HIGH ASPECT RATIO WINGS FORFORMULA ONE RACERS

Short, stubby, low aspect ratio wings havecharacterized Formula One racers sincetime immemorial. A little number crunchingshows they would get around the coursequicker if they carried high aspect ratiowings instead; not "high" as in sailplane, butmuch higher than they are now.

Consideration of the fact that in pylon rac-ing these spirited little bullets spend morethan half their time pulling high G turns leadsto the conclusion that speed could be im-proved by emphasizing in design the condi-tions prevailing in the turns instead of thestraightaways. To the technical observer, theemphasis seems to be placed on the straight-aways - where the problem isn't.

At a given power, as the aircraft turns theincreasing drag slows it down, and as itstraightens out, the now decreasing drag al-lows the aircraft to speed up again.

The slowing down in the turns can be de-creased and the speeding up in the straight-aways increased by going to longer and nar-rower wings; to higher aspect ratios. Highaspect ratio has long been the turf ofsailplanes and long range airplanes, but italso has application to closed-course racers.In fact, high aspect ratio was "made" for theracer's drag problem.

To illustrate: According to the bar chart inFigure 1 the aspect ratio 2.83 Cassutt Spec-ial II, rounding the pylons at maximum speedon a 1400 foot radius, sees a drag increaseof almost 60% over its straight and levelvalue. By tripling the aspect ratio to 8.49, theincrease is held to around 23%. In thestraightaways the drag is reduced about5%. This, and pilot skill, is the key to winningraces.

Tripling the aspect ratio on the Cassuttdoesn't, of course, mean tripling the span. Itmeans increasing it by the square root of 3,or 73%, and reducing the chord by whateverit takes to yield the original wing area, in thiscase 42%.

Elementary physics tells us that the wingon an aircraft turning at constant altitudegenerates more lift than when flying straightand level. This lift induces an increment ofdrag all by itself, which adds to the drag al-ready there. This induced drag varies as thesquare of the lift coefficient. If, for example,the racer is pulling 3 G's in rounding the py-lons (a fairly typical value, by the way), thedrag induced by lift is 9 times higher thanin 1 G flight.

Consider now the concept of Aspect Ratio,which states that the higher this ratio thelower the drag induced by lift. Sailplanescapitalize on this principle, and aspect ratiosof 40 are drawing the attention of designersthese days. After all, any aircraft capable offlying over a thousand miles without power(the present record) has to have somethinggoing for it. That "something" is aspect ratio(and smooth, laminar surfaces).

There is no suggestion here that FormulaOne racers emulate their engineless breth-

by Stan Hall1530 Belleville WaySunnyvale, CA 94087

em by gcing to such extremes. The benefitis certain to be zero - or worse. But doublingor tripling the 2.83 aspect ratio on the vener-able but still popular Cassutt or other racersof the genre would seem a practical and po-tentially winning strategy - and their aspectratios wouldn't be too far removed fromthose presently seen on the single engineCessnas and Pipers with which we are all sofamiliar.

Reported here in support of this idea is asummary of a straight forward paper studyconducted by the author of 6 different wingsfor the Cassutt. Involved were three rectan-gular (constant chord) wings and three ta-pered wings, each tapered at a ratio of 2:1.The Cassutt was chosen simply because (1)it is still winning races after all these yearsand, (2) data on the aircraft were readilyavailable in Jane's All The World's Aircraft.

Each of these wings (with airplane at-tached) was run via pocket calculator aroundsix, sea level laps of an arbitrary but not atyp-ical, 3-mile closed course, and the speedscompared.

Everything was held constant except the

aspect ratio - same power (100 hp), samewing area, same airfoil, same gross weight,same pilot, same constant turn radiusaround the pylons, same everything - exceptthe aspect ratio.

