt daarmee je grenslaag weer, met als gevolg bijna geen grenslaag, en dus bijna geen wrijvingsweerstand.
Deze worden redelijk vaak gecombineerd, als je iets afzuigt moet je het ook ergens laten en omgekeerd.
Grote nadeel van deze twee technieken is dat kleine gaatjes/spleetjes kunnen verstoppen, en je dus uit praktische overwegingen
met grotere spleten/gaten moet werken
-Bewegen van de wand. Laat je de wand meebewegen met de stroming dan is er geen snelheidsverschil en daarmee geen wrijving.
-Versnellen van de moleculen vlak bij de wand door statische elctriciteit gecombineerd met ionisatie/plasma. Zie voor meer
informatie bijvoorbeeld: JLN lab
-Ter plaatse van je grenslaag iets laten stromen wat minder visceus is. Dit kan betekenen dat je een minimaal visceuze vloeistof
aan de voorkant van je schip laat sijpelen, of bijvoorbeeld lucht perst onder je schip, of bijvoorbeeld de romp opwarmt. (warm
water is minder visceus)
-De wervels in de grenslaag weer netjes in de lengterichting legt, met kleine langsgroefjes. De "haaie huid" bij de nieuwste
zwempakken is hier een voorbeeld van. 3M heeft ook wel eens haaiefolie gemaakt voor wedstrijdroeiboten, wat direct daarna werd
verboden door de roeibond.
Drukweerstand
Loopt de stroom mooi om het voorwerp heen dan is de weerstand laag.
Wordt de stroom beinvloed dan is de vormweerstand hoog.
Deze weerstand wordt ook wel vormweerstand genoemd.
Deze is afhankelijk van de vorm van de stroomlijnen.
Als je weet hoe de stroomlijn loopt weet je ook de drukweerstand.
Bekijk eens onderstaande tekening met de theorieën van hoe werkt een zeil in gedachte:
Je kunt op twee manieren zien dat de driehoek meer drukweerstand heeft als de cirkel: een manier is dat bij de driehoek de
stroomlijnen na de driehoek anders liggen. er is dus iets verplaatst, en de kracht voor die verplaatsing is de druk weerstand.
Andere redenering is dat bij de driehoek kracht C, welke naar gedeeltelijk naar voren is gericht ontbreekt
De route van de stroomlijn is echter volgens de coanda theorie mede afhankelijk van de grenslaag. Zou de cirkel veel grenslaag
hebben dan zou de stroomlijn er ook zo uit kunnen zien.
In de praktijk is gebleken dat een turbulente laag door zijn snelheidsverdeling waarbij maar weinig echt heel langzaan gaat, de
stroming beter blijft aanliggen.
Voor de drukweerstand is een turbulente grenslaag daardoor beter als een laminaire grenslaag.
Vandaar dat bij top schaatsers strippen op de pakken worden geplakt om ervoor te zorgen dat de stroming turbulent wordt, en
daardoor de schaatser een een lagere drukweerstand krijgt. Hetzelfde trucje verklaart de putjes van de golfbal.
Dit zijn leuke truuken, maar helaas niet toepasbaar op een scheepsromp, daar is de stroming na ca. een meter toch al turbulent.
Strippen opplakken maakt de grenslaag dan alleen maar dikker, en dus een snellere loslating en dus de drukweerstand hoger. De
romp moet dus gewoon zo gestroomlijnd mogelijk zijn.
Opvallend is dat bij veel schepen de drukweerstand lager is als ze achteruitvaren, of onder een grote helling lager is. Dit zie je ook
vaak bij autos terug.
Meest gehoorde verklaring hiervoor is dat er voor een groot gedeelte op gevoel wordt ontworpen, en het gevoel zegt toch dat een
driehoek met de punt naar voren minder druk opmaakt als andersom. Terwijl de werkelijkheid andersom zegt.
Ook bij druk weerstand geld net zoals bij een zeil dat de achterkant het belangrijkst is omdat daar onderdruk heerst en daar dus de
hoogste snelheden zijn.
Golf makende weerstand.
Een schip maakt golven als zij vaart. In die golven zit energie. Die energie is de golfweerstand.
golf ontstaat door de scheepsronding, want die geeft een drukverschil, die zich nu behalve in een snelheids verandering ook uit in
een niveau verschil.
Hoe sneller en hoe meer het water de bocht om moet, hoe hoger het nivoverschil.
Een hoge druk uit zich natuurlijk in een niveau verschil omhoog, zoals bij de boeg, waar het water door de boeg van de hartlijn van
het schip wordt afgebogen, dus wordt weggedrukt. Dit noem ik nu even boeg berg.
Een lage druk uit zich natuurlijk in een nivo verschil omlaag, zoals op de grootste breedte van het schip, waar het water juist weer
naar binnen wordt afgebogen, dus weer richting romp wordt getrokken.
Dit noem ik nu even schouderdal
bij de kont wordt het richting hartlijn stromende water weer naar buiten afgebogen, het wordt door het water wat van de andere
kant komt weggedrukt, dus nivoverhoging bij de kont. Dit noem ik nu even achterberg
Nu heeft water de eigenschap dat een nivoverhoging graag geegaliseerd wil worden, vandaar dat je sluizen enzo nodig hebt en het
water niet gewoon met een graafmachine kunt ophogen.
Het bergje valt dus als het ware naar beneden door de zwaartekracht, en schiet zelfs door als het het niveau van het omringende
water heeft bereikt. De golftop wordt dus na een tijdje een golfdal, en even later weer een golftop
In dat tijdje heb je wel een stukje gevaren. Heb je in het tijdje dat je boegberg een boegdal werd een halve scheepslente gevaren,
dan valt je boegdal dus samen met je schouderdal. Hierdoor heb je dus een dieper dal halverwege je schip. In diezelde tijd is je
schouderdal een schouderberg geworden, en valt samen met je achterberg, waardoor je achterberg dus extra hoog wordt.
In deze situatie maak je dus heel veel golven, en heb je dus een heel hoge golfmakende weerstand.
Deze stuatie is bekend onder de naam rompsnelheid.
Je golfpatroon ziet er dan ongeveer zo uit:
((De rompsnelheid van een schip is in km/u als je lengte in meters invult ongeveer: 4,5*wortel(lengte). Een valk (6m) heeft dus
een rompsnelheid van 11 km/u)).
Vaar je in de tijd dat je boegberg een boegdal en weer een boegberg werd een halve scheepslengte dan heft je boegberg juist je
schouderdal op en maak je dus heel weinig golven, en heb je dus een lage golmakende weerstand.
Vaar je sneller dan de rompsnelheid, dan noemt men dat planeren.
Typisch zie je dan juist een kuil direct achter het schip ontstaan en maak je opeens veel minder golven. Je vaart als het ware op je
boeggolf.
hierdoor kom je een stukje omhoog (in vergelijking met je rompsnelheid, waarbij je eigenlijk in je boegdal vaart).
Dit omhoogkomen is wat anders dan de kracht waarmee waterskiers niet zinken!
Het niet zinken van een waterskier komt omdat de achterkant van de skie lager zit als de voorkant, en daardoor het water naar
beneden wordt afgebogen, en dus de reactiekracht op de skie omhoog is.
Dit "waterski-effect" moet je wel enigzins hebben bij een planerende boot, anders "zuigt" de boot zich verder naar beneden, zoals
bijvoorbeeld bij sleepboten gebeurt, die wel vaak wel grote motoren hebben, maar een oplopende kont welke het water juist
omhoog richt, en de boot dus naar beneden trekt.
Vandaar dat sommige sloepen "planeer vlakken" hebben (onder water bij de spiegel). Dit is om niet te veel naar beneden te worden
gezogen, zodat ze dus wel kunnen planeren.
Een catamaran, kano, of wedstrijdroeiboot romp heeft heel weinig ronding in de lengterichting. Dit betekent dat de boegbergen,
schouderdalen en hekbergen in vergelijking met een gewone romp erg klein zijn. De golfmakende weerstand is daardoor maar een
klein gedeelte van de totale weerstand.
Hierdoor is de overgang tussen rompsnelheid en planeren lang niet zo duidelijk als bij een zwaardboot, en zul je deze mensen wat
minder over planeren horen praten.
Bij sommige boten worden de rondingen in het water minder door haar scheef te hangen, wat kan resulteren in een lagere
golfmakende weerstand. (en vorm en wrijvings weerstand).
Tegelijkertijd wordt dan het waterskie-effect minder door het mindere oppervlakte waardoor planeren wel kansloos is.
Vandaar dat een zwaardboot bij weinig wind vaak toch beter vaart onder een kleine hoek.
Bij een valk is dit volgens sommige een van de redenen dat hij onder helling hoger aan de wind kan varen.
Andere reden is dat de valk onder grote helling loefgieriger is, en dus om rechtdoor te blijven varen zo roer moet worden gegeven
dat je met het roer het water afbuigt naar lij, en dus als het ware de boot naar loef duwt. Dit roergeven remt de boot weer af
waardoor de schijnbare wind ook wat ruimer inkomt.
Ook wordt de romp assymetrisch waardoor deze misschien het water naar lij afbuigt, en de boot dus naar loef duwt, maar dat lijkt
me sterk
Laatste mogelijke verklaring (die ik het best vindt) is dat de bolling van het zeil anders wordt gevolgd, doordat de wind als het ware
vanuit de halshoek naar boven gaat, en dus minder bolling tegenkomt, waardoor het zeil vlakker lijkt voor de wind, en je dus hoger
kan. Dit vlakkere zeil wordt nog eens extra vlak doordat bij grote hellingshoeken de twist van het grootzeil beduidend meer wordt
doordat de gaffel onder die hoeken meer naar beneden valt. Vandaar dat juist bij gaffelgetuigde schepen zonder neerhouder dit
effect dat ze hoger kunnen varen onder grotere hellingshoeken optreedt.
Weerstand door drift.
Vooral bij aan de wind varen is er een grote zijdelingse kracht en slechts een kleine voorwaartse kracht.
Daardoor wordt een zeilboot eigenlijk scheef door het water getrokken in plaats van rechtdoor.
Hierdoor ontstaat drift.
Heb je veel drift dan heb je ook een hoge weerstand door drift.
Dit is vergelijkbaar met de remmende werking van roergeven.
Als we inzoomen op de kiel:
De kracht op de kiel werkt (net zo als bij een zeil) loodrecht op de kiel. Bij drift is dit niet meer loodrecht op de vaarrichting.
Dat betekent dat de dwarskracht van de kiel een beetje tegen de vaarrichting komt in te staan.
Anders gezegd, om de boot dwars door het water te trekken heb je vrij veel kracht nodig
Wat je eigenlijk wil is dus zo min mogelijk drift.
Dat kan je bereiken door een grote, goed gevormde kiel te kiezen welke al bij een kleine drifthoek voldoende kracht geeft om de
dwarskracht van je zeil op te vangen.
Hierbij geld net zoals bij een zeil dat een diepstekende in de lengterichting korte kiel dat het beste doet.
Kun je niet zo diep, dan moet je het in de lengte zoeken.
Een diepstekende kiel brengt echter het aangrijpingspunt van de dwarskracht lager, wat resulteerd in een groter hellend koppel.
dit wordt wel weer enigszins gecompenseerd door hel lagere zwaartepunt.
Meestal kun je echter niet makkelijk iets aan de kiel veranderen, Het enige wat je dant kunt doen is ervoor zorgen dat de kiel mooi
glad is, zodat de stroming goed blijft aanliggen. Dit kan soms best veel schelen. Vergeet niet dat de krachten op je zeil ongeveer
even groot zijn als op je kiel.
Overigens helpt je romp ook tegen verlijeren, principe van driftweerstand blijft echter hetzelfde.
De dwarskracht van je romp door het water is soms wel te beinvloedden.
Denk bijvoorbeeld eens aan een knikspant welke meer "knik" aan lij in het water duwt bij grote hoeken, of aan een catamaran met
a-symmetrische rompen, etc
Terug naar index
http://zeilplan.net/leren/theorie/tekst.php?tekst=stabiliteit.txt
Terug naar index
Terug naar index
Stabiliteit
Ook stabiliteit wordt door veel mensen gezien als iets heel ingewikkelds.
Omdat naar mijn mening de de zeilboeken vooral dwaalsporen geven vertel ik het hier nog een sop een andere
manier.
Stabiliteit is de mate waarin het schip weer overeind wil komen.
Met aanvangstabiliteit wordt bedoelt de mate waarin een schip overeind wil komen bij kleine hoeken. Met stabiliteits
omvang wordt bedoelt tot welke hoek het schip nog overeind wil komen.
Globaal is stabiliteit opgebouwd uit:
vormstabiliteit
gewichts stabiliteit
Snelheids stabiliteit
Elke boot heeft met al deze stabiliteitsvormen te maken. Soms is een veruit het belangrijkst en wordt gezegd dat die
boot "zus en zo" stabilititeit heeft.
Vormstabiliteit
Als je een bal onderwater duwt heb je hiervoor een kracht nodig.
Bij een skippy bal heb je meer kracht nodig dan een pinpongbal.
De skippybal kun je maar een klein stukje onder water trekken.
Eigenlijk is het zo dat hoe meer volume je onderdompelt hoe meer kracht je nodig hebt.
(Om een melkpak van 1 liter onder te dompelen door zijn eigen gewicht moet je het vullen met 1 kg water.)
(Dit is nou de wet van Archimedes).
Stel je nou de volgende situatie voor: Ik heb een vlotje gebouwd met twee dicht bij elkaar elkaar geknoopte ballen.
De ballen worden enigzins in het water geduwd door het gewicht van het vlot. Als ik het scheef trek gaat de ene bal
dieper en de andere bal juist ondieper.
Dat betekent dat de bal die dieper gaat graag weer omhoog wil, en de bal die uit het water is niet meer omhoog wil.
De lage kant wil dus omhoog.
Dat is nu de basis van vormstabiliteit.
Dan nu het plaatje met met een vierkante bakken, allebij even scheef getrokken, maar de een veel breder als de
ander
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Je ziet duidelijk dat aan de lage kant de bak verder het water wordt ingedrukt, en aan de hoge kant minder het
water wordt ingedrukt. de verandering tov rechtop is aangegeven met de blauwe vlakjes.
Ook zie je dat bij de brede bak de blauwe vakjes veel groter zijn, en ze liggen ook verder van het midden als bij de
smalle bak, de opdrijfkracht komt daardoor ver uit het midden te liggen.
De drijfkracht verschuift daardoor veel meer bij de brede bak als bij de smalle bak.
Dit effect zie je net zo goed bij een ronde vorm.
Vormstabiliteit is dus afhankelijk van je breedte!
Hoe zit dat nu met dat verhaal uit de zeilboeken dat vormstabiliteit afneemt als je erg scheef ligt?
kijk maar naar onderstaand plaatje en let op de grote en vooral afstand tot het midden van de blauwe vlakken:
Tot nu toe is het eigenlijk hetzelfde verhaal als in het zeilboek alleen op een andere manier verteld.
In de zeilboeken heeft men het over het verschuiven van het drukkingspunt, waarbij het drukkingspunt het
aangrijpingspunt van de opdrijvende kracht is.
Een hele mond vol, maar hoe weet je nu waar het drukkingspunt zit?
welnu, het drukkingspunt is het midden van het onderwaterschip. Dus zoals op onderstaand plaatje voor een rechte
bak (let op de gestippelde hulplijnen)
In deze tekening kun je zien dat het drukkingspunt inderdaad iets verschuift als er helling onstaat. Zonder de
hulplijnen teken je jezelf echter als snel klem
Je zult zien als je een flink bredere bak tekent dat inderdaad het drukkingspunt bij een brede bak meer van het
midden komt te liggen.
Teken dit zelf maar eens.
Gewichtsstabiliteit
in het verhaaltje over vormstabiliteit kijk ik alleen maar naar hoe opdrijvende krachten van het midden schuiven.
Het omgekeerde van de opdrijvingskracht is de zwaartekracht. (Als het goed is, anders zink je of ga je juist vliegen)
Zit er een afstand tussen de werklijnen van de opdrijvende kracht en de zwaartekracht dan heb je een koppel, dat is
nu het oprichtend koppel (of kenterend koppel.)
Ga je hier nu fijn aan zitten tekenen, dan zul je zien dat bij grotere hoeken de hoogte van je zwaartepunt er erg toe
doet.
Hoe lager je zwaartepunt hoe meer opichtend koppel.
Zie het plaatje hieronder met links een mega zware kiel en rechts iemand boven in de mast. Werklijnen zijn de rode
stippel lijnen.
Snelheids stabiliteit
Dit heeft te maken met het waterski effect, buigt de boot het water naar beneden af en komt ze schuin te liggen dan
krijg je aan de lage kant meer lift met als gevolg een richtend moment.
Buigt de boot het water juist omhoog af zoals de sleepboot, dan heeft dit juist een negatieve uitwerking op de
stabiliteit.
Terug naar index
http://zeilplan.net/leren/theorie/tekst.php?tekst=trim.txt
Terug naar index
Trimmen
Ook dit theorie onderdeel wordt als erg ingewikkeld gezien.
De beste zeiltrim is erg moeilijk omdat er zoveel factoren zijn die ook nog constant veranderen.
Veel zeilers komen niet veel verder dan: "Bij harde wind moet je alles strak zetten, en bij weinig
wind alles zo zetten dat net je vouwen uit je zeil zijn."
Veel zitten deze mensen er niet naast, maar ze missen wel de uitdaging om "de boot zo lekker
mogelijk te laten lopen", wat een hele nieuwe dimensie aan zeilen toevoegt.
Een belangrijk hulpmiddel hierbij zijn de telltales, die de stroming om het zeil vertellen.
Dat je behalve met je zeilen ook met je gewicht kunt trimmen wordt vaak niet eens beseft.
Volgens mij is het idee achter trim door bijna alle zeilers te volgen die al zo goed zijn dat ze
zelfstandig kunnen varen:
Over hoe je je zeil in de juiste vorm krijgt ga ik niet op in aangezien dit teveel mogelijkheden
zijn en omdat de precieze uitwerking nogal eens per boot verschilt.
Als voorbeeld: zet je de neerhouder wat losser om meer twist te krijgen dan krijg je bij een
flexibele mast ook minder mastbuiging en daarmee meer bolling.
Zeiltrim
Bij optimale zeiltrim wordt zoveel mogelijk wind zoveel mogelijk naar achter afgebogen.
Hoe buig je nou zoveel mogelijk wind om naar achter:
Neem zoveel mogelijk bolling en zorg dat je achterlijk zoveel mogelijk naar achter wijst.
maar let op het volgende:
●
●
●
●
De stroming om het zeil niet mag niet loslaten, wat je kunt zien aan je achterste telltales
die niet meer naar achter gaan.
Als dit gebeurt kan dit komen omdat:
❍
je je zeil te ver hebt aangetrokken, de intredehoek is te groot ten opzichte van de
hoek met de wind
❍
Je bollingscurve ergens te veel is voor de stroming om nog te volgen.
Het voorlijk mag niet killen.
Als dit gebeurt kan dit komen omdat:
❍
je zeil niet genoeg is aangetrokken. De wind komt dan in het voorste stukje
simpelweg de verkeerde kant het zeil binnen.
❍
De intredehoek van het zeil te groot is (Dit geld natuurlijk als je je zeil al zover hebt
aangetrokken dat het achterlijk al naar achter wijst).
De telltales horen over de volle hoogte van het zeil naar achter te wijzen.
Als dit niet zo is kan dit komen omdat:
❍
als alleen je bovenste telltales naar lij gaan: te weinig twist.
❍
als allen je onderste telltales naar lij gaan: te veel twist.
Dat je de boot nog kunt houden, en je niet teveel helling krijgt.
Je bent dan overpowered, je buigt dus teveel wind teveel om, je kunt dan:
❍
Je zeil wat losser te laten, dan buig je de lucht wat minder om.(en dan begint je
voorlijk te klapperen, en hoor je intredehoek dus verkleinen)
❍
Meer twist te nemen waardoor de bovenkant van het zeil (wat het grootste hellend
koppel levert) wat minder wind ombuigt.
❍
Te reven, waardoor je gewoonweg minder wind ombuigt, en juist het meest hellend
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koppel leverend stuk zeil bovenin omlaag schuift.
Als je nu afgehaakt bent komt dit waarschijnlijk door de enorme berg begrippen in bovenstaand
verhaal.
Zie hieronder wat ik met deze begrippen bedoel.
begrippen:
Over de begrippen is meestal nogal wat verwarring omdat een eigenschap meestal samenhang
met een andere eigenschap.
Zo heeft bijvoorbeeld een zeil met de bolling ver naar achter een wat meer scheppend achterlijk.
De term achterlijk open zetten kun je op twee manieren zien:
●
●
Twist zorgt ervoor dat je achterlijk als het ware wegwaait, wat een lagere uittredehoek
geeft.
Je uittredehoek verkleinen door je bolling minder te maken en verder naar voren te zetten
geeft ook een lagere uittredehoek.
Twist
Hoe hoger je komt hoe harder het waait. De wind wordt namelijk afgeremd door de wrijving met
het water.
Hoe verder van het water hoe minder afgeremd. (dit is dus eigenlijk ook een grenslaag).
Als je halve wind vaart komt de schijnbare wind bovenin je zeil dus ruimer in als onderin je zeil.
Bovenin moet je zeil dus meer uitstaan.
Halve wind is een verdraaiing van je bovenste zeillat van ca 15 graden normaal, aan de wind is 5
graden normaal.
Natuurlijk is dit maar een richtwaarde, die van meerdere dingen afhankelijk is.
Een beetje twist is dus goed.
Opvallend is dat twist onder helling een grote invloed heeft.
Als het schip onder helling komt lijkt de lucht meer vanaf onderen te komen, dat wil zeggen uit
de richting van de giek.
Het profiel van het zeil wordt dan dus wat anders gevolgd.
Bij veel twist en grote hellingshoeken heeft dit een zeer grote invloed:
In de plaatjes hieronder in blauw de route van de lucht langs het zeil.
Beide van boven af gezien, rechtse schip ligt onder helling.
Nu hetzelfde maar dan met twist:
Hopelijk heb ik hiermee duidelijk gemaakt dat twist een heel grote invloed heeft onder helling.
Wanneer is de twist juist gekozen:
Als alle telltales in je achterlijk naar achter gaan.
Heb je geen telltales in het achterlijk (zoals bij je fok)dan is het een goede vuistregel dat als je
wat oploeft het zeil gelijkmatig van boven tot onder begint te killen, en niet eerst boven of onder.
ourworld.compuserve.com/homepages/lestergilbert/
plaatje van http://
Telltales
Telltales zijn verklikkers die de stromingsrichting weergeven. Ze bestaan in vele afmetingen en
uitvoeringen.
Een telltale is niets anders dan een dun,licht touwtje of dun strookje dat aan je zeil is
vastgemaakt.
Aangezien je lucht niet kunt zien heb je telltales nodig om te zien hoe de stroming om je zeil
heen verloopt. De basis voor een goede zeiltrim.
Ze zijn verkrijgbaar in de betere watersportwinkel.
Uiteraard kun je ze ook zelf maken, wat veel goedkoper is aangezien een dun touwtje/reepje
nogal gevoelig is voor beschadiging.
Simpelste uitvoering is een wollen draadje (liefst synthetisch in verband met rot) dat met een
naald door je zeil wordt gehaald, en aan bijde zijden een knoopje zodat het niet los kan schieten.
Ik ben geen voorstander van gaatjes in je zeil prikken dus mijn versie is een synthetisch wollen
draadje vastgeplakt met een rondje geknipt uit zeilreparatie tape.
Op huurboten gebruik ik meestal een stukje cassetteband (heb ik in overvloed aangezien mijn
autoradio graag bandjes lust)met een gewoon stukje plakband.
Gebruik liever geen grijze tape (ducktape) of bruine tape (dozentape) omdat deze soms enorm
smerige lijmsporen achterlaten bij verwijderen.
Een strookje knippen van licht spinnakerdoek (5 oz)is nog mooier aangezien deze bij regen deze
iets minder snel an je zeil kleven.
Ik probeer de telltales niet in de buurt te plakken van stiksels aangezien ze hier nogal eens aan
willen blijven kleven.
Als laatste zou ik willen opmerken om ze donker van kleur te maken zodat je ze goed kunt zien.
Plaats van de telltales:
Eigenlijk ben je alleen geïnteresseerd in of de stroming bij de achterkant van het zeil nog mooi
verloopt.
Logisch is dus om ze daar te zetten, 3 is meestal voldoende, mooi verdeelt over je achterlijk.
Bij je fok echter is dit meestal vrij zinloos omdat je ze dan niet kunt zien als je je aan loef bevind
doordat ze dan achter het grootzeil zitten.
Daarom zet je ze bij de fok zover naar voren dat je ze als stuurman kunt zien.
Ga je voor de eerste keer fanatiek aan de gang met de zeiltrim dan is het aan te bevelen om er
meerdere horizontaal te plaatsen zodat je de stroming om het zeil goed kunt zien.
dat ziet er helaas al snel uit alsof er iemand jarig is aan boord, dus is het aan te raden dese
tijdelijk te gebruiken.
Ga je zo eens rondvaren dan zul je waarschijnlijk merken dat het heel moeilijk is om alle telltales
naar achter te krijgen.
Bedenk dan dat de stroming aan lij het belangrijkst is aangezien deze de hoogste snelheid heeft.
Aan loef in je voorlijk lukt het vaak niet om de telltales naar achter te krijgen.
Dit komt omdat als het goed is de stroming aan loef langzamer gaat als aan lij, al gauw is dit
zoveel langzamer dat de stroming daar zelfs stil komt te staan, en je telltales gewoon wat
ronddwarrelen.
Let dus alleen op je telltales aan lij en aan je telltales aan je achterlijk.
Krijg je ook je telltales aan lij niet goed bedenk dan dat het eigenlijk alleen gaat om je telltales
aan je achterlijk.
Het gaat erom wat je zeil in totaal doet en niet wat het voorste stukje doet.
Uiteraard is het wel het streven om de telltales aan lij en in het achterlijk goed te krijgen.
Zeiltrim hoog aan de wind
Snelheid versus hoogte.
Hoog aan de wind is het meestal de bedoeling om zo hard en zo hoog mogelijk te gaan.
Vaak zie je de neiging om het zeil dan ook maar helemaal binnen te trekken.
Dit heeft geen zin als daarbij de lucht naar loef wordt afgebogen, dan ben namelijk lucht naar
loef aan het ombuigen, en maak je dus meer zijwaartse kracht, die leid tot een grotere
driftweerstand.
Met een vlakker zeil kun je het zeil wel verder aantrekken.
Helaas is het zo dat een vlakker zeil de lucht minder ombuigt en je dus minder kracht krijgt.
Vaak is het niet mogelijk om even snel het zeil vlakker te maken, denk dan ook eens aan de truc
om iets meer helling te nemen, dan gaat de lucht "vlakker langs je zeil zoals hierboven in het
verhaal over twist beschreven.
Dus: hoe vlakker het zeil, hoe verder je het mag aantrekken, hoe minder kracht je krijgt.
Let trouwens ook eens op bovenstaand plaatje op de lucht voordat die bij het zeil is.
De lucht voelt namelijk al voor het zeil de onderdruk aan lij en wil daar naar toe stromen.
Dit effect noemt men ook wel "upwash". de ombuiging achter het zeil noemt men "downwash".
Deze termen komen uit de wereld van vliegtuigvleugels, waar de up en de down wat logischer is.
Als laatste is op te merken dat aan de wind de bolling iets verder naar voren wordt gezet.
Dit zorgt (naast afvlakking van het achterlijk, dus minder afbuiging naar loef) ervoor dat je
zeilkracht iets meer naar voren wordt gericht.
Zeiltrim ruimere koersen
Op ruimere koersen speelt hoogte halen natuurlijk weinig rol.
Ook is de helling meestal niet zo gauw een probleem omdat de zeilkracht nauwelijks naar de
zijkant gaat.
Op ruimere koersen gaat het dus om zoveel mogelijk kracht.
. Dit betekent dus een zo groot mogelijke intredehoek en een zo groot mogelijke uitredehoek en
geen loslating van de stroming.
Dus een zo groot mogelijke diepte en een een curve die maar langzaam afneemt.
Extra bolle zeilen zoals bolle jannen, gennakers en spinnakers kunnen nu meestal hun werking
doen.
Bij deze extra bolle zeilen dient natuurlijk ook gelet te worden dat de lucht niet naar loef wordt
afgebogen, maaar een beetje is niet zo erg zolang er maar wat lucht naar achter wordt
omgebogen.
Het alternatief is al gauw dat zeil te strijken, waarmee het natuurlijk helemaal niks meer doet.
Zeiltrim met golven
Golven zorgen ervoor dat het schip en daarmee de zeilen heen en weer bewegen. Zowel ten
opzichte van de wind als ten opzichte van het water.
Als je zeil heen en weer beweegt betekent dit dat de wind door het schommelen ook steeds iets
anders binnenkomt.
Voor je zeiltrim betekent dit dus dat deze niet superkritisch kan zijn.
Als de wind iets voorlijker inkomt of iets dwarser inkomt moet ze zeiltrim ook nog redelijk zijn.
Aan de wind dus iets meer op snelheid varen in plaats van op hoogte.
Voor je kiel geld dat deze ook heen en weer beweegt.
Je kiel ziet dit als een constant veranderende drifthoek, soms een negatieve drifthoek (geeft ook
drift weerstand) en vaak een heel grote drifthoek.
Een grote drifthoek geeft veel driftweerstand. Je hebt dus meer driftweerstand, met als gevolg
dat je langzamer gaat varen en nog meer driftweerstand krijgt.
Dit is het simpelst te verbeteren door iets meer op snelheid te varen waardoor de drifthoek en
daarmee de driftweerstand minder wordt.
Je bent het grootse gedeelte van de tijd bezig om golven te beklimmen, aangezien golfaf sneller
gaat, en golfaf dus minder tijd kost.
anneer er tegen een golf op wordt gevaren zal met name de snelheid van de top van de mast
erg laag zijn.
Hierdoor zal de schijnbare wind in de top veel ruimer inkomen. Met wat extra twist staat je zeil
op dat moment optimaal.
Verder is het gebruikelijk om de bolling iets verder naar voren te zetten.
Ik weet niet precies waarom maar een redenering hierachter is dat hoe verder de bolling naar
voren staat hoe beter de bolling op die plek blijft.
