# High Aspect Ratio Wings For Formula One Racers

## Transcription

High Aspect Ratio Wings For Formula One Racers
HIGH ASPECT RATIO WINGS FOR
FORMULA ONE RACERS
Short, stubby, low aspect ratio wings have
characterized Formula One racers since
time immemorial. A little number crunching
shows they would get around the course
quicker if they carried high aspect ratio
wings instead; not "high" as in sailplane, but
much higher than they are now.
Consideration of the fact that in pylon racing these spirited little bullets spend more
than half their time pulling high G turns leads
to the conclusion that speed could be improved by emphasizing in design the conditions prevailing in the turns instead of the
straightaways. To the technical observer, the
emphasis seems to be placed on the straightaways - where the problem isn't.
At a given power, as the aircraft turns the
increasing drag slows it down, and as it
straightens out, the now decreasing drag allows the aircraft to speed up again.
The slowing down in the turns can be decreased and the speeding up in the straightaways increased by going to longer and narrower wings; to higher aspect ratios. High
aspect ratio has long been the turf of
sailplanes and long range airplanes, but it
also has application to closed-course racers.
In fact, high aspect ratio was "made" for the
racer's drag problem.
To illustrate: According to the bar chart in
Figure 1 the aspect ratio 2.83 Cassutt Special II, rounding the pylons at maximum speed
on a 1400 foot radius, sees a drag increase
of almost 60% over its straight and level
value. By tripling the aspect ratio to 8.49, the
increase is held to around 23%. In the
straightaways the drag is reduced about
5%. This, and pilot skill, is the key to winning
races.
Tripling the aspect ratio on the Cassutt
doesn't, of course, mean tripling the span. It
means increasing it by the square root of 3,
or 73%, and reducing the chord by whatever
it takes to yield the original wing area, in this
case 42%.
Elementary physics tells us that the wing
on an aircraft turning at constant altitude
generates more lift than when flying straight
and level. This lift induces an increment of
drag all by itself, which adds to the drag already there. This induced drag varies as the
square of the lift coefficient. If, for example,
the racer is pulling 3 G's in rounding the pylons (a fairly typical value, by the way), the
drag induced by lift is 9 times higher than
in 1 G flight.
Consider now the concept of Aspect Ratio,
which states that the higher this ratio the
lower the drag induced by lift. Sailplanes
capitalize on this principle, and aspect ratios
of 40 are drawing the attention of designers
these days. After all, any aircraft capable of
flying over a thousand miles without power
(the present record) has to have something
going for it. That "something" is aspect ratio
(and smooth, laminar surfaces).
There is no suggestion here that Formula
One racers emulate their engineless breth-
by Stan Hall
1530 Belleville Way
Sunnyvale, CA 94087
em by gcing to such extremes. The benefit
is certain to be zero - or worse. But doubling
or tripling the 2.83 aspect ratio on the venerable but still popular Cassutt or other racers
of the genre would seem a practical and potentially winning strategy - and their aspect
ratios wouldn't be too far removed from
those presently seen on the single engine
Cessnas and Pipers with which we are all so
familiar.
Reported here in support of this idea is a
summary of a straight forward paper study
conducted by the author of 6 different wings
for the Cassutt. Involved were three rectangular (constant chord) wings and three tapered wings, each tapered at a ratio of 2:1.
The Cassutt was chosen simply because (1)
it is still winning races after all these years
and, (2) data on the aircraft were readily
available in Jane's All The World's Aircraft.
Each of these wings (with airplane attached) was run via pocket calculator around
six, sea level laps of an arbitrary but not atypical, 3-mile closed course, and the speeds
compared.
Everything was held constant except the
aspect ratio - same power (100 hp), same
wing area, same airfoil, same gross weight,
same pilot, same constant turn radius
around the pylons, same everything - except
the aspect ratio.
The aspect ratios were set at 2.83, 5.66
and 8.49, the latter two representing a doubling and tripling of the Cassutt's original 2.83.
