;/'11' Inverse Pressure

Gradient Matching... and other ideas for designing fast,

low wing airplanes that climb and turn like madBY MIKE ARNOLD

In 1993, shortly after I set theClaO record in the AR-5, myfriends and I made a video tape

("Why it goes so fast"1) in which,among a lot of other things, I ex-plained my reasons for configuringthe wing/body interface as I had. Twent on for 20 minutes about cluesI'd discovered in Hoerner2 that ledme to make the sides of the fuselageparallel, from the thickest part of theairfoil, all the way back to where thetrailing edge of the wings intersectthe body. Bruce CarmichaeP and I

spoke about the importance of thisfuselage shape, and of the expandingradius wing root fairings, in reduc-ing the rapid deceleration of flowover the after part of the wing, at theroot. This deceleration leads to dragand separation, especially at high an-gles of attack. 1 also noted (afterBruce's visit) that I had sized andplaced the canopy in such a way thatit filled out the fuselage cross sectionfrom a point directly over the thick-est part of the wing, all the way backto a point directly over the trailing

edge, where the canopy peaks. I saidthat I thought all this attention to thewing/body intersection, and the posi-tion of the canopy relative to it, paidoff in an improved rate of climb andsmaller turning radius (I wanted adogfighter), and lower drag at topspeed. The AR-5 climbs well, consid-ering its horsepower; it turns insideall the airplanes I've flown it against,and it holds a world speed record4.So, I thought I was really on to some-thing. But, I'm not an engineer.What do I know?

INTERFERENCE, THENEGLECTED DRAG?

Bruce didn't really have a comment onthe importance of incorporating the canopy

/ in the overall wing/body design. He wasenthusiastic about the parallel fuselagesides and the expanding-radius wing-rootfairings3a, but 1 think he felt the canopywas too far away from the wing to havemuch effect on the intersection ("I thinkpressure drops as the square of the distancefrom its source." — Bruce Carmichael). Sodid most of the other eight designers 1called. In fact, the general consensus wasthat 1 was making too big a deal of interfer-ence drag itself, it being such a smallpercentage of the overall drag of the air-plane. But, I'd seen color renderings ofpressure distributions over airliners and,even at cruise speeds, I could see that thelow pressure fields over the top of the wingwent right up the fuselage sides and met atthe top. Something was definitely goingon up there where I wanted to put a canopy,and I couldn't just ignore it.

Airfoil designer and self-proclaimedirascible curmudgeon Harry Riblett5

thought the canopy stuff was a good ideathough, and Irv Culver6 did, too. I framedmy case for Irv in more depth than I had for

the others. I talked more about pressure gra-dients with him, which I hadn't done in thearticle I wrote for Sport Aviation1 and hadonly touched on in the video. I'd had thegood fortune to work with Irv briefly on an-other project, and I knew he had a specialinterest in interference drag since before hisdays with Kelly Johnson at the SkunkWorks, so his support was very comforting.But 1 was kind of hoping that everyone elsewould see the logic in what I was doing,too, and they'd all come right out and saywhat a great idea it was, and we'd all be de-signing airplanes that looked vaguely likethe AR-5, happily ever after (and I'd be fa-mous, and people would bring me sacks ofmoney, and so on). But it wasn't happening.Three years had gone by and no one wassaying anything about it. The videos weresent out and people wrote rave reviewsabout them, but they rarely mentioned theinterference drag stuff. No one else eitherchallenged or confirmed the idea thatcanopy position was an important ingredi-ent in the wing/body soup, or even that thewing/body drag question itself was impor-tant. Two known rebels and I thought it wasa good idea, and I was still as broke as ever.

The problem with trying to talk aboutwing/body interference drag is that it's sohard to measure that kind of drag, unless

you have a super powerful computer, or awind tunnel handy, and even then it's nopiece of cake. Most of us will be forced tofall back on a few tried and thought-to-be-true formulas, based on previous estimatesthat seemed to work, to calculate the inter-ference at the wing root of our designs.Hoerner suggests simply calling the drag ofthe wing surface covered by the fuselageequal to the wing root interference drag, butmany folks just guess about this one. Mostof the designers I talked to said that interfer-ence drag is generally thought to be(guesstimated to be) 4% to 6% of the totaldrag of an average airplane, so we're onlytalking about a couple of miles an hour any-way, so why waste your time? But here'swhat 1 saw in Hoerner that makes me thinkit's important to keep interference drag aslow as possible on an already clean design.