The aspect ratios were set at 2.83, 5.66and 8.49, the latter two representing a doubl-ing and tripling of the Cassutt's original 2.83.To help with the bookkeeping, the wingswere identified by their aspect ratios andtheir planforms ("R" for rectangular, "T fortapered). 5.66T would, for example, repre-sent a tapered wing having an aspect ratioof 5.66.

The results were as expected. As Figure2 shows, the racer with the 8.49T wing wonthe "race". It led the standard 2.83R Cassuttby well over a mile at the finish. Its nearestcompetitor was 8.49R, another long-winger,which led the standard Cassutt by only 400feet or so less.

Considering the whisker finishes we oftensee at Reno, one might conclude that leadsof this magnitude constitute something of ablowout. The blowing-out is done in theturns.

Although there is but a negligible speeddifference between the tapered and rectan-gular 8.49 wings, it would seem imprudent,in interests of capitalizing on the simpler con-struction of the rectangular wing, to ignoreother, strong virtues inherent in the taperedwing.These are discussed later.

TABLE 1

Approximate Horizontal Tail Volume Coefficients and Stick-Fixed, Power OffNeutral Points and Static Margins for Cassutt II Special, eg at 25% m.a.c.,Using Wings of Various Planforms.

Planform*

2.83R

5.66R

8.49R

2.83T

5.66T

8.49T

.199

.282

.345

.192

.270

.333

Neutral Point

29.7%

32.3

34.9

29.6

32.0

34.4

Static Margin

4.7%

7.3

9.9

4.6

7.0

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 : Cassutt 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 ) - 364 fpaUlTi| Araa (S) - 66 iq.fi. Nai. BMP - 100Aapact Hallo (At) - 2.13 Nai. THP - 100 I 0.15 - 15

Calculation of Coafficianta Fro* Data Shown Abova

o Dra| (D) • THF « 550 • 15 « 550 . 121.4 Ibi.

Datarainc Ti«« Around Tha Couna By Flllint Out Tablai Shown BaloOn« For Each l-aca Court* Sljuant. Only Flnt Two (Abbravlatad)T.bl.i Sho.n Her«.

• THF « 550 - 15 « 5Dacalaratinj In Turn Mo. 1

CD- _°'ASV'

128.4.00119 i 66 i 364*_____100.00119 • 66 » 364*

• .0123©

3.14 • 2.13 • .10V _>

Al

2.13'4i1

10

tract.)

.10-''.15

.15

.10

.74

(taparad 2:1)

.15

.90

.91

.17

.12

(pi llbi

3 (.4.02 34 2471

©co.

.2312 .0010 .0195 202.6

fl./l.C*

• add to pravioui apaad aach tioa (watch

361.o|2307|244J 1.2387 1.0010 1.0195 Il99.6 |ll«.s|.70.1 \'-~l~-—J——J-—I——-L——J__~L-—-| I- I

'—I T—I—i—~~T—T~—r—T~T~=:JT:713 |337.2|;012|2166 |.2426 j.0013 |. 0191 |l 76.5 |l3l. 6 | -37 .9 |[-1

Total-4540 ft. (raq'd turn dlatanca - 4391 f t . )

Tlaia In turn

- .0123 - .0001

• |.011i|

|St.p 2 |

Davaiop Followlnj Input Data for Tablai Shown In Stay 3

i . 13 . [4540 - 439»"| • 12.51 tK.I "'•' J

Accalaratlng in Straightaway Bo. 1

C,

Q) Ct (Saa Stap 1) -

© CD| (S.. st.p 1) -

© CD • tapir (Saa Stap 1) 4 CD, • |.0115 • C0

D

© Thrutt (T) • TUP i J50 - 15 « 550 -

r~——^———r11 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 - "47 - ]73i . 10.97 ,.c. |L 3*5 J ——— I

•» - - - To dacalaratlnf. In turn no. 2. ate,*----

Total Tina, lit

Averaga Spaad •

Lap •

47.16

12.

