# High Aspect Ratio Wings For Formula One Racers

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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. Nai. Laval Fll|ht Spaad (V 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. Only Flnt Two (Abbravlatad) 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 • add to pravioui apaad aach tioa (watch tract.) (taparad 2:1) 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 Averaga Spaad • 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 One premise of this article is that the 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). What About the Vertical Tail? 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 Readers interested in computing the speed advantage of incorporating high aspect ratio wings in their own racers can use the same technique the author employed in preparing this article. An engineering back- 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. What About the Bipes and the Big Iron? Although this article is about Formula One 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." Published by the author. P. O. Box 10051, San Diego, CA 92138.