To help with the bookkeeping, the wings
were identified by their aspect ratios and
their planforms ("R" for rectangular, "T for
tapered). 5.66T would, for example, represent a tapered wing having an aspect ratio
of 5.66.
The results were as expected. As Figure
2 shows, the racer with the 8.49T wing won
the "race". It led the standard 2.83R Cassutt
by well over a mile at the finish. Its nearest
competitor was 8.49R, another long-winger,
which led the standard Cassutt by only 400
feet or so less.
Considering the whisker finishes we often
see at Reno, one might conclude that leads
of this magnitude constitute something of a
blowout. The blowing-out is done in the
turns.
Although there is but a negligible speed
difference between the tapered and rectangular 8.49 wings, it would seem imprudent,
in interests of capitalizing on the simpler construction of the rectangular wing, to ignore
other, strong virtues inherent in the tapered
wing.These are discussed later.
TABLE 1
Approximate Horizontal Tail Volume Coefficients and Stick-Fixed, Power Off
Neutral Points and Static Margins for Cassutt II Special, eg at 25% m.a.c.,
Using Wings of Various Planforms.
Planform*
Neutral Point
Static Margin
2.83R
.199
29.7%
4.7%
5.66R
.282
32.3
7.3
8.49R
.345
34.9
9.9
2.83T
.192
29.6
4.6
5.66T
.270
32.0
7.0
8.49T
.333
34.4
9.4
* R = Rectangular; T = Tapered 2:1. Front spar located at 0.25 chord.
SPORT AVIATION 33
Table 2 - Procedure for Developing Time History Around the Course.
Example A i r c r a f t : C a s s u t t 11 Special (? Sea Level.
EitUata raraaita Drat CoafMclant (C-
r)
from HiiM Tait
Aircraft Data
Cron Ut. (U) - 100 Ibi.
UlTi| Araa (S) - 66 iq.fi. Nai. BMP - 100
Aapact Hallo (At) - 2.13
Nai. THP - 100 I 0.15 - 15
) - 364 fpa
Datarainc Ti«« Around Tha Couna By Flllint Out Tablai Shown Balo
On« For Each l-aca Court* Sljuant.
T.bl.i Sho.n Her«.
Calculation of Coafficianta Fro* Data Shown Abova
Dacalaratinj In Turn Mo. 1
o
Dra| (D) •• THF
THF «« 550 -• 15 « 5550
CD- _°
.
121.4 Ibi.
c
o.
(pi llbi
_____100
.00119 • 66 » 364*
3 (.4.02 34
fl./l.C*
2471 .2312 .0010 .0195 202.6
Al
• .0123
128.4
.00119 i 66 i 364*
'ASV'
.10
3.14 • 2.13 • .10 ' 4 -''.15
V
_>
i
.15
1
.10
.15
361.o|2307|244J 1.2387 1.0010 1.0195 Il99.6 |ll«.s|.70.1 \'-~l~
.90
'—I
T—I—i—~~T—T~—r—T~T~=:JT:7
13 |337.2|;012|2166 |.2426 j.0013 |. 0191 |l 76.5 |l3l. 6 | - 3 7 . 9 |[-1
.74
.12
2.13
10
.91
.17
I
Total-4540 ft. (raq'd turn dlatanca - 4391 f t . )
Tlaia In turni
. 13 .
[4540 - 439»"| • 12.51 tK.
"'•'
I
- .0123 - .0001
• |.011i|
I-
-—J——J-—I——-L——J__~L-—-|
J
Accalaratlng in Straightaway Bo. 1
|St.p 2 |
C,
Davaiop Followlnj Input Data for Tablai Shown In S t a y 3
r~——^———r
11
Q)
Ct (Saa Stap 1) -
CD| (S.. st.p 1) -
CD • tapir (Saa
I 345.0 I .
Total - 3 7 4 7 f t . (raq'd atral|hta»ay dlatanca - 3735 f t . ) i
TIM In atral|hta»ay - 11 -
L
Stap 1) 4 CD, •
"47
3 5 -
*
]73i
J
.
10.97
,.c.