THE SUPERMESSERSCHMITT

Hoerner did a lot of wind tunnel work inGermany during the war, and in Fluid Dy-namic Drag he presents some fascinatingdrag breakdowns of the Me 109, both fromcalculations, and from experimental datafrom the tunnel. Each nut and bump and an-tenna is examined and its drag area andcoefficient calculated. It's been very useful

SPORT AVIATION 61

AR-6 Formula 1 design, showing engine cowl fairing in to fuselage sides over point ofmax. thickness on wing. Fuselage sides are then parallel back to trailing edge.

AR-6 showing sort-of-round cowl, and wing root leading edge fairings needed in thehigh pressure area created by back of cowl.

AR-6 showing high pressure area on horizontal stabilizer (aft half of airfoil) meeting lowpressure area on vertical stabilizer (around point of maximum thickness on vert. stab.).62 MAY 1997

for me to see exactly what contributes drag,how much drag, and why. Great stuff. Atthe end of the chapter he mentions that thespeed of the 109 would jump from 378mph to 396 mph if the same airplane, withthe same shape and airfoils, could be madecompletely smooth . . . no antennas or gunports or rivets or gaps . . . absolutelysmooth. He dropped it there, but it mademe think about what that means in terms ofthe AR-5 and interference drag. The AR-5is essentially that cleaned up Me 109. It hasno antennas or gun ports or rivets or gaps... it's just what Hoerncr wanted. It does allthat is necessary to cut the drag in half, justlike what happens on his imaginary, SuperMe 109. So what happens to the interfer-ence drag on these two airplanes when youcut the drag in half? There's been no changein the shape, so the drag of the intersectionwill remain the same, but its percentage ofthe total drag of the new, cleaned up air-plane will have doubled! Hoerner estimatedthat interference drag on the dirty Me 109was 4.3% of the total drag of the airplane,so that means it goes up to 8.6% of the totaldrag on the Super Me 109 (roughly). Now,that's getting to be significant!

To add to that, here are some thoughtsfrom Irv Culver who reminds us that inter-ference drag can be very low if you get itright (or, even, negative; that is, the wingand fuselage together can actually havelower drag than the sum of the wing andfuselage measured separately). Or, it canbe very high if you get it wrong (and bothairplanes will look fine, unless you knowwhat to look for). If it's wrong, you couldeasily double the drag (2 x 8.6% = 17.2%).But, if it's a good intersection, you couldtheoretically reduce interference drag tozero (or less). In our Super Messerschmitt,that would be the difference between nointerference drag, and an additional dragequal to around 17.2% of the total drag,being generated at the wing root and addedto the total drag of the airplane!

And all of this is happening in levelflight. We haven't even begun to apply theback pressure on the stick that starts multi-plying that 17.2% in some terrible,sickening way, until the airplane bogsdown in its own over-expanded wake.When I designed the AR-5,1 didn't fullyappreciate how much this drag really didincrease at higher angles of attack. I could-n't find anything definitive on it in mybooks, and none of the other designersseemed to know much about it. But, Irvtells a story about one designer's attemptto get his new ship off the ground, whichhe was unable to do until Irv came along

HIGH PRESSURE LOW PRESSURE

AR-6 Formula 1 racer design, showing wing/canopy relationship.

and made a new wing root fairing for it (anexpanding radius one). The designer laterbecame famous, but the interference dragcaused by the lovely P-40 style, round-bot-tomed, tapered fuselage on this particulardesign was so great it had grounded the air-plane. I didn't know exactly how muchdrag that was, but it sounded like some-thing to pay attention to, if you ask me.

"INTERFERENCE DRAG GOESUP APPROXIMATELY AS THE

SQUARE OF THE CL"9

Whamo! I've been reading Hoerner nowfor about 15 years. I do it for fun. Some-times I'm just looking up something out ofidle curiosity, trying to get some minor littlething clear in my mind, when somethingcomes right out and smacks me. I love FluidDynamic Drag for that. In it, a few yearsback I came across this line about how in-terference drag goes up with increases inlift. I had just finished reading an article byStan Hall in Sport Aviation^ about the im-portance of high aspect ratio wings onFormula 1 airplanes. He had pointed outthat, because a pylon racer spends so muchof its time turning, it had better have lowdrag in the turns as well as on the straights,and that the way to do that was to reduce theInduced Drag (the drag induced by lifting)by using higher aspect ratio wings. He con-cluded that an 8:1 aspect ratio wing wasprobably a good compromise betweenstrength, weight, and induced drag reduc-