ft.aac

51 • 10

• J39

97 « 13

9 fpa -

10 « 11.21 • 47_..16 aac

As a bonus, increasing the aspect ratiogives added "free" horsepower. Recall thatpower varies as the cube of speed. Thus, ifit were possible to increase the speed of thestandard Cassutt by 17 mph, which is thespeed advantage held by 8.49T, it would re-quire an additional 24 horsepower to do it.Since 8.49T will fly 17 mph faster on thesame power, that 24 horsepower comes asa bonus. How much work, expense andfrustration would be involved in trying tosqueeze another 24 horsepower out of anyFormula One racing engine and still meetthe regulations of the International FormulaOne (IF1) racing organization? In all likeli-hood such increase would be beyond thecapability of "blueprinting", tweaking andother strategems. Doing the squeezing withthe wing would surely be more productive,particularly in view of the fact that where theIF1 limits the wing area, its rules are silenton ?ny other aspect of the wing.' ,om both the aerodynamic and structural

points of view, there is a practical limit onhow much aspect ratio can be used on theCassutt or other racers of similar size. Figure3 shows that the speed advantage disap-pears at an aspect ratio of around 11. In fact,tripling the Cassutt's original 2.83 to 8.49would seem a reasonable limit, consideringthe structural penalties a designer faces ingoing to longer, narrower and thinner wings.

As Figure 3 also shows, the largest speedimprovements actually develop at the lower

aspect ratios. However, the term Improve-ment might be better interpreted, not in ab-solute terms but in terms of how much isneeded to get to the checkered flag first.

Structural ConsiderationsIncreasing the aspect ratio calls attention

to a number of factors involving the wingstructure. One is the added weight, whichturns out to have a minor effect on speed.Another is flutter, which requires carefulscrutiny.

To dispose of the weight factor first, in-creasing the aspect ratio will increase thestructural weight, with the tapered wing com-ing off lighter than a rectangular wing of thesame aspect ratio. However, considering theamount of weight change likely to be in-volved, the effect on speed in either case islikely to be small.

Of greater significance is the effect ofweight on take-off performance. An addi-tional hundred pounds in the standard Cas-sutt would, for instance, add around 20% tothe take-off run. Note, however, that thetake-off speed is also higher, so the effecton racing performance around the coursemay not be large - IF the aircraft is out therealone, racing against itself.

According to Bill Rogers, Secretary/Trea-surer of the International Formula Onegroup, 12 times racing champion Ray Cote'sexperience is that a speed advantage of from

3 to 5 mph is needed in order to pass. Thus,even a slight delay in getting off the groundin the usual racehorse start could make thejob of overtaking and ultimately passing thecompetition more difficult in a heavierairplane.

From the structural standpoint, however,the biggest concern of increased aspect ratiorelates to the matter of wing stiffness, whichis an element of vital significance in flutter.Although the subject of flutter is a highlycomplex one, what it boils down to insofaras the designer is concerned is that the nat-ural periods of vibration (frequency) of thewing bending and torsional modes need be(1) as high as practicable and (2) not tooclose together. In fact, the natural frequen-cies should be as far apart as reason per-mits. Frequencies too close together invite a"coupling" of one mode with another, thussetting the stage for flutter. And fastairplanes are replete with potential modalbooby traps.

At the right speed, structures can couple,often in several modes at the same time.Wings, ailerons, fuselages and even propel-lers can couple, one with the other or in com-bination; a vibrating structure in one placeon the airplane can excite vibration some-where else. If violent enough, disaster is notfar away.

Increasing the aspect ratio calls for atten-tion to these phenomenon. Taking a simplis-tic approach, observe that a long fishing rod

34 SEPTEMBER 1988

•PARASITE DRAG

AR = 2.83(CASSUTT SPECIAL)

cDpar = .0015Di (INDUCED DRAG)

. 0008 IN STRAIGHTAWAY

.0015 TURNING

.0015

AR = 8.49

.0015 |to024l

.0003 IN STRAIGHTAWAY

TURNING

FIG. 1 — TYPICAL MAXIMUM SPEED DRAG COEFFICIENTS FOR TWOASPECT RATIOS IN STRAIGHTAWAY AND IN TURNING ON 1400 FT. RADIUS

will bend more and have a lower bendingfrequency than a short one under the sameload. Long wings and short wings mimic thisbehavior.