——— I
|
•» - - - To dacalaratlnf. In turn no. 2. ate,*----
|.0115 • C0
D
Total Tina, lit Lap • 12. 51 • 10 97 « 13 10 « 11.21 • 47_..16 aac
Thrutt (T) • TUP i J50 -
15 « 550
-
As a bonus, increasing the aspect ratio
gives added "free" horsepower. Recall that
power varies as the cube of speed. Thus, if
it were possible to increase the speed of the
standard Cassutt by 17 mph, which is the
speed advantage held by 8.49T, it would require an additional 24 horsepower to do it.
Since 8.49T will fly 17 mph faster on the
same power, that 24 horsepower comes as
a bonus. How much work, expense and
frustration would be involved in trying to
squeeze another 24 horsepower out of any
Formula One racing engine and still meet
the regulations of the International Formula
One (IF1) racing organization? In all likelihood such increase would be beyond the
capability of "blueprinting", tweaking and
other strategems. Doing the squeezing with
the wing would surely be more productive,
particularly in view of the fact that where the
IF1 limits the wing area, its rules are silent
on ?ny other aspect of the wing.
' ,om both the aerodynamic and structural
points of view, there is a practical limit on
how much aspect ratio can be used on the
Cassutt or other racers of similar size. Figure
3 shows that the speed advantage disappears at an aspect ratio of around 11. In fact,
tripling the Cassutt's original 2.83 to 8.49
would seem a reasonable limit, considering
the structural penalties a designer faces in
going to longer, narrower and thinner wings.
As Figure 3 also shows, the largest speed
improvements actually develop at the lower
34 SEPTEMBER 1988
aspect ratios. However, the term Improvement might be better interpreted, not in absolute terms but in terms of how much is
needed to get to the checkered flag first.
Structural Considerations
Increasing the aspect ratio calls attention
to a number of factors involving the wing
structure. One is the added weight, which
turns out to have a minor effect on speed.
Another is flutter, which requires careful
scrutiny.
To dispose of the weight factor first, increasing the aspect ratio will increase the
structural weight, with the tapered wing coming off lighter than a rectangular wing of the
same aspect ratio. However, considering the
amount of weight change likely to be involved, the effect on speed in either case is
likely to be small.
Of greater significance is the effect of
weight on take-off performance. An additional hundred pounds in the standard Cas-
sutt would, for instance, add around 20% to
the take-off run. Note, however, that the
take-off speed is also higher, so the effect
on racing performance around the course
may not be large - IF the aircraft is out there
alone, racing against itself.
According to Bill Rogers, Secretary/Treasurer of the International Formula One
group, 12 times racing champion Ray Cote's
experience is that a speed advantage of from
ft.
47.16 aac
• J399 fpa -
3 to 5 mph is needed in order to pass. Thus,
even a slight delay in getting off the ground
in the usual racehorse start could make the
job of overtaking and ultimately passing the
competition more difficult in a heavier
airplane.
From the structural standpoint, however,
the biggest concern of increased aspect ratio
relates to the matter of wing stiffness, which
is an element of vital significance in flutter.
Although the subject of flutter is a highly
complex one, what it boils down to insofar
as the designer is concerned is that the natural periods of vibration (frequency) of the
wing bending and torsional modes need be
(1) as high as practicable and (2) not too
close together. In fact, the natural frequencies should be as far apart as reason per-
mits. Frequencies too close together invite a
"coupling" of one mode with another, thus
setting the stage for flutter. And fast
airplanes are replete with potential modal
booby traps.
At the right speed, structures can couple,
often in several modes at the same time.
Wings, ailerons, fuselages and even propellers can couple, one with the other or in combination; a vibrating structure in one place
on the airplane can excite vibration somewhere else. If violent enough, disaster is not
far away.