Als je bolling steeds van voor naar achter beweegt heeft de stroming wat meer moeite om aan te
blijven liggen.
Weer een andere redenering om de bolling wat verder naar voren te leggen is dat de stroming
wat onregelmatiger is, en hoe verder de bolling naar voren in het zeil ligt hoe minder snel de
stroming daar loslaat, omdat daar minder grenslaag is en omdat de fok daar helpt om de
stroming aan te laten liggen.
Een andere redenering die ik wel eens van een grootzeil trimmer heb gehoord is dat de
zeilkracht daarmee wat meer naar voren wordt gericht.
Die laatste heb ik mijn twijfels bij omdat je je dan kunt afvragen of dit niet altijd verstandig is.
Balanceren zeilkracht en onderwaterkracht.
Heb je nu eindelijk een heleboel power in je zeil getrimd, dan kan het gebeuren dat de boot
vreselijk loefgierig is zodat je een flinke roeruitslag moet geven.
Veel roeruitslag geven remt natuurlijk, dus dat is geen optimale trim.
Een beetje druk op je roer (loefgierig natuurlijk) is gunstig.
Dit is makkelijker voor te stellen als je de werking van het grootzeil en de fok vergelijkt met de
werking van kiel en roer.
Je vaart toch ook niet met de fok los!
Helmaal uit den boze is een lijgierig schip, dat kun je vergelijken met rondvaren met een
onderwaterschip met de fok bak.
Je kunt het ook anders zien: Buig je met het roer water naar lij om dan duw je de boot naar loef,
je verlijerd dan dus minder en je hebt dan ook minder driftweerstand.
De discussie is eigenlijk hoeveel roeruitslag moet je hebben bij het rechtdoor varen.
Om dit voor te kunnen stellen ga ik weer naar de vergelijking met de zeilen.
Je fok heeft de wind al wat omgebogen voor je grootzeil. Daarom is het grootzeil altijd al wat
extra naar binnen getrokken ten opzichte van de fok.
(overigens zou je ook kunnen zeggen dat de fok wat losser staat als het grootzeil omdat de fok
in de upwash van het grootzeil zit.) Je kunt net zo goed zeggen dat de kiel het water voor het
roer al wat heeft omgebogen, en je roer dus wat "strakker" moet.
Gevangen in een sterk overdreven plaatje de juiste stand waarbij het de blauwe lijn de route van
het water voorsteld:
De roerstand hoort dus een stukje naar lij (=helmstok naar loef)te zijn, maar minder dan de
drifthoek.
Als de drifthoek dus 5º is zal de helmstok ca 1-4 graden naar loef horen te zijn.
De kleine loefgierigheid die hierbij hoort is te verwezenlijken door met de plaats van de
zeilkracht te spelen,
Dit kan met de helling gebeuren (=dwarscheepse verplaatsing van het zeilpunt)
en/of met de zeilen en/of bolling naar voor of achter schuiven (=verschuiven van zeilpunt in
lengterichting).
Trimmen met de helling
Los van de grote invloed van de helling op de zeilen, kan dit een grote invloed op de
scheepsweerstand hebben.
Meestal is het zo dat een schip het beste vaart met een kleine helling omdat het nat oppervlak
iets kleiner wordt.
Is men aan het planeren dan moet men juist zo recht mogelijk varen, omdat men de liftkracht
naar beneden wil richten.
Ook gaat het water scheef over je kiel wat ook invloed heeft.
Meer durf ik hier nu niet over te zeggen omdat dit erg scheepstype afhankelijk is.
Trimmen met de helling in lengterichting
Als de boot wat achterover hangt dreigt als snel de spiegel in het water te komen.
Als de spiegel gedeeltelijk onder water komt betekent dit meestal dat het water daar een raar
hoekje om moet, en daarmee extra weerstand maakt.
Als de spiegel te ver boven water steekt zit er een heel stuk romp niet in het water.
Dit heeft tot gevolg heeft dat de lengte van de waterlijn korter is en daardoor de golfmakende
weerstand dreigt toe te nemen.
Meer durf ik hier nu niet over te zeggen omdat dit erg scheepstype afhankelijk is.
Waarmee te trimmen
Zoals ik bovenaan al zei is dit erg bootafhankelijk.
Beste is dus naar mijn mening hier gewoon eens mee te spelen op een dag met weinig wind
zodat je goed kunt zien wat er gebeurt als je aan een lijntje trekt. Liefst zelfs zonder "advies"
van pottenkijkers die het "beter" weten hoe het moet, zodat je nooit eens dingen kunt
overdrijven als experiment.
Enige tips die ik geef is dat als je je neerhouder strak doorzet als je ook je grootschoot helemaal
hebt aangetrokken, en dan de grootschoot weer loslaat er een kans bestaat dat je mast knikt bij
de giek.
Andere tip is dat dat je een stijve vast niet moet proberen te buigen.
Voor de rest niet te bang zijn om een lijntje goed strak te zetten, maar blijf je gezond verstand
gebruiken.
Volgende stap is dat je een zelfde boot zoek en daar dicht bij gaat varen zodat je kunt zien bij
welke trim je sneller gaat.
Veelal is de gelegenheid hiertoe op een dagtocht bij een zeilschool, of indien je een eigen boot
hebt op gezellige wedstrijden die meestal wel door een lokale club worden georganiseerd.
Meestal zijn die lokale competities ook leuk voor beginners omdat het nivo meestal niet
belachelijk hoog is en er veel verschil zit tussen de boten, er zit altijd wel iemand tussen waaran
je gewaagd bent, en anders kun je altijd de schuld geven aan het materiaal.
Ook heeft dit als voordeel dat je aan de bar de wedstrijd in een ontspannen sfeer kunt
evalueren, (wat voor veel mensen misschien nog wel belangrijker is als het zeilen zelf).
Is je materiaal echt bar slecht dan kun je vast wel iemand vinden die volgende week een
fokkemaat nodig heeft.
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Terug naar index
Veelgestelde vragen
Uiteraard kun je nieuwe vragen aan mij mailen.
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1 Waarom verlijer ik zoveel na de overstag?
2 Hoe werkt een vleugelkiel?
3 Wanneer moet ik kiezen voor een High Aspect fok en wanneer voor de genua?
4 Molens draaien altijd linksom en mijn boot loopt ook lekkerder over bakboord,
Is dit om dezelfde reden?
5 Ga ik harder in de vaargeul of op het meer?
6 Als ik ruime wind in de trapeze blijf hangen, en de stuurman naar de andere
kant gaat zodat we toch rechtop blijven, ga ik harder. Hoe kan dit?
7 Kan een boot sneller dan de wind varen?
8 Kan ik bij de hogerwal aanleg met sliplanding niet beter de fok wegrollen?
9 Iemand heeft heeft het drukverschil tussen loef en lij gemeten en kwam op 0
uit. Hoe kan dat?
10 In je koppels en krachten verhaal zeg je dat de zeilkracht loodrecht op de giek
is. In je verhaal over zeiltrim zeg je dat de bolling naar voren plaatsen de
zeilkracht meer naar voren richt. Je verhaal klopt dus niet en je bent een prutser!
11 Met dat theorie verhaal van jou kom ik nergens tegen dat de fok meer doet dan
het grootzeil. Toch heb ik dat al meerdere keren gehoord. hoe zit dat ?
12 In het blad "Zeilen" stond dat een cunningham hole weinig zin heeft bij
moderne boten. hoe zit dat?
13 Hoe werkt een zelflozer?
14 Een opgeklapt roer (wat nog steeds onder water zit) stuurt slechter als een
roer dat netjes naar beneden zit. Hoe kan dat?
15 Die foto van dat vliegtuig die een sleuf achter zich maakt in de wolken, is die
echt?
16 mag ik dingen kopieren uit je site?
17 Je zegt dat de stroming achter op je zeil turbulent is, en dat de stroming moet
blijven aanliggen. Dat kan toch niet?
1 Waarom verlijer ik zoveel na de overstag?
Lees het stuk zeilpuntverplaatsing en onderwaterschip.
Het heeft dus te maken met het overtrokken zijn van je kiel en/of overtrokken zijn van je zeil.
Als je je zeilstand netjes aanpast (ook je fok)aan hoe de wind tijdens je overstag staat, en pas
weer hoog stuurt als je snelheid hebt zou dit moeten ophouden.
2 Hoe werkt een vleugelkiel?
Een vleugelkiel trekt de boot dieper het water in, de vleugel trekt de boot dus naar loef bij grotere
helling waardoor de rest van de kiel minder kracht naar loef hoeft te geven.
http://zeilplan.net/leren/theorie/tekst.php?tekst=faq.txt (1 of 5)24-1-2004 17:32:51
Meestal is de prestatie van een schip met een vleugelkiel slechter als van een schip met een
diepstekende kiel.
Een vleugelkiel steekt meestal minder diep, waardoor het de oplossing kan zijn voor boten die
wat ondieper vaarwater willen kunnen aandoen.
3 Wanneer moet ik kiezen voor een High Aspect fok en wanneer voor de genua?
Als je hoog wil kunnen gaan is de HA beter, zeker als het hard waait op vlak water. Wil je wat
meer op snelheid varen, zoals bij golven dan is de Genua beter.
Dit komt omdat je Genua meer "tipwervels" heeft, en vaak wat boller is. Minder efficient dus als
je hoog wil.
Daarentegen is een Genua wel gewoon groter, en daarom gunstiger op de ruime koersen.
4 Molens draaien altijd linksom en mijn boot loopt ook lekkerder over bakboord, Is dit
om dezelfde reden?
Nee, Molens draaien linksom omdat dit historisch zo gegroeid is omdat maalstenen vroeger maar
op een manier werden gemaakt.
Eigenlijk draaien alleen de molens in Nederland en Belgie linksom. (bron Informatie-XVI het gilde
van vrijwillige molenaars, Evert Smit, die dit heel duidelijk uitlegt in ca 50 kantjes die ik jullie wil
besparen)
Waarschijnlijk staat je mast scheef, is krom, of je boot is scheef, of je gewicht is scheef verdeeld.
Overigens is het wel zo dat windvlagen over de ene boeg ruim inkomen, en over de andere boeg
juist hoger, afhankelijk aan welke kant van het lagedrukgebied je zit. Zie zeilplan.net onder
weer, en onder wedstijdzeilen en vervolgens tactiek.
Dit effect zorgt ervoor dat de boot over de ene boeg lekkerder loopt.
Ook zou het zo kunnen zijn dat bij de bovenkant van je zeil de wind onder een iets andere hoek
binnenkomt, waardoor je over de ene boeg met teveel twist vaart, en over de andere boeg met te
weinig twist.
5 Ga ik harder in de vaargeul of op het meer?
In de vaargeul ga je harder (als deze dieper is als het meer) Dat komt omdat in ondiep water
golven langzamer gaan.
Je kunt dit ook zien bij de kust waar het ondieper wordt, daar komen de golven dichter achter
elkaar te zitten terwijl het er niet meer worden. De golven gaan dus langzamer.
Dit betekent ook dat je rompsnelheid lager wordt.
Is het meer erg ondiep dan krijg je ook nog eens het effect wat je ook in een kleine sloot hebt:
Zuiging
Als je door een kleine sloot vaart moet het water onder de boot door naar achteren.
Het water wordt dan als het ware door de spleet tussen bodem en boot geperst. Deze "pers druk"
is extra weerstand.
6 Als ik ruime wind in de trapeze blijf hangen, en de stuurman naar de andere kant gaat
zodat we toch rechtop blijven, ga ik harder. Hoe kan dit?
Waarschijnlijk omdat dan de boot minder beweegt en je dus minder last hebt van beweging van
je zeil die de stroming verstoord.
Verder zou ik me kunnen voorstellen dat je zelf meer wind vangt als je in de trapeze hangt.
Als laatste zou ik me kunnen voorstellen dat je minder mastbuiging hebt doordat je trapezedraad
de functie van zijstag enigszins overneemt, en dat beter doet dan het zijstag omdat je
trapezedraad horizontaler trekt dan het zijstag.
7 Kan een boot sneller dan de wind varen?
Voor de wind: natuurlijk niet (nou ja zonder motor en andere flauwe grappen dan).
Rond halve wind: als je een boot hebt met niet te veel weerstand moet dit makkelijk kunnen.
Surfers en catamarans varen regelmatig twee keer harder dan de wind.
Met een gewone zeilboot haal je dit meestal niet.
Misschien kun je begrijpen dat als je halve wind vaart, met dezelfde snelheid als de wind, de
schijnbare wind schuin van voren komt, en je net zoals bij aan de wind varen daar gewoon mee
kunt doorgaan.
8 Kan ik bij de hogerwal aanleg met sliplanding niet beter de fok wegrollen?
Als je de fok laat klapperen kun je hem beter wegrollen.
Als je hem netjes bedient zal je een stuk minder verlijeren.
Laten staan dus.
9 Iemand heeft heeft het drukverschil tussen loef en lij gemeten en kwam op 0 uit. Hoe
kan dat?
Omdat de drukken niet zo hoog zijn en daarmee moeilijk te meten. Makkelijker is het gemiddelde
uitrekenen door de kracht op je zeilen te meten en te delen door het zeiloppervlak.
10 In je koppels en krachten verhaal zeg je dat de zeilkracht loodrecht op de giek is. In
je verhaal over zeiltrim zeg je dat de bolling naar voren plaatsen de zeilkracht meer
naar voren richt. Je verhaal klopt dus niet en je bent een prutser!
Ik ben inderdaad een prutser, maar van prutsen kun je heel wat leren.
Het koppels en krachten verhaal wou ik begrijpbaar houden, en dus niet ingewikkelder maken
door te zeggen dat de zeilkracht meestal iets meer naar voren gericht is ten opzichte van je giek.
De zeilkracht is inderdaad iets meer naar voren gericht als loodrecht op de giek. Dit komt door:
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Twist, De bovenkant van je zeil is wat meer naar voren gericht, en je zeilkracht dus ook.
Bolling voor het midden. De zeilkracht is afhankelijk van hoeveel je ombuigt en dus van je
curve.
Voorin heb je de meeste curve en dus de meeste kracht, en het zeil is voorin meer vaar
voren gericht.
Overdreven:
Wat je hieruit leert is vooral dat je eigenlijk niet naar je giek moet kijken maar naar je zeil.
Gebruik je het voor koppels en krachten dan wordt je al gauw gek, dan niet doen dus.
11 Met dat theorie verhaal van jou kom ik nergens tegen dat de fok meer doet dan het
grootzeil. Toch heb ik dat al meerdere keren gehoord. hoe zit dat ?
De fok levert inderdaad een relatief grotere kracht dan je grootzeil. Dit komt omdat de fok in de
snellere lucht van het grootzeil zit, en het grootzeil in de langzamere lucht van de fok.
leest het bernoulli verhaal maar door.
Je fok doet dus meer door het grootzeil, en je grootzeil minder door de fok.
Kortom, de prestatie van je fok is dus sterk afhankelijk van wat je precies met je grootzeil doet.
Als ik een uitspraak zou doen dat de fok meer doet dan het grootzeil, dan betekent dat dus niet
dat je je helemaal moet focussen op de fok.
12 In het blad "Zeilen" stond dat een cunningham hole weinig zin heeft bij moderne
boten. hoe zit dat?
Sorry, dat weet ik niet want ik heb dat nooit gelezen.
Lijkt mij dat een cunningham handig blijft, zelfs bij zeilen die niet rekken en die al een boel
andere trimmogelijkheden hebben.
Een cunningham is erg makkelijk om spanning op je voorlijk te trekken. Met je val is dit vaak
lastiger omdat deze niet (of weinig) vertraagd is.
13 Hoe werkt een zelflozer?
Er zijn twee soorten zelflozers.
De een steekt niet door de romp heen.
De ander steekt wel door de romp heen of heeft een kapje op de romp.
De versie welke niet door de romp steekt zuigt eigenlijk niet, terwijl de versie welke wel
doorsteekt zuigt als een tiet.
Hoe kan dat nu?
De niet doorstekende zelflozer buigt geen water om.
Volgens De wet van Bernoulli is er dus ook geen drukverandering.
De wel doorstekende zelflozer buigt het water wel om.
Dit geeft natuurlijk krachten.
Het looswater komt er op een plek uit waar het water in de richting van de romp wordt
omgebogen, daar waar dus een reactiekracht is van de romp af is.
Dit is nou ook de reden dat een hoogtemeter van een vliegtuig(welke eigenlijk de luchtdruk meet)
op een vlak gedeelte van een vliegtuig zit.
Dan wordt hij namelijk niet beinvloed door de snelheid.
14 Een opgeklapt roer (wat nog steeds onder water zit) stuurt slechter als een roer dat
netjes naar beneden zit. Hoe kan dat?
Dit komt namelijk doordat de druk welke je opbouwt "weglekt" om de bovenkant en onderkant
van je roerblad heen: De "tipwervels". Bij een opgeklapt roer heeft het water veel meerde tijd en
ruimte om tipwervels te maken omdat je naar verhouding veel meer tip hebt.
15 Die foto van dat vliegtuig die een sleuf achter zich maakt in de wolken, is die echt?
Zover ik weet wel, Het enige wat eraan getruukt is is dat er een vliegtuig voor vliegt. De fotograaf
zat namelijk in dat vliegtuig ervoor.
Zover ik weet vloog dit vliegtuig ook gewoon rechtdoor en steeg niet op ofzo.
Dit heb ik niet gecheckt. Foto is van het bedrijf die dat vliegtuig bouwt (Cessna.
16 mag ik dingen kopieren uit je site?
Ja hoor, daar is hij voor. Wel zou ik het fijn vinden als je het internetadres erbij vermeld, in plaats
van mijn naam.
Dit omdat als je een stukje uit zijn verband trekt ik liever heb dat mensen het hele verhaal
kunnen lezen, dan dat ze denken dat ik dom ben.
17 Je zegt dat de stroming achter op je zeil turbulent is, en dat de stroming moet
blijven aanliggen. Dat kan toch niet?
Ik zeg niet dat de hele stroming achter op je zeil turbulent is, ik zeg dat de grenslaag bij je
achterlijk turbulent is geworden.
Let op dat als het dunne (enkele mm)luchtlaagje wat op je zeil "kleeft" turbulent is dit absoluut
niet betekent dat de stroming daar als geheel turbulent is.
Terug naar index
http://zeilplan.net/leren/theorie/tekst.php?tekst=links.txt
Terug naar index
Enkele links
misinterpretations of bernoulli lawDit is eigenlijk hetzelfde als mijn verhaal over hoe een
zeil werkt, alleen heb ik de wiskunde geskipt.
geen aanrader als je niet van wiskunde houd (Weet je ook meteen waar mijn coanda plaatje
vandaan komt).
a physical description of lift
Dit is een verhaal over hoe een vleugel werkt wat wiskundig niet zo diep gaat, en daardoor
wat makkelijker leesbaar is. Wel is het coanda verhaal hier niet helemaal duidelijk.
see how it flies
Deze vlieger kan het mooi vertellen. Let op hoe hij de magere uitleg van vorige link over
coanda weet te gebruiken om te vertellen dat dit nergens op slaat. Lees je mijn verhaal, of
de eerste link, dan zie je dat zijn huis-tuin en keuken proefje dit juist bewijst. Rest van de
site is best intressant als je ook over vliegtuigen wilt meepraten, verder is dit iemand die de
circulatie theorie ziet als werkelijkheid.
jef raskin
Geloof je toch nog een beetje dat een vleugel werkt doordat de weg boven de vleugel langer
is, dan wordt dat helemaal de grond ingestampt. Erg leuk geschreven vind ik. Door deze site
ben ik aan het denken gezet en heb heel dit verhaal geschreven.
veenhoop
Deze zeilschool vertelt op zijn website iets over theorie.
Dit is wel een typisch voorbeeld van toveren met de circulatie theorie van prandtl, waar je
dus eigenlijk niks aan hebt. Rest van het verhaal vind ik heel goed. Weet je ook meteen
waar ik die foto van dat jacht met reefknuttels vandaan heb.
vleugel in rook
Hier wat plaatjes van vleugels met wat rook. aan lijzijde is bovenkant gaat de lucht veel
sneller
draaiende ballonnen theorie
Een hele intressante theorie die de werking van een vleugel verklaard op een andere manier.
niet alleen de vliegtuigvleugel wordt fout uitgelegd
Voor de technische nerd (zoals ik) leuk om eens door te lezen, ook de rest van deze site
heeft leuke dingen, zoals practical jokes
http://www.amasci.com/
virtuele windtunnel
Deze mensen hebben een virtuele windtunnel op hun site staan.
Je kunt hem zelf downloaden op nasa simulator site
http://zeilplan.net/leren/theorie/tekst.php?tekst=links.txt (1 of 2)24-1-2004 17:33:43
http://zeilplan.net/leren/theorie/tekst.php?tekst=links.txt
Had je zelf nog een mooie toevoeging/opmerking/vraag mail me dan op [email protected]
(domme vragen bestaan niet)
Ook kun je een bericht achterlaten op het forum.
Ik ben erg benieuwd vanaf waar je niks meer snapt van bovenstaand verhaal, dan moet ik
dat nog eens wat beter neerzetten. Ik wil heel graag feedback!!
Terug naar index
http://zeilplan.net/leren/theorie/tekst.php?tekst=links.txt (2 of 2)24-1-2004 17:33:43
Misinterpretations of Bernoulli's Equation
Misinterpretations of Bernoulli's Law
Weltner, Klaus and Ingelman-Sundberg, Martin
Department of Physics, University Frankfurt, Postfach 11 19 32, 60054 Frankfurt, Germany; Stockholm
Abstract. Bernoulli's law and experiments attributed to it are fascinating. Unfortunately some of these
experiments are explained erraneously, e.g.: the function of a vaporizer and the soaring of a ping-pong
ball in a jet stream of a hair dryer can not be used as applications of Bernoulli's law. The static pressure
in a free jet stream is equal to the static pressure in the environmental atmosphere regardless of the
streaming velocity of the jet. This can be shown by classroom experiments.
Acceleration of air is caused by pressure gradients. Air is accelerated in direction of the velocity if the
pressure goes down. Thus the decrease of pressure is the cause of a higher velocity. It is wrong to say
that a lower pressure is caused by a higher velocity.
Pressure gradients perpendicular to the streamlines are caused by the deflection of streaming air. The
deflection of air generates regions of lower and higher pressure according to the curvature of the
streamlines. Vaporizer, the soaring ping-pong ball as well as the physics of flight are only to be
explained regarding the acceleration perpendicular to the streamlines.
1. Common derivation and applications of Bernoulli's law
In a recent paper Baumann and Schwaneberg [1] state:
Bernoulli's Equation is one of the more popular topics in elementary physics. It provides striking
lecture demonstrations, challenging practice problems, and plentiful examples of practical
applications from curving baseballs to aerodynamic lift. Nevertheless, Students and Instructors
are often left with an uncomfortable feeling that the equation is clear and its predictions are
verified, but the real underlying cause of the predicted pressure changes is obscure.
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Figure 1
This statement is correct and it should be added that the common treatment of Bernoulli's equation is
also misleading. Generally a flow of an incompressible fluid through a tube with different cross-sections
is observed and the theory of conservation of energy is applied to the flow.
The energy of a volume V at any point is the sum of its kinetic energy
and its potential energy
(pV). Effects of gravitation and viscosity are neglected. The energy of a given volume of the fluid which
moves from point 1 to point 2 is the same at both points. The related energy equation is
(1)
Using
and rearranging we arrive at Bernoulli's Law:
(2)
The equation states a reversed relation between static pressure and streaming velocity which is often
demonstratet by experiments like
●
Soaring ball: A light ball (e.g. ping pong ball) can be kept soaring in an upwards directed air
stream of a hair dryer. The ball remains within the stream even if the stream is inclined and not
vertical. The explanation given is that the static pressure within the stream is less due to the
higher velocity.
●
Evaporator: If a fast stream of air passes over the opening of a pipe, the pressure inside is
lowered and it is possible to suck in liquids. This effect is used as an application of Bernoulli's
law [2] referring to the high streaming velocity within the air stream and claiming pstream <
patmosphere .
Figure 2
●
Aerodynamic lift: The higher streaming velocity of the air at the upper surface of the wing is
stated to be the cause of the lower pressure. Different reasons are given for the generation of the
higher streaming velocity. The most popular one is a comparison of path lengths of the flow
above and below the aerofoil and the statement that due to a longer path length at the upper side
the flow has to be faster [3], [1].
2. Misinterpretations and misapplications of Bernoulli's law
2.1 Static pressure in a free air stream
Static pressure is the pressure inside the stream measured by a manometer moving with the flow. At the
same time, the static pressure is the pressure which is excerted on a plane parallel to the flow. Thus the
static pressure within an air stream has to be measured carefully using a special probe. A thin disk must
cover the probe except for the opening. The disk must be positioned parallel to the streaming flow, so
that the flow is not interfered with.
If the static pressure is measured in the way outlined above within a free air stream generated by a fan or
a hair dryer it can be shown that the static pressure is the same as in the surrounding atmosphere.
Bernoulli's law cannot be applied to a free air stream because friction plays an important role. It may be
noted that the situation is similar to the laminar flow of a liquid with viscosity inside a tube. The
different velocity of the stream layers is caused by viscosity. The static pressure is the same throughout
the whole cross-section. A free air stream in the atmosphere is exlusively decelerated by friction. If
static pressure in a free air stream is equal to atmospheric pressure, some of the striking lecture
demonstrations are interpreted incorrectly since the effects observed are not caused by Bernoulli's law.
2.2. Aerodynamic lift
The explications referring to differences of path lengths are wrong. Air volumes which are adjacent
before separation at the leading edge of the aerofoil do not meet again at the trailing edge [4]. This
explanation is erranous. The higher streaming velocity at the upper surface of the aerofoil is not the
cause of lower pressure. It is the other way round as will be shown below. As a matter of fact the higher
streaming velocity is the consequence of the lower pressure at the upper surface of the wing [4].
These contradictions and misunderstandings can only be clarified by means of the basic physics of fluid
mechanics.
3. Fluid dynamics, Newtons laws and the Euler equations
Fluid dynamic is an extension of Newton’s mechanic. It was Euler who applied the fundamental laws of
Newton to fluid motion. He succeeded in establishing equations for the three dimensional fluid motion the Euler equations. For simplicity reasons we restrict our considerations to stationary flow and we
neglect effects of gravitation and viscosity [5]. We refer to an elementary cubical volume within curved
streamlines. Figure 3. The reference system is chosen deliberately to separate the direction of velocity
and its perpendicular. We analyse the acceleration of a mass element
components of the acceleration:
. We separate the
Tangential acceleration = acceleration in direction of the velocity (Figure 3)
Normal acceleration = acceleration perpendicular to the direction of velocity (Figure 4)
Tangential acceleration in s-direction.
Figure 3
An acceleration is the result of a force acting on the mass element. A force in direction of the velocity
can only be generated by a pressure difference. The static pressure acting on the aera A at the back must
exceed the pressure on the aera A at the front.
Acceleration in direction of the motion is the effect of a decrease of pressure. The force F is given by:
(3)
Thus Newton’s equation reads
(4)
Using
and
we obtain
(5)
This equation can be transformed to
(6)
The definite integral for two positions 1 and 2 is
(7)
The solution is
(8)
This is Bernoulli's law.
This derivation of Bernoulli's law is more instructive compared to the derivation generally used in
textbooks because it shows the physics behind the law. The streaming fluid accelerates as a result of
decreasing pressure (i.e. or a negative pressure gradient). This derivation clearly shows that an
acceleration can never be the cause of decreasing pressure.
Normal acceleration exists if streamlines are curved. A normal acceleration is the effect of a force in
direction of the radius of curvature. In the case of the elementary volume the pressure acting on the
outside area must exceed the pressure on the inside area.
Figure 4
The force referring to the z-axis is:
The negative sign is due to the fact that the force
has the opposite direction of a positive pressure gradient.
Newton’s equation reads
(9)
The normal acceleration is well known for circular motions with a radius R and a velocity v:
(10)
Inserting
and
in (9) we obtain the pressure gradient in z-direction.
(11)
Unfortunately this equation can only be integrated if the total field of the flow is known. However the
relation can be demonstrated in a simple and impressing way. If we make water rotate in a disk or a pot,
the surface of the water rises at the outer parts. The level of the surface is a manometer indicating the
pressure beneath. Assuming homogenous angular velocity of the circular flow of water the velocity is
. Thus equation (9) may be solved for a horizontal level beneath the surface neglecting
gravitational pressure:
(12)
(13)
The pressure is proportional to the square of the radius generating a parabolic surface.
(14)
This result is also well known for centrifuges.
As a rule, physics textbooks neglect the treatment of normal acceleration of fluids. They do not discuss
the pressure gradients normal to the velocity if streamlines are curved. By the way, this is different from
textbooks on technical fluid dynamics which treat the flow of fluids in curved tubes. The neglect of
pressure gradients related to curved streamlines is disastrous because the mechanism producing low
pressure is thus made impossible to understand. Obstacles cause curved streamlines and generate
pressure gradients of air and as a consequence regions of higher or lower pressure. The deflection of the
streaming is the cause for the generation of pressure gradients perpendicular to the streamlines and thus
the cause for the generation of pressure differences.
3.2 Coanda-effect.
The flow near limiting surfaces follows the geometrical shape of these surfaces. This behaviour is called
Coanda-effect. It is neither trivial nor general. The flow must not be forced to change its direction
abruptly as to avoid the generation of turbulence and separation. The classic example for the Coandaeffect is a flow blown across a flat plane with an adjacent half cylinder. At first the flow follows the
surface of the cylinder and separates later.
Figure 5
Figure 6
This is important because this behaviour holds for all flows limited by smoothly curved surfaces like
aerofoils, streamlined obstacles, sails and - with a certain reservation - roofs.
The Coanda-effect can be understood taking viscosity into consideration. In figure 6 we assume the
stream to start. It will flow horizontally. But due to viscosity some layers of the adjacent air will be
taken away by the stream. In this adjacent region - dotted in figure 6 - the air is sucked away and hence,
gives rise to a reduction of pressure, consequently producing a normal acceleration of the stream. By the
end of the process the stream fits the shape of the curved surface. This Gedankenversuch illustrates the
importance of viscosity in generating of stationary flow. Also the stationary flow around an aerofoil
which produces lift is only possible due to the Coanda-effect and the air's viscosity.