tion. He showed how important induceddrag was when you pull the stick back in a 3G turn. That little 2% to 4% of the total dragof the racer that was the induced drag inlevel flight, suddenly becomes 9 timesgreater in the turn! It can add a third or moreto the total drag of the airplane! That's likethrowing out speed brakes in every turn! In-duced drag goes up as the square of the liftcoefficient (CL) goes up. That's a terrifyingrate of increase, but it's in all the books. It'san easy thing to calculate. Nobody ques-tions it. It's why sailplanes that operate atslow speeds (and high lift coefficients) havelong, skinny wings.

So here I am reading Hoerner one night,poking around for crumbs in the Interfer-ence Drag Chapter, when I see this ratioagain, "Interference Drag goes up approxi-mately as the square of the CL." Only thistime it's interference drag that's going upArnold AR-5, Mitsu-bishi Zero, and Super-marine Spitfire, show-ing expanding radiuswing root fairings.Rounding the trailingedge of the fairingas it blends into thefuselage (as on AR-5and Zero) helps pre-vent early stall (andalso allows a shorterfairing).

at that dizzy rate, not induced drag. Amaz-ing! I hadn't seen that anywhere elsebefore. It was Hoerner all the time!

If this is correct, or even close to it (notall engineers take Hoerner as gospel), itmeans that not only does induced drag (thedrag you make the wings skinny to com-pensate for) go up 9 times in a 3 G rum —now, he's telling me that wing root inter-ference drag goes up the same dreadfulamount! Worse even than I imagined!And, of course, everything that's true in ahigh G turn is true in a climb too because,after all, when you pull a 3 G turn, you'rejust climbing around in a circle. That'swhy airplanes that need to climb well, andbe able to claw along at high altitudes (andhigh lift coefficients), like the U-2, needlong skinny wings, too. When the lift coef-ficient goes up a little, the induced draggoes up a whole lot. And the wing rootdrag does the same thing!

So, now I'm really asking myself, whydo we go to all the trouble and expense ofbuilding our wings as long and as skinny asthey can get (before we start running intoweight and structural problems), to combata relatively small drag (induced drag is es-timated to be around 3% of the total dragof the AR-5, at top speed), and not pay thesame amount of attention to interferencedrag (as previously mentioned, thought tobe about 4%-6% on most modern, lowwing airplanes, at high speeds), which is

SPORT AVIATION 63

AR-5, climbing, showing "inverse pressure gradient matching" asI think it should be (gradients canceling each other).

AR-5, with canopy moved forward just one foot, showing pres-sure gradients lined up (adding to each other. Boo!).

larger, and which goes up the same way in-duced drag does, at the same time (that is,at higher Cls, as when taking off, climbing,turning or flying at high altitudes)? Seemsto me that low drag wing roots are everybit as important as long, skinny wings.

SEARCHING FORREASSURANCE

When I designed the AR-5,1 lookedfor any other examples of airplanes that ap-peared to be designed around the wing rootas the AR-5 is. 1 found that the very suc-cessful Kawasaki Ki 100, Japanese Armyfighter, had straight fuselage sides from thethickest point on the wing to the trailingedge, and that the radial engine was fairedinto the fuselage sides before the thickestpart of the wing, as I had come to believe itshould be. But the airplane was a modifica-tion of the Ki 61 "Tony", an inline enginedfighter, so of course the fuselage sides werealready narrow and straight. It doesn't ap-pear to have been done on purpose. It justworked out that way. The airplane had avery good rate of climb though. And, eventhough the bulky radial engine increasedthe frontal area and wasn't nearly asstreamlined as the inline engine, the speed64 MAY 1997

remained about the same. Interesting, butit's hard to draw any conclusions from it.

Although it doesn't show in most draw-ings, the F8F Bearcat's otherwisecompound curved fuselage is flattenednoticeably on its sides, over the wing,from the leading edge, all the way back tothe trailing edge. This was obviously doneon purpose. Grumman went to some trou-ble to do it. But the canopy isn't placedexactly where I think it should be and, aswas customary on mid-wing designs backthen, it doesn't have any wing root fair-ings, at all. (Hoerner's data13 indicatesthat, even a constant radius fillet, all theway around the wing root reduces drag ona flat tunnel wall. He recommends a ra-dius of around 6% of the wing chord atthe