Increasing the aspect ratio calls for attention to these phenomenon. Taking a simplistic approach, observe that a long fishing rod
•PARASITE DRAG
D
c
D p a r = .0015
i (INDUCED DRAG)
. 0008 IN STRAIGHTAWAY
AR = 2.83
(CASSUTT SPECIAL)
.0015
TURNING
.0015
.0003 IN STRAIGHTAWAY
AR = 8.49
.0015
|to024l TURNING
FIG. 1 — TYPICAL MAXIMUM SPEED DRAG COEFFICIENTS FOR TWO
ASPECT RATIOS IN STRAIGHTAWAY AND IN TURNING ON 1400 FT. RADIUS
will bend more and have a lower bending
frequency than a short one under the same
load. Long wings and short wings mimic this
behavior.
The problem is compounded by the fact
that the higher aspect ratio wing is thinner
than one of lower aspect ratio, which not only
causes the spar(s) to be shallower and thus
more flexible on that account alone but
equally as important, the cross section area
of that portion of the wing section called upon
to handle the torsion loads (in stressed-skin
structures) is also less. And, in any torsionresisting structure, cross section area is a
vital ingredient to achieving stiffness. To
demonstrate: a large diameter tube will twist
less under a given torque than a small
diameter tube having the same length and
wall thickness. It's the cross section area that
does it. Doubling the diameter will increase
the stiffness by a factor of four, which is
exactly how much the cross section area is
increased.
This is where the tapered wing pays off;
its cross section area at the root, where the
torsion loads and stresses are ultimately
reacted, is greater than in the rectangular
wing. The spar is also deeper there. These
factors combine to stiffen the wing in both
bending and torsion.
It should be noted that the higher the natural periods of vibration the higher the
speeds required to excite them and the
closer the bending and torsional frequencies
can be before becoming too close for comfort.
For those readers, designers or builders
interested in a technique for measuring the
torsional stiffness of a wing already built, an
article on the subject, written by the author,
appeared in the August 1987 issue of
SPORT AVIATION (ref. 1). The procedure is
based on an FAA report which states that if
in test the wing torsional stiffness meets certain, specified numerical criteria it will meet
the FAA's flutter requirements. Even so, the
IF1 rules require that new racers demonstrate freedom from flutter via actual flight
test.
Aside from considerations of weight and
stiffness, there is the problem of distance between the spars of 2-spar wings; the pilot
sits between them. As the aspect ratio increases, the distance between the spars reduces (if, as usual, the chord-percentages of
their location remain the same), and there
may not be enough to accommodate the
pilot. This would be particularly true in rectangular wings, less so on tapered wings.
The designer, then, is left with having to
make perhaps significant changes in the
means used to attach the wing to the fuselage.
One solution is to go to a single spar, torsion-box, diagonal drag spar structure. Older
sailplanes use this technique widely.
Effect of Aspect Ratio on
Static Stability in Pitch
builder wants to retrofit a higher aspect ratio
to his racer in place of the original, lower
aspect ratio wing. Obviously, he would
greatly prefer maintaining the same spar(s)
position in the fuselage so as to minimize
changes in the fuselage structure.
Good design judgment suggests that the
spar be located in the wing at the same percentage of the chord as before and that the
chord be disposed about the spar in the
same manner. The aircraft CG is not likely
to change significantly in this arrangement.
Under this circumstance, then, if the new
wing's aerodynamic center (see following)
remains fixed at the same fuselage station
as before, or moves aft, the pitch stability will
increase along with aspect ratio. In
aerodynamic effect, the wing moves aft as
the aspect ratio increases, making the aircraft more nose heavy and thus more stable.
It is not difficult, in this scenario, to conceive of a practical wing having an aspect
ratio so high as to make the aircraft uncomfortable to fly - unless the CG is moved aft
to compensate.
If the aerodynamic center moves forward,
the contribution of aspect ratio to stability will
still be felt but its effect will become progressively overshadowed by the effect of moving
the aerodynamic center forward - which
tends to make the aircraft tail heavy.
To better appreciate the effect on stability
of changing the aspect ratio, consider the
concept of the neutral point, a term having
much to do with stability.
The neutral point represents the center of
all the aerodynamic forces and moments on
the airplane as a whole, not just the wing.
For stability, the CG must always be located
forward of the neutral point, and the farther
forward the more stable.