4. Generation of high and low pressure within a flow
4.1 Measurement of static pressure within a free stream of air
A sufficiently sensitive manometer can be produced easily if not available in the lab. A fine pipe of glas
is bent at one side to dip in a cup and to be fixed according to figure 7. The meniscus must be positioned
in the middle of the pipe. The suitable inclination should be 1:15 - 1:30. A rubber tube connects the glas
pipe with a probe. As has been pointed out before a flat disk must be glued on top of the probe leaving
the opening free. The disk has to be held parallel to the streaming. If the static pressure is measured in
such a way it can be shown that it is equal to the pressure in the environmental atmosphere.
Figure 7
4.2 Generation of high and low pressure by deflection of an air stream
According to figure 8 we place a curved plane into the air stream of a fan. A curved plane can be
produced by glueing two postcards on top of each other. By fixing them around a bottle with a rubber,
an appropriate curvature can be achieved.
Figure 8
Due to the Coanda-effect, the air stream follows the shape of the curved plane at the lower side. The
stream follows the upper side because there is no other way left to move.
Figure 9
The curved plane forces a curved flow resulting in a radial pressure gradient. Outside of the flow there is
atmospheric pressure.
Due to the pressure gradient inside the curved air stream an increase of pressure is to be expected at the
inner or convex side of the plane in relation to the center center of curvature. Figure 8. At the outer or
concave side a decrease of pressure is to be expected. Figure 9. This increase and decrease exists indeed
and can be demonstrated using the manometer described above. See figure 8 and figure 9. The
experiment shows that by deflecting of an air stream regions of increased or decreased pressure may be
generated. This experiment is fundamental for the understanding of the production of pressure
differences if air passes obstacles. By analysing the curvature of the evasive flow we can predict
pressure distribution. It should be added that in this case Bernoulli's law still holds since friction may be
neglected. Since in figure 8 the pressure increases at the inner surface the local streaming velocity is
reduced.
In figure 9 the pressure decreases at the outer surface and the streaming velocity increases. The physical
mechanism is quite obvious. The curved plane causes a curved streaming flow and a decrease of
pressure. Hence incoming air is accelerated by the decrease of pressure.
The experiment requires an air stream the cross section of which should exceed the width of the
postcard. If a hair-dryer is used which produces a narrow air stream it is advisable to glue the curved
plane between two even planes of glass or plastic to confine the air stream. The distance of the limiting
planes should be equal to the diameter of the air stream produced by the hair-dryer.
4.3 Examples and applications
Hill: If air passes a hill - figure 10- it follows the shape of it. A deformation of the original horizontal
flow occurs only in the surroundings of the hill. Further away we observe normal atmospheric pressure
and horizontal flow.
Figure 10
We first analyse the curvature following the trajectory A.The trajectory starts from the bottom of the hill
and is continued perpendicular to the streamlines. The streaming air is deflected upwards. The air is
accelerated upwards too. Starting from the bottom and going outwards the pressure has to decrease in
order to produce the acceleration upwards. Because of the atmospheric pressure further away there must
be a higher pressure at the bottom of the trajectory A.
In the case of trajectory B starting from the top of the hill the curvature of the streamlines is reversed.
The streaming air is accelerated downwards throughout the whole trajectory. Following this trajectory
the pressure increases starting from the top until it reaches its normal value further away. Thus at the top
of the hill we expect a reduced pressure. In the case of the trajectory C we expect the same as for
trajectory A. Modelling the hill with bent postcards these results can be demonstrated experimentally as
well.
Evaporator: These considerations give an explanation of the mechanism for the evaporator. A pipe
dipping in a flow of air forces an evasive flow (see figure 11). This is a situation similar to that of the
hill. The streaming is curved over the nozzle of the pipe and the acceleration directs to the aperture.
Therefore lower pressure is generated at the nozzle.
Figure 11
Forces on a roof: If wind passes a house the stream is to flow around it. Due to the curvature of the
evasive flow there is higher pressure at the front side and lower pressure at the peak of the roof.
Figure 12
The flow is by no means smooth and laminar. At the peak of the roof it definitely becomes turbulent and
separates. (Thus at the rear side we cannot expect the same as for the hill.) Behind the peak of the roof
the same reduced pressure can be found as at the peak. This is why the situation at the rear side of the
house cannot be the same as for the hill.
The effect of pressure differences on the roof is maximized if front doors or windows are opened. In this
case there is high pressure inside the house. The pressure difference acting on the roof is increased.
If windows or doors at the rear are opened there is a lower pressure inside the house that reduces the
pressure difference acting on the roof.
Aerodynamic lift: The aerodynamic lift, too, is a result of the evasive flow caused by the aerofoil. The
streamlines near the wing are determined by the latter’s shape and position. As a whole the stream is
deflected downwards. (See figure 8 and figure 9.)
Propulsion by a sail: The same phenomenon can be observed in the case of a sail. A sail is a curved
plane similar to figure 8 and 9. The sail deflects the air flow and produces an increase of pressure at the
inner side in relation to the center of curvature and a decrease of pressure at the outer side. By this way it
generates a force normal to the sail. Skilled sailors keep the streaming of the air smooth and laminar and
avoid turbulent and separating flow.
6. Conclusion
The deliberation of Bernoulli's law in schools and textbooks has serious drawbacks. Unfortunately many
applications are erranous and misleading. One source of confusion is the derivation of Bernoulli's law
based on the theorem of energy conservation. Bernoulli's law should be derived from the tangential
acceleration as a consequence of declining pressure. Another source of difficulties is the fact that many
physics textbooks do not mention normal acceleration of flow and the resulting pressure gradients
perpendicular to the flow.
Both, Bernoulli's law and the generation of pressure gradients perpendicular to the flow are
consequences of Newton’s laws. None of them contradicts those.
Bernoulli's law is insufficient to explain the generation of low pressure. A faster streaming velocity
never produces or causes lower pressure. The physical cause of low or high pressure is the forced
normal acceleration of streaming air caused by obstacles or curved planes in combination with the
Coanda-effect. Pressure gradients generated by the deflection of streaming air can be clearly
demonstrated by simple experiments which would substantially improve the discussion of fluid
mechanics in schools and textbooks.
Literature
[1] Baumann, R.; Schwaneberg, R.: "Interpretation of Bernoulli's Equation", The Physics Teacher, Vol.
32, Nov. 1994, pp. 478 - 488
[2] Paus, H.J.: "Physik in Experimenten und Beispielen" München/Wien, 1995.
[3] Mansfield, M; O’Sullivan, C.: "Understanding Physics", Chichester, New York, 1998
[4] Weltner, K.; Ingelman-Sundberg, M.: "Physics of Flight - reviewed", submitted to Eurpean Journal
of Physics
Stalls and Spins [Ch. 18 of See How It Flies]
_ [Previous] [Contents] [Next]
[Comments or questions]
Copyright © 1996-2001 jsd
*
18 Stalls and Spins
Caution: Cape does not enable user to fly.
—
warning label on Superman costume sold at Walmart
Spins are tricky. After reading several aerodynamics texts and hundreds of pages of NASA spin-tunnel
research reports, I find it striking how much remains unknown about what happens in a spin.
18.1 Stalls: Causes and Effects
Here's a basic yet important fact: if you don't stall the airplane, it won't spin. Therefore, let's begin by
reviewing stalls.
As discussed in section 5.3, the stall occurs at the critical angle of attack, which is defined to be the point
where a further increase in angle of attack does not produce a further increase in coefficient of lift.
Nothing magical happens at the critical angle of attack. Lift does not go to zero; indeed the coefficient of
lift is at its maximum there. Vertical damping goes smoothly through zero as the airplane goes through
the critical angle of attack, and roll damping goes through zero shortly thereafter. An airplane flying 0.1
degree beyond the critical angle of attack will behave itself only very slightly worse than it would 0.1
degree below.
If we go far beyond the critical angle of attack (the ``deeply stalled'' regime) the coefficient of lift is
greatly reduced, and the coefficient of drag is greatly increased. The airplane will descend rapidly,
perhaps at thousands of feet per minute. Remember, though: the wing is still supporting the weight of the
airplane. If it were not, then there would be an unbalanced vertical force, and by Newton's law the
airplane would be not only descending but accelerating downward. If the wings were really producing
zero force (for instance, if you snapped the wings off the airplane) the fuselage would accelerate
downward until it reached a vertical velocity (several hundred knots) such that weight was balanced by
fuselage drag.
18.2 Stalling Part vs. All of the Wing
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We can arbitrarily divide the wing into sections; each section contributes something to the lift of the
whole wing. It is highly desirable (as discussed in section 5.4.3) to have the coefficient of lift for
sections near the wing-root reach its maximum early, and start decreasing, while the coefficient of lift
1
for sections near the tips continues increasing (as a function of angle of attack).
Therefore it makes perfect sense to say that the sections near the roots are stalled while the sections near
the tips are not stalled. If only a small region near the root is stalled, the wing as a whole will still have
an increasing coefficient of lift — and will therefore not be stalled.
We see that the wing will continue to produce lots of lift well beyond the point where part of it is
stalling. This is the extreme slow-flight regime — you can fly around all day with half of each wing
stalled (although it takes a bit of skill and might overheat the engine).
18.3 Boundary Layers
There is a very simple rule in aerodynamics that says the velocity of the fluid right next to the wing (or
any other surface) is zero. This is called the no-slip boundary condition. Next to the surface there is a
thin layer, called the boundary layer, in which the velocity increases from zero to its full value.
18.3.1 Separated versus Attached Flow
The wing works best when the airflow is attached to the wing surface by a simple boundary layer. The
opposite of attached flow is separated flow.
For attached flow, as we move through the boundary layer from the wing surface out to the full-speed
flow, there is practically no pressure change. Sometimes it helps to think about attached flow in the
following way: Imagine removing the boundary layer and replacing it with a layer of putty that redefines
the shape of the wing. Then imagine ``lubricating'' the new wing so that the air slides freely past it; the
no-slip condition no longer applies. Bernoulli's principle can be used to calculate the pressure on the
surface of the putty; obviously it could never be applied inside the boundary layer. The putty-covered
wing may not be the most desirable shape, but it won't necessarily be terrible.
For separated flow, the putty model does not work. Suppose I want to pick up a piece of lint from the
floor using a high-powered vacuum cleaner. If I keep the hose 3 feet away from the floor, it will never
work; I could have absolute zero pressure at the mouth of the hose, but the low pressure region would be
``separated'' from the floor and the lint. If I move the hose closer to the floor, eventually it will develop
low pressure near the floor. This is part of the problem with separated flow: there is low pressure
somewhere, but not where you need it. Separation can have multiple evil effects:
●
Separation means the air doesn't follow the contour of the wing. This is somewhat like having a
really thick boundary layer. The wing can't force the air into the optimal flow pattern, so not as
●
●
much low pressure is produced.
Whatever low pressure is produced isn't all attached to the wing surface. This is a new problem
that an attached flow would not have, no matter how thick the boundary layer.
On a non-streamlined object such as a golf ball, there is a lot of drag (specifically: form drag, as
discussed in section 4.4) because separation disrupts a desirable high-pressure area behind the
ball.
18.3.2 Laminar versus Turbulent Flow
In the simplest case, there is laminar flow, in which every small parcel of air has a definite velocity, and
the velocity varies smoothly from place to place. The other possibility is called turbulent flow, in which:
●
●
at any given point the velocity fluctuates as a function of time, and
at any given time the velocity changes rapidly as we move from point to point, even for nearby
points.
The closer we look, the more fluctuations we see.
Attached turbulent flow produces a lot of
mixing. Some bits of air move up, down,
left, right, faster, and slower relative to the
average rearward flow.
For separated laminar flow, there will be
some reverse flow (noseward, opposing the
overall rearward flow) but the pattern in
space will be much smoother than it would
be for turbulent flow, and it will not
fluctuate in time.
You can tell whether a situation is likely to be turbulent if you know the Reynolds number. You don't
need to know the details, but roughly speaking small objects moving slowly through viscous fluids (like
honey) have low Reynolds numbers, while large objects moving quickly through thin fluids (like air)
have high Reynolds numbers. Any system with a Reynolds number less than about 10 is expected to
have laminar flow everywhere. If you drop your FAA ``Pilot Proficiency Award'' wings into a jar of
honey, they will settle to the bottom very slowly. The flow will be laminar everywhere, since the
Reynolds is slightly less than 1. There will be no separation, no turbulence, and no form drag — just lots
of skin-friction drag.
Systems with Reynolds numbers greater than 10 or so are expected to create at least some turbulence.
Airplanes operate at Reynolds numbers in the millions. The wing will have a laminar boundary layer
near the leading edge, but as the air moves back over the wing, at some point the boundary layer will
become turbulent. This is called the transition to turbulence or simply the boundary layer transition.
Also at some point (before or after the transition to turbulence) the airflow will become separated. The
designers try to keep the region of separation rather small and near the trailing edge. In order to make a
wing develop a lot of lift without stalling, it helps to minimize the amount of separation.
18.3.3 Boundary Layer Control
2
One scheme for controlling separation involves the use of vortex generators (VGs). The VGs are the
little blades you see on the top of some wings, sticking up into the airstream at funny angles. Each blade
works like a turnplow, reaching out into the high-velocity airstream and turning the layers over —
plowing energy into the inner layers.
Re-energizing the boundary layer allows the wing to fly at higher angles of attack (and therefore higher
coefficients of lift) without stalling. This improves your ability to operate out of short and/or obstructed
fields.
The vorticity created by these little VGs should not be confused with the bound vortex, the big vortex
that generates the circulation that supports the weight of the airplane. As discussed in section 3.12, to
create lift you have to make the air circulate around the wing; that is, there must be vortex line running
3
along the span. VGs don't do that; their vortex lines run chordwise, not spanwise.
Boundary-layer turbulence (whether created by VGs or otherwise) also helps prevent separation, once
again by stirring additional energy into the inner sublayers of the boundary layer.
On a golf ball, 99% of the drag is form drag, and only 1% is skin-friction drag. The dimples in the golf
ball provoke turbulence, adding energy to the boundary layer. This allows the flow to stay attached
longer, maintaining the high-pressure region behind the ball, thereby decreasing the amount of form
drag. The turbulence of course increases the amount of skin-friction drag, but it is worth it.
4
Bernoulli's principle does not apply inside the boundary layer, separated or otherwise. As discussed in
section 3.4, Bernoulli's principle applies in situations where pressure (potential energy) and airspeed
squared (kinetic energy) add up to a constant. This is not the case in the boundary layer, because friction
there converts a significant amount of the energy into heat.
Do VGs play the same role as dimples on a golf ball? Not exactly. Unlike a golf ball, a wing is supposed
to produce lift. Also unlike a golf ball, a wing is highly streamlined; consequently, its form drag is not
predominant over skin-friction drag. VGs are typically used to improve lift at high angles of attack (by
fending off loss of lift due to separation). They may or may not improve performance at low angle of
attack (by decreasing form drag at the expense of skin-friction drag).
If you want ultra-low drag, and don't care about short-field performance, you want a wing with as much
laminar flow as possible. Designing a ``laminar flow wing'' is exquisitely difficult, especially in the real
world where the laminar flow could be disturbed by rain, ice, mud, and splattered bugs on the leading
edge.
There is always some separation on every airfoil section. The separation grows as the angle of attack
increases. If there is too much separation, it cuts into the wing's ability to produce lift. If there were no
separation, the wing could continue producing lift up to very high angles of attack (thereby achieving
very high coefficients of lift).
5
Having lots of separation is the dominant cause (but not the definition) of stalling. Remember: the stall
occurs at the critical angle of attack, i.e. the point where max coefficient of lift is attained.
18.3.4 Summary
A full discussion of turbulence and/or separated flow is beyond the scope of this book; indeed, trying to
really understand and control these phenomena is a topic of current research. There is nothing simple
about it. But there are a few things we can say.
●
●
●
●
●
The opposite of separated flow is attached flow.
The opposite of turbulent flow is laminar flow.
Separated flow need not be very turbulent, nor vice versa.
Laminar flow need not be attached, nor vice versa.
Turbulence doesn't cause separation (and indeed oftenhelps prevent it).
For more information, see e.g. reference 17.
18.4 Coanda Effect, etc.
The name Coanda effect is generally applied to any situation where a thin, high-speed jet of fluid meets
a solid surface and follows the surface around a curve. Depending on the situation, one or more of
several different physical processes might be involved in making the jet follow the surface.
As a pilot, you absolutely do not need to know about the Coanda effect or what causes it. Indeed, many
professional aerodynamicists get along just fine without really understanding such things. The main
purpose of this section is to dispel the notion that a normal wing produces lift ``because'' of some type of
Coanda effect.
Using the Coanda effect to explain the operation of a normal wing makes about as much sense as using
bowling to explain walking. To be sure, bowling and walking use some of the same muscle groups, and
both at some level depend on Newton's laws, but if you don't already know how to walk you won't learn
much by considering the additional complexity of the bowling situation.
18.4.1 Tissue-paper Demonstration
You can demonstrate one type of Coanda effect for yourself using a piece of paper. Limp paper, such as
tissue paper, works better than stiff paper. Drape the paper over your fingers, and then blow
horizontally, as shown in the following figures.
6
Figure 18.1: Tissue Paper; No Coanda Effect
If the jet passes just above the paper, as shown in figure 18.1, nothing very interesting happens. The jet
just keeps on going. The paper is undisturbed.
Figure 18.2: Tissue Paper; Coanda Effect
On the other hand, if the jet actually hits the paper as shown at point C in figure 18.2, the downstream
part of the paper will rise up. This is because the air follows the curved surface; as it does so, it creates
enough low pressure to lift the weight of the paper.
The air in your lungs, at point A, is at a pressure somewhat above atmospheric. At point B, after
emerging from the nozzle, the air in the jet is at atmospheric pressure.
As discussed in section 3.3, the fact that the fluid follows a curved path proves that there is a force on it.
This force must be due to a pressure difference. In this case, the pressure on the lower edge of the jet
(where it follows the curve of the tissue paper near point D) is less than atmospheric, while the pressure
on the upper edge of the jet (near point E) remains more-or-less atmospheric. This pressure difference
pulls down on the jet, making it curve. By the same token it also pulls up on the paper, creating lift.
People who only half-understand Bernoulli's principle will be surprised to hear that the jet leaves the
nozzle at high speed at atmospheric pressure. It's true, though. In particular, the crude statement that
``high velocity means low pressure'' is an oversimplification that cannot be used in this situation. The
correct basis of Bernoulli's principle is that for a particular parcel of air the mechanical energy
(pressure plus kinetic energy per unit volume) remains more-or-less constant. If you want to compare
two different parcels of air, you'd better make sure that they started out with the same mechanical
energy.
In this case, the air in the jet leaves the nozzle with a higher mechanical energy than the ambient air.
Your lung-muscles are the source of the extra energy.
When this high-velocity, atmospheric-pressure air smacks into the paper at point C, it actually creates
above-atmospheric pressure there. Indeed, we can use the streamline-curvature argument again: if the air
turns a sharp corner, there must be a very large pressure difference.
In order to make this sharp turn, the air needs something to push against. A good bit of the required
momentum comes from the air that splatters backward, as suggested by the squiggles just below and
upstream of the point of contact. This process is extremely messy. It is much more complicated than
anything that happens near a wing in normal flight. To visualize this splatter, blow a jet of air onto a
7
dusty surface. Even if you blow at a very low angle, some of the dust particles blow away in the
direction opposite to the main flow.
18.4.2 Blowing the Boundary Layer
Since we saw in section 18.3 that de-energizing the boundary layer is bad, you might think adding
energy to the boundary layer should be good... and indeed it is. One way of doing so uses vortex
generators, as discussed in section 18.3. Figure 18.3 shows an even more direct approach.
●
●
We use a pump to create a supply of air at very high pressure.
The air comes out a nozzle. The result is a jet of high-velocity air at the same pressure as the
8
●
local air.
The jet shoots out of a slot in the top of the wing, adding energy to the boundary layer at a place
where this could be very helpful.
Figure 18.3: Blowing the Boundary Layer
Once again, the Coanda effect cannot explain how the wing works; you have to understand how the
wing works before you consider the added complexity of the blower.
In this case we expect one spectacular added complexity, namely curvature-enhanced turbulent mixing.
This phenomenon will not be discussed in this book, except to say that it does not occur near a normal
wing, while it is likely to be quite significant in the situation shown in figure 18.3.
Curving flows with lots of shear can be put to a number of other fascinating uses, but a discussion is
beyond the scope of this book. See reference 9.
18.4.3 Teaspoon Demonstration
Another example of a jet following a curved surface uses a jet of water. You can easily perform the
following experiment: let a thin stream of water come out of the kitchen faucet. Then touch the left side
of the stream with the convex back side of a spoon. The stream will not be pushed to the right, but
instead it will follow the curve of the spoon and be pulled to the left. The stream can be deflected by
quite a large amount. In accordance with Newton's third law of motion, the spoon will be pulled to the
right.
I don't understand everything I know about this situation, but it is safe to say the following:
1. This water-in-air jet differs in fundamental ways from the air-in-air jet situation described above.
2. This effect has practically nothing to do with the way a normal wing produces lift.
To convince yourself of these facts, it helps to have a higher velocity and/or a larger diameter than you
can conveniently get from a kitchen faucet. A garden hose will give you a bigger diameter, and if you
add a nozzle you can get a higher velocity. You can easily observe:
●
●
●
●
●
9
The amount of lift you can produce is pathetically small, compared to the dynamic pressure and
area of the water jet.
The lift-to-drag ratio is terrible. Indeed this makes it very hard to measure the lift; if you get the
angle slightly wrong you will inadvertently measure a drag component instead.
The water spreads out when it hits the surface, making a thin coating over a wide area of the
surface. This is in marked contrast to what happens in the air-in-air jet, as you can demonstrate
by placing thin strips of tissue paper side by side. You can easily blow on one strip and lift it
without disturbing its neighbors.
Some of the spreading layer flows backwards, ahead of the point of contact of the jet,
corresponding to a negative amount of upwash. This is grossly different from what happens near
a real wing.
The effect does not depend on curvature-enhanced turbulent mixing with the ambient air. This is
quite unlike what happens in a real airplane with boundary-layer blowing.
It appears that surface tension plays two very important roles:
1. At the water/air interface it prevents mixing of the air and water.
2. At the water/wing interface it plays a dominant role in making the water stick to the surface.
In both respects this is quite unlike the air-in-air jet, where the air/wing surface tension has no effect and
there is no such thing as air/air surface tension.
To convince yourself of this: Take a thin sheet of plastic. Get it wet on both sides, and drape it over a
cylinder. You will not be able to lift it off the cylinder using a tangential water jet. The surface tension
holding the wet plastic to the cylinder is just as strong as the tension between the plastic and the jet. In
contrast, when the same piece of plastic has air on both sides, you can easily lift it off the cylinder using
an air jet.
18.4.4 Fallacious Model of Lift Production
You may have heard stories saying that the Coanda effect explains how a wing works. Alas, these are
just fairy tales. They are worse than useless.
1. For starters, these fairy tales often claim that blowing on tissue paper (as described just above)
proves that ``high velocity means low pressure'' which is absolutely not what is being
demonstrated. The high-velocity air coming out of your mouth is at atmospheric pressure. If you
blow across the top of a flat piece of paper, it will not rise, no matter what you do. There is no
low pressure in the jet (unless and until it gets pulled around a corner). Therefore the Coanda
stories give a wrong explanation of normal wings and basic aerodynamics. And by the way, such
stories cannot even begin to explain the operation of flat wings — yet we have seen in section
3.10.1 that a barn door doesn't behave very differently from other airfoils.
2. The Coanda-like notion of airflow following a curved surface cannot possibly explain why there
is upwash in front of the wing. In figure 18.2 there must be a stagnation point on the upper
surface of the paper near point C. This is completely different from the situation near a normal
wing, where the stagnation line must be somewhere below the leading edge of the wing. Upwash
is important, since it contributes to lift while creating a negative amount of induced drag. A
further consequence, by the way, is that these Coanda-like stories cannot possibly explain the
operation of stall-warning devices, as discussed in section 3.5.
3. As mentioned above, the distribution of velocities necessary to create curvature-enhanced
turbulent mixing is produced by a high-speed jet but is not produced by a normal wing.
4. Sometimes the fairy tales say that the jet ``sticks'' to the surface because of viscosity. This implies
that if the viscosity of the fluid changes, the amount of lift an airfoil produces should change in
proportion. In fact, though, the amount of lift produced by a real wing is independent of viscosity
over a wide range. Also, many of the processes responsible for the real Coanda effect require the
10
production of turbulence, so they only work if the viscosity is sufficiently low.
5. In the real Coanda effect, we know where the high-velocity air comes from. It comes from a
nozzle. Upstream of the nozzle is a pump (or a rocket engine, or some other device) to supply the
necessary energy. The jet makes high-velocity air above the wing, not below, because that's
where we aim the nozzle. An ordinary wing is completely different. It is wonderfully effective at
creating high-velocity air above itself, without nozzles, without pumps, and without transferring
11
energy to the air.
6. The fairy tales generally neglect the fact that the wing speeds up the air in its vicinity, and just
assume that the relative wind meets the wing at the free-stream velocity and follows the curve in
a Coanda-like way. As a consequence, they miscalculate the pressure gradients by a factor of ten
or so.
7. Finally, in the real Coanda effect we know how big the jet is. Its initial size is determined by the
nozzle. The amount of mixing depends on the speed of the jet, the speed of the ambient air, the
curvature of the surface, and other known quantities. Awareness of the Coanda effect is a small
part of — not a replacement for — a full analysis of the wing in figure 18.3. In contrast, (a) the
typical fairy tales imply that the entire flow pattern of a normal wing can be explained by
mentioning the magic words ``Coanda effect'', yet (b) they cannot explain how thick a chunk of
air is deflected by the wing. One inch? Six inches? A chord-length? A span-length? Some amount
proportional to the viscosity of the air? It would be very hard to calculate how much.
12
18.4.5 Summary
Don't let anybody tell you that squirting a spoon or blowing on tissue paper is a good model of how a
wing works.
If you want to ``get the feel'' of lift production, the obvious methods are the best. These include holding
a model airfoil
13
downstream of a household fan, or sticking it out of a car window.
18.5 Spin Entry
Case 1: In normal flight, rolling motions are very heavily damped, as discussed in section 5.4. Even
though the static stability of the bank angle is small or even negative, you cannot get a large roll rate
without a large roll-inducing force; when you take away the force the roll rate goes away.
Case 2: Near the critical angle of attack, the roll damping goes away. Suppose you start the aircraft
rolling to the right. The roll rate will just continue all by itself. The right wing will be stalled (beyond
max lift angle of attack) and the left wing will be unstalled (below max lift angle of attack).
Case 3: At a sufficiently high initial angle of attack (somewhat greater than the critical angle of attack),
14
the roll will not just continue but accelerate, all by itself. This is an example of the ``departure'' that
constitutes the beginning of a snap roll or spin. The resulting undamped rolling motion is called
autorotation.
At a high enough angle of attack, the ailerons lose effectiveness, and at some point they start working in
15
reverse. Figure 18.4 shows how this reversal occurs. Suppose you deflect the ailerons to the left. This
raises the angle of attack at the right wingtip and lowers it at the left wingtip. Normally, this would
increase the lift on the right wing (and lower it on the left), creating a rolling moment toward the left.
Near the critical angle of attack, though (as seen in the left panel of the figure), raising or lowering the
angle of attack has about the same effect on the coefficient of lift, so no rolling moment is produced (for
now, at least).
Figure 18.4: Lift and Drag at Departure
We see that at this angle of attack, anything that creates a rolling mo-ment will cause the aircraft to roll
like crazy, and indeed to keep accelerating in the roll-wise direction. There will be no natural roll
damping, and you will be unable to oppose the roll with the ailerons.
There are two main ways of provoking a spin at this point:
1. Suppose the airplane is in a steady slip to the left. That is, you are steadily pushing on the right
rudder pedal. Then the slip/roll cou-pling (as discussed in section 9.1 and section 9.2) will cause
it to spin to the right.
2. Suppose the airplane is not in much of a slip, but you suddenly cause it to yaw to the right. The
left wingtip will temporarily be moving faster, and the right wingtip will temporarily be moving
slower. This difference in airspeeds will create a difference in lift, causing a spin to the right. The
initial yawing motion could come from a sudden application of rudder, or from adverse yaw, or
what-ever. Note that in the right panel of figure 18.4, the ai-leron deflection has a tremendous
effect on the drag. This means that ailerons deflected to the left cause a yaw to the right which in
turn provokes a roll to the just the opposite of what ailerons normally do.
18.6 Types of Spin
18.6.1 Spin Modes
The word ``spin'' can be used in several different ways, which we will discuss below. The spin family
tree includes:
●
●
●
``departure'', i.e. onset of undamped rolling;
incipient spin — i.e. one that has just gotten started; or
well-developed spin, which could be
❍ a steep spin, or
❍ a flat spin.
Figure 18.5 shows an airplane in a steady spin. You can see that the direction of flight has two
components: a vertical component (down, parallel to the spin axis) and a horizontal component (forward
and around).
Figure 18.5: Airplane in a Steady Spin
Figure 18.6 is a close-up of a wing in a steep spin. We have welded a pointer to each wingtip, indicating
the direction from which the relative wind would come if the wing were producing zero lift; we call this
the Zero-Lift Direction (ZLD). (For a symmetric airfoil, the ZLD would be aligned with the chord line
of the wing.) Remember that the angle between the direction of flight and the ZLD pointer is the angle
of attack.
Figure 18.6: Steep Spin — Geometry
Figure 18.7: Steep Spin — Coefficient of Lift
In this situation, both wingtips have the same vertical speed, but they have significantly different
horizontal speeds — because of the rotation. Consequently they have different directions of flight, as
shown in the figure. This in turn means that the two wingtips have significantly different angles of
attack, as shown in figure 18.7. The two wings are producing equal amounts of lift, even though one is
in the stalled regime and one in the unstalled regime.
Figure 18.8 shows another spin mode. This time the rotation rate is higher than previously. The spin axis
is very close to the right wingtip. The outside wing is still unstalled, while the inside wing is very, very
deeply stalled, as shown in figure 18.9.