The problem is compounded by the factthat the higher aspect ratio wing is thinnerthan one of lower aspect ratio, which not onlycauses the spar(s) to be shallower and thusmore flexible on that account alone butequally as important, the cross section areaof that portion of the wing section called uponto handle the torsion loads (in stressed-skinstructures) is also less. And, in any torsion-resisting structure, cross section area is avital ingredient to achieving stiffness. Todemonstrate: a large diameter tube will twistless under a given torque than a smalldiameter tube having the same length andwall thickness. It's the cross section area thatdoes it. Doubling the diameter will increasethe stiffness by a factor of four, which isexactly how much the cross section area isincreased.

This is where the tapered wing pays off;its cross section area at the root, where thetorsion loads and stresses are ultimatelyreacted, is greater than in the rectangularwing. The spar is also deeper there. Thesefactors combine to stiffen the wing in bothbending and torsion.

It should be noted that the higher the nat-ural periods of vibration the higher thespeeds required to excite them and thecloser the bending and torsional frequenciescan be before becoming too close for com-fort.

For those readers, designers or buildersinterested in a technique for measuring the

torsional stiffness of a wing already built, anarticle on the subject, written by the author,appeared in the August 1987 issue ofSPORT AVIATION (ref. 1). The procedure isbased on an FAA report which states that ifin test the wing torsional stiffness meets cer-tain, specified numerical criteria it will meetthe FAA's flutter requirements. Even so, theIF1 rules require that new racers demon-strate freedom from flutter via actual flighttest.

Aside from considerations of weight andstiffness, there is the problem of distance be-tween the spars of 2-spar wings; the pilotsits between them. As the aspect ratio in-creases, the distance between the spars re-duces (if, as usual, the chord-percentages oftheir location remain the same), and theremay not be enough to accommodate thepilot. This would be particularly true in rec-tangular wings, less so on tapered wings.The designer, then, is left with having tomake perhaps significant changes in themeans used to attach the wing to the fuse-lage.

One solution is to go to a single spar, tor-sion-box, diagonal drag spar structure. Oldersailplanes use this technique widely.

Effect of Aspect Ratio onStatic Stability in Pitch

One premise of this article is that thebuilder wants to retrofit a higher aspect ratioto his racer in place of the original, loweraspect ratio wing. Obviously, he wouldgreatly 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 per-centage of the chord as before and that thechord be disposed about the spar in thesame manner. The aircraft CG is not likelyto change significantly in this arrangement.

Under this circumstance, then, if the newwing's aerodynamic center (see following)remains fixed at the same fuselage stationas before, or moves aft, the pitch stability willincrease along with aspect ratio. Inaerodynamic effect, the wing moves aft asthe aspect ratio increases, making the air-craft more nose heavy and thus more stable.

It is not difficult, in this scenario, to con-ceive of a practical wing having an aspectratio so high as to make the aircraft uncom-fortable to fly - unless the CG is moved aftto compensate.

If the aerodynamic center moves forward,the contribution of aspect ratio to stability willstill be felt but its effect will become progres-sively overshadowed by the effect of movingthe aerodynamic center forward - whichtends to make the aircraft tail heavy.

To better appreciate the effect on stabilityof changing the aspect ratio, consider theconcept of the neutral point, a term havingmuch to do with stability.

The neutral point represents the center ofall the aerodynamic forces and moments onthe airplane as a whole, not just the wing.For stability, the CG must always be locatedforward of the neutral point, and the fartherforward the more stable.

Neutral point not only considers the forcesand moments on the wing but those on the

SPORT AVIATION 35

TURN NO. 2

• — 4398 FT.