Neutral point not only considers the forces
and moments on the wing but those on the
SPORT AVIATION 35
3735 FT.
STRAIGHTAWAY NO. 1
TURN NO. 2
RACEPLANE PATH AROUND COURSE
• — 4398 FT.
5.66 R
246 MPH
8.49 R
248 MPH .
FIG. 2 - Order of finish and leads (to scale) after 6 laps around 3 mile course. Speeds assumed to have stabilized
at end of first lap.
fuselage, the horizontal tail and even the propeller. If the wing's aerodynamic center
moves, so does the neutral point. The
aerodynamic center (a.c.) is usually located
at or near the 1/4-chord point on the wing's
mean aerodynamic chord (m.a.c.).
If the tail location, aspect ratio and/or area
are changed, if the number of propeller
blades is changed, if the propeller diameter
is changed - all these plus other factors
cause the neutral point to change and with
This makes the percentage distance between the CG and the neutral point greater
than before and the aircraft now has a higher
static margin.
The main reason for this is that the neutral
point shifts aft with increasing aspect ratio
because, as the span increases, the downwash over the tail reduces.
If the aircraft turns out to be too stable for
comfort and/or adequate control, one obvi-
ous solution is to move the CG aft. Since, as
indicated earlier, the CG, fixed at a given
fuselage station, is (under the Figure 4 conditions) closer to the wing leading edge than
originally, it can be moved aft even if it were
originally located as far aft as permitted by
the IF1 rules (25%). Here, under the conditions shown in the figure, 25% of the Cas-
it, the static stability.
Static stability is measured in terms of how
far apart the CG and neutral point are, expressed in percent of the ma.c. aft of its leading edge. If, for example, the CG were located at 25% m.a.c. and the neutral point at
35%, there would exist a 10% "static stability
margin" or, simply, "static margin" (sometimes called the "CG margin").
The preceding remarks, and the following
ones, supplemented by study of Figure 4,
250—,
TAPERED
MPH
RECTANGULAR
240—
now make one important effect of aspect
ratio on stability clear.
Here one notes that, if the aircraft CG is
fixed as a given fuselage station and is forward of the spar, as the aspect ratio increases, the position of the CG in percent
m.a.c. decreases. This because the m.a.c.
is shorter and the CG now finds itself closer
to the leading edge of the new wing than
before on the old one. (If the CG is on the
spar, there will be no change. If the CG is
aft of the spar, its m.a.c. percentage will increase. This applies, of course, only to wings
where the spar on the new wing is set at the
same chord percentage as the old wing.)
36 SEPTEMBER 1988
230-
6
8
10
ASPECT RATIO
FIG. 3 - Effect of aspect ratio and taper on average course speed of Cassutt
Special II.
12
suit's AR2.83 chord is only 10% of the
AR8.49 chord, so the airplane's CG can be
moved aft another 15% of the higher AR
wing.
A shortcut to computing the effect of adding, removing or moving ballast is shown in
an article written by the author in reference 2.
If moving the CG doesn't solve the noseheaviness problem, the wing needs to be
moved forward.
Computing the position of the neutral point
is not a simple chore for the uninitiated. For
those readers interested in pursuing the matter further, Perkins and Hage (ref. 3) shows
the way. However, a feel for whether the stability is likely to be acceptable or not may be
realized by determining the Horizontal Tail
Volume Coefficient (Vh) instead, which is
quick and easy. Vh won't locate the neutral
point all by itself because other factors are
involved but it appears in the equation for
neutral point and has a strong influence
thereon.
Vh simply equates to the ratio of tail area
to wing area, multiplied by the ratio of tail
arm to wing m.a.c. length. Tail arm is measured fore and aft, from the wing's a.c. to the
tail's a.c.
To determine if the V,, is adequate, compare it with what it was originally on the lower
aspect ratio-winged airplane or with the Vh
of other racers known to have acceptable
stability.
For reference, tail volume coefficients for
several representative aircraft (not racers)
are shown in L. Pazmany's "Light Aircraft
Design" (ref. 4).