Figure 18.8: Flat Spin — Geometry
Figure 18.9: Flat Spin — Coefficient of Lift
Figure 18.10: Doubly Stalled Flat Spin — Coefficient of Lift
Figure 18.10 shows yet another possible spin mode. In this case, the outside wing is stalled, while the
inside wing is, of course, much more deeply stalled. Whether this spin mode, or the one shown in figure
18.9 (or both or neither) is stable depends on dozens of details (aircraft shape, weight distribution, et
cetera). There is a common misconception that in a spin, one wing is stalled and the other wing is always
unstalled. This is true of ``most'' spins but it is not a defining property. It would be safer to use the
following definition:
In a spin, at least one wing is stalled,
and the two wings are operating at very different angles of
attack.
18.6.2 Samaras, Flat Spins, and Centrifugal Force
A samara is a winged seed. Maples are a particularly well known and interesting example.
Maple samaras have only one wing, with the seed all the way at one end. Its mode of flight is analogous
to an airplane in a flat spin. In an airplane, the inside wing is deeply stalled, while in the samara the
inside wing is missing entirely.
In a non-spinning airplane, if one wing were producing more lift than the other, that wing would rise. So
the question is, why is a flat spin stable? Why doesn't the outside wing continue to roll to ever-higher
16
bank angles? The secret is centrifugal force. Suppose you hold a broomstick by one end while you
spin around and around; the broomstick will be centrifuged outward and toward the horizontal.
In an airplane spinning about a vertical axis, the high (outside) wing will be centrifuged outward and
downward (toward the horizontal), while the low (inside) wing will be centrifuged outward and upward
(again toward the horizontal). In a steady flat spin, these centrifugal forces cancel the rolling moment
that results from one wing producing a lot more lift than the other. This is the only example I can
imagine where an airplane is in a steady regime of flight but one wing is producing more lift than the
other.
As discussed in reference 6, an aircraft with a lot of mass in the wings will have a stronger centrifugal
force than one with all the mass near the centerline of the fuselage. In particular, an aircraft with one
pilot and lots of fuel in the wing tanks could have completely different spin characteristics than the same
aircraft with two pilots and less fuel aboard.
18.6.3 NASA Spin Studies
In the 1970s, NASA conduced a series of experiments on the spin behavior of general-aviation aircraft;
see reference 8 and reference 7 and other papers cited therein. They noted that there was ``considerable
confusion'' surrounding the definition of steep versus flat spin modes, and offered the classification
scheme shown in table 18.1.
spin mode
Steep
Mod'ly Steep Mod'ly Flat
angle of attack
20 to 30
30 to 45
45 to 65
Flat
65 to 90
nose attitude
extreme nose-down
less nose-down
rate of descent
very rapid
less rapid
rate of roll
extreme
moderate
rate of yaw
moderate
extreme
wingtip-to-wingtip difference in angle of attack
modest
large
nose-to-tail difference in slip
large
large
Table 18.1: Spin Mode Classification
The angle of attack that appears in this table is measured in the aircraft's plane of symmetry; the actual
angle of attack at other positions along the span will depend on position.
The NASA tests demonstrated that general aviation aircraft not approved for intentional spins commonly
had unrecoverable flat spin modes.
18.6.4 Effects of Changes in Orientation of Spin
In all cases NASA studied, the flat spin had a faster rate of rotation (and a slower rate of descent) than
the steep spin. Meanwhile, reference 15 reports experiments in which the flatter pitch attitudes were
associated with the slower rates of rotation. This is not a contradiction, because the latter dealt with an
unsteady spin (with frequent changes in pitch attitude), rather than a fully stabilized flat spin. A sudden
change to a flatter pitch attitude will cause a temporary reduction in spin rate, for the following reason.
In any system where angular momentum is not changing, the system will spin faster when the mass is
more concentrated near the axis of rotation. The general concept is discussed in section 19.8. By the
same token, if the mass of a spinning object is redistributed farther from the axis, the rotation will slow
down.
When the spinning airplane pitches up into a flatter attitude, whatever mass is in the nose and tail will
move farther from the axis of rotation. Angular momentum doesn't change in the short run, so the
rotation will slow down in the short run.
In the longer run — in a steady flat spin — the aerodynamics of the spin will pump more angular
momentum into the system, and the rotation rate will increase quite a lot. The rotation rate of the
established flat spin is typically twice that of the steep spin.
Recovering from an established flat spin requires forcing the nose down. This brings the mass in the
nose and tail closer to the axis of rotation. Once again using the principle of conservation of angular
momentum, you can see that the rotation rate will increase (at least in the short run) as you do so —
which can be disconcerting.
18.7 Recovering from a Spin
If you find yourself in an unusual turning, descending situation, the first thing to do is decide whether
you are in a spiral dive or in a spin. In a spiral dive, the airspeed will be high and increasing; in a spin
the airspeed will be low. You should be able to hear the difference. Also, the rate of rotation in a spiral
is much less; the high speed means the airplane has lots of momentum and can't turn on a dime. In a
spin, the aircraft will be turning a couple hundred degrees per second.
17
To get out of a spin, follow the spin-recovery procedures given in the Pilot's Operating Handbook for
your airplane. The literature is full of home-brew spin recovery procedures that probably work most of
the time in most airplanes, but if you want a procedure that works for sure, follow the handbook for your
airplane.
For typical airplanes, the spin recovery procedure contains the following items:
●
●
●
●
●
Retard the throttle to idle
Retract the flaps
Neutralize the ailerons
Apply full rudder in the direction opposing the spin
Briskly move the yoke to select zero angle of attack.
Now let's discuss each of these items in a little more detail.
Retarding the throttle is a moderately good idea for a couple of reasons. For one thing (especially if you
have a fixed-pitch prop) it keeps the engine from overspeeding during the later stages of the spin
recovery. More importantly, gyroscopic precession of the rotating engine and propeller can hold the
nose up, flattening the spin and interfering with the recovery (depending on the direction of spin).
Propwash might increase the effectiveness of the horizontal tail and therefore assist in the spin recovery,
but (especially in a flat spin) the propwash could be blown somewhere else by the abnormal airflow —
so you may not be able to count on this.
Retracting the flaps is a moderately good idea because you might exceed the ``max flaps-extended
speed'' if you mishandle the later stages of the spin recovery and you don't want to damage the flaps.
Retracting the flaps may help with the spin recovery itself. Recall from section 5.4.3 that the flaps
effectively increase the washout of the wings. Washout ensures that the airplane will stall before it runs
out of roll damping. (This produces a nice straight-ahead stall.) In the spin, though, when you have lost
all vertical damping and roll damping, the washout doesn't help. The early stages of spin recovery are
not like the early stages of stall entry.
Neutralizing the ailerons is usually a good idea for the simple reason that it is hard to think of anything
better to do with them. Deflecting the ailerons effectively increases the angle of attack of one wingtip
and decreases the angle of attack of the other wingtip. In a spin, the part of the wing where the ailerons
are may (or may not) be in the stalled regime — so deflecting the ailerons to the left may (or may not)
produce a paradoxical rolling moment to the right.
Depressing the rudder to oppose the spin is obviously a good thing to do.
Finally, you want to move the yoke to select zero angle of attack. In typical trainers, this means shoving
the yoke all the way forward, but in other aircraft, especially aerobatic aircraft, all the way forward
might select a large negative angle of attack. Shoving the yoke all the way forward in such a plane
would likely convert the spin to an inverted spin — hardly an improvement. This is just one example of
why you want to know and follow the spin recovery procedure for your specific airplane.
The relative significance of the rudder compared to the flippers in breaking the spin depends radically on
the design of the airplane, the loading of the airplane, and on the spin mode, as discussed in reference 6.
In normal non-spinning flight, you should apply smooth pressures to the controls. Spin recovery is the
exception: it calls for brisk, mechanical motions of the controls, almost without regard to the pressures
involved.
If you get into a spin in instrument conditions, you should rely primarily on the airspeed indicator and
the rate-of-turn gyro. The inclinometer ball cannot be trusted; it is likely to be centrifuged away from the
center of the airplane — giving an indication that depends on where the instrument is installed, telling
you nothing about the direction of spin. The artificial horizon (attitude indicator) cannot be trusted since
it may have tumbled. The rate-of-turn gyro is more trustworthy, since it is a rate gyro, not a free gyro;
that is, it has no gimbals and cannot possibly suffer from gimbal lock.
Recovery from a so-called incipient spin (one that has just gotten started) is easier than from a well18
developed spin. Normal-category single-engine certification requirements say that an airplane must be
able to recover from a one-turn spin (or a 3-second spin, whichever takes longer) in not more than one
additional turn. If you let the spin go on for several turns, you might progress from a steep spin to a flat
spin. Recovery could take a lot longer — if it is possible at all.
If you load the airplane beyond the aft limit of the weight and balance envelope, even the incipient spin
may be unrecoverable; see section 6.1.1. Imperfect repairs to the wing, or slack in the control cables,
could also impede spin recovery.
Finally, the spin is yet another reason why it is NOT SAFE to think of the yoke as simply the up/down
19
control. In a spin you have a low airspeed and a high rate of descent. If you think of the yoke as the up/
down control, you will be tempted to pull back on the yoke, which is exactly the wrong thing to do. On
the other hand, if you think of the yoke as (primarily) the fast/slow control, you will realize that you
need to push forward on the yoke, to solve the airspeed problem.
18.8 Don't Mess With Spins
It is quite impressive how well a samara works. A maple seed descends very slowly, riding the wind
much better than a parachute of similar size and weight ever could. Flat spins can be extremely stable; a
wing by itself loves to spin. That's why spins (and flat spins in particular) are so dangerous: it takes a lot
of rudder force to persuade a wing to stop spinning.
Spins are extremely complex. Even designers and top-notch test pilots are routinely surprised by the
behavior of spinning airplanes. Spin-test airplanes are equipped with cannon-powered spin-recovery
parachutes on the airframe, and quick-release doors in view of the distinct possibility that the pilot will
have to bail out. Tests are conducted at high altitude over absolutely unpopulated areas. Therefore please
don't experiment with spinning a plane except exactly as approved by the manufacturer — one
unrecoverable spin mode can ruin your whole day.
1
This happens naturally on a rectangular wing; it can be enhanced by washout and other designers'
tricks.
2
An even more direct method of adding energy to the boundary layer uses a jet of high-velocity
air, as discussed in section 18.4.2.
3
Of course, the VGs contribute indirectly to maintaining the health of the big bound vortex, since
they help maintain attachment and therefore help create lots of circulation.
4
See reference 17 for a nice discussion of golf balls, cricket balls, and boundary layers in general.
5
... just as having lots of water is the cause, but not the definition, of drowning — you can get very
wet without drowning.
6
You can blow directly from your lips, but it's better to use a flexible straw or a thin piece of
tubing, so that you can get a better view of what's happening. If you put a nozzle at the end of the
tube, the jet will keep its shape better.
7
Ground pepper is a convenient source of suitable dust.
8
This won't be exactly atmospheric, since the local pressure has been affected by the wing.
9
Remember, lift is the force perpendicular to the flow and perpendicular to the surface.
10
Indeed, as long as the viscosity is not exactly zero, the smaller the viscosity, the greater the
turbulence.
11
Of course some energy is transferred, in the form of friction and induced drag, but this is very
small, out of all proportion to the energy that the air parcel transfers from its own speed to
pressure and back again.
12
Nonsensical things are often rather hard to calculate.
13
If you don't have a good model airfoil, start with a flat piece of cardboard.
14
This refers to ``departure from normal flight''. It has nothing to do with takeoff or with a
``departure stall'' which merely refers to a stall in the takeoff configuration.
15
Under present-day certification rules, the ailerons are required to work normally up to at least
stalling angle of attack. However, some older airplanes were built under older rules. These
planes, including many aerobatic aircraft, have much less washout, and therefore lose aileron
effectiveness earlier. All planes lose effectiveness eventually. For simplicity, this section ignores
washout.
16
See section 19.4 for a discussion of the nature of centrifugal fields.
17
Recovery from a spiral dive is discussed in section 6.2.4.
18
Multi-engine aircraft are not required to be recoverable from any sort of spin, incipient or
otherwise.
19
This point is discussed in chapter 7.
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[Comments or questions] _
Copyright © 1996-2001 jsd
A Physical Description of Lift
This material can be found in more detail in "Understanding Flight",
by David Anderson and Scott Eberhardt, McGraw-Hill, 2001, ISBN: 0-07-136377-7
Reviews
Review from
Discovery
Review from Pilot
Training
A Physical Description of Flight ©
David Anderson
Fermi National Accelerator Laboratory
Ret.
[email protected]
&
Scott Eberhardt
Dept. of Aeronautics and Astronautics University of Washington
Seattle WA 91895-2400
[email protected]
http://www.aa.washington.edu/faculty/eberhardt/lift.htm (1 of 18)24-1-2004 18:04:54
Almost everyone today has flown in an airplane. Many ask the simple question "what makes an airplane
fly?" The answer one frequently gets is misleading and often just plain wrong. We hope that the answers
provided here will clarify many misconceptions about lift and that you will adopt our explanation when
explaining lift to others. We are going to show you that lift is easier to understand if one starts with
Newton’s laws rather than the Bernoulli principle. We will also show you that the popular explanation
that most of us were taught is misleading at best and that lift is due to the wing diverting air down. Most
of this diverted air is pulled down from above the wing.
Let us start by defining three descriptions of lift commonly used in textbooks and training manuals. The
first we will call the Mathematical Aerodynamics Description of lift, which is used by aeronautical
engineers. This description uses complex mathematics and/or computer simulations to calculate the lift
of a wing. It often uses a mathematical concept called "circulation" to calculate the acceleration of the
air over the wing. Circulation is a measure of the apparent rotation of the air around the wing. While
useful for calculations of lift, this description does not lend themselves to an intuitive understanding of
flight.
The second description we will call the Popular Description, which is based on the Bernoulli principle.
The primary advantage of this description is that it is easy to understand and has been taught for many
years. Because of its simplicity, it is used to describe lift in most flight training manuals. The major
disadvantage is that it relies on the "principle of equal transit times", or at least on the assumption that
because the air must travel farther over the top of the wing it must go faster. This description focuses on
the shape of the wing and prevents one from understanding such important phenomena as inverted
flight, power, ground effect, and the dependence of lift on the angle of attack of the wing.
The third description, which we are advocating here, we will call the Physical Description of lift. This
description of lift is based primarily on Newton's three laws and a phenomenon called the Coanda effect.
This description is uniquely useful for understanding the phenomena associated with flight. It is useful
for an accurate understanding the relationships in flight, such as how power increases with load or how
the stall speed increases with altitude. It is also a useful tool for making rough estimates ("back-of-theenvelope calculations") of lift. The Physical Description of lift is also of great use to a pilot who needs
an intuitive understanding of how to fly the airplane.
The popular description of lift
Students of physics and aerodynamics are taught that an airplane flies as a result of the Bernoulli
principle, which says that if air speeds up the pressure is lowered. (In fact this is not always true. The air
flows fast over the airplane’s static port but the altimeter still reads the correct altitude.) The argument
goes that a wing has lift because the air goes faster over the top creating a region of low pressure. This
explanation usually satisfies the curious and few challenge the conclusions. Some may wonder why the
air goes faster over the top of the wing and this is where the popular explanation of lift falls apart.
In order to explain why the air goes faster over the top of the wing, many have resorted to the geometric
argument that the distance the air must travel is directly related to its speed. The usual claim is that when
the air separates at the leading edge, the part that goes over the top must converge at the trailing edge
with the part that goes under the bottom. This is the so-called "principle of equal transit times".
One might ask if the numbers calculated by the Popular Description really work. Let us look at an
example. Take the case of a Cessna 172, which is popular, high-winged, four-seat airplane. The wings
must lift 2300 lb (1045 kg) at its maximum flying weight. The path length for the air over the top of the
wing is only about 1.5% greater than under the wing. Using the Popular Description of lift, the wing
would develop only about 2% of the needed lift at 65 mph (104 km/h), which is "slow flight" for this
airplane. In fact, the calculations say that the minimum speed for this wing to develop sufficient lift is
over 400 mph (640 km/h). If one works the problem the other way and asks what the difference in path
length would have to be for the Popular Description to account for lift in slow flight, the answer would
be 50%. The thickness of the wing would be almost the same as the chord length.
But, who says the separated air must meet at the trailing edge at the same time? Figure 1 shows the
airflow over a wing in a simulated wind tunnel. In the simulation, smoke is introduced periodically. One
can see that the air that goes over the top of the wing gets to the trailing edge considerably before the air
that goes under the wing. In fact, the air is accelerated much faster than would be predicted by equal
transit times. Also, on close inspection one sees that the air going under the wing is slowed down from
the "free-stream" velocity of the air. The principle of equal transit times holds only for a wing with zero
lift.
Fig 1 Simulation of the airflow over a wing in a wind tunnel, with "smoke".
The popular explanation also implies that inverted flight is impossible. It certainly does not address
acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the same shape), or how a
wing adjusts for the great changes in load such as when pulling out of a dive or in a steep turn?
So, why has the popular explanation prevailed for so long? One answer is that the Bernoulli principle is
easy to understand. There is nothing wrong with the Bernoulli principle, or with the statement that the
air goes faster over the top of the wing. But, as the above discussion suggests, our understanding is not
complete with this explanation. The problem is that we are missing a vital piece when we apply
Bernoulli’s principle. We can calculate the pressures around the wing if we know the speed of the air
over and under the wing, but how do we determine the speed? As we will soon see, the air accelerates
over the wing because the pressure is lower, not the other way around.
Another fundamental shortcoming of the popular explanation is that it ignores the work that is done. Lift
requires power (which is work per time). As will be seen later, an understanding of power is key to the
understanding of many of the interesting phenomena of lift.
Newton’s laws and lift
So, how does a wing generate lift? To begin to understand lift we must review Newton’s first and third
laws. (We will introduce Newton’s second law a little later.) Newton’s first law states a body at rest will
remain at rest, or a body in motion will continue in straight-line motion unless subjected to an external
applied force. That means, if one sees a bend in the flow of air, or if air originally at rest is accelerated
into motion, a force is acting on it. Newton’s third law states that for every action there is an equal and
opposite reaction. As an example, an object sitting on a table exerts a force on the table (its weight) and
the table puts an equal and opposite force on the object to hold it up. In order to generate lift a wing must
do something to the air. What the wing does to the air is the action while lift is the reaction.
Let’s compare two figures used to show streamlines over a wing. In figure 2 the air comes straight at the
wing, bends around it, and then leaves straight behind the wing. We have all seen similar pictures, even
in flight manuals. But, the air leaves the wing exactly as it appeared ahead of the wing. There is no net
action on the air so there can be no lift! Figure 3 shows the streamlines, as they should be drawn. The air
passes over the wing and is bent down. Newton’s first law says that them must be a force on the air to
bend it down (the action). Newton’s third law says that there must be an equal and opposite force (up)
on the wing (the reaction). To generate lift a wing must divert lots of air down.
Fig 2 Common depiction of airflow over a wing. This wing has no lift.
Fig 3 True airflow over a wing with lift, showing upwash and downwash.
The lift of a wing is equal to the change in momentum of the air it is diverting down. Momentum is the
product of mass and velocity (mv). The most common form of Newton’s second law is F= ma, or force
equal mass times acceleration. The law in this form gives the force necessary to accelerate an object of a
certain mass. An alternate form of Newton’s second law can be written: The lift of a wing is
proportional to the amount of air diverted down times the vertical velocity of that air. It is that simple.
For more lift the wing can either divert more air (mass) or increase its vertical velocity. This vertical
velocity behind the wing is the vertical component of the "downwash". Figure 4 shows how the
downwash appears to the pilot (or in a wind tunnel). The figure also shows how the downwash appears
to an observer on the ground watching the wing go by. To the pilot the air is coming off the wing at
roughly the angle of attack and at about the speed of the airplane. To the observer on the ground, if he or
she could see the air, it would be coming off the wing almost vertically at a relatively slow speed. The
greater the angle of attack of the wing the greater the vertical velocity of the air. Likewise, for a given
angle of attack, the greater the speed of the wing the greater the vertical velocity of the air. Both the
increase in the speed and the increase of the angle of attack increase the length of the vertical velocity
arrow. It is this vertical velocity that gives the wing lift.
Fig 4 How downwash appears to a pilot and to an observer on the ground.
As stated, an observer on the ground would see the air going almost straight down behind the plane. This
can be demonstrated by observing the tight column of air behind a propeller, a household fan, or under
the rotors of a helicopter; all of which are rotating wings. If the air were coming off the blades at an
angle the air would produce a cone rather than a tight column. The wing develops lift by transferring
momentum to the air. For straight and level flight this momentum eventually strikes the earth in. If an
airplane were to fly over a very large scale, the scale would weigh the airplane.
Let us do a back-of-the-envelope calculation to see how much air a wing might divert. Take for example
a Cessna 172 that weighs about 2300 lb (1045 kg). Traveling at a speed of 140 mph (220 km/h), and
assuming an effective angle of attack of 5 degrees, we get a vertical velocity for the air of about 11.5
mph (18 km/h) right at the wing. If we assume that the average vertical velocity of the air diverted is
half that value we calculate from Newton's second law that the amount of air diverted is on the order of
5 ton/s. Thus, a Cessna 172 at cruise is diverting about five times its own weight in air per second to
produce lift. Think how much air is diverted by a 250-ton Boeing 777 on takeoff.
Diverting so much air down is a strong argument against lift being just a surface effect (that is only a
small amount of air around the wing accounts for the lift), as implied by the popular explanation. In fact,
in order to divert 5 ton/sec the wing of the Cessna 172 must accelerate all of the air within 18 feet (7.3
m) above the wing. One should remember that the density of air at sea level is about 2 lb per cubic yard
(about 1kg per cubic meter). Figure 5 illustrates the effect of the air being diverted down from a wing. A
huge hole is punched through the fog by the downwash from the airplane that has just flown over it.
Fig 5 Downwash and wing vortices in the fog. (Photographer Paul Bowen, courtesy of Cessna Aircraft,
Co.)
So how does a thin wing divert so much air? When the air is bent around the top of the wing, it pulls on
the air above it accelerating that air downward. Otherwise there would be voids in the air above the
wing. Air is pulled from above. This pulling causes the pressure to become lower above the wing. It is
the acceleration of the air above the wing in the downward direction that gives lift. (Why the wing bends
the air with enough force to generate lift will be discussed in the next section.)
As seen in figure 3, a complication in the picture of a wing is the effect of "upwash" at the leading edge
of the wing. As the wing moves along, air is not only diverted down at the rear of the wing, but air is
pulled up at the leading edge. This upwash actually contributes to negative lift and more air must be
diverted down to compensate for it. This will be discussed later when we consider ground effect.
Normally, one looks at the air flowing over the wing in the frame of reference of the wing. In other
words, to the pilot the air is moving and the wing is standing still. We have already stated that an
observer on the ground would see the air coming off the wing almost vertically. But what is the air doing
below the wing? Figure 6 shows an instantaneous snapshot of how air molecules are moving as a wing
passes by. Remember in this figure the air is initially at rest and it is the wing moving. Arrow "1" will
become arrow "2" and so on. Ahead of the leading edge, air is moving up (upwash). At the trailing edge,
air is diverted down (downwash). Over the top the air is accelerated towards the trailing edge.
Underneath, the air is accelerated forward slightly.
Fig 6 Direction of air movement around a wing as seen by an observer on the ground.
So, why does the air follow this pattern? First, we have to bear in mind that air is considered an
incompressible fluid for low-speed flight. That means that it cannot change its volume and that there is a
resistance to the formation of voids. Now the air has been accelerated over the top of the wing by of the
reduction in pressure. This draws air from in front of the wing and expels if back and down behind the
wing. This air must be compensated for, so the air shifts around the wing to fill in. This is similar to the
circulation of the water around a canoe paddle. This circulation around the wing is no more the driving
force for the lift on the wing than is the circulation in the water drives the paddle. Though, it is true that
if one is able to determine the circulation around a wing the lift of the wing can be calculated. Lift and
circulation are proportional to each other.
One observation that can be made from figure 6 is that the top surface of the wing does much more to
move the air than the bottom. So the top is the more critical surface. Thus, airplanes can carry external
stores, such as drop tanks, under the wings but not on top where they would interfere with lift. That is
also why wing struts under the wing are common but struts on the top of the wing have been historically
rare. A strut, or any obstruction, on the top of the wing would interfere with the lift.
Coanda Effect
A natural question is "how does the wing divert the air down?" When a moving fluid, such as air or
water, comes into contact with a curved surface it will try to follow that surface. To demonstrate this
effect, hold a water glass horizontally under a faucet such that a small stream of water just touches the
side of the glass. Instead of flowing straight down, the presence of the glass causes the water to wrap
around the glass as is shown in figure 7. This tendency of fluids to follow a curved surface is known as
the Coanda effect. From Newton’s first law we know that for the fluid to bend there must be a force
acting on it. From Newton’s third law we know that the fluid must put an equal and opposite force on
the glass.
Fig 7 Coanda effect.
So why should a fluid follow a curved surface? The answer is viscosity; the resistance to flow which
also gives the air a kind of "stickiness". Viscosity in air is very small but it is enough for the air
molecules to want to stick to the surface. At the surface the relative velocity between the surface and the
nearest air molecules is exactly zero. (That is why one cannot hose the dust off of a car.) Just above the
surface the fluid has some small velocity. The farther one goes from the surface the faster the fluid is
moving until the external velocity is reached. Because the fluid near the surface has a change in velocity,
the fluid flow is bent towards the surface by shear forces. Unless the bend is too tight, the fluid will
follow the surface. This volume of air around the wing that appears to be partially stuck to the wing is
called the "boundary layer" and is less than one inch (2.5 cm) thick, even for a large wing.
Look again at Figure 3. The magnitude of the forces on the air (and on the wing) are proportional to the
"tightness" of the bend. The tighter the air bends the greater the force on it. One thing to notice in the
figure is that most of the lift is on the forward part of the wing. In fact, half of the total lift on a wing is
typically produced in the first 1/4 of the chord length.
Lift as a function of angle of attack
There are many types of wing: conventional, symmetric, conventional in inverted flight, the early
biplane wings that looked like warped boards, and even the proverbial "barn door". In all cases, the wing
is forcing the air down, or more accurately pulling air down from above. (Though the early wings did
have a significant contribution from the bottom.) What each of these wings has in common is an angle of
attack with respect to the oncoming air. It is the angle of attack that is the primary parameter in
determining lift.
To better understand the role of the angle of attack it is useful to introduce an "effective" angle of attack,
defined such that the angle of the wing to the oncoming air that gives zero lift is defined to be zero
degrees. If one then changes the angle of attack both up and down one finds that the lift is proportional
to the angle. Figure 8 shows the lift of a typical wing as a function of the effective angle of attack. A
similar lift versus angle of attack relationship is found for all wings, independent of their design. This is
true for the wing of a 747, an inverted wing, or your hand out the car window. The inverted wing can be
explained by its angle of attack, despite the apparent contradiction with the popular explanation of lift. A
pilot adjusts the angle of attack to adjust the lift for the speed and load. The role of the angle of attack is
more important than the details of the wings shape in understanding lift. The shape comes into play in
the understanding of stall characteristics and drag at high speed.
Fig 8 Lift versus the effective angle of attack.
Typically, the lift begins to decrease at a "critical angle" of attack of about 15 degrees. The forces
necessary to bend the air to such a steep angle are greater than the viscosity of the air will support, and
the air begins to separate from the wing. This separation of the airflow from the top of the wing is a stall.
The wing as air "scoop"
We now would like to introduce a new mental image of a wing. One is used to thinking of a wing as a
thin blade that slices though the air and develops lift somewhat by magic. The new image that we would
like you to adopt is that of the wing as a scoop diverting a certain amount of air from the horizontal to
roughly the angle of attack, as depicted in Figure 9. For wings of typical airplanes it is a good
approximation to say that the area of the scoop is proportional to the area of the wing. The shape of the
scoop is approximately elliptical for all wings, as shown in the figure. Since the lift of the wing is
proportional to the amount of air diverted, the lift of is also proportional to the wing’s area.
Fig 9 The wing as a scoop.
As stated before, the lift of a wing is proportional to the amount of air diverted down times the vertical
velocity of that air. As a plane increases speed, the scoop diverts more air. Since the load on the wing
does not increase, the vertical velocity of the diverted air must be decreased proportionately. Thus, the
angle of attack is reduced to maintain a constant lift. When the plane goes higher, the air becomes less
dense so the scoop diverts less air at a given speed. Thus, to compensate the angle of attack must be
increased. The concepts of this section will be used to understand lift in a way not possible with the
popular explanation.
Lift requires power
When a plane passes overhead the formally still air gains a downward velocity. Thus, the air is left in
motion after the plane leaves. The air has been given energy. Power is energy, or work, per time. So, lift
requires power. This power is supplied by the airplane’s engine (or by gravity and thermals for a
sailplane).
How much power will we need to fly? If one fires a bullet with a mass, m, and a velocity, v, the energy
given to the bullet is simply ½mv2. Likewise, the energy given to the air by the wing is proportional to
the amount of air diverted down times the vertical velocity squared of that diverted air. We have already
stated that the lift of a wing is proportional to the amount of air diverted times the vertical velocity of
that air. Thus, the power needed to lift the airplane is proportional to the load (or weight) times the
vertical velocity of the air. If the speed of the plane is doubled the amount of air diverted down doubles.
Thus to maintain a constant lift, the angle of attack must be reduced to give a vertical velocity that is half
the original. The power required for lift has been cut in half. This shows that the power required for lift
becomes less as the airplane's speed increases. In fact, we have shown that this power to create lift is
proportional to 1/speed of the plane.
But, we all know that to go faster (in cruise) we must apply more power. So there must be more to
power than the power required for lift. The power associated with lift is often called the "induced"
power. Power is also needed to overcome what is called "parasitic" drag, which is the drag associated
with moving the wheels, struts, antenna, etc. through the air. The energy the airplane imparts to an air
molecule on impact is proportional to the speed2 (form ½mv2) . The number of molecules struck per
time is proportional to the speed. The faster one goes the higher the rate of impacts. Thus the parasitic
power required to overcome parasitic drag increases as the speed3.
Figure 10 shows the "power curves" for induced power, parasitic power, and total power (the sum of
induced power and parasitic power). Again, the induced power goes as 1/speed and the parasitic power
goes as the speed3. At low speed the power requirements of flight are dominated by the induced power.
The slower one flies the less air is diverted and thus the angle of attack must be increased to increase the
vertical velocity of that air. Pilots practice flying on the "backside of the power curve" so that they
recognize that the angle of attack and the power required to stay in the air at very low speeds are
considerable.
Fig 10 Power requirements versus speed.