3735 FT.

STRAIGHTAWAY NO. 1

RACEPLANE PATH AROUND COURSE

5.66 R246 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 stabilizedat end of first lap.

fuselage, the horizontal tail and even the pro-peller. If the wing's aerodynamic centermoves, so does the neutral point. Theaerodynamic center (a.c.) is usually locatedat or near the 1/4-chord point on the wing'smean aerodynamic chord (m.a.c.).

If the tail location, aspect ratio and/or areaare changed, if the number of propellerblades is changed, if the propeller diameteris changed - all these plus other factorscause the neutral point to change and withit, the static stability.

Static stability is measured in terms of howfar apart the CG and neutral point are, ex-pressed in percent of the ma.c. aft of its lead-ing edge. If, for example, the CG were lo-cated at 25% m.a.c. and the neutral point at35%, there would exist a 10% "static stabilitymargin" or, simply, "static margin" (some-times called the "CG margin").

The preceding remarks, and the followingones, supplemented by study of Figure 4,now make one important effect of aspectratio on stability clear.

Here one notes that, if the aircraft CG isfixed as a given fuselage station and is for-ward of the spar, as the aspect ratio in-creases, the position of the CG in percentm.a.c. decreases. This because the m.a.c.is shorter and the CG now finds itself closerto the leading edge of the new wing thanbefore on the old one. (If the CG is on thespar, there will be no change. If the CG isaft of the spar, its m.a.c. percentage will in-crease. This applies, of course, only to wingswhere the spar on the new wing is set at thesame chord percentage as the old wing.)

This makes the percentage distance be-tween the CG and the neutral point greaterthan before and the aircraft now has a higherstatic margin.

The main reason for this is that the neutralpoint shifts aft with increasing aspect ratiobecause, as the span increases, the down-wash 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, asindicated earlier, the CG, fixed at a givenfuselage station, is (under the Figure 4 con-ditions) closer to the wing leading edge thanoriginally, it can be moved aft even if it wereoriginally located as far aft as permitted bythe IF1 rules (25%). Here, under the condi-tions shown in the figure, 25% of the Cas-

250—,

MPH

240—

230-

TAPERED

RECTANGULAR

6 8

ASPECT RATIO

10 12

FIG. 3 - Effect of aspect ratio and taper on average course speed of CassuttSpecial II.

36 SEPTEMBER 1988

suit's AR2.83 chord is only 10% of theAR8.49 chord, so the airplane's CG can bemoved aft another 15% of the higher ARwing.

A shortcut to computing the effect of ad-ding, removing or moving ballast is shown inan article written by the author in reference 2.

If moving the CG doesn't solve the nose-heaviness problem, the wing needs to bemoved forward.

Computing the position of the neutral pointis not a simple chore for the uninitiated. Forthose readers interested in pursuing the mat-ter further, Perkins and Hage (ref. 3) showsthe way. However, a feel for whether the sta-bility is likely to be acceptable or not may berealized by determining the Horizontal TailVolume Coefficient (Vh) instead, which isquick and easy. Vh won't locate the neutralpoint all by itself because other factors areinvolved but it appears in the equation forneutral point and has a strong influencethereon.

Vh simply equates to the ratio of tail areato wing area, multiplied by the ratio of tailarm to wing m.a.c. length. Tail arm is mea-sured fore and aft, from the wing's a.c. to thetail's a.c.

To determine if the V,, is adequate, com-pare it with what it was originally on the loweraspect ratio-winged airplane or with the Vhof other racers known to have acceptablestability.

For reference, tail volume coefficients forseveral representative aircraft (not racers)are shown in L. Pazmany's "Light AircraftDesign" (ref. 4).

Table 1 shows the approximate tail volumecoefficients for the Cassutt, using wings ofvarying aspect ratio. The table also showsthe Cassutt's power-off, stick-fixed neutralpoint and static stability margin for each ofthe aspect and taper ratios studied, wherethe CG is arbitrarily set at the aft IF1 limit of25%. The most striking feature of this listingis how low the values are for the standard(low aspect ratio) Cassutt. With either therectangular or tapered wing, it is less than5%. Note again that this is power-off, stick-fixed and approximate. The margins couldbe less than those shown.