Table 1 shows the approximate tail volume
coefficients for the Cassutt, using wings of
varying aspect ratio. The table also shows
the Cassutt's power-off, stick-fixed neutral
point and static stability margin for each of
the aspect and taper ratios studied, where
the CG is arbitrarily set at the aft IF1 limit of
25%. The most striking feature of this listing
is how low the values are for the standard
(low aspect ratio) Cassutt. With either the
rectangular or tapered wing, it is less than
5%. Note again that this is power-off, stickfixed and approximate. The margins could
be less than those shown.
If Formula One racers typically operate at
such small margins, there may be cause for
concern. Perkins and Hage suggest that full
throttle power in a tractor propeller can be
counted on to shift the neutral point forward
by some 4% in representative single-engine,
high performance aircraft. If the power off
be improved by shifting the neutral point aft.
Enlarging the horizontal tail will do it. So will
increasing the tail's aspect ratio. And so will
lengthening the fuselage tail arm (lengthen-
ing the aft fuselage).
Increasing the wing aspect ratio also has
an influence on the yaw/roll stability. Determining the extent of this influence in numerical terms is an exceedingly complex chore
because yaw and roll interact.
It is likely sufficient, however, to determine
the Vertical Tail Volume Coefficient (Vv) of
the original aircraft and, if its stability were
to be judged satisfactory, to alter the size
and/or aspect ratio of the new vertical tail so
as to maintain the original Vv.
The vertical tail volume coefficient equates
to the ratio of the vertical tail area to the wing
area, multiplied by the ratio of tail length
(again, a.c. to a.c.) to the wing span. Here
one notes, Vv is proportional to wing span,
which is to say that if the same or close to
the same yaw stability as before is desired
and the wing span is increased by, say, 50%
over the original, the vertical tail area needs
to be increased by the same percentage,
holding the same aspect ratio and vertical
tail a.c. position as before.
Pazmany's book shows representative
values for Vv as well for several light aircraft.
Roll Rate
If in increasing the aspect ratio the aileron
dimensions are maintained at the same percentages of wing span and chord, the roll
rate at a given airspeed and aileron deflec-
tion will decrease. If it is important to maintain the original roll rate, there are two useful
options - the pilot can simply apply more aileron in fuming (if he isn't already against the
stops) or the designer can make the ailerons
longer, percentage-wise, in the first
place. For large span increases, lengthening
the ailerons is likely the preferred option.
A first approximation to how much longer
to make the ailerons might be - for every
percent the wing span is increased the aileron span should be increased about 2% over
what it was on the lower aspect ratio wing.
This value has no readily obvious theoretical
justification; it simply came out in a computation of the roll rates of several representative
wings.
As the angular throw and/or aileron span
are increased, the stick forces will increase
right along, and if they become excessive it
may be desirable that the pilot and designer
get together and re-examine the need for
duplicating the roll rate of the shorter wing.
Or come up with an alternative solution.
In a high aspect ratio wing, maintaining
the same aileron chord and span percentages will, of course, cause the ailerons to
be longer, narrower and thinner than in a low
aspect ratio wing. Bringing the long-wing roll
rate back to the short-wing rate will, as
suggested above, require that the aileron become longer still, and this makes attention
to aileron stiffness and balance of particular
importance. It is a matter of record that ailerons tend to flutter more often than do wings,
and a particularly hazardous and not uncommon situation exists where aileron flutter
modes couple with the wing modes, wreak-
STATIC MARGIN = .c3 m.a.c.
stability is only 4% to begin with, adding full
power can render the aircraft neutrally stable
(have no stability at all) or actually render it
unstable. Thus, even though the IF1 rules
permit a 25% CG position, in some aircraft
configurations this may be too far aft.
There are varying opinions among racing
people as to what the static margin ought to
.10 m.a.c.
STATIC MARGIN = .21 m.a.c.
be. One opinion is that low margins improve
pilot skill (agreed!). Another opinion holds
that the constant pitch changes and control
inputs brought about by low margins slow
the airplane down. Still another opinion is
that higher margins improve the airplane's
ability to take care of itself, thus permitting
the pilot to more fully concentrate on racing
strategy. Properly, it seems a matter of pilot
choice.