At cruise, the power requirement is dominated by parasitic power. Since this goes as the speed3 an
increase in engine size gives one a faster rate of climb but does little to improve the cruise speed of the
plane. Doubling the size of the engine will only increase the cruise speed by about 25%.
Since we now know how the power requirements vary with speed, we can understand drag, which is a
force. Drag is simply power divided by speed. Figure 11 shows the induced, parasitic, and total drag as a
function of speed. Here the induced drag varies as 1/speed2 and parasitic drag varies as the speed2.
Taking a look at these figures one can deduce a few things about how airplanes are designed. Slower
airplanes, such as gliders, are designed to minimize induced power, which dominates at lower speeds.
Faster propeller-driven airplanes are more concerned with parasite power, and jets are dominated by
parasitic drag. (This distinction is outside of the scope of this article.)
Fig 11 Drag versus speed.
Wing efficiency
At cruise, a non-negligible amount of the drag of a modern wing is induced drag. Parasitic drag of a
Boeing 747 wing is only equivalent to that of a 1/2-inch cable of the same length. One might ask what
affects the efficiency of a wing. We saw that the induced power of a wing is proportional to the vertical
velocity of the air. If the area of a wing were to be increased, the size of our scoop would also increase,
diverting more air. So, for the same lift the vertical velocity (and thus the angle of attack) would have to
be reduced. Since the induced power is proportional to the vertical velocity of the air, it is also reduced.
Thus, the lifting efficiency of a wing increases with increasing wing area. The larger the wing the less
induced power required to produce the same lift, though this is achieved with and increase in parasitic
drag.
As will be briefly discussed in the section on ground effect, the additional loading on the wing in straight
and level flight due to upwash is equal to the weight of the airplane time 2/AR. Where AR is the wing’s
aspect ratio (span divided by the mean chord). Thus, when considering two wings with the same area but
different aspect ratios, the wing with the greater aspect ratio will be the most efficient.
There is a misconception by some that lift does not require power. This comes from aeronautics in the
study of the idealized theory of wing sections (airfoils). When dealing with an airfoil, the picture is
actually that of a wing with infinite span. Since we have seen that the power necessary for lift decrease
with increasing area of the wing, a wing of infinite span does not require power for lift. If lift did not
require power airplanes would have the same range full as they do empty, and helicopters could hover at
any altitude and load. Best of all, propellers (which are rotating wings) would not require power to
produce thrust. Unfortunately, we live in the real world where both lift and propulsion require power.
Power and wing loading
Now let us consider the relationship between wing loading and power. At a constant speed, if the wing
loading is increased the vertical velocity must be increased to compensate. This is accomplished by
increasing the angle of attack of the wing. If the total weight of the airplane were doubled (say, in a 2g
turn), and the speed remains constant, the vertical velocity of the air is doubled to compensate for the
increased wing loading. The induced power is proportional to the load times the vertical velocity of the
diverted air, which have both doubled. Thus the induced power requirement has increased by a factor of
four! So induced power is proportional to the load2.
One way to measure the total power is to look at the rate of fuel consumption. Figure 12 shows the fuel
consumption versus gross weight for a large transport airplane traveling at a constant speed (obtained
from actual data). Since the speed is constant the change in fuel consumption is due to the change in
induced power. The data are fitted by a constant (parasitic power) and a term that goes as the load2. This
second term is just what was predicted in our Newtonian discussion of the effect of load on induced
power.
Fig 12 Fuel consumption versus load for a large transport airplane traveling at a constant speed.
The increase in the angle of attack with increased load has a downside other than just the need for more
power. As shown in figure 8 a wing will eventually stall when the air can no longer follow the upper
surface. That is, when the critical angle is reached. Figure 13 shows the angle of attack as a function of
airspeed for a fixed load and for a 2-g turn. The angle of attack at which the plane stalls is constant and
is not a function of wing loading. The angle of attack increases as the load and the stall speed increases
as the square root of the load. Thus, increasing the load in a 2-g turn increases the speed at which the
wing will stall by 40%. An increase in altitude will further increase the angle of attack in a 2-g turn. This
is why pilots practice "accelerated stalls" which illustrates that an airplane can stall at any speed, since
for any speed there is a load that will induce a stall.
Fig 13 Angle of attack versus speed for straight and level flight and for a 2-g turn.
Wing vortices
One might ask what the downwash from a wing looks like. The downwash comes off the wing as a sheet
and is related to the details on the load distribution on the wing. Figure 14 shows, through condensation,
the distribution of lift on an airplane during a high-g maneuver. From the figure one can see that the
distribution of load changes from the root of the wing to the tip. Thus, the amount of air in the
downwash must also change along the wing. The wing near the root is "scooping" up much more air
than the tip. Since the wing near the root is diverting so much air the net effect is that the downwash
sheet will begin to curl outward around itself, just as the air bends around the top of the wing because of
the change in the velocity of the air. This is the wing vortex. The tightness of the curling of the wing
vortex is proportional to the rate of change in lift along the wing. At the wing tip the lift must rapidly
become zero causing the tightest curl. This is the wing tip vortex and is just a small (though often most
visible) part of the wing vortex. Returning to figure 5 one can clearly see the development of the wing
vortices in the downwash as well as the wing tip vortices.
Fig 14 Condensation showing the distribution of lift along a wing. (from Patterns in the Sky, J.F.
Campbell and J.R. Chambers, NASA SP-514.)
Winglets (those small vertical extensions on the tips of some wings) are used to improve the efficiency
of the wing by increasing the effective length, and thus area, of the wing. The lift of a normal wing must
go to zero at the tip because the bottom and the top communicate around the end. The winglet blocks
this communication so the lift can extend farther out on the wing. Since the efficiency of a wing
increases with area, this gives increased efficiency. One caveat is that winglet design is tricky and
winglets can actually be detrimental if not properly designed.
Ground effect
Another common phenomenon that is often misunderstood is that of ground effect. That is the increased
efficiency of a wing when flying within a wing length of the ground. A low-wing airplane will
experience a reduction in drag by as much as 50% just before it touches down. This reduction in drag
just above a surface is used by large birds, which can often be seen flying just above the surface of the
water. Pilots taking off from deep-grass or soft runways also use ground effect. Many pilots mistakenly
believe that ground effect is the result of air being compressed between the wing and the ground.
To understand ground effect it is necessary to look again at the upwash. Notice in Figure 15 that the air
bends up from its horizontal flow to form the upwash. Newton's first law says that there must be a force
acting on the air to bend it. Since the air is bent up the force must be up as shown by the arrow. Newton's
third laws says that there is an equal and opposite force on the wing which is down. The result is that the
upwash increases the load on the wing. To compensate for this increased load, the wing must fly at a
greater angle of attack, and thus a greater induced power. As the wing approaches the ground the
circulation below the wing is inhibited. As shown in Figure 16, there is a reduction in the upwash and in
the additional loading on the wing caused by the upwash. To compensate, the angle of attack is reduced
and so is the induced power. The wing becomes more efficient.
Fig 15 Wing out of ground effect
Fig 16 Wing in ground effect
The additional load due to upwash is equal to the weight of the airplane time 2/AR. Most small airplanes
have aspect ratios of 7-8. An airplane with an aspect ratio of 8 can experience as much as a 25%
reduction in wing loading due to ground effect. Since induced power is proportional to the load2, this
corresponds to a 50% reduction in induced power. Earlier, we estimated that a Cessna 172 flying at 110
knots must divert about 5 ton/sec to provide lift. In our calculations we neglected the contribution of
upwash. The amount of air diverted is probably closer to 6 ton/sec.
Conclusions
Let us review what we have learned and get some idea of how the physical description has given us a
greater ability to understand flight. First what have we learned:
●
●
●
●
The amount of air diverted by the wing is proportional to the speed of the wing and the air
density.
The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of
attack.
The lift is proportional to the amount of air diverted times the vertical velocity of the air.
The power needed for lift is proportional to the lift times the vertical velocity of the air.
Now let us look at some situations from the physical point of view and from the perspective of the
popular explanation.
●
The plane’s speed is reduced. The physical view says that the amount of air diverted is reduced
so the angle of attack is increased to compensate. The power needed for lift is also increased. The
popular explanation cannot address this.
●
●
The load of the plane is increased. The physical view says that the amount of air diverted is the
same but the angle of attack must be increased to give additional lift. The power needed for lift
has also increased. Again, the popular explanation cannot address this.
A plane flies upside down. The physical view has no problem with this. The plane adjusts the
angle of attack of the inverted wing to give the desired lift. The popular explanation implies that
inverted flight is impossible.
As one can see, the popular explanation, which fixates on the shape of the wing, may satisfy many but it
does not give one the tools to really understand flight. The physical description of lift is easy to
understand and much more powerful.
This material can be found in more detail in "Understanding Flight",
by David Anderson and Scott Eberhardt, McGraw-Hill, 2001, ISBN: 0-07-136377-7
Jef Raskin
Jef Raskin's
Coanda Effect: Understanding Why Wings
Work
Site Directory
MODEL AIRPLANES, THE BERNOULLI EQUATION,
AND THE COANDA EFFECT © 1994 by Jef Raskin
"In aerodynamics, theory is what makes the invisible
plain. Trying
to fly an airplane without theory is like getting into a
fistfight
with a poltergeist."
--David Thornburg [1992].
"That we have written an equation does not remove from
the flow of
fluids its charm or mystery or its surprise."
--Richard Feynman [1964]
INTRODUCTION
http://www.jefraskin.com/forjef2/jefweb-compiled/published/coanda_effect.html (1 of 29)24-1-2004 18:11:58
Jef Raskin
A sound theoretical understanding of lift had been
achieved
within two decades of the Wright brothers' first flight
(Prandtl's
work was most influential 1), but the most common
explanation of
lift seen in elementary texts and popular articles today
is
The common explanation, from The Way Things Work [Macaulay
1988]
The reasoning--though incomplete--i s based on the
Bernoulli
effect, which correctly correlates the increased speed
with which
air moves over a surface and the lowered air pressure
measured at
that surface.
In fact, most airplane wings do have considerably
more
curvature on the top than the bottom, lending credence
to this
explanation. But, even as a child, I found that it
presented me
with a puzzle: how can a plane fly inverted (upside
down). When I
1IMAGE
Ludwig imgs/conda02.
Prandtl (1875-1953), a German physicist, often called the
gif
"father of aerodynamics." His famous book on the theory of
wings, Tragflü geltheorie, was published in 1918.
Jef Raskin
1
pressed my 6th grade science teacher on this question,
he just got
mad, denied that planes could fly inverted and tried to
continue
his lecture. I was very frustrated and argued until he
said, "Shut
up, Raskin!" I will relate what happened next later in
this essay.
A few years later I carried out a calculation
according to a
naive interpretation of the common explanation of how a
wing
works. Using data from a model airplane I found that the
calculated lift was only 2% of that needed to fly the
model. [See
Appendix 1 for the calculation]. Given that Bernoulli's
equation
is correct (indeed, it is a form of the law of
conservation of
energy), I was left with my original question
unanswered: where
does the lift come from?
In the next few sections we look at attempts to
explain two
related phenomena--what makes a spinning ball curve and
how a
wing's shape influences lift--and see how the common
explanation of
lift has led a surprising number of scientists
(including some
famous ones) astray.
THE SPINNING BALL
The path of a ball spinning around a vertical axis
and moving
forward through the air is deflected to the right or the
left of a
straight path. Experiment shows that this effect depends
both on
the fact it is spinning and that it is immersed in a
fluid (air).
Non-spinning balls or spinning balls in a vacuum go
straight. You
might, before going on, want to decide for yourself
Jef Raskin
which way a
ball spinning counterclockwise (when seen from above)
will turn.
Let's see what five books say about this problem.
Three are
by physicists, one is a standard reference work, and the
last,
just for kicks, is from a book by my son's soccer coach.
We'll
start with physicist James Trefil, who writes [Trefil
1984],
Before leaving the Bernoulli effect, I'd like to
point
out one more area where its consequences should be
explored, and that is the somewhat unexpected activity
of a baseball. Consider, if you will, the curve ball.
This particular pitch is thrown so that the ball spins
around an axis as it moves forward, as shown in the top
in figure 11-4. Because the surface of the ball is
rough, the effect of viscous forces is to create a thin
layer of air which rotates with the surface. Looking at
the diagram, we see that the air at the point labeled A
will be moving faster than the the air at the point
labeled B, because in the first case the motion of the
ball's surface is added to the ball's overall velocity,
while in the second it is subtracted. The effect, then
is a 'lift' force, which tends to move the ball in the
direction shown. 2
imgs/conda02.
2IMAGE
The surface roughness is not essential. The effect is observed no
gif
smooth the ball.
matter how
Jef Raskin
2
Trefil's figure 11-4. It does not agree with some other sources.
Baseball aficionados would say that the ball curves
toward third
base. Trefil then shows a diagram of a fast ball, shown
as
deflecting downward when spinning so that the bottom of
the ball
is rotating forward. It is the same phenomenon with the
axis of
rotation shifted 90 degrees.
In The Physics of Baseball , Robert K. Adair [Adair
1990]
imagines a ball thrown toward home plate, so that it
rotates
counterclockwise as seen from above--as in Trefil's
diagram. To the
left of the pitcher is first base, to his right is third
base.
Adair writes:
We can then expect the air pressure on the third-base
side of the ball, which is travelling faster through
the
air, to be greater than the pressure on the on the
first-base side, which is travelling more slowly, and
the ball will be deflected toward first base.
This is exactly the opposite of Trefil's conclusion
though they
agree that the side spinning forward is moving faster
Jef Raskin
through the
air. We have learned from these two sources that going
faster
through the air either increases or decreases the
pressure on that
side. I won't take sides in this argument as yet.
The Encyclopedia Brittanica [1979] gives an
explanation which
introduces the concept of drag into the discussion.
"The drag of the side of the ball turning into the
air
(into the direction the ball is travelling) retards
the
airflow, whereas on the other side the drag speeds up
the airflow. Greater pressure on the side where the
airflow is slowed down forces the ball in the
direction
of the low-pressure region on the opposite side,
where a
relative increase in airflow occurs."
Now we have read that spinning the ball causes the air
to move
either faster or slower past the side spinning forward,
and that
faster moving air increases or decreases the pressure,
depending
on the authority you choose to follow. Speaking of
authority, it
3
might be appropriate to turn to one of the giants of
physics of
this century, Richard Feynman. He takes the side of
Trefil, and
uses a cylinder rather than a sphere [Feynman et. al.
1964.
Italics are theirs. The lift force referred to is
shown pointing
upwards.]:
"The flow velocity is higher on the upper side
of a
cylinder [shown rotating so that its top is
moving in
the same direction as its forward travel] than on
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the
lower side. The pressures are therefore
lower on
the
upper side than on the lower side. So when we
have a
combination of a circulation around a cylinder
and a net
horizontal flow, there is a net vertical force
on the
cylinder--it is called a lift force ."
Now for my son's coach's book. The coach in this case
is the
world-class soccer player, George Lamptey. There is
almost no
theory given, but we can be reasonably sure that
Lamptey has
repeatedly tried the experiment and should therefore
report the
direction the ball turns correctly. He writes
[Lamptey 1985]:
"The banana kick is more or less an off-center
instep
drive kick which adds a spin to the soccer ball.
Kick
off center to the right, the soccer ball curves
to the
left. Kick off center to the left, the soccer ball
curves to the right... The amount the soccer ball
curves
depends on the speed of the spin."
Jef Raskin
Lamptey, like Adair, has the high pressure on the
side moving
into the air. I will not relate more accounts, some
having the
ball swerve one way, some the other. Some explanations
depend on
the author's interpretation of the Bernoulli effect,
some on
viscosity, some on drag, some on turbulence.
We will return to the subject of spinning balls,
but we are
not yet finished finding problems with the common
explanation of
lift.
OTHER PARADOXES
The common explanation of how a wing works leads
us to
conclude, for example, that a wing which is somewhat
concave on
the bottom, often called an "undercambered" wing, will
always
generate less lift (under otherwise fixed conditions)
than a flat
4
bottomed one. This conclusion is
wrong.
We then have to ask how a flat wing like that of a
paper
airplane, with no curves anywhere, can generate lift.
Note that
the flat wing has been drawn at a tilt, this tilt is
called "angle
of attack" and is necessary for the flat wing to
generate lift.
The topic of angle of attack will be returned to
presently.
Jef Raskin
A flat wing can generate lift. This is a bit difficult to explain
given the traditional mental model.
The cross-sectional shapes of wings, like those
illustrated
here, are called "airfoils." A very efficient airfoil
for small,
slow-flying models is an arched piece of thin sheet
material, but
it is not clear at all from the common explanation how
it can
generate lift at all since the top and bottom of the
airfoil are
the same length.
If the common explanation is all there were to it,
then we
should be making the tops of wings even curvier than
they now are.
Then the air would have to go even faster, and we'd get
more lift.
In this diagram the wiggliness is exaggerated. More
realistic
lumpy examples will be encountered in a few moments.
If we make the top of the wing like this, the air on top has a
lot longer path to follow, so the air will go even faster than
with a conventional wing. You might conclude that this kind
of airfoil should have lots of lift. In fact, it is a disaster.
Enough examples. While Bernoulli's equations are
correct,
their proper application to aerodynamic lift proceeds
quite
differently than the common explanation. Applied
properly or not,
the equations result in no convenient visualization
that links the
5
Jef Raskin
shape of an airfoil with its lift, and reveal nothing
about drag.
This lack of a readily-visualized mental model, combined
with the
prevalence of the plausible-sounding common explanation,
is
probably why even some excellent physicists have been
misled.
ALBERT EINSTEIN'S WING
My friend Yesso, who works for the aircraft
industry (though
not as a designer), came up with a proposed improved
airfoil.
Reasoning along the lines of the common explanation he
suggested
that you should get more lift from an airfoil if you
restarted the
top's curve part of the way along:
An extra lump for extra lift?
This is just a "reasonable" version of the lumpy airfoil
that I
presented above. Yesso's idea was, of course, based on
the concept
that a longer upper surface should give more lift. I was
about to
tell Yesso why his foil idea wouldn't work when I
happened to talk to Jö rgen Skogh 3. He told me of a
humped airfoil Albert Einstein 4
designed during WWI that was based on much the same
reasoning
Yesso had used [Grosz 1988].
Jef Raskin
Albert Einstein's airfoil. It had no
aerodynamic virtues.
This meant that instead of telling Yesso merely that
his idea
wouldn't work, I could tell him that he had created a
modernized
version of Einstein's error! Einstein later noted, with
chagrin, that he had goofed 5. [Skogh 1993]
EVIDENCE FROM EXPERIMENTS
If it were the case that airfoils generate lift
solely
because the airflow across a surface lowers the
pressure on that
imgs/conda02.
3IMAGE
Mr. Skogh
worked on aircraft design for Saab in Sweden and for
gif
Lockheed in the United States.
4Albert Einstein [1879-1955], a German-American physicist, was one of
the greatest scientists of all time. His small error in wing
design does not detract from the massive revolution his
thinking brought about in physics.
5Jö rgen Skogh writes, "During the First World War Albert Einstein was
for a time hired by the LVG (Luft-Verkehrs-Gesellshaft) as a
consultant. At LVG he designed an airfoil with a pronounced
mid-chord hump, an innovation intended to enhance lift. The
airfoil was tested in the Gö ttingen wind tunnel and also on
an actual aircraft and found, in both cases, to be a flop."
In 1954 Einstein wrote "Although it is probably true that
the principle of flight can be most simply explained in this
[Bernoullian] way it by no means is wise to construct a wing
in such a manner!" See [Grosz, 1988] for the full text.
6
Jef Raskin
surface then, if the surface is curved, it does not
matter whether
it is straight, concave, or convex; the common
explanation
depends only on flow parallel to the surface. Here are
some
experiments that you can easily reproduce to test this
idea.
1. Make a strip of writing paper about 5 cm X 25
cm. Hold it
in front of your lips so that it hangs out and down
making a
convex upward surface. When you blow across the top of
the paper,
it rises. Many books attribute this to the lowering of
the air
pressure on top solely to the Bernoulli effect.
blow
air
Now use your fingers to form the paper into a curve
that it is
slightly concave upward along its whole length and
again blow
along the top of this strip. The paper now bends
downward.
2. As per the diagrams below, build a box of thin
plywood or
cardboard with a balsa airfoil held in place with pins
that allow
it to flap freely up and down. Air is introduced with a
soda
straw. That's one of the nice things about science. You
don't have to take anybody's word for a claim, you can
try it yourself! 6 In
this wind tunnel the air flows only across the top of
the shape. A
student friend of mine made another where a leaf blower
blew on
both top and bottom and he got the same results, but
that design
takes more effort to build and the airfoil models
require leading
Jef Raskin
and trailing edge refinement. Incidentally, I tried to
convince a
company that makes science demonstrators to include
this in their
offerings. They weren't interested in it because "it
didn't give
the right results." "Then how does it work?" I asked.
"I don't
know," said the head designer.
An experiment may be difficult to interpret but,
unless it is
fraudulent, it cannot give the wrong results.
imgs/conda02.
6IMAGE
In some fields, e.g. the study of sub-atomic particles, you
gif
megabucks and a staff of thousands to build
might need
an accelerator to do an independent check, but the
principle is still there.
7
CROSS
SECTION
Jef Raskin
SIDE VIEW
AIRFOIL DEMONSTRATOR. These drawings are full size, but
the exact
size and shape aren't important. I made a number of
airfoils to
test. Here are drawings of the ones I made:
8
NORMAL
CONCAVE
RECURVED
FLAT
FLAT WITH
DOWNTURN
FLAT WITH
UPTURN
EXPERIMENTAL RESULTS
When the straw is blown into, the normal airf oil
promptly
lifts off the bottom and floats up. When the blowing
stops, it
goes back down. This is exactly what everybody expects.
Now
consider the concave shape; the curve is exactly the
same as the
first airfoil , though turned upside down. If the common
explanation were true, then, since the length along the
curve is
the same as with the "normal" example, you'd expect this
one to
rise, too. After all, the airflow along the surface must
be
lowering the pressure, allowing the normal ambient air
Jef Raskin
pressure
below to push it up. Nonetheless, the concave airfoil
stays firmly
down; if you hold the apparatus vertically, it will be
seen to
move away from the airflow.
In other words, an often-cited experiment which is
usually
taken as demonstrating the common explanation of lift
does not do
so; another effect is far stronger. The rest of the
airfoils are
for fun--try to anticipate the direction each will move
before you
put them in the apparatus. It has been noted that
"progress in
science comes when experiments contradict
theory" [Gleick 1992]
although in this case the science has been long known,
and the
experiment contradicts not aerodynamic theory, but the
oftentaught common interpretation. Nonetheless, even if
science does
not progress in this case, an individual's understanding
of it
may. Another simple experiment will lead us toward an
explanation
that may help to give a better feel for these
aerodynamic effects.
THE COANDA EFFECT
9
Jef Raskin
If a stream of water is flowing along a solid
surface which
is curved slightly away from the stream, the water will
tend to follow the surface. This is an example of the
Coanda effect 7 and is
easily demonstrated by holding the back of a spoon
vertically
under a thin stream of water from a faucet. If you hold
the spoon
so that it can swing, you will feel it being pulled
toward the
stream of water. The effect has limits: if you use a
sphere
instead of a spoon, you will find that the water will
only follow
a part of the way around. Further, if the surface is too
sharply
curved, the water will not follow but will just bend a
bit and
break away from the surface.
The Coanda effect works with any of our usual fluids,
such as air
at usual temperatures, pressures, and speeds. I make
these
qualifications because (to give a few examples) liquid
helium,
gasses at extremes of low or high pressure or
temperature, and
fluids at supersonic speeds often behave rather
differently.
Fortunately, we don't have to worry about all of those
extremes
Jef Raskin
with model planes.
imgs/conda02.
7IMAGE
In the 1930's the Romanian aerodynamicist Henri-Marie Coanda
gif
(1885-
1972) observed that a stream of air (or other fluid) emerging
from a nozzle tends to follow a nearby curved or flat
surface, if the curvature of the surface or angle the
surface makes with the stream is not too sharp.
10
A stream of air, such as
what you'd get if you blow
through a straw, goes in a
straight line
A stream of air alongside
a straight surface still goes
in a straight line
A stream of air alongside
a curved surface tends to
follow the curvature of the
surface. Seems natural
enough.
Strangely, a stream of air
alongside a curved surface
that bends away from it still
tends to follow the curvature
of the surface. This is the
Coanda effect.
Another thing we don't have to wonder about is why
the Coanda
effect works, we can take it as an experimentally given
fact. But
I hope your curiosity is unsatisfied on this point and
that you
will seek further.
A word often used to describe the Coanda effect is
to say
that the airstream is "entrained" by the surface. One
advantage of
Jef Raskin
discussing lift and drag in terms of the Coanda effect
is that we
can visualize the forces involved in a rather
straightforward way.
The common explanation (and the methods used in serious
texts on
aerodynamics) are anything but clear in showing how the
motion of
the air is physically coupled to the wing. This is
partly because
much of the approach taken in the 1920s was shaped by
the need for
the resulting differential equations (mostly based on
the Kutta- Joukowski theorem 8) to have closed-form
solutions or to yield
useful numerical results with paper-and-pencil methods.
Modern
approaches use computers and are based on only slightly
more
intuitive constructs. We will now develop an alternative
way of
visualizing lift that makes predicting the basic
phenomena
associated with it easier.
imgs/conda02.
8IMAGE
Discovered independently by the German mathematician M. Wilheim
gif
1944) and the Russian physicist Nikolai
Kutta (1867-
Joukowski (1847-1921).
11
A MENTAL MODEL OF HOW A WING GENERATES LIFT AND DRAG
As is typical of physicists, I have often spoken
of the air
moving past the wing. In aircraft wings usually move
through the
air. It makes no real difference, as flying a slow
plane into the
wind so that the plane's ground speed is zero
demonstrates. So I
will speak of the airplane moving or the wind moving
whichever
makes the point more clearly at the time.
In the next illustration , it becomes convenient
to look at
Jef Raskin
the air molecules, attracted to the
surface, are pulled down.
Think of the wing moving to the left, with the air
standing still.
The air moves toward the wing much as if it was attached
to the
wing with invisible rubber bands. It is often helpful to
think of
lift as the action of the rubber bands that are pulling
the wing
up.
Another detail is important: the air gets pulled
along in the
direction of the wing's motion as well. So the action is
really
more like the following picture.
The air is pulled forward as well
as down by the motion of the
wing.
If you were in a canoe and tried pulling someone in the
water
toward you with a rope, your canoe would move toward the
person.
It is classic action and reaction. You move a mass of
air down and
the wing moves up. This is a useful visualization of the
lift
generated by the top of the wing.
As the diagram suggests, the wing has also spent
some of its
energy, necessarily, in moving the air forward. The
imaginary
rubber bands pull it back some. That's a way to think
about the
drag that is caused by the lift the wing generates. Lift
cannot be
had without drag.
The acceleration of the air around the sharper
curvature near
the front of the top of the wing also imparts a downward
and
Jef Raskin
forward component to the motion of the molecules of air
(actually
a slowing of their upward and backward motion, which is
equivalent) and thus contributes to lift. The bottom of
the wing
is easier to understand, and an explanation is left to
the reader.
The experiments with the miniature wind tunnel
described
earlier are readily understood in terms of the Coanda
effect: the
downward-curved wing entrained the airflow to move
downward, and a
force upward is developed in reaction. The upward-curved
(concave)
airfoil entrained the airflow to move upwards, and a
force
downward was the result. The lumpy wing generates a lot
of drag by
moving air molecules up and down repeatedly. This eats
up energy
(by generating frictional heat) but doesn't create a net
downward
motion of the air and therefore doesn't create a net
upward
12
movement of the wing. It is easy, based on the Coanda
effect, to
visualize why angle of attack (the fore-and-aft tilt
of the wing,
as illustrated earlier) is crucially important to a
symmetrical
airfoil, why planes can fly inverted, why flat and
thin wings
work, and why Experiment 1 with its convex and concave
strips of
paper works as it does.
What has been presented so far is by no means a
physical
account of lift and drag, but it does tend to give a
good picture
of the phenomena. We will now use this grasp to get a
reasonable
hold on the spinning ball problem.
Jef Raskin
WHY THE SPINNING BALL'S PATH CURVES, IN TERMS OF THE
COANDA EFFECT
The Coanda effect tells us the air tends to follow
the
surface of the ball. Consider Trefil's side A which is
rotating in
the direction of flight. It is trying to entrain air with
it as it
spins, this action is opposed by the oncoming air. Thus,
to
entrain the air around the ball on this side, it must
first
decelerate it and then reaccelerate it in the opposite
direction.
On the B side, which is rotating opposite the direction
of flight,
the air is already moving (relative to the ball) in the
same
direction, and is thus more easily entrained. The air
more readily
follows the curvature of the B side around and acquires a
velocity
toward the A side. The ball therefore moves toward the B
side by
reaction.
It is again time for a simple experiment. It is
difficult to
experiment with baseballs because their weight is large
compared
to the aerodynamic forces on them and it is very hard to
control
the magnitude and direction of the spin, so let us look
at a case
where the ball is lighter and aerodynamic effects easier
to see. I
use a cheap beach ball (expensive ones are made of
heavier
materials and show aerodynamic effects less). Thrown with
enough
bottom spin (bottom moving forward) such a ball will
actually rise
in a curve as it travels forward.The lift due to spin can
be so
strong that it is greater than the downward force of
gravity!
Soon, air resistance stops both the spin and the forward
Jef Raskin
motion of
the ball and it falls, but not before it has shown that
Trefil's
explanation of how spin affects the flight of a ball is
wrong.
The lift due to spinning while moving through the air
is
usually called the "Magnus 9 effect." Some books on
aerodynamics
also describe the "Flettner Rotor," which is a long-since
abandoned attempt to use the Magnus effect to make an
efficient
boat sail. Many sources besides Trefil get the effect
backwards
including the usually reliable Hoerner [Hoerner 1965].
Collegelevel texts tend to get it right [Kuethe and Chow 1976;
Houghton
and Carruthers 1982] but, as noted above, Feynman's
Lectures on
Physics has the rotation backwards. I was relieved to see
that the
classic Aerodynamics [von Ká rmá n 1954] gets the lift
force on a
imgs/conda02.
9IMAGE
H. G. Magnus
(1802-1870), a German physicist and chemist, demonstrated
gif
this effect in 1853.
13
spinning ball in the correct direction though the
reasoning seems
a bit strained.