If Formula One racers typically operate atsuch small margins, there may be cause forconcern. Perkins and Hage suggest that fullthrottle power in a tractor propeller can becounted on to shift the neutral point forwardby some 4% in representative single-engine,high performance aircraft. If the power offstability is only 4% to begin with, adding fullpower can render the aircraft neutrally stable(have no stability at all) or actually render itunstable. Thus, even though the IF1 rulespermit a 25% CG position, in some aircraftconfigurations this may be too far aft.

There are varying opinions among racingpeople as to what the static margin ought tobe. One opinion is that low margins improvepilot skill (agreed!). Another opinion holdsthat the constant pitch changes and controlinputs brought about by low margins slowthe airplane down. Still another opinion isthat higher margins improve the airplane'sability to take care of itself, thus permittingthe pilot to more fully concentrate on racingstrategy. Properly, it seems a matter of pilotchoice.

If, based on flight test or low computed Vh,the pitch stability is judged insufficient, it can

be improved by shifting the neutral point aft.Enlarging the horizontal tail will do it. So willincreasing the tail's aspect ratio. And so willlengthening 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. Deter-mining the extent of this influence in numer-ical terms is an exceedingly complex chorebecause yaw and roll interact.

It is likely sufficient, however, to determinethe Vertical Tail Volume Coefficient (Vv) ofthe original aircraft and, if its stability wereto be judged satisfactory, to alter the sizeand/or aspect ratio of the new vertical tail soas to maintain the original Vv.

The vertical tail volume coefficient equatesto the ratio of the vertical tail area to the wingarea, multiplied by the ratio of tail length(again, a.c. to a.c.) to the wing span. Hereone notes, Vv is proportional to wing span,which is to say that if the same or close tothe same yaw stability as before is desiredand the wing span is increased by, say, 50%over the original, the vertical tail area needsto be increased by the same percentage,holding the same aspect ratio and verticaltail a.c. position as before.

Pazmany's book shows representativevalues for Vv as well for several light aircraft.

Roll RateIf in increasing the aspect ratio the aileron

dimensions are maintained at the same per-centages of wing span and chord, the rollrate at a given airspeed and aileron deflec-

tion will decrease. If it is important to main-tain the original roll rate, there are two usefuloptions - the pilot can simply apply more aile-ron in fuming (if he isn't already against thestops) or the designer can make the aileronslonger, percentage-wise, in the firstplace. For large span increases, lengtheningthe ailerons is likely the preferred option.

A first approximation to how much longerto make the ailerons might be - for everypercent the wing span is increased the aile-ron span should be increased about 2% overwhat it was on the lower aspect ratio wing.This value has no readily obvious theoreticaljustification; it simply came out in a computa-tion of the roll rates of several representativewings.

As the angular throw and/or aileron spanare increased, the stick forces will increaseright along, and if they become excessive itmay be desirable that the pilot and designerget together and re-examine the need forduplicating the roll rate of the shorter wing.Or come up with an alternative solution.

In a high aspect ratio wing, maintainingthe same aileron chord and span percen-tages will, of course, cause the ailerons tobe longer, narrower and thinner than in a lowaspect ratio wing. Bringing the long-wing rollrate back to the short-wing rate will, assuggested above, require that the aileron be-come longer still, and this makes attentionto aileron stiffness and balance of particularimportance. It is a matter of record that ailer-ons tend to flutter more often than do wings,and a particularly hazardous and not uncom-mon situation exists where aileron fluttermodes couple with the wing modes, wreak-

STATIC MARGIN = .c3 m.a.c.

STATIC MARGIN = .21 m.a.c..10 m.a.c.

FIG. 4 - Demonstration of how neutral points and static stability marginschange with aspect ratio, eg and spar fixed with reference to fuselage.

SPORT AVIATION 37

ing all kinds of havoc in the process. It wouldbe difficult to exaggerate the importance ofmaintaining very stiff, well-supported andwell balanced ailerons - and all surfaces forthat matter, including tails.

The importance of wing torsional stiffnessto roll rate can be seen in historical perspec-tive. At 400 mph the British Spitfire fighter isreported to have lost some 65% of itsmaximum design roll rate due primarily tothe wing twisting under the influence of aile-ron application.

A common term used in situations of thiskind is "aileron reversal speed", which is thespeed at which the wing twists so much asto cancel the aileron effect entirely. Anyfurther increase in speed would cause theaircraft to roll in a direction opposite to thatintended. An unwelcome situation, indeed.

As suggested earlier, high aspect ratiowings tend to be less stiff in torsion than lowaspect ratio wings, unless proper accountingfor this fact is taken in design.

Procedure For Computing theTime History Around the Course

Readers interested in computing thespeed advantage of incorporating high as-pect ratio wings in their own racers can usethe same technique the author employed inpreparing this article. An engineering back-ground is not required, only time, patience -and plenty of paper. The procedure is shownby example in Table 2. The procedure ismuch easier to follow than the appearanceof the table would suggest; there are mostlyrepetitive calculations.

First, measure the maximum speed of theoriginal aircraft in straight and level flight,and from this and the maximum thrust horse-power (THP), compute the drag. The THPwill be the maximum brake horsepower(BMP) times the propeller efficiency, this lat-ter being around 0.85 for a good propeller.The drag of the aircraft in pounds will be 550times the THP, divided by the speed of theaircraft in feet per second.

The objective of this initial exercise is todetermine the aircraft's parasite drag coeffi-cient (CD ), which is simply the differencebetween tfie total drag coefficient (CD) andthe drag coefficient induced by lift (CD). Al-though the total drag coefficient changeswith speed, the parasite drag coefficientdoesn't - at least not much.

At appropriate points in the subsequentanalysis, the CDpw is added back in. If onlythe wing's aspect ratio is changed, the air-craft's CD will remain the same for all ver-sions of {fie aircraft. That's why it is "ex-tracted" from the total drag coefficient in thefirst place - just so it can be added back inlater.

The procedure entails dividing the racecourse into four segments, two 180 degreeturns and two straightaways. The "race" (theanalysis) starts at the beginning of the firstturn, and the aircraft is assumed to be flyingat its maximum level flight speed at thispoint.

From here on, the aircraft's speed is com-puted at one second intervals for the firstlap. Although probably not exactly true in reallife, the aircraft's speed is assumed to havestabilized at the end of the first lap, and theaverage speed over all subsequent laps isassumed to be the same as that of the firstone.

As the pilot hits the starting point, he rollsinto his first turn, holding a constant 1400foot radius throughout. To simplify the proce-dure, the roll is assumed to develop fully,instantaneously (this is not too far from theactual truth!).

In turning, the aircraft develops a cen-trifugal force, and the wing lift generatedthereby is the opposing resultant of the cen-trifugal force and the aircraft's gross weight.

From the lift is computed the lift coefficient(CL) and from this, the induced drag coeffi-cient (CDi). Note again that induced drag hasaspect ratio as one of its determinants. Ad-ding in the C0 gives the total drag coeffi-cient which now, of course, turns out to behigher than before the turn started. Thismeans more drag. Since the drag is nowhigher than the thrust, the airplane slowsdown.

So much for the first second. The speedat the start of second number two will be thespeed at the start of second number one,less the amount the aircraft slowed downduring that first second. And so on, secondby second, until the turn is completed. Thelast column in the table, identified as "a",shows the amount the aircraft slowed down(or speeded up) during the second beingconsidered.

Then the pilot rolls out, again instantane-ously, into the first straightaway. The cen-trifugal force disappears, the induced dragdrops precipitously and there is now morethrust than drag, and so the aircraft speedsup.

The same procedure is used in the straight-away as in the turn, except that the centri-fugal force is no longer involved.

At the end of the first straightaway, thefirst half of the first lap is now analyzed. Theprocedure for the second half is merely arepeat of the first, only with different num-bers. The key to the procedure is that thespeed at the beginning of each second isalways the speed at the beginning of the pre-vious second, minus the speed lost or gainedat the end of that previous second. Thus, theaircraft is seen to slow down, second by sec-ond in the turn and speed up, second bysecond in the straightaway. A really efficientairplane would, at the end of the first lap,have regained most of the speed lost in theturns.

The first "trip" around the course assumesthe original aspect ratio. Subsequent tripscan be analyzed the same way, using differ-ent aspect ratios for comparison. The speedadvantage of higher aspect ratio will becomeclear. It will also become clear that we'reworking with small differences in big num-bers, but perhaps not too small to win therace.

It should be emphasized that all this isbased on drag data taken from an aircraftalready built and flying, where the intent isto determine the effect of substituting theoriginal wing with one of higher aspect ratio.Aircraft still on the drawing board can usethe same procedure but first the drag charac-teristics must be computed where beforethey were derived from measurement of ac-tual speed.

Readers intending to go through the pro-cedure again, for another aspect ratio,should be reminded that the entry into thefirst turn will be at a higher speed than beforebecause 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 atable of V, CL, CD, CD, D and T along thelines shown in Table 2 and assume differentspeeds. The maximum speed will be whereD and T (drag and thrust) are equal.

Other Factors Deserving AttentionCertainly not all aspect ratio-related fac-

tors were addressed in the study sum-marized here, first because not all are knownand second because some of the more obvi-ous ones are hard to assign numbers to. Oneof the latter is the effect of the fuselage on(or in ) the wing. Another is the effect of thepropeller slipstream. The fact that the influ-ences of both interact doesn't help in tryingto quantify the overall effect.

The high turbulence of the fuselage/pro-peller combination will involve less of thewing if the wing is long and narrow ratherthan short and wide, thus causing less dragdue to flow separation off the wing and wing/fuselage juncture interference effects.

A third non-quantifiable effect of high as-pect ratio relates to pilot visibility forward anddown; narrow wings simply block out lessvisibility in this critical direction than do wideones. The IF1 rules require that vision beprovided at no less than 25 degrees belowthe horizontal over the wing leading edge.

What About the Bipesand the Big Iron?

Although this article is about Formula Oneracers, the principles outlined should beequally applicable to closed-course racers ofany kind, including the little biplanes and thehuge Unlimiteds. In fact, the biplanes mightbenefit more from increased aspect ratiothan the single-wingers because their aspectratios tend to be less. Note that the aspectratio of a biplane equates approximately tothe square of the span of the longer wing,divided by the area of both wings. The ef-fects 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 un-dertaking have to be seen to be appreciated.

AcknowledgementsThe author wishes to thank Lockheed aero-

nautical engineer Jim McVernon and BillRogers, engineer, SecretaryrTreasurer andTechnical Inspector of the International For-mula One racing organization for lookingover his shoulder and providing valuablecontributions during the preparation of thisarticle. Readers interested in pursuing theFormula One challenge further can contactBill Rogers at 926 Rawhide Place, NewburyPark, CA 91320.

References1. Hall, Stan, Testing of Structurally-Scaled,Sacrificial Models As An Aid To Full-ScaleDesign." SPORT AVIATION, August 1987.2. Hall, Stan, "How To Move the CG? - Trythe Quick Reference Chart." SPORT AVIA-TION, May 1986.3. Perkins and Hage, "Airplane Perfor-mance, Stability and Control." John Wileyand Sons, New York.4. Pazmany, L, "Light Airplane Design."Published by the author. P. O. Box 10051,San Diego, CA 92138.

38 SEPTEMBER 1988