If, based on flight test or low computed Vh,
the pitch stability is judged insufficient, it can
FIG. 4 - Demonstration of how neutral points and static stability margins
change with aspect ratio, eg and spar fixed with reference to fuselage.
SPORT AVIATION 37
ing all kinds of havoc in the process. It would
be difficult to exaggerate the importance of
maintaining very stiff, well-supported and
well balanced ailerons - and all surfaces for
that matter, including tails.
The importance of wing torsional stiffness
to roll rate can be seen in historical perspective. At 400 mph the British Spitfire fighter is
reported to have lost some 65% of its
maximum design roll rate due primarily to
the wing twisting under the influence of aileron application.
A common term used in situations of this
kind is "aileron reversal speed", which is the
speed at which the wing twists so much as
to cancel the aileron effect entirely. Any
further increase in speed would cause the
aircraft to roll in a direction opposite to that
intended. An unwelcome situation, indeed.
As suggested earlier, high aspect ratio
wings tend to be less stiff in torsion than low
aspect ratio wings, unless proper accounting
for this fact is taken in design.
Procedure For Computing the
Time History Around the Course
speed advantage of incorporating high aspect ratio wings in their own racers can use
the same technique the author employed in
ground is not required, only time, patience and plenty of paper. The procedure is shown
by example in Table 2. The procedure is
much easier to follow than the appearance
of the table would suggest; there are mostly
repetitive calculations.
First, measure the maximum speed of the
original aircraft in straight and level flight,
and from this and the maximum thrust horse-
power (THP), compute the drag. The THP
will be the maximum brake horsepower
(BMP) times the propeller efficiency, this latter being around 0.85 for a good propeller.
The drag of the aircraft in pounds will be 550
times the THP, divided by the speed of the
aircraft in feet per second.
The objective of this initial exercise is to
determine the aircraft's parasite drag coefficient (CD ), which is simply the difference
between tfie total drag coefficient (CD) and
the drag coefficient induced by lift (CD). Although the total drag coefficient changes
with speed, the parasite drag coefficient
doesn't - at least not much.
At appropriate points in the subsequent
analysis, the CDpw is added back in. If only
the wing's aspect ratio is changed, the aircraft's CD will remain the same for all versions of {fie aircraft. That's why it is "extracted" from the total drag coefficient in the
first place - just so it can be added back in
later.
The procedure entails dividing the race
course into four segments, two 180 degree
turns and two straightaways. The "race" (the
analysis) starts at the beginning of the first
turn, and the aircraft is assumed to be flying
at its maximum level flight speed at this
point.
From here on, the aircraft's speed is computed at one second intervals for the first
lap. Although probably not exactly true in real
life, the aircraft's speed is assumed to have
stabilized at the end of the first lap, and the
average speed over all subsequent laps is
assumed to be the same as that of the first
one.
38 SEPTEMBER 1988
As the pilot hits the starting point, he rolls
into his first turn, holding a constant 1400
foot radius throughout. To simplify the proce-
dure, the roll is assumed to develop fully,
instantaneously (this is not too far from the
actual truth!).
In turning, the aircraft develops a centrifugal force, and the wing lift generated
thereby is the opposing resultant of the centrifugal force and the aircraft's gross weight.
From the lift is computed the lift coefficient
(CL) and from this, the induced drag coefficient (CDi). Note again that induced drag has
aspect ratio as one of its determinants. Adding in the C0 gives the total drag coefficient which now, of course, turns out to be
higher than before the turn started. This
means more drag. Since the drag is now
higher than the thrust, the airplane slows
down.
So much for the first second. The speed
at the start of second number two will be the
speed at the start of second number one,
less the amount the aircraft slowed down
during that first second. And so on, second
by second, until the turn is completed. The
last column in the table, identified as "a",
shows the amount the aircraft slowed down
(or speeded up) during the second being
considered.