I wish I could send this essay to the 6th grade
science
teacher who could not take the time to listen to my
reasoning.
Here's what happened: he sent me to the principal's
office when I
came in the next day with a balsa model plane with dead
flat
wings. It would fly with either side up depending on
how an
aluminum foil elevator adjustment was set. I used it to
demonstrate that the explanation the class had been
Jef Raskin
given must
have been wrong, somehow. The principal, however, was
informed
that my offense was "flying paper airplanes in class"
as though
done with disruptive intent. After being warned that I
was to
improve my behavior, I went to my beloved math teacher
who
suggested that I go to the library to find out how
airplanes
fly--only to discover that all the books agreed with my
science
teacher! It was a shock to realize that my teacher and
even the
library books could be wrong. And it was a revelation
that I could
trust my own thinking in the face of such concerted
opposition. My
playing with model airplanes had led me to take a major
step
toward intellectual independence--and a spirit of
innovation that
later led me to create the Macintosh computer project
(and other,
less-well-known inventions) as an adult.
APPENDIX 1
A QUANTITATIVE APPLICATION OF THE COMMON (INCORRECT)
EXPLANATION
If the pressure, in Newtons per square meter (Nm -2
kgm-1s- 2), on the top of a wing is notated p top , the
=
pbottom , the velocity (ms -1) on the
top of the wing v
, and the velocity on the bottom
v
top
bottom, and where __ is the
pressure on the bottom
density of air (approximately 1.2 kgm -3), then the
pressure
difference across the wing is given by the first term of
Bernoulli's equation:
ptop - pbottom = 1/2 _ (vtop2 - vbottom2)
A rectangular planform (top view) wing of one meter
span was
measured as having a length chordwise along the bottom of
0.1624 m
Jef Raskin
while the length across the top was 0.1636 m. The ratio of
the
lengths is 1.0074. This ratio is typical for many model and
fullsize aircraft wings. According to the common explanation
which has
two adjacent molecules separated at the leading edge
mysteriously
meeting at the trailing edge, the average air velocities on
the
top and bottom are also in the ratio of 1.0074.
A typical speed for a model plane of 1m span and 0.16m
chord with a mass of 0.7 kg (a weight of 6.9 N) is 10 ms -1
, so v
is 10 ms-1
which makes v top 10.074 ms -1. Given these
numbers, webottom
find a pressure difference from the equation of about 0.9
kgm -1 - 2. The area of the wing is 0.16 m 2
s
giving a total force of 0.14
N.
This is not nearly enough--it misses lifting the weight of
6.9 N by
a factor of about 50. We would need an air velocity
difference of
14
about 3 ms -1 to lift the plane.
The calculation is, of course, an approximation
since
Bernoulli's equation assumes nonviscous, incompressible
flow and
air is both viscous and compressible. But the viscosity
is small
and at the speeds we are speaking of air does not
compress
significantly. Accounting for these details changes the
outcome at
most a percent or so. This treatment also ignores the
second term
(not shown) of the Bernoulli equation--the static
Jef Raskin
pressure
difference between the top and bottom of the wing due
to their
trivially different altitudes. Its contribution to lift
is even
smaller than the effects already ignored. The use of an
average
velocity assumes a circular arc for the top of the
wing. This is
not optimal but it will fly. None of these details
affect the
conclusion that the common explanation of how a wing
generates
lift--with its naï ve application of the Bernoulli
equation--fails
quantitatively.
FURTHER READING: There are many fine books and articles
on the
subject of model airplane aerodynamics (and many more
on
aerodynamics in general). Commendably accurate and
readable are
books and articles for modelers by Professor Martin
Simons [e.g.
Simons 1987]. Much can be learned from Frank Zaic's
delightful, if
not terribly technical, series [Zaic 1936 to Zaic 1964]
(Available
from the Academy of Model Aeronautics in the United
States), and
no treatments are more professional or useful than
those of
Professor Michael Selig and his colleagues [e.g. Selig
et. al.
1989]. All of these authors are also well-known
modelers. The
other references on aerodynamics, e.g. Kuethe and Chow
[1976] and Houghton and Carruthers [1982] are graduate
or upper-level
undergraduate texts, they require a knowledge of
physics and
calculus including partial differential equations.
Jones [1988] is
an informal treatment by a master and Hoerner [1965] is
a
Jef Raskin
magnificent compendium of experimental results, but has 5
little
theory--practical designers find his work invaluable.
15
REFERENCES
* Adair, Robert K. The Physics of Baseball , Harper and
Row, NY,
1990. pg. 13
* Feynman, R. et. al. Lectures on Physics, Vol II ,
Addison-Wesley
1964 pg. 40-9, 40-10, 41-11
* Gleick, J. Genius. Pantheon Books, NY 1992 pg. 234
* Grosz, Peter M. "Herr Dr Prof Albert Who? Einstein the
Aerodynamicist, That's Who!" WWI Aero No. 118, Feb. 1988
pg. 42 ff
* Hoerner, S.F. Fluid-Dynamic Drag , Hoerner Fluid
Dynamics, 1965
pg. 7-11
* Houghton and Carruthers. Aerodynamics for Engineering
Students ,
Edward Arnold Publishers, Ltd. London, 1982
* Jones, R.T. Modern Subsonic Aerodynamics . Aircraft
Designs Inc.,
1988. pg.36
* Lamptey, George. The Ten Bridges to Professional
Soccer, Book 1:
Bridge of Kicking . Academy Press, Santa Clara CA, 1985.
* Levy, Steven. "Insanely Great." Popular Science,
February, 1994.
pg. 56 ff.
* Linzmayer, Owen. The Mac Bathroom Reader , Sybex 1994
* Kuethe and Chow. Foundations of Aerodynamics , Wiley,
1976
* Macaulay, David. The Way Things Work . Houghton Mifflin
Co.
Boston, 1988. pg. 115
Jef Raskin
* Selig, M. et. al. Airfoils at Low Speeds . Soartech 8.
Herk
Stokely, 1504 Horseshoe Circle, Virginia Beach VA 23451,
1989
* Simons, M. Model Aircraft Aerodynamics , 2nd ed.. Argus
Books
Ltd., London, 1987.
* Skogh, Jö rgen. Einstein's Folly and The Area of a
Rectangle , in
publication
* Thornburg, Dave. Do You Speak Model Airplane? Pony X
Press, 5
Monticello Drive, Albuquerque NM 87123, 1992
* Trefil, James S. A Scientist At The Seashore. Collier
Books,
Macmillan Publishing Co., 1984, pp 148-149
* von Ká rmá n, T. Aerodynamics . Oxford Univ. Press 1954
pg. 33
* Zaic, Frank. Model Aeronautic Yearbooks. Published from
the 30's
to the 60's
* Zaic, Frank. Circular Airflow . Model Aeronautic
Publications,
1964.
ACKNOWLEDGMENTS
I am very appreciative of the suggestions I have
received from a
number of careful readers, including Dr. Bill Aldridge,
Professors
16
Jef Raskin
Michael Selig, Steve Berry, and Vincent Panico, and
Linda Blum.
They have materially improved both the content and the
exposition,
but where I have foolishly not taken their advice my
own errors
may yet shine through.
AUTHOR'S BIOGRAPHY
Jef Raskin was a professor at the University of
California at
San Diego and originated the Macintosh computer at
Apple Computer
Inc [Levy 1994; Linzmayer 1994]. He is a widelypublished writer,
an avid model airplane builder and competitor, and an
active
musician and composer.
17
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GIF Collection, Airfoil Misconception
UP to SCIENCE HOBBYIST | UP to LIFTING FORCE MISCONCEPTIONS
AIRFOIL DIAGRAMS
fig. 1
Diagrams in grade K-6 textbooks. The air in the lefthand diagram approaches the wing horizontally and
also leaves the wing horizontally. This violates Newton's laws, since by F=ma there cannot be a lifting
force unless air is accelerated downwards. The wing must deflect the horizontally-moving air downwards,
as shown in the righthand diagram.
http://www.eskimo.com/~billb/wing/airgif.html (1 of 5)24-1-2004 18:14:12
fig. 2
Actual windtunnel photograph of air flowing around a wing. Pulsed smoke streams illustrate that parcels
of air which are divided by the leading edge DO NOT recombine at the trailing edge. Therefor the "wing
shape" explanation of lifting force falls apart.
fig. 3
A flim clip of windtunnel experiments shows a single "plane" of air as it
approaches an airfoil and is sliced into upper and lower portions. Note
that the air flowing above the wing quickly outraces the air flowing
below. The air flowing above and below the wing never rejoin again.
The real reason for the rapid flow of air above the wing is never
explained in "bernoulli"-based textbooks.
fig. 4
The confusing aspects of "airfoil shape" shown here can
totally obscure the true nature of aerodynamic lift.
Many authors point out that airfoils give positive lift even
if the attack angle is zero (so presumably the explanation
of choice should be "wing shape", and not "attack
angle".) But there is a problem here. To determine if an
airfoil is tilted, we cannot rely on construction of the
geometrical attack angle. Geometrical attack angle is very
sensitive to tiny bumps on the wing's leading edge, since
tiny bumps can change where we draw the main 'chord.'
Yet tiny bumps on the leading edge can have little effect
on deflection of air, while the tilting of the airfoil shown
in the fourth section can have an enormous effect upon
the deflection of air and upon lifting force. SMALL
FEATURES ON THE LEADING EDGE CAN CAUSE
US TO TILT THE ENTIRE WING, WHILE WE DENY THAT WE HAVE DONE SO.
To determine the effective attack angle, we cannot trust the simple geometrical rules. To determine
whether an asymmetrical wing is REALLY set to zero attack angle, we instead must inspect the trailing
edge of the airfoil to see if it directs air downwards more than the leading edge pulls air upwards.
fig. 5
Fluid simulation from SAAB
Aircraft shows phase lag between
upper and lower air parcels after an
airfoil has passed. Air travels much
faster over the top of the airfoil, and
then it never rejoins the air which
has travelled below. Note that the
airfoil has deflected the air
downwards.
fig. 6
An air flow simulation from J. S. Denker's HOW IT
FLYS, in the Airfoils chapter.
Note that in the top diagram, the asymmetrical
(cambered) wing has been adjusted to produce zero
lifting force. There is no "slip" or "phase delay"
between upper and lower airflows. In the middle and
bottom diagrams, the angle of attack is progressively
increased, which creates an increasing lifting force.
Increasing the angle of attack also increases the phase
delay between upper and lower air flows.
So not only is the common "wingshape / Bernoulli"
explanation wrong, but it even covers up one of the
most interesting phenomena in airfoil physics: the fact
that the time delay between upper and lower airflows
is proportional to the attack angle and the lifting
force!
Maintained by Bill Beaty. Mail me at: [email protected].
If you are using Lynx, type "c" to email.
The Airfoil Misconception in K-6 Textbooks
AIRFOIL MISCONCEPTIONS | SCIENCE HOBBYIST
AIRPLANE FLIGHT ANALOGY
1997
William Beaty
(See also J. Denker's critique and my response, 8/99)
The controversy about wings and the lifting force has a definite origin. It arises because
we are taught about the flow patterns surrounding two-dimensional airfoil crossections...
and then we apply those concepts to 3D wings.
This is a major mistake. The behavior of 3D wings is fundamentally different than the
behavior of 2D airfoils.
In a 3D world, an airplane produces a downstream wake with net downwash, but in a 2D
wind-tunnel there is no such wake, and the 2D upwash must always be equal to the 2D
downwash. Even more important, 3D wings have finite area, while 2D wings act as if they
are infinitely long. An infinite wing gives some strange results which finite 3D wings
never produce. For example, if a 2D infinite wing should ever deflect even a tiny portion
of the oncoming air downwards, it would deflect an infinite amount of air and produce an
infinite lifting force. As a result, a 2D infinite airfoil does an odd thing: it applies a
sensible, FINITE force to an infinite mass of air, and yet a net amount of air does NOT
move downwards. It acts like a reaction engine, but where the "exhaust" has zero velocity
and infinite mass. This strange effect only applies to 2D airfoils, and is never seen with 3D
airplanes flying through 3D air.
The controversy about "Bernoulli versus Newton" is really a controversy about two-D
versus three-D. It's a controversy over the physics of airfoils in two-dimensional "flatland"
worlds, versus the more ordinary physics of short 3D wings in a 3D world.
I could attempt to explain the problem in words, but words are easily misunderstood
(especially when emotions run high.) A visual analogy works much better. Below is my
explanation for how a three-dimensional airplane flys through 3D space. It is very
different than the typical 2D explanations found in most textboooks. My "circulation" is
flipped ninety degrees!
http://www.amasci.com/wing/rotbal.html (1 of 8)24-1-2004 18:16:35
Imagine a huge, disk-shaped helium balloon floating in the air. The disk stands on edge. It
is weighted for neutral buoyancy. A small platform sticks out of its rim. (If you feel the
need, you should imagine a counterweight on the opposite rim to the platform, so the
balloon hovers without rotating.) See fig. 1 below
_____
_--
--_
/
__|
|
\
.
fig. 1
\_
|
|
DISK-BALLOON WITH
A SMALL PLATFORM
_/
--_____--
Now suppose I were to leap from the top of a ladder and onto the balloon's small platform.
The balloon would move downwards. It would also rotate rapidly counterclockwise, and I
would be dumped off.
Next, suppose we have TWO giant disk-shaped balloons stacked adjacent to each other
like pancakes standing on edge.
____
_-- _____
/ _---_
__| /
\
__|
.
|
|
|
\_
_/
--_____--
fig. 2 TWO DISK-BALLOONS,
STACKED ADJACENTLY
They do not touch each other. Both have platforms. If I jump onto the first platform, but
then I immediately leap onto the next platform, I can stay up there for a tiny bit longer.
Next, suppose we have a row of these disk-balloons one KM long. It looks like fig. 2
above, but with hundreds of hovering balloons. Now I can run from platform to platform,
and I will stay aloft until I run out of balloons. Behind me I leave a trail of rotating,
downward-moving balloons. I can remain suspended against gravity because I am flinging
mass downwards. The mass takes the form of helium mass trapped inside the balloons. I
am also doing much more work than necessary, since the energy I expend in rotating the
balloons does not contribute to my fight against gravity. (In truth, all my work is really not
necessary, I could simply walk along the Earth's surface with no need to move any
massive gasbags!)
To make the situation more symmetrical, let me add a second row of platform-bearing
balloons in parallel to the first row:
_____
_--
_____
--_
/
_--
TWO LONG
|
BALLOONS
|
\
/
.
|__
|
\_
--_
_/
--_____--
fig. 3
END VIEW OF
__|
\
.
|
|
ROWS OF DISK-
|
\_
_/
--_____--
There's one platform for each of my feet. I can run forwards, leaving a trail of "wake
turbulence" behind me. The "wake" is composed of rotating, descending balloons. Fig. 4
below show an animated GIF of this process.
Fig. 4 Forcing the balloons downwards
Also see: Smoke Ring animation
"DISK BALLOONS" BEHIND AIRPLANES
An aircraft does much the same thing as me and my balloons: it remains aloft by throwing
down a spinning region of mass. This mass consists of two long, thin, vortex-threads and
the tubular regions of air which are constrained to circulate around them. The balloons
crudely represent the separatrix of a vortex-pair: the cylindrical parcels of air which must
move with closed streamlines.
How do airplanes fly? Real aircraft use "invisible disk-balloons" to stay aloft. The two
rows of "invisible balloons" form a single, very long, downwards-moving cylinder of air.
This single cylinder has significant mass and carries a large momentum downwards.
_____
_--
_____
--_
_--
/
\
|
/
AIRCRAFT, W/
|
___
|
|
|
___
ROTATED BY THE
|
---____/ \____--http://www.amasci.com/wing/rotbal.html (4 of 8)24-1-2004 18:16:35
--_
fig. 5
FRONT VIEW OF
\
|
AIR MASSES
|
WINGS'
PRESSURE DIFFERENCE
\_
_/
--_____--
\_/
\_
_/
--_____--
\
|
|
|
|
\
______
/ ___ \
SECTION OF AN
/
/
\
\
HAS STREAMLINES
| | o | |
PERFECTLY
\
\___/
/
PAIR OF ROTATING
\_______/
THE BALLOONS ARE
|
|
/
/
|
|
______
/ ___ \
|
|
|
/
|
|
|
|
|
|
|
|
|
/
|
|
\
|
|
\
o
|
\___/
\_______/
\
\
ACTUAL WAKE
|
WHICH DO NOT
/
RESEMBLE A
BALLOONS.
A CRUDE
ANALOGY.
/
/
fig. 6
THE CROSS-
\
Fig. 7 Actual downwash made visible
(See efluids.com photo gallery and another photo
FLY FASTER FOR LESS DRAG
My forward speed makes a difference in how much work I perform. If I walk slowly along
my rows of balloons, each platform sinks downwards significantly. I must always leap
upwards to the next platform, and each balloon is thrown violently downward as I leap. I
tire quickly. On the other hand, if I run very fast, my feet touch each platform briefly, the
balloons barely move, and the situation resembles my running along the solid ground.
Similarly, if a real aircraft flys slowly, it must fling the vortex-pairs violently downward.
It performs extra work and experiences a very large "induced drag." If it flys fast, it
spreads out the necessary momentum-changes, and therefore it needs only to barely touch
each parcel of mass (each "balloon.") Hence, faster flight is desirable because it requires
far less work to be performed in moving the air downwards. And if a slow-flying, heavilyloaded aircraft should fly very low over you, its powerful wake vortices will blow you
over and put dust in your eyes.
All of my reasoning implies that modern aircraft actually remain aloft by launching
"smoke rings" downwards. Imagine one of the flying cars in the old 'Jetsons' cartoon, the
ones with those little white rings shooting down out of the underside. But rather than
launching a great number of individual rings, modern aircraft throw just one very long
ring downwards, and they are lifted by the upward reaction force.
A CRUDE PREDICTION
How well does the "disk balloons" model correspond to the real world? Well, we can pull
an equation out of the motions of the balloons, and use it to predict both aircraft energy
use and induced drag. If the equation is at all similar to the actual aerodynamics of a realworld airplane, then the "disk balloons" are a useful model. If the equation is faulty, then
the model only has weak ties with reality.
Suppose the "disk-balloons" contain air which rotates as a solid object, (or imagine radial
membranes in the balloons.) If I add together the work done in creating the circulatory
flow, plus the work done in projecting the constrained air downwards, I arrive at a
predicted aircraft power expenditure of:
Power = 8 * (M * g)^2 / [ pi * span^2 * V * density ]
M * g being aircraft weight, V is velocity of horizontal flight, and "density" is the density
of air. Induced drag should then be power/V:
Induced Drag = 8 * (M * g)^2 / [ pi * span^2 * V^2 * density ]
What happens if I assume that the air within the disk-balloons is not "solid", but instead it
is made to whirl faster near the center of the balloon, such that the tangential velocity of
the air is constant regardless of its distance from the center of the balloon? (Imagine a
wing which produces a downward velocity of net downwash which is constant at each
point along the whole span of the wing.) If the "downwash" is constant across the
wingspan, then the modified "balloon equation" predicts a power expenditure of 2x that
above.
How does this match reality? I'm looking for information on this at the moment. I'm told
that these two equations are identical to the equations of real aircraft, except that the
number "8" is replaced by a factor which is dependent upon the particular geometry of the
wing. Pretty good for an "amateur aerodynamicist", eh?
One final note. The downwash of real airplanes contains rapidly rotating air. This
represents wasted energy, since only the "shell" of each "balloon" needs to rotate as the air
moves downwards. Is there a wing which can produce a downwash vortex-pair without
any spinning cores? Maybe it would use less fuel than modern wings.
LINKS
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Water Striders fling underwater vortices (Nature 8/03)
Harvard U: Fish Gotta Swim
Wakes in flapping flight
Applet: flow around doublet/vortex etc.
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●
Created and maintained by Bill Beaty. Mail me at: [email protected].
If you are using Lynx, type "c" to email.
BAD PHYSICS: Misconceptions spread by K-6 textbooks
up to SCI. MISCONCEPTION COMMENTS GOOD STUFF NEW STUFF
SEARCH
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RECURRING SCIENCE MISCONCEPTIONS IN K-6 TEXTBOOKS
William J. Beaty
ALWAYS UNDER CONSTRUCTION
WARNING: This file is currently being written, edited, corrected, etc. It does still contain some mistakes of its own. I
placed it online as a sort of 'trial by fire' in order to hear readers' responses so I could target weak or unclear sections for
improvement. (And, as my site points out, NOBODY is perfect so we should always practice critical thinking. Take all
information with a grain of salt, including everything here!) Please feel free to send public comments to me with the
COMMENT BOOK. If you prefer that nobody else sees your comments, send private comments to me via this form.
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THE MISCONCEPTIONS
MAIN MISCONCEPTIONS PAGE
Jump to ELECTRICITY MISCONCEPTION PAGE
COMMENT BOOK, publicly express your opinions on all this
Suggest Your Own K-6 Textbook Miscon
Try "SCIENCE MYTHS" SPREAD BY K-6 TEXTBOOKS
AM I JUST A NITPICKER?
"Errors, like straws, upon the surface flow; He who would search for pearls must dive below." - John Dryden
THE MISCONCEPTIONS:
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SCIENTISTS USE THE SCIENTIFIC METHOD? not quite.
CLOUDS REMAIN ALOFT BECAUSE WATER DROPLETS ARE TINY? Wrong!
THE SKY IS BLUE BECAUSE OF COMPLICATED PHYSICS No, it's simple.
A LEMON-BATTERY CAN LIGHT A FLASHLIGHT BULB? doesn't work!
SOUND TRAVELS BETTER THROUGH SOLIDS & LIQUIDS? No it doesn't.
GRAVITY IN SPACE IS ZERO? It's actuallly strong.
FILLED AND EMPTY BALLOONS DEMONSTRATE THE WEIGHT OF AIR? Misleading.
GASES ALWAYS EXPAND TO FILL THEIR CONTAINERS? Not quite.
FRICTION IS CAUSED BY SURFACE ROUGHNESS? Obsolete idea!
ICE SKATES FUNCTION BY MELTING ICE VIA PRESSURE? nope.
THE EARTH HAS 92 CHEMICAL ELEMENTS?
LIGHT FROM THE SUN IS PARALLEL LIGHT?
A WING'S LIFTING FORCE IS CAUSED BY ITS SHAPE?
FOR EVERY ACTION, THERE IS AN EQUAL AND OPPOSITE REACTION?
BEN FRANKLIN'S KITE WAS STRUCK BY LIGHTNING?
THE MAIN LENS OF YOUR EYE IS INSIDE THE EYE?
WHEN ONE PRISM SPLITS LIGHT INTO COLORS, A SECOND IDENTICAL PRISM CAN RECOMBINE
THEM?
CLOUDS, FOG, AND SHOWER-ROOM MIST ARE MADE OF WATER VAPOR?
http://www.amasci.com/miscon/miscon4.html (1 of 32)24-1-2004 18:18:25
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RAINDROPS HAVE POINTS?
AIR IS ALMOST ENTIRELY WEIGHTLESS?
SHADOWS VANISH ON CLOUDY DAYS BECAUSE THE SUN ISN'T BRIGHT ENOUGH?
INFRARED LIGHT IS A FORM OF HEAT?
THERE ARE SEVEN COLORS IN THE RAINBOW?
THE EARTH'S NORTH AND SOUTH MAGNETIC POLES RESIDE JUST BELOW THE SURFACE?
LASER LIGHT IS "IN PHASE" LIGHT?
LASER LIGHT IS PARALLEL LIGHT?
LASERS ARE COHERENT BECAUSE ATOMS EMIT IN PHASE?
IRON AND STEEL ARE THE ONLY STRONGLY MAGNETIC MATERIALS?
RE-ENTERING SPACECRAFT ARE HEATED BY AIR FRICTION?
CARS AND AIRPLANES ARE SLOWED DOWN BY AIR FRICTION?
THE NORTH MAGNETIC POLE OF THE EARTH IS IN THE NORTH?
SALT WATER IS FULL OF SODIUM CHLORIDE MOLECULES?
LIGHT AND RADIO WAVES ALWAYS TRAVEL AT "THE SPEED OFLIGHT"?
That's the way all the books were: They said things that were useless, mixed-up, ambiguous, confusing, and
partially incorrect. How anybody can learn science from these books, I don't know, because it's not science.
- Dr. Richard Feynman, in "Surely you're Joking, Mr. Feynman"
CORRECT: THERE IS NO SINGLE LIST CALLED "THE SCIENTIFIC METHOD." IT IS A MYTH
The rules of a science-fair typically require that students follow THE SCIENTIFIC METHOD, or in other words,
hypothesis-experiment-conclusion. The students must propose a hypothesis and test it by experiment. This supposedly is
"The Scientific Method" used by all scientists. Supposedly, if you don't follow "The Scientific Method" listed in K-6
texts, then you're not doing science. (Some science fairs even ban astronomy and paleontology projects. Where's the
experiment in these?)
Unfortunately this is wrong, and there is no single "Scientific Method" as such. Scientists don't follow a rigid procedurelist called "The Scientific Method" in their daily work. The procedure-list is a myth spread by K-6 texts. It is an extremely
widespread myth, but this doesn't make it any more real. "The Scientific Method" is part of school and school books, and
is not how real science is done. Real scientists use a large variety of methods (perhaps call them methods of science rather
than "The Scientific Method.") Hypothesis/experiment/conclusion is one of these, but it certainly is not the only one, and
it would be a mistake to elevate it above all others. We shouldn't force children to memorize it. And we shouldn't use it to
exclude certain types of projects from science fairs! If "The Scientific Method" proves that Astronomy is not a science,
then it's "The Scientific Method" which is unscientific, not Astronomy.
"Ask a scientist what he conceives the scientific method to be and he adopts an expression that is at once
solemn and shifty-eyed: solemn, because he feels he ought to declare an opinion; shifty-eyed because he is
wondering how to conceal the fact that he has no opinion to declare." - Sir Peter Medawar
There are many parts of science that cannot easily be forced into the "hypothesis/experiment/conclusion" mold.
Astronomy is not an experimental science, and Paleontologists don't perform Paleontology experiments... so studying
dinosaurs or stars must not be science?
Or, if a scientist has a good idea for designing a new kind of measurment instrument (e.g. a telescope), that certainly is
"doing science." But where is The Hypothesis? Where is The Experiment? The Atomic Force Microscope (STM/AFM)
revolutionized science. Yet wouldn't building such a device be rejected from many science fairs? After all, it's not an
experiment. So, were the creators of the STM not doing science when they came up with that device? The Nobel prize
committee disagrees.
Forcing kids to follow a caricature of scientific research distorts science, and it really isn't necessary in the first place.
Another example: great discoveries often come about when scientists notice anomalies. Isaac Asimov said it well: "The
most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' (I found it!) but 'That's
funny...' " This suggests that lots of important science comes NOT from proposing hypotheses or even from performing
experiments, but instead comes from learning to see what nobody else can see. Scientific discovery comes from
something resembling "informed messing around," or unguided play. Yet "The Scientific Method" listed in textbooks
says nothing about this. As a result, educators treat science as deadly serious business, and "messing around" is
sometimes dealt with harshly.
ARTICLES:
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Ten Science Myths (McComas)
Scientific Methods (Denker)
The Scientific Method (Simanek)
On Scientific Method (Bridgman)
Theories DON'T become laws
Dispelling Common Science Myths
"Why should there be the method of science? There is not just one way to build a house, or even to grow
tomatoes. We should not expect something as motley as the growth of knowledge to be strapped to one
methodology." -Ian Hacking
CORRECT: THE SKY IS BLUE BECAUSE AIR IS BLUE.
This one isn't purely an error. Still, it involves misconceptions on the part of authors.
Why is the sky blue? Usually the books start going on about wavelengths of light, Tyndall effect, and Rayleigh scattering.
They teach some complicated physics first, then use it to explain blue sky and sunsets. Their explanations are correct. But
what if you don't understand the physics? DOesn't this make their explanation useless? And do you just give up?
They're wrong: you don't need complicated physics to understand this. The sky is blue for a very simple reason:
AIR IS NOT A TRANSPARENT MATERIAL. INSTEAD IT IS BLUE!
The sky is blue for much the same reason that a cloud of powder is white. Powder isn't invisible. Throw some dust into
the air on a sunny day and you'll see a visible cloud. But what happens if you could throw some AIR? You might think
that a cloud of air would be invisible. You'd be wrong. Air isn't invisible, instead it's a powdery-blue substance.
True, small amounts of air are almost perfectly transparent. So are small amounts of water. Go to an opaque muddy river
or pond and use a glass to dip out a cup of water. The water looks clear, no? Yet the river is opaque brown. When you try
to look through ten cups of water, or a hundred cups, the water seems to turn into brown paint. Air behaves like this too.
A mile of air looks clear, but ten miles of air looks misty blue, and a thousand miles of air looks opaque white. The air is
acting like the dirty river water, where a thin layer looks clear but a thick layer doesn't.
The sky is blue because air is a powdery blue material, and when the sun shines on it, you can see this blue color. Stare
upwards on a sunny day, and you're looking into a thick cloud of air. There really is no "sky" up there. You're not looking
at a blue surface. Instead you're just seeing the Earth's layer of blue air against the blackness of outer space.
Suppose you could go far out into space away from the Earth, then build yourself a thin hollow glass bubble a thousand
miles wide. Viewed from the Earth, your thin glass bubble would be almost invisible. OK, now fill your bubble with air.
It won't be invisible any more. It will look like a giant droplet of bright blue paint. It might even look whitish in the
middle, since very thick layers of air seem as white as milk. What if you let your giant glass bubble crash into the moon?
The air inside would pour out over the moon's surface and form a thick layer of atmosphere. The moon wouldn't look
white anymore. It would turn blue.
OK, now here's a question. Smoke is white, milk is white, and powder is white. A big cloud of particles should look like
white smoke, not like a blue dye. Why is air blue instead of white? And even more important, why are sunsets red? (Does
this mean that air is a red substance?!!) Ah, if you start wondering about such things, then *now* you finally need the
advanced physics explanations.
CORRECT: CLOUDS ACTUALLY REMAIN ALOFT BECAUSE THEY ARE WARM INSIDE.
Clouds are heavy. Evaporated water (H2O gas) is less dense than air, so moist air rises, but when the H2O gas condenses
to form clouds, it contracts by about 1000 times and turns into very dense liquid water. (Imagine that the helium in a
balloon condensed into a liquid. Would it still be buoyant?) Even a small cloud contains many tons of liquid water. How
can clouds remain aloft?
Many sources claim that clouds remain aloft because the water droplets are so small and widely separated that gravity has
less effect on them. This is wrong. It doesn't matter if you break up a body of water into tiny droplets; its weight remains
the same. You can't fool gravity. If a cloud contains tons of water, it will be pulled down to the Earth's surface with the
same force whether the water forms a cloud or whether it forms raindrops. The answer lies elsewhere.
Some sources claim that clouds remain aloft because of updrafts: because the air had been rising, and the rising air blows
the cloud droplets upwards. Wrong again: it would take an upwards hurricane-wind to keep so many tons of water
suspended. [WRONG! G. Beaulieu points out that cloud-stuff is only 1/10 percent more dense than air.] An updraft
should be instantly halted as soon as the low-density water vapor turns into a dense liquid. [Correct. The excess weight
will slow the updraft, stop it, then reverse it.]
Still other sources claim that clouds stay up there because the droplets are very tiny, so they settle through the air very
slowly. This is true, but it doesn't explain how weighty water can remain aloft. Stop and think a bit... if we have hundreds
of tons of water, will its weight disappear simply because it has been divided into tiny droplets? No, instead the heavy
droplets drag the air downwards as they fall. Air that contains water droplets is denser than normal air (its weight is
increased by almost exactly the weight of the suspended water droplets, which works out to around 1/10 percent of the
weight of the air in a particular volume.) Dense air falls fast! In other words, the tiny droplets will still race downwards
because they form dense cloud-matter, and both the droplets and the air between them will be dragged downwards by
gravity. Anyone playing with humidifier fog knows this. Yet even some professional meteorologists are saying these
things. They should know better.
So why *DO* clouds stay up there? Why don't they pour downwards to form a ground-hugging fog? The answer is
simple: the weight of the water droplets is countered by the buoyancy of heated air between the droplets. Clouds are like
hot air balloons.
Whenever liquid water condenses from H2O gas, it releases thermal energy. When moist air turns into droplet-filled air,
the droplets are hot, and they warm the air too. Clouds stay up there because they're less dense on average than
surrounding air. In fact, if the water droplets should fall out of the cloud as rain, then the remaining hot air is no longer
weighed down by tons and tons of water, and it races upwards. This rising hot air is the "engine" which drives the violent
updrafts in thunderstorms and hurricanes. Hot air with its water removed no longer floats serenely along as clouds,
instead it forms upward jets with hurricane velocity.
Try making this "Touch The Clouds" device and you'll discover that droplet-filled air can be very dense. You can easily
pour it from a pitcher and fill some cups. But we also know that hot air is less dense that cool air of the same pressure, so
hot must rise through cooler air. Mix the two ideas together: dense air which is full of water droplets becomes less dense
when heated, and at a certain high temperature it should be buoyed upwards by the atmosphere even though it's full of
heavy water droplets.
More thinking: helium gas rises in air, but liquid helium does not. Liquid helium is heavy like liquid water (though not
quite as heavy as an equal quantity of water.) This is because each gram of liquid helium occupies a certain small volume,
while each gram of helium gas occupies a much large volume, and the is bouyed upwards by the surrounding air. So,
what happens when helium condenses into liquid? It shrinks greatly, becoming more dense than the surrounding air, then
it dribbles downwards. It falls downwards even if it's a large blob of liquid, and it falls downward even if it takes the form
of tiny droplets. THE SAME IS TRUE OF WATER. Water vapor (h2o gas) like helium is lighter than air, and it will rise.
However, if that vapor should condense into droplets, it greatly contracts in size and greatly increases in density. A cloud
of water droplets is heavy, and it SHOULD fall downwards. Even if the droplets are so tiny that they individually settle
slowly, the droplet together have significant weight, so the droplets should drag the air downwards as they go. The dense,
droplet-filled air can fall very fast, even though the individual droplets remain "stuck in the air" because of forces of
viscosity.
Whenever vapor condenses to form droplets, it releases "heat of condensation" which causes the remaining air to expand.
The warm air can even expand MORE than the volume left empty by the condensing vapor, causing the average density
to fall and causing clouds to rise upwards rather than just float. When clouds form, they usually pour upwards, not
downwards. They are a bit too hot, so they try to rise to a higher level.
Wrong: Scientific American "Ask an Expert" Tell them to calculate the heat released by condensation of cloud water,
the temperature of resulting air, and the weight of a 1KM cloud compared to 1KM of nearby air which is cooler yet
droplet-free.
● Wrong: New Scientist "Last Word"
● Wrong: National Geographic Kids
● Wrong: UK ScienceLine
● Wrong: Star Tribune: kid's weather questions
● Wrong: Madsci: ask an expert
● Wrong: U. Indiana Moment in Science
● Wrong: U. Corp. Atmos Research
● Wrong: NASA p.u.m.a.s. (they even mention "lighter than air"... then deny it!
● Wrong:
● Wrong: Starbase outreach pgm
●
Correct:
● Steve's Weather FAQ
● n
CORRECTED: A SINGLE LEMON BATTERY CANNOT LIGHT A FLASHLIGHT BULB
Gradeschool science books sometimes contain "experiments" which do not work. The prism experiment below is one of
them. Another is the "lemon battery" or "potato battery" used to run a light bulb. Stick some copper and zinc into a single
lemon, and this "battery" does create a small voltage. Touch your lemon-cell to the wires of a loudspeaker or headphones
and you'll hear a clicking sound. Connect it to an old-style panel meter (voltmeter or milliamp-meter, the kind with the
moving needle,) and your lemon can make the meter needle move. Three or four lemon-cells connected in series can run
an LCD digital clock or light a red Light Emitting Diode LED. (If you try the digital clock or LED, remember that
polarity is important, and if it doesn't work, try reversing the connections.)
However, the lemon's electrical output is far too feeble to light a standard flashlight bulb. Same with motors, buzzers, etc.
The lemon battery is too weak. The experiment described in the books doesn't work.
Example: stick a fairly wide copper strip and a similar zinc strip into a lemon. (This works much better than copper
pennies or zinc nails.) First use the strips to tear up the inside of the lemon, then insert the metal strips very close together
to give best results. The area of each "battery plate" is around 1 inch square. Measured voltage: 0.91V. Measured shorthttp://www.amasci.com/miscon/miscon4.html (7 of 32)24-1-2004 18:18:25
circuit current: two milliamps (0.002 Amps) immediately decreasing to a constant half a milliam (0.0005 amps.) What
does this mean? Well, a typical flashlight bulb draws an ENTIRE 1/4 AMPERE when lit. Not half a milliamp, but 250
milliamps or 0.250 Amps. You'd need 500 lemons wired in parallel! 0.2500amps / 0.0005amps = 500 lemons.
However, there are specialized light bulbs which draw very tiny currents. From Radio Shack we can get a #272-1139
incandescent bulb which only draws around fifteen milliams (0.015 amps) at 0.7 volts when lit very dimly in a darkened
room. To light this bulb we only need 0.0150A/0.0005A = 30 lemons wired in parallel. But wasn't the lemon's electric
current higher at the start? 0.002 amps, not 0.0005 amps? Yes, so with only TEN lemons wired in parallel, maybe we
could cause a special hyper-sensitive light bulb to blink on for a second or two before going dark.
This still translates into "the experiment doesn't work." One single lemon cannot light up any sort of incandescent bulb.
At best we can use several lemons to light an LED. If a textbook contains the bulb-lightning experiment, it means that the
author never performed the experiment to see if it works. LOTS of books and websites say that a lemon can light a
flashlight bulb. Every single one of these is wrong. The mistake is like a kind of infection. If you aren't careful, then your
science website can catch a disease!
Can't we build a larger lemon-juice battery in a jar which will light a small bulb? Yes, but your battery needs to be fairly
large; much larger than a couple of metal parts stuck into a lemon. At the very least you'll need a jar for the juice, plus
some sheets of copper and zinc several inches wide. If you don't have that special Radio Shack bulb, then you'll need
more than one lemon-juice jar hooked in series to make the 1.5 volts needed by a standard flashlight bulb.
If you really want to light up a small lightbulb, why not build an ELECTRIC GENERATOR instead?
How to cheat!
There is a secret way to make a lemon-cell light up an incandescent bulb. You have to cheat! Buy yourself a "super
capacitor" or "memory backup capacitor" via mail-order surplus. They cost a few dollars. You want a value between 0.1
farad and 0.5 farads. Try one of these suppliers:
●
●
●
All Electronics
Electronics Goldmine
Jameco Electronics
Build a lemon battery and connect it to the terminals of the super capacitor. (Me, I use alligator clip-leads bought from
Radio Shack.) Wait for a few minutes. Now connect your flashlight bulb to the supercapacitor terminals and it should
light brightly for a few seconds. (If not, then remove the bulb and try connecting your lemon cell to the capacitor for 15
minutes to make sure the capacitor gathers enough energy.) The capacitor slowly collects electrical energy from the
lemon battery, then it dumps that energy into the flashlight bulb over a very short time. You can even use this trick to let
your lemon battery run a low-voltage buzzer or turn a small motor (look for "solar cell motors" from various mail order
suppliers or Radio Shack.) As with the bulb, you must charge up the capacitor for many minutes, then use it to run your
bulb or motor for a few seconds.
It's not an ideal experiment, and it's hard to explain how capacitors work. But it's easier than trying to connect thirty
lemon-cells in parallel!
●
●
●
●
Four lemons light an LED
Note about Lemon energy
Tongue tingle, but no lightbulb
Digital watch yes, lightbulb no
CORRECTED: ICE SKATES DO NOT FUNCTION BY MELTING ICE VIA PRESSURE
It is commonly stated that ice skates have low friction because ice melts when pressure is applied to it. This is not quite
correct. A demonstration using an ice cube, a wire, and two weights is often provided to illustrate the phenomena.
However, while pressure does affect the melting point of ice, the pressure provided by the skates is not enough to melt ice
except when the temperature is a fraction of a degree below 0C. Also, the icecube and wire demonstration is very
misleading because it is always performed in a heated room, and the wire doesn't melt ice entirely by pressure, it melts
the ice by thermal conduction of warm room temperature along the wire. (Also, narrow gaps in ice always freeze closed
because the simultaneous melt/freeze process at water/ice boundary acts to flatten points and fill crevices) Another point:
the weight of small objects is too low to create high pressure, yet small objects do experience low friction when on ice.
The low friction of ice is probably caused by a layer of liquid water a few hundred molecules thick which always
spontaneously develops on the surface of ice. Also, melting from frictional heating can provide liquid water as
lubrication. Here's more on this whole debate, and also a bit from BAD CHEMISTRY
CORRECTED: THERE ARE NOT 92 ELEMENTS ON EARTH
Uranium has the highest atomic number of the elements commonly found in the environment, and some books will tell
you that there are 92 elements found on earth: atomic numbers 1 through 92 (hydrogen through uranium). This is wrong.
Unfortunately there are two elements below Uranium which are radioactive and have extremely short half lives. These are
Technetium and Promethium. These two elements do not occur naturally on Earth, and this reduces the total number of
elements found in the environment to 90. However, in the 1970s a natural uranium reactor was found in an ancient
streambed in Africa, and the mineral deposits at the site contained traces of a long-lived Plutonium isotope (atomic
number 94.) This brings the total number of elements on the Earth back up to 91. (Note: Technicium, though not found
naturally on Earth, is present in some stars, detected by spectral analysis.) See THE PHYSICS TEACHER, Vol.27 No.4
p282
LIGHT FROM THE SUN IS PARALLEL? NOPE.
Some books state that because the sun is so far away, sunlight arriving at the Earth is almost perfectly parallel. This is
incorrect. The books reason that the more distant the object, the more parallel the light, and since the sun is so far away,
sunlight is perfectly parallel. They make a mistake. While it is true that light from *each tiny point* on the sun's surface is
just about perfectly parallel by the time it reaches our eyes, light from the sun as a whole is not. This is because the sun,
though very distant, is very large. A similar situation exists with light from the sky. We wouldn't say that the blue sky
emits parallel light. Yet light from the sky comes from many miles away.
If sunlight were perfectly parallel, there would be some interesting effects which are usually smeared out by the sun's
disklike image. First of all, if the sun were tiny, then to us it would look like a very bright point, like an intensely bright
star or a welding arc. Also, shadows on the ground would lack penumbras and be almost perfectly sharp. Without the
penumbras, diffraction of waves would be revealed, and parallel dark and bright lines would appear at the edges of
shadows. At nightfall the advancing shadows of distant mountains would be seen to race across the ground. During sunset
the sun wouldn't gradually sink below the horizon, instead it would wink out. During the day the variations in air density
would cause the ground to be covered by moving patterns of light; patterns similar to those seen on the bottom of a
swimming pool but in this case made by "waves" in the sky. Solar and lunar eclipses would lack penumbrae. Looking at
the sun might burn your retina, since the parallel light would be focused to a tiny point. And if sunlight were perfectly
parallel, a large convex lens could concentrate sunlight into an intense pinpoint rather than into a small disk. Also, a if a
small concave lens were placed near the focus of a large convex lens, the pair lenses could be used to concentrate sunlight
and form it into a thin, dangerously powerful parallel beam. Try to do this with the real sun, and all you get is a large,
projected image of the sun's disk.
CORRECTED: WITH AN AIRCRAFT WING, THE LIFTING FORCE DOES NOT COME FROM THE
DIFFERENCE IN CURVATURE BETWEEN THE TOP AND BOTTOM SURFACES
Also: wings/lift webpage
Some books explain that the lifting force on an aircraft wing is created because the upper wing surface is longer and more
curved than the lower. They state that air dividing at the leading edge of the wing must rejoin at the trailing edge,
therefore the upper air stream must move faster, and so the wing is pulled upwards by the Bernoulli effect. This is not
correct: the air divided by the leading edge does NOT rejoin at the trailing edge, and there is no "race" to catch up. The
same books often contain a misleading diagram showing a flat-bottomed wing with flow lines of the surrounding air. (see
below.) This diagram actually shows a zero-lift condition. In order to create lift, a wing must deflect air downwards.
Both the explanation and the diagram have serious problems. They wrongly imply that inverted flight is impossible and
that an aircraft with equal pathlengths of upper and lower wing surfaces will not fly. They also wrongly suggest that
aircraft can violate conservation of momentum by remaining aloft without reacting against the air, and without causing a
downward motion of the air. Yet upside-down flight is far from impossible; it is a common aerobatic move. And many
wings have equal pathlengths, including even the thin cloth wings of the Wright Brothers' flyer! And anyone standing
under a slow, low-flying plane or below the thin, fast wings of a helicopter will know that there is a very great downward
flow of air below the wings. All of this indicates that there is a serious problem with the "curved top, flat bottom"
explanation. Below is an alternative.
As a plane flies, its wings cut through the air at an angle. This "angle of attack" causes the wing to apply a
downward force to the air. Or rather than being tilted, the wings can be curved or "cambered", and this makes
the trailing edge of the wing tilt down at an angle. As a result, the moving air streams downwards at an angle.
As a result, the wing is pushed upwards and backwards. (These two forces are called "lift" and "induced
drag.")
The lower surface of the wing causes air to move down, but that's not the only important effect. Because the
flowing air adheres to the TOP of the wing, the tilt of the wing also causes the upper surface of the wing to
pull downwards upon the air above it. The air ABOVE the wing moves down and the wing is forced
upwards.
As any plane flies, a stream of air is sent diagonally downwards by its wings, and the wing acts like a 'reaction engine'
much like a jet engine or a rocket. Unless a wing is either tilted or cambered, it cannot force the air downwards and
cannot generate any "lift."
It may help to imagine a hovering helicopter: a helicopter can hover because its rotor applies a downward force to the air,
and the air applies an upward force to the rotor. As a result, the air flows downwards and the upward force supports the
craft. But like any airplane, a helicopter rotor is a moving wing, and it's this small wing which sends the air downwards.
Like any wing, helicopter rotors are reaction engines, they push air downwards, and the air pushes them upwards. They
are not "sucked upwards," and neither are airplanes.
You may have seen a plane's downwash of air in movies: a "cropduster" plane sends out a trail of fertilizer mist, and the
trail of mist does not float, instead it moves immediately down into the crops, driven downward by the moving air. Air
from wings can even be dangerous: if a plane flies too low, the downwash from its wings can knock people over.
The "Bernoulli effect" is still true. It explains how the top of the wing is able to "pull downwards" on the air flowing over
it. And the Bernoulli Effect proves extremely useful in calculations of the lifting force during classes in airplane physics
and during experimental work in aerodynamics. But airplanes also obey Newton's laws: accelerate some air downwards,
and you'll experience an upwards force.
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WEBSITE: Airfoil misconceptions in K-6 textbooks
SOME EMAIL DEBATE
My improved explanation:DISK BALLOONS
SOUND TRAVELS BETTER THROUGH SOLIDS? NO.
Many elementary textbooks say that sound travels better through solids and liquids than through air, but they are
incorrect. In fact, air, solids, and liquids are nearly transparent to sound waves. Some authors use an experiment to
convince us differently: place a solid ruler so it touches both a ticking watch and your ear, and the sound becomes louder.
Doesn't this prove that wood is better than air at conducting sound? Not really, because sound has an interesting property
not usually mentioned in the books: waves of sound traveling inside a solid will bounce off the air outside the solid. The
experiment with the ruler merely proves that a wooden rod can act as a sort of "tube," and it will guide sounds to your
head which would otherwise spread in all directions in the air. A hollow pipe can also be used to guide the ticking sounds
to your head, thus illustrating that air is a good conductor after all. Sound in a solid has difficulty getting past a crack in
the solid, just as sound in the air has difficulty getting past a wall. Solids, liquids, and air are nearly equal as sound
conductors.
It's true that the speed of sound differs in each material, but this does not affect how well they conduct. "Faster" doesn't
mean "better." It is true that their transparency is not exactly the same, but this only is important when sound travels a
relatively great distance through each material. It's also true that complex combinations of materials conduct sound
differently and may act as sound absorbers (examples: water with clouds of bubbles, mixtures of various solids, air filled
with rain or snow.) And last: when you strike one object with another, the sound created inside the solid object is louder
than the sound created in the surrounding air. So, before we try to prove that solids are better conductors, we had better
make sure that we aren't accidentally putting louder sound into the solids in the first place.
GRAVITY IN SPACE IS ZERO? WRONG.
Everyone knows that the gravity in outer space is zero. Everyone is wrong. Gravity in space is not zero, it can actually be
fairly strong. Suppose you climbed to the top of a ladder that's 300 miles tall. You would be up in the vacuum of space,
but you would not be weightless at all. You'd only weigh about fifteen percent less than you do on the ground. While 300
miles out in space, a 115lb person would weigh 100lb. Yet a spacecraft can orbit 'weightlessly' at the height of your
ladder! While you're up there, you might see the Space Shuttle zip right by you. The people inside it would seem as
weightless as always. Yet on your tall ladder, you'd feel nearly normal weight. What's going on?
The reason that the shuttle astronauts act weightless is that they're inside a container which is FALLING! If the shuttle
were to sit unmoving on top of your ladder (it's a strong ladder,) the shuttle would no longer be falling, and its occupants
would feel nearly normal weight. And if you were to leap from your ladder, you would feel just as weightless as an
astronaut (at least you'd feel weightless until you hit the ground!)
So, if the orbiting shuttle is really falling, why doesn't it hit the earth? It's because the shuttle is not only falling down, it is
moving very fast sideways as it falls, so it falls in a curve. It moves so fast that the curved path of its fall is the same as
the curve of the earth, so the Shuttle falls and falls and never comes down. Gravity strongly affects the astronauts in a
spacecraft: the Earth is strongly pulling on them so they fall towards it. But they are moving sideways so fast that they
continually miss the Earth. This process is called "orbiting," and the proper word for the seeming lack of gravity is called
"Free Fall." You shouldn't say that astronauts are "weightless," because if you do, then anyone and anything that is falling
would also be "weightless." When you jump out of an airplane, do you become weightless? And if you drop a book, does
gravity stop affecting it; should you say it becomes weightless? If so, then why does it fall? If "weight" is the force which
pulls objects towards the Earth, then this force is still there even when objects fall.
So, to experience GENUINE free fall just like the astronauts, simply jump into the air! Better yet, jump off a diving board
at the pool, or bounce on a trampoline, or go skydiving. Bungee-jumpers know what the astronauts experience.
Space isn't remote at all. It's only an hour's drive away if your car could go straight upwards. --Fred Hoyle
CORRECTED: FOR EVERY ACTION, THERE IS NOT AN EQUAL AND OPPOSITE REACTION
Newton originally published his laws of motion in Latin, and in the English translation, the word "action" was used in a
different way than it's usually used today. It was not used to suggest motion. Instead it was used to mean "an acting
upon." It was used in much the same way that the word "force" is used today. What Newton's third law of motion means
is this:
For every "acting upon", there must be an equal "acting upon" in the opposite direction.
Or in modern terms...
For every FORCE applied, there must be an equal FORCE in the opposite direction.
So while it's true that a skateboard does fly backwards when the rider steps off it, these MOTIONS of "action" and
"reaction" are not what Newton was investigating. Newton was actually referring to the fact that when you push on
something, it pushes back upon you equally, EVEN IF IT DOES NOT MOVE. When a bowling ball pushes down on the
Earth, the Earth pushes up on the bowling ball by the same amount. That is a good illustration of Newton's third Law.
Newton's Third Law can be rewritten to say:
FOR EVERY FORCE THERE IS AN EQUAL AND OPPOSITE FORCE.
Or "you cannot touch without being touched."
Or even simpler: Forces always exist in pairs.
CORRECTED: BEN FRANKLIN'S KITE WAS NEVER STRUCK BY LIGHTNING
Many people believe that Ben Franklin's kite was hit by a lightning bolt, and this is how he proved that lightning is
electrical. A number of books and even some encyclopedias say the same thing. They are wrong. When lightning strikes a
kite, the electric current in the string is so high that just the spreading electric currents in the ground can kill anyone
standing nearby, to say nothing of the person holding the string! What Franklin actually did was to show that a kite would
collect a tiny bit of electrical charge-imbalance out of the sky during a thunderstorm.
Air is not a perfect insulator. The charges in a thunderstorm are constantly leaking downwards through the air and into
the ground. Electric leakage through the air caused Franklin's kite and string to become charged, and the hairs on the
twine stood outwards. The twine was then used to charge a metal key, and tiny sparks could then be drawn from the key.
Those tiny sparks were the only "lightning" in his experiment. (He used a metal object because sparks cannot be directly
drawn from the twine; it's conductive, but not conductive enough to make sparks.)
His experiment told Franlkin that some stormclouds carry strong electrical charges, and it IMPLIED that lightning was
just a large electric spark.
The common belief that Franklin easily survived a lightning strike is not just wrong, it is dangerous: it may convince kids
that it's OK to duplicate the kite experiment as long as they "protect" themselves by holding a silk ribbon and employing
a metal key. Make no mistake, Franklin's experiment was extremely dangerous. Lightning goes through miles of
insulating air, and will not be stopped by a piece of ribbon. If lightning had actually hit his kite, he would have been
gravely injured, and most probably would have died instantly. See LIGHTNING SURVIVOR RESOURCES
THE MAIN LENS OF YOUR EYE IS INSIDE THE EYE? NOT QUITE.
Some textbooks assume that the small lens found deep within the eyeball is the eye's main lens, and the cornea of the eye
is simply a protective window. The textbook diagrams even depict light rays passing into the eye and only bending as
they pass through this internal lens. But in the human eye, the small lens found within the eyeball is not the main imaging
lens. The cornea is actually the main lens; it is the strongly curved transparent front surface of the eye. Most of the
bending of the light occurs at the place where the light enters the surface of the cornea. When you look at your eye in the
mirror, you are looking directly at the eye's main lens. When you want to change the focusing power of your eye, you
apply "contact lenses" to the cornea surface, or you undergo surgery which re-sculpts the cornea's curvature. The smaller
lens inside the eye acts only to alter the focus of the eye as a whole. Muscles change its shape in order to correct the focus
for near and far viewing. Without this small internal lens, human vision would be blurry, and vision would be unable to
accommodate for near and far views. But without the cornea lens, [the human eye would be blind] IMPROVED
VERSION: witthout the cornea lens, human vision would rely upon the pinhole-camera effect of the eye's pupil, and
vision would be incredibly blurry. Open your eyes underwater in dimly-lit conditions to see what vision would be like
without a cornea.
CORRECTED: WHEN ONE PRISM SPLITS LIGHT INTO COLORS, A SECOND IDENTICAL PRISM
CANNOT RECOMBINE THEM
A single prism can split a sunbeam into a rainbow. Many children's science books show how a second similar prism can
be used to recombine the colors. This is incorrect, two prisms do not work as shown. Prisms of two DIFFERENT sizes
can split and then focus the colors into momentary recombination at a particular distance. With THREE prisms in a
special arrangement, the splitting and complete recombining of colors can be accomplished. But books which depict one
prism splitting the colors and a second identical prism recombining the colors into a single white beam are in error, and
are no doubt the source of endless frustration for those of us who try to duplicate the effect with real prisms.
The "rainbows" can also be recombined by placing a screen at just the right place, and by bouncing the colors off many
small mirrors so the colored beams converge upon a screen. Recombination can also be done with a convex lens or a
concave mirror and a screen. I hope that very few students will attempt to perform the color recombination experiment
depicted in their books, for disappointment awaits. (MORE)
CLOUDS, FOG, AND SHOWER-ROOM MIST ARE WATER VAPOR? NO.
All three things are made of small droplets of liquid water hanging in the air. When water evaporates, it turns into a
transparent gas called "water vapor." When it condenses again, it can take the form of rain, snow, rivers, and oceans, but
it also can take the form of clouds, mist, fog, etc. Fog can make surfaces wet, but not because of condensation. Instead,
the fog droplets collide with the solid surface. Fog is liquid water, not a vapor. Fly an ultralight aircraft slowly through a
large dense cloud, and you'll become damp. To look for water vapor, look at the bubbles in rapidly boiling water. Look at
the small empty space at the spout of a boiling teakettle. Look at the far end of the teakettle's plume of mist, where the
mist seems to vanish into the air. Look at the empty air above a wet surface. In these situations you see nothing, and that's
where the vapor is. Water vapor seems invisible because it is transparent. Clouds and fog are not transparent. They are
composed of liquid droplets.
CORRECTED: RAINDROPS DON'T HAVE POINTS!!
Nearly every drawing of raindrops depicts them as having a sharp upper point. This is wrong. Surface tension of water
acts like a stretched "bag" around the water, and unless some other force is acting, it pulls the water into a spherical
shape. Our eyes do see tiny droplets as a blur, but a flash photograph reveals that small raindrops are nearly spherical.
The larger ones are distorted by the pressure of moving air, but this doesn't make points, it makes them somewhat
flattened. Think of it this way: underwater bubbles are not pointed as they rise, just as falling water drops are not pointed
as they fall. And while it's true that the SYMBOL for water is a droplet with a point, REAL water droplets look nothing
like the symbol. And when water drips from a faucet, it never actually has a point. Instead it has a narrow neck, and after
the neck has snapped, it is yanked back into the falling ball of water. See Dr. Fraser's BAD SCIENCE for lots more about
this.
AIR IS WEIGHTLESS? NO.
We are not conscious of air's weight because we are immersed within it. In the same way, even a large bag of water
seems weightless when it is immersed in a water tank. The bag of water in the tank is supported by buoyancy. In a similar
way, buoyancy from the atmosphere makes a bag of air seem weightless when it's surrounded by air. One way to discover
the real weight of air would be to take a bag of air into a vacuum chamber. Another way is to weigh a pressurized and an
unpressurized football. A cubic meter of air at sea-level pressure and 0C temperature has a mass of 1.2KG. The nonmetric rule of thumb says that the air that would fill a bathtub weighs about one pound. Here's a simple way to detect the
mass of air even though the air seems weightless: open an umbrella, wiggle it slightly forwards and back, then close it
and wiggle it again. When you wiggle it when open, you can feel its increased mass because of the air the umbrella must
carry with it. (Ah, but then we must explain the difference between weight and mass!)
CORRECTED: FILLED AND EMPTY BALLOONS DO NOT DEMONSTRATE THE WEIGHT OF AIR
Many books contain a incorrect experiment which purports to directly demonstrate that air has weight. A crude beambalance is constructed using a meter stick. Deflated rubber balloons are attached to the ends, and the balance is adjusted.
One balloon is then inflated, and that end of the balance-beam is supposed to sag downwards. A large amount of air
supposedly weighs more than a small amount of air.
Unfortunately this experiment lies. When immersed in atmosphere, buoyancy causes full and empty balloons to weigh the
same. But then why does the above experiment work? It doesn't! The experiment will fail unless you know the trick: blow
the balloon up near to bursting. It secretly relies on the fact that the air within a high-pressure balloon is denser than air
within a low pressure balloon. Obviously this does not DIRECTLY demonstration anything about the weigh of air, and
it's dishonest to tell students that it does.
To illustrate the problem, try this instead: attach two opened paper bags to the balance, adjust it, then crush one bag so it
contains little air. The balance WILL NOT MOVE. What does this teach your class; that air is... weightless? Yet air does
have significant weight. We just can't detect this weight directly by using balloons or paper bags.
Here's a way to make the experiment more honest. Perform the balance-beam experiment again, but blow one balloon
REALLY full so the rubber feels hard and the balloon is about to pop. Blow up the second balloon so it is ALMOST full,
but still a bit stretchy. Try to keep the balloons the same size. Now the balance will show that, even though the balloons
are nearly the same size, the "hard" balloon is heavier. Does this teach misleading things to your class? No, instead it
exposes the dishonesty of the original demonstration. In truth, balloons full of air do not weigh more than empty ones.
However, COMPRESSED air does weigh more than UNCOMPRESSED air.
What if we lived underwater, how could we use the balance-beam to measure the weight of water directly? The answer is
that we cannot. If a water-filled balloon and an uninflated balloon were compared underwater, the experiment would
show that they weigh the same, which seems to prove that water is weightless. When underwater, a bag full of water
weighs just the same as a flattened bag which contains nothing. The situation with air is identical: if we live our lives
immersed within a sea of air, we cannot use a balance to easily detect the actual weight of the air. (In fact, a bathtub full
of air weighs about a half kilogram, but we cannot sense this weight while living in an atmosphere.)
It's hard to teach the weight of water to the fishes, and hard to teach the weight of air to human grade-schoolers. These
experiments could only work if performed in a vacuum environment (say, on the moon's surface.) We humans are like
fish underwater: we're not aware that our ocean of air has any weight.
To better demonstrate the weight of air directly, hook a heavy bottle to a vacuum pump, pump all the air out, seal it, then
weigh the bottle. Break the seal and let the air in, then weigh it again. The difference in weight is the weight of the air
contained in the bottle. Another: use a balance to compare the weight of two vacuum-containing bottles, then open one of
them so it becomes filled with air. The bottles will then weigh differently, and the difference is the true weight of the air
in one bottle. Or another: build a balance using upside-down paper bags, then place a candle below one of them, then
remove the candle again. That bag rises, indicating that a volume of warm air weighs slightly less than a volume of cool
air. (Don't set the bag on fire!!) But note that this candle experiment says nothing simple and direct about the actual
weight of a volume of unheated air.
CORRECTED: IN THE EVERYDAY WORLD, GASES DO NOT EXPAND TO FILL THEIR CONTAINERS
What is the difference between a liquid and a gas? Both are "fluids", both can flow. Gases are USUALLY less dense than
liquids, although gases under fiercely high pressure can approach the density of liquids, so that's not a good criterion. The
main difference is that gases are a different phase of matter: a gas can be made to condense into a liquid form, and a
liquid can be made to evaporate into gas. Another major characteristic: because there are bonds between its particles,
when a liquid IS PLACED INTO A VACUUM ENVIRONMENT, it will not expand continuously, while a gas in a
vacuum chamber will expand continuously until it hits the walls.
This is very different than the oft-quoted rule that "gases always expand to fill their containers." This rule only works
correctly if the container is totally empty: the container must "contain" a good vacuum beforehand. However, we all live
in a gas-filled environment. All our containers are pre-filled with air. In our environment, any new quantity of gas will
not expand, it will just sit there. If you squirt some carbon dioxide out of a CO2 fire extinguisher, it will not instantly
expand to fill the room. Instead it will pour downwards like an invisible fluid and form a pool on the floor. It behaves
similarly to dense sugar-water which was injected into a tank of water: it pours downwards, and only after a very long
time it will mix with the rest of the water. "Mixing" is very different than "expanding to fill!" The rule about gases does
not involve mixing, instead it involves compressibility and instant expansion into a vacuum.
In an air-filled room, dense gases act much like liquids; they can be poured into a cup or bowl, poured out out onto a
tabletop, and then they run off the edge onto the floor where they form an invisible mess. :) Less dense gases will stay
where they are put, like smoke or like food coloring which has just been injected into a fishtank. Gas of even lesser
density rises and forms a pool on the ceiling. Only in the world of the physicist, where "empty container" always implies
a vacuum, does the rule about gasses work properly.
CORRECTED: SHADOWS DO VANISH ON CLOUDY DAYS, BUT NOT BECAUSE THE SUN ISN'T
BRIGHT ENOUGH
Shadows appear when an object blocks a light source. The shape of the shadow is created by the shape of the opaque
object AND by the shape of the light source. On a cloudy day the whole sky acts as a light source, and a person's shadow
spreads out and becomes a dim fuzzy patch which surrounds the person on the ground on all sides. The shadow is so
spread-out that it seems absent entirely. When the sun is visible, the same shadow is concentrated in one specific place
and becomes easy to see. But even the shadows made by sunlight will have fuzzy borders, since the sun is a small disk
rather than a tiny dot. On cloudy days, the fuzzy borders of your body's shadow become much much larger than the
shadow itself, so that the shadow seems to vanish.
CORRECTED: FRICTION IS NOT CAUSED BY SURFACE ROUGHNESS
Some books point to surface roughness as the explanation of sliding friction. Surface roughness merely makes the moving
surfaces bounce up and down as they move, and any energy lost in pushing the surfaces apart is regained when they fall
together again. Friction is mostly caused by chemical bonding between the moving surfaces; it is caused by stickyness.
Even scientists once believed this misconception, and they explained friction as being caused by "interlocking asperites",
the "asperites" being microscopic bumps on surfaces. But the modern sciences of surfaces, of abrasion, and of lubrication
explain sliding friction in terms of chemical bonding and "stick & slip" processes. The subject is still full of unknowns,
and new discoveries await those who make surface science their profession
When thinking about friction, don't think about grains of sand on sandpaper. Instead think about sticky adhesive tape
being dragged along a surface.
CORRECTED: NO, INFRARED LIGHT IS NOT A KIND OF HEAT
Infrared light is invisible light. When any type of light is absorbed by an object, that object will be heated. The infrared
light from an electric heater feels hot because the light is EXTREMELY BRIGHT LIGHT. Just because human eyes
cannot see the light which causes the heating does not mean that the light is made of some mysterious entity called "heat
radiation." When bright light shines on an absorbtive surface, that surface heats up.
And this is no benign misconception. Those who fall under its sway may also come to believe that *visible* light cannot
heat surfaces (after all, visible light is not "heat radiation.") Misguided science students may wrongly believe that warm
objects emit no microwaves (since only IR light is "heat radiation"), even though hot objects actually do emit
microwaves. Or they may believe that the glow of red hot objects is somehow different than the infrared glow of cooler
objects. Or they may believe that IR light is a form of "heat," and is therefore fundamentally different than any other type
of electromagnetic radiation.
In his book "Clouds in a Glass of Beer," Physicist C. Bohren points out that this "heat" misconception may have been
started long ago, when early physicists believed in the existence of three separate types of radiation: heat radiation, light,
and actinic radiation. Eventually they discovered that all three were actually the same stuff: light. "Heat radiation" and
"actinic radiation" are simply invisible light of various frequencies. Today we say "UV light" rather than "actinic
radiation." Yet the obsolete term "heat radiation" still lingers. Since human beings can only see certain frequencies of
light, it's easy to see how this sort of confusion got started. Invisible light seems bizarre and mysterious when compared
to visible light. But "invisibility" is caused by the human eye, and is not a property carried by the light. If humans could
see all the light in the infrared spectrum, we would say things like this: "of COURSE the electric heater makes things hot
at a distance, it is intensely BRIGHT, and bright light can heat up any surface which absorbs it."
PS, if you're interested in physical science misconceptions, Bohren's Book is an excellent resource. He's like me, and
complai ns about several specific misconceptions which keep his students from understanding science.
CORRECTED: THERE ARE NOT SEVEN COLORS IN THE RAINBOW
Actually here is a very large number of distinct colors in any rainbow. And neither are there sharp divisions between the
bands of color, yet numerous textbooks depict them. In reality, between yellow and green we find yellow-green, and
between green and yellowgreen is GREENISH yellowgreen, and on and on. How many colors are in a rainbow? Thirty?
Sixty? It's not easy to say, for it depends on the particular eye, and the particular rainbow. What of the teachers and
students who look in vain for the yellow-green in their textbook's depiction of rainbows? They've crashed into a longrunning textbook misconception: the strange idea that rainbows have exactly seven distinct bands of color and no more,
and with nothing in between those uniform bands of 'official' color.
CORRECTED: ACTUALLY, THE EARTH'S NORTH AND SOUTH MAGNETIC POLES RESIDE DEEP
WITHIN THE EARTH'S CORE
Many textbooks have an erroneous diagram of the earth which shows a bar magnet within it, and the ends of this bar
magnet extend to just beneath the earth's surface. These diagrams depict the magnet's field lines as radiating from spots
on the earth's surface. This is very misleading. The earth's magnetic poles actually behave as if they're deep within the
earth, down inside the core. The Earth's magnetic field does not come from a giant bar magnet, but if we IMAGINE that
it does, then the imaginary "bar magnet" inside the earth is short, stubby, disk-shaped, and part of the iron core deep
inside the planet.
The typical textbook diagram is incorrect, and there are NO INTENSE MAGNETIC FIELDS at the land surface near the
earth's "north pole" and "south pole." If you stand at the Earth's south magnetic pole, metals aren't attracted to the ground
more strongly than anywhere else. The Geomagnetic "poles" on the earth's surface are not places where the field is strong.
They are simply the points on the landscape where the field lines are perfectly vertical.
Proper diagrams should instead show the field lines to be radiating from poles inside the earth's core. They should show
the field lines around the northern and southern areas of the earth's surface as being approximately vertical and parallel,
not "radial" like a spiderweb and not concentrated into special points on the surface.
Another error associated with the above: some books claim that the earth's field at the magnetic poles is much stronger
than elsewhere. This is untrue. The field strength at the north magnetic pole above Canada is about the same as the field
strength in Virginia! And the strongest field in the Earth's northern hemisphere does not appear at the north magnetic pole
at all, the north pole actually has a weaker field than elsewhere. The strongest fields in the northern hemisphere are not in
one but in two places: west of Hudson bay in Canada, and in Siberia.
LINKS
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Correct diagram of Earth's field
NOAA questions about Earth's field
Field strength map
The Great Magnet, the Earth
LASER LIGHT IS "IN PHASE" LIGHT? WRONG.
It's incorrect to say that "in laser light the waves are all in phase." When two light waves travelling in the same direction
combine, they inextricably add together, they do not travel as two independent "in-phase" waves. The photons in laser
light are in phase, but the WAVES are not. Instead, ideal laser light acts like a single, perfect wave.
When the light wave within a laser causes atoms to emit smaller, in phase light waves, the result is not "in phase" light.
Instead the result is a single, more intense, amplified wave of light. In-phase emission leads to amplification, not to
multiple in-phase waves. If the atoms' emissions weren't in phase, the result would NOT be light that's out of phase.
Instead the the atoms would absorb light rather than amplifying it.
Each atom in a laser contributes a tiny bit of light, but their light vanishes into the main traveling wave. The light from
each atom strengthens the main beam, but loses its individuality in the process. 99 plus 1 equals 100, but if someone gives
us 100, we cannot know if it is made from 99 plus 1, or 98 plus 2, or 50 plus 50, etc.
All the *PHOTONS* in a single wave of light are in phase. This might be one reason that people say that laser light is "in
phase" light. However, in-phase photons are nothing unique, and they don't really explain coherence. Any EM spherewave or plane-wave is made of in-phase photons. For example, all the photons radiated from a radio broadcast antenna
are also in phase, but we don't say that these are special "in phase" radio waves, instead we just say that they are waves
with a spherical wavefront. Even if all the photons in laser light are in phase, it is still incorrect to say "all the WAVES are
in phase." Photons are not waves. They are quanta, they are particles, and they do not behave as small, individual
"waves." Yes, all the photons are in phase, but only because they are part of a single plane-waves.
The light from a laser is basically a single, very powerful light wave. Single waves are always in phase with themselves,
but it's misleading to imply that a single plane-wave or sphere-wave is something called an "in phase" wave. Laser light
could more accurately be called "pointsource" light. Sphere waves or plane waves behave as if they were emitted from a
single tiny point. The physics term for this is "spatially coherent" light. Light from light bulbs, flames, the sun, etc. are the
opposite, and are called "extended-source" light. Extended-source light comes from a wide source, not from a pointsource, and the waves coming from different parts of the source will cross each other. Starlight and the light from arc
welders is "point-source" light and is quite similar to laser light. Light from arc-welders and from distant stars has a
higher spatial coherence than light from most everyday light sources. (Note: the sun is a star, correctly implying that light
becomes more and more spatially coherent as it moves far from its source. This is a clue as to the REAL reason that lasers
give spatially coherent light! (See below)
CORRECTED: LASER LIGHT IS NOT PARALLEL LIGHT
Light from most lasers is not parallel light. However, if laser light is passed through the correct lenses, it can be formed
into a tight, parallel beam. The same is not true for light from an ordinary light bulb. If light from a light bulb were passed
through the same lenses, it would form a spreading beam, and an image of the lightbulb would be projected into the
distance. Laser light can form beams because a laser is a pointsource, and when you project the image of a pointsource
into the distance, you form a narrow parallel beam! However, it is simply wrong to state that laser light is inherently
parallel light. Laser light can be FORMED INTO parallel light, while the light from ordinary sources cannot.
Most types of lasers actually emit spreading, non-parallel light. Lasers in CD players and in "laser pointers" are
semiconductor diode lasers. They create cone-shaped light beams, and if a parallel beam is desired, they require a
focusing lens. The same is true for the lasers in inexpensive "laser pointers." Take apart an old laser-pointer, and you'll
find the plastic lens in front of the diode laser inside.
Classroom "HeNe" lasers also create spreading light. The laser tube within a typical classroom laser contains at least one
curved mirror (called a "confocal" arrangement,) and it creates light in the form of a spreading cone. It's a little-known
fact that manufacturers of classroom lasers traditionally place a convex lens on the end of their laser tubes in order to
shape the spreading light into a parallel beam. While it's true that a narrow beam is convenient, I suspect that part of their
reason is to force the laser to fit our stereotype that all lasers produce thin, narrow light beams. The manufacturers could
save money by selling "real" lensless laser tubes having spreading beams. But customers would complain, wouldn't they?
We have been brought up to believe that laser light is parallel light.
CORRECTED: LASERS EMIT COHERENT LIGHT, BUT NOT BECAUSE THE ATOMS EMIT IN-PHASE
LIGHT WAVES
In-phase emission causes the AMPLIFICATION of light, it doesn't cause coherent light. Because the atoms emit light in
phase with incoming light, they will amplify the light, but they amplify incoherent light too, and they don't make it
coherent. The coherence of laser light has another source... Laser light has two main characteristics: it is
"monochromatic" or very pure in frequency (this also is called "temporally coherent.") Laser light also has a point-source
character of sphere waves and plane waves (also called "spatially coherent.")
Even fairly advanced textbooks fail to give the real reason why laser light is spatially coherent. They usually point out
that the laser's atoms all emit their light in phase, and pretend that this leads to spacial coherence. Wrong. It is true that
the fluorescing atoms in a laser all emit light that's in-phase with the waves already traveling between the mirrors. But the
in-phase emission only creates amplification of the traveling waves, it does not create spatially coherent light. For
example, if you were to feed incoherent light into a HeNe laser tube, the atoms would emit in-phase waves, and the laser
would amplify the light. But the brighter light would still be incoherent! Lasers certainly can amplify the COHERENT
wave which is trapped between their mirrors. But how did the light within the laser get to be coherent in the first place?
Lasers create coherent light because of their mirrors.
The mirrors in a laser form a resonant cavity which preserves coherent light while rejecting incoherent light. How does it
work? Imagine a simplified laser having flat, parallel mirrors. As light bounces between the mirrors, the light "thinks"
that it's traveling down an infinitely long "virtual tunnel". (Have you ever held up two mirrors facing each other? Then
you've seen this infinite tunnel.) When a laser is first turned on, it fluoresces; it emits light which is NOT coherent.
Different random light waves start out from different parts of the laser. After a few thousand mirror bounces, all the
waves have added and subtracted to form just one single wave. In the case of flat-mirror lasers, this wave is a nearly
perfect plane wave. A single plane wave is coherent (to be incoherent, you must have at least two different waves.)
This can be a bit confusing. After all, the individual atoms each emit a wave. Don't all these waves add up to messy
incoherent light? No. The in-phase emission preserves coherence as it amplifies. It's true that each atom emits light waves
in all directions. However, these sideways waves cancel each other out, and only the waves that travel in the same
direction as the incoming light will be preserved. It's as if the atoms "know" which direction to send out a beam. But in
reality, the atoms don't know this. Instead, they just emit a light wave which is in phase with the incoming light, and for
this reason the wave from the atom will cancel out everywhere except in a line with the incoming light. If the light in a
laser were ALREADY coherent, then the atoms will amplify it but won't make it more coherent. The coherence comes
from the great distance that the light has travelled as it bounced between the mirrors.
A similar thing happens with starlight: starlight is coherent! Starlight travels far from its original source and all the waves
add up to form a wave with a single wavefront. Light from distant stars is spatially coherent, even though sunlight is not,
yet the sun is a star. The farther the light travels from its source, the more it approaches the shape of a perfect plane wave.
And a perfect plane wave is perfectly coherent. Laser light is spatially coherent because, among other things, the
bouncing light has traveled millions of miles between mirrors, and all the various competing waves have melded together
to form a single pure plane-wave or sphere-wave.
P.S. The pure color (monochrome) laser light is ALSO created by the mirrors. Huh? Yes, but the reason for this is not
totally straightforward (and it's quite a bit beyond the K-6 level of these webpages!)
The two mirrors of a laser can trap a standing wave of light. The space between the mirrors is like the string of a guitar:
there can be a fundamental wave, or overtone waves, or complicated waves which are a mixture of these. But waves of
non-overtone frequencies cannot exist between the mirrors. Since the distance between the crests of a lightwave is very
small, LOTS of different overtones can fit between the mirrors, and each overtone is a slightly-different pure color of
light. Light from a neon sign is reddish, but it doesn't have the extreme purity of laser light. Now for the weird part: when
a Helium-Neon laser first operates, many different overtones of red light are amplified and the beam contains many
slightly-different colors of red at the same time. It's not yet monochromatic. As time goes on, some of these colors are
amplified a bit more than others, and this uses up the available energy coming from the power supply. In other words, the
different waves start competing for limited resources! Just one wave "wins" in the end, and all of the other overtones drop
out of the running. The laser light is not just red light. Instead it is a SINGLE PURE OVERTONE-WAVE, a pure
frequency where the string of waves just perfectly fits in the space between the two mirrors. Change the spacing of the
laser's mirrors, and you change the frequency of the light.
CORRECTED: IRON AND STEEL ARE NOT THE ONLY STRONGLY MAGNETIC MATERIALS
There are numerous others. Nickel and Cobalt metals are very magnetic. (U.S. "nickel" coins contain copper which spoils
the effect, so try Canadian nickels made before 1985.) Most other materials are "diamagnetic," and are repelled visibly by
very strong magnets, although some materials are "paramagnetic" and are attracted. Supercold liquid oxygen is attracted
by magnets. Some but not all types of stainless steel are nonmagnetic. There are even some metals which are individually
nonmagnetic, but which become strongly magnetic when mixed together, chromium and platinum for example, and
compounds of manganese and bismuth.
CORRECTED: RE-ENTERING SPACE CAPSULES ARE NOT HEATED BY AIR FRICTION
They are heated as they plow into the atmosphere and compress the air ahead of them. Ever pump up a bicycle tire and
discover that the pump and the tire have become hot? The same effect causes spacecraft and supersonic aircraft to heat up
as they compress the air at their leading edges. The heat doesn't come from *rubbing* upon the air, it comes from
*squeezing* the air. This applies mostly to blunt objects such as Apollo reentry vehicles. It does not apply as much to the
Space Shuttle: with wings oriented mostly edge-on to the moving air, the surfaces of the Shuttle ARE heated by friction.
But when the Shuttle first reenters the atmosphere, the bottom of the craft faces forwards, and in that case the Shuttle is
heated by air compression, NOT by friction.
CORRECTED: CARS AND AIRPLANES ARE NOT SLOWED DOWN BY AIR FRICTION
They are slowed because it takes energy to stir the air. While direct friction between the air and the car's surface does play
a part, the work done in stirring the air far exceeds the work done in direct frictional heating. If vehicles did not send air
swirls and vortices spinning off as they moved, they would barely be slowed by the air at all. Eventually the swirling air
is slowed by friction and ends up warmer, but this occurs long after the vehicle has passed.
CORRECTED: THE NORTH MAGNETIC POLE OF THE EARTH IS NOT IN THE NORTH
Opposite poles attract. If we hold two bar magnets near each other, the "N" pole of one magnet is attracted by the "S"
pole of another. If we suspend a bar magnet by a thread, the "N" pole of that magnet will point... toward's Earth's north!
Something is wrong here. Shouldn't the "N" pole of a magnet point towards the "S" of the Earth? Alike poles should not
attract. Either the "N" and "S" printed on all bar magnets is reversed, or the "N" and "S" on the Earth is backwards.
Which is it?
Physics defines "N-type" magnetic poles as being the north-pointing ends of compasses and magnets. Wind an
electromagnet coil, see which end points towards the north, and that end is the N pole of the electromagnet. Therefore, the
magnetic pole inside the northern hemisphere of the Earth is a south-type magnetic pole. The Earth's northern magnetic
pole is an S! It has to be this way, otherwise it would not attract the N-pole of a compass.
This is a long-standing but arbitrary physical standard, much the same as defining electrons as being negative. Like it or
not, we are stuck with negative electrons, and seconds which last about 1/100,000 of a day, with backwards Earth poles,
with centimeters which are about as wide as a small finger, etc.
Interesting email msgs on magnetic polarity
Also see Dexter Magnetics for more on this.
CORRECTED: ACTUALLY THERE ARE NO SODIUM CHLORIDE MOLECULES IN SALT WATER
Salt is not made of NaCl molecules. Salt is made of a three-dimensional checkerboard of oppositely charged atoms of
sodium and chlorine. A salt crystal is like a single gigantic molecule of ClNaClNaClNaClNaClNaClNa. When salt
dissolves, it turns into independent atoms. Salt water is not full of "sodium chloride." Instead it is full of sodium and
chlorine! The atoms are not poisonous and reactive like sodium metal and chlorine gas because they are electrically
charged atoms called "ions." The sodium atoms are missing their outer electron. Because of this, the remaining electrons
behave as a filled electron shell, so they cannot easily react and form chemical bonds with other atoms except by
electrical attraction. The chlorine has one extra electron and its outer electron shell is complete, so like sodium it too
cannot bond with other atoms. These oppositely charged atoms can attract each other and form a salt crystal, but when
that crystal dissolves in water, the electrified atoms are pulled away from each other as the water molecules surround
them, and they float through the water separately.
CORRECTED: LIGHT AND RADIO WAVES DO NOT ALWAYS TRAVEL AT "THE SPEED OF LIGHT"
They only travel at the "speed of light" (186,000 miles per second) while moving through a perfect vacuum. Light waves
travel a bit slower in the air, and they travel LOTS slower when moving through glass. Why does light bend when it
enters glass at an angle? Because the waves SLOW DOWN. Why can a prism split white light into a spectrum? Because
within the glass THE SPEED OF LIGHT WAVES IS DIFFERENT FOR DIFFERENT WAVELENGTHS. And while
the numerical value for the speed of light in a vacuum, "c," is very important in all facets of physics, as far as light waves
are concerned there is no single unique speed called "The Speed Of Light." [note for advanced students: ok ok, I'll add
this: light *waves* within a transparent medium are slow, even though the wave's photons are thought to jump from atom
to atom always at a speed of c.]
Created and maintained by Bill Beaty. Mail me at: [email protected].
If you are using Lynx, type C to email.
Hoe vliegt een vliegtuig?
De virtuele windtunnel
Onder deze tekst ziet u de virtuele windtunnel (al dan niet geladen), ontworpen door de NASA. Het is
niet zo heel moeilijk de windtunnel te bedienen, maar u zult misschien enige uitleg nodig hebben voor
het optimaal benutten ervan:
Linksboven ziet u de weergave van het object dat zich momenteel in de windtunnel bevindt, rechtsboven
is een schermpje met enkele grafieken. Daaronder is een gedeelte met knoppen om de vorm van het
voorwerp in te stellen, en helemaal onderaan bevindt zich een scherm om opgeroepen data in te tonen.
In het eerste schermpje staat zoals al gezegd een afbeelding van het voorwerp; met de bovenste knoppen
in dat schermpje, Edge, Top, Side-3D, Find en Zoom kan men instellen vanaf welke positie men het
voorwerp in de windtunnel bekijkt. 'Edge' betekend dat het voorwerp vanaf de zijkant wordt getoond,
hierbij is de luchtstroom (die zo van links naar rechts stroomt) ideaal zichtbaar. Als men op 'Top' klikt
zal de bovenkant zichtbaar worden, hierdoor zal de luchtstroom echter wel stoppen. Als u op Side-3D
klikt zal het voorwerp in 3D worden weergegeven, de luchtstroom gaat nu wel door (mits u niet eerst op
'Top' heeft geklikt). Let op: de luchtstroom zal exact door het midden van het 3D voorwerp gaan en dus
niet om het witte gedeelte heen. Met de knop 'Find' kunt u de ideale uitvergroting (waarop het meeste te
zien is) bekijken, en met de knop 'Zoom' kan man zelf de vergroting kiezen, door de schuif onder de
knop te bewegen.
Onder in het schermpje staan nog een aantal knoppen: Streamlines, Moving, Frozen en Geometry.
'Sreamlines' betekend stroomlijnen, als deze knop geactiveerd is kunt u zien hoe de lucht langs het
voorwerp beweegt, als u echter op 'Moving' klikt kunt u niet alleen dat zien maar ook hoe snel de lucht
zich op verschillende plaatsen beweegt en hoe groot de luchtdichtheid, die mede de lift bepaald, daar is.
Wanneer de knop 'Frozen' aan staan wordt het beeld dat vlak voor het activeren van die functie bij
'Moving' te zien was stilgelegd, zodat u dat moment op uw gemak kan bekijken. Door het activeren van
de knop 'Geometry' worden meer inputgegevens zichtbaar alsmede andere gegevens zoals de Chord line
en de Mean Chamber Line.
In het volgende scherm is waarschijnlijk een grafiek te zien. Met de knop 'Rescale' kunt u de
schaalverdeling opnieuw idealiseren, dit is handig wanneer u de instellingen heeft veranderd.
Onder deze twee schermpjes is het belangrijkste bedieningspaneel, met daarop de volgende knoppen:
Met de eerste knop kan men switchen tussen 'Lift' en 'Cl-no units'.
Met de tweede kan bepaald worden of er een ideale of meer realistische luchtstroom optreed.
'Show Geom' laat de eigenschappen van het voorwerp dat zich in de windtunnel bevindt en die van de
omgeving in het onderste gedeelte zien.
http://members.chello.nl/~j.hummelink1/anw_vw.htm (1 of 3)24-1-2004 18:20:25
'Show Data' toont de standaard of later ingestelde gegevens van het voorwerp en omgeving.
Met de knop 'Reset' kunnen de gegevens weer naar hun standaardvorm worden teruggebracht (dat is de
vleugel die u bij het opstarten van de virtuele windtunnel ziet).
Het zwarte schermpje met de groene cijfers boven 'Input' laat de lift of het aantal Cl-no units zien.
Onder 'input':
Als met de knop 'Flight Test' indrukt kan men met de schuifjes die er naast zullen verschijnen de
windsnelheid en hoogte waarop het voorwerp zich bevindt instellen, ook kan men met het menu'tje
boven de schuifjes de omgeving bepalen. In het menu daarboven kunt u bovendien de omgeving
bepalen:
Earth - Average Day = de aarde op een gemiddelde dag
Mars - Average Day = de planeet Mars op een gemiddelde dag
Water-Const Density = Water met constante dichtheid
Specify Air T & P = Lucht met zelf in te stellen temperatuur en druk.
Specify Fluid Density = vloeistof met zelf te bepalen dichtheid
Onder de schuifjes zijn drie vakjes met daarin de eigenschappen van de omgeving: de druk in kPa (=
Press-kPa), de temperatuur in graden Celcius (= Temp-C) en de dichtheid in Kgom-3 (= Density…kg/cu
m)
Met de knop 'Shape' de vorm van het voorwerp bepalen, in het menu kan het soort object worden
bepaald; van boven naar beneden: 'Airfoil' is de vleugel zoals wij die kennen, 'Ellipse' betekend Ellips,
een 'Plate' is natuurlijk een gewone plaat, 'Cylinder' is in het Nederlands cilinder en een 'Ball' is een bal.
Met de schuifjes eronder kan de vorm van het gekozen voorwerp worden en bij sommige voorwerpen
zoals de bal en cilinder kan in plaats van de hoek waaronder het voorwerp geplaatst is (= Angle-deg = de
hoek in graden) de rotatiesnelheid vastgesteld worden (= Spin rpm = aantal rotaties per minuut) en in
plaats van de kromming (= Chamber-%c) kan de diameter in meter (= Radius m) worden ingesteld. Bij
de cilinder is het mogelijk de breedte (= Span m = breedte in meters) vast te stellen in plaats van de dikte
(= Thick-%crd), bij een bal is die natuurlijk gelijk aan de diameter.
Wanneer men 'Size' heeft aangeklikt kan men de grootte van de vleugel bepalen, dit geldt niet als met
een bal of cilinder als voorwerp heeft gekozen omdat de grootte dan al bij 'Shape' is ingesteld, u zal hier
dus dezelfde instellingen te zien krijgen als bij 'Shape'. Met het schuifje 'Chord-m' kan de lengte van de
Chord line in meters aangepast worden, 'Span-m' staat voor de spanwijdte in meters en 'Area-sq m' voor
de oppervlakte van de vleugel in m2. Bij 'Aspect Rat' is de grootte van de Chord line ten opzichte van de
spanwijdte weergegeven (Aspect Rat = Span-m/Chord-m).
Met het menu'tje boven 'Output' kan geswitcht worden tussen de lift in Newtons of in Pounds. Wanneer
u de lift in kg wilt weten moet u de lift in Newtons delen door 9,81.
Onder 'Output':
Met de knop 'Plots' veranderd het scherm met de grafieken in een vlak met verschillende grafiekopties, u
kunt hier uit een diagram met oppervlaktedruk of oppervlaktesnelheid kiezen. En wanneer de omgeving
op 'Mars/Earth - Average Day' ingesteld staat en het voorwerp niet een bal of cilinder is, is het ook nog
mogelijk grafieken te verkrijgen met lift of Cl-no units uitgezet tegen snelheid (= Speed), hoogte (=
Altitude), dichtheid (= Density), vleugeloppervlakte (= Wing Area), hoek (= Angle), Kromming (=
Chamber) en dikte (= Thickness).
Als men op de knop 'Probe' klikt zal er een violet puntje op het zwarte scherm komen dat met de
schuifbalken in het vak rechtsboven geregeld kan worden, hier vanuit kan informatie worden gewonnen
over die specifieke plek met de knoppen 'Velocity' en 'Pressure' (= snelheid en druk). Met de knop
'Smoke' kan een klein straaltje rook gegenereerd worden uit het paarse punt.
Op de 'Lift Meter' is te zien hoeveel lift er ontstaat door de gecreëerde vleugel.
Bovenstaande handleiding hebben we zelf gemaakt, de windtunnel hebben we niet zelf gemaakt. Niets van deze
pagina mag zonder toestemming van de makers gekopieerd worden.

Zeiltheorie inleiding Hier wil ik de betere theorieën achter het zeilen

Transcription

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