Then the pilot rolls out, again instantaneously, into the first straightaway. The centrifugal force disappears, the induced drag
drops precipitously and there is now more
thrust than drag, and so the aircraft speeds
up.
The same procedure is used in the straightaway as in the turn, except that the centri-
fugal force is no longer involved.
At the end of the first straightaway, the
first half of the first lap is now analyzed. The
procedure for the second half is merely a
repeat of the first, only with different numbers. The key to the procedure is that the
speed at the beginning of each second is
always the speed at the beginning of the previous second, minus the speed lost or gained
at the end of that previous second. Thus, the
aircraft is seen to slow down, second by second in the turn and speed up, second by
second in the straightaway. A really efficient
airplane would, at the end of the first lap,
have regained most of the speed lost in the
turns.
The first "trip" around the course assumes
the original aspect ratio. Subsequent trips
can be analyzed the same way, using differ-
ent aspect ratios for comparison. The speed
advantage of higher aspect ratio will become
clear. It will also become clear that we're
working with small differences in big numbers, but perhaps not too small to win the
race.
It should be emphasized that all this is
based on drag data taken from an aircraft
already built and flying, where the intent is
to determine the effect of substituting the
original wing with one of higher aspect ratio.
Aircraft still on the drawing board can use
the same procedure but first the drag characteristics must be computed where before
they were derived from measurement of actual speed.
Readers intending to go through the procedure again, for another aspect ratio,
should be reminded that the entry into the
first turn will be at a higher speed than before
because the higher aspect ratio wing is now
"cleaner" and thus faster.
The easiest way to determine this new
speed is by trial and error. Simply set up a
table of V, CL, CD, CD, D and T along the
lines shown in Table 2 and assume different
speeds. The maximum speed will be where
D and T (drag and thrust) are equal.
Other Factors Deserving Attention
Certainly not all aspect ratio-related factors were addressed in the study summarized here, first because not all are known
and second because some of the more obvious ones are hard to assign numbers to. One
of the latter is the effect of the fuselage on
(or in ) the wing. Another is the effect of the
propeller slipstream. The fact that the influences of both interact doesn't help in trying
to quantify the overall effect.
The high turbulence of the fuselage/propeller combination will involve less of the
wing if the wing is long and narrow rather
than short and wide, thus causing less drag
due to flow separation off the wing and wing/
fuselage juncture interference effects.
A third non-quantifiable effect of high aspect ratio relates to pilot visibility forward and
down; narrow wings simply block out less
visibility in this critical direction than do wide
ones. The IF1 rules require that vision be
provided at no less than 25 degrees below
the horizontal over the wing leading edge.
and the Big Iron?
racers, the principles outlined should be
equally applicable to closed-course racers of
any kind, including the little biplanes and the
huge Unlimiteds. In fact, the biplanes might
benefit more from increased aspect ratio
than the single-wingers because their aspect
ratios tend to be less. Note that the aspect
ratio of a biplane equates approximately to
the square of the span of the longer wing,
divided by the area of both wings. The effects of wing interference, one with the other,
however, needs careful scrutiny to see if in-
creasing the aspect ratio is really worthwhile.
The thorny problems involved in such an undertaking have to be seen to be appreciated.
Acknowledgements
The author wishes to thank Lockheed aeronautical engineer Jim McVernon and Bill
Rogers, engineer, SecretaryrTreasurer and
Technical Inspector of the International Formula One racing organization for looking
over his shoulder and providing valuable
contributions during the preparation of this
article. Readers interested in pursuing the
Formula One challenge further can contact
Bill Rogers at 926 Rawhide Place, Newbury
Park, CA 91320.
References
1. Hall, Stan, Testing of Structurally-Scaled,
Sacrificial Models As An Aid To Full-Scale
Design." SPORT AVIATION, August 1987.
2. Hall, Stan, "How To Move the CG? - Try
the Quick Reference Chart." SPORT AVIATION, May 1986.
3. Perkins and Hage, "Airplane Performance, Stability and Control." John Wiley
and Sons, New York.
4. Pazmany, L, "Light Airplane Design."
San Diego, CA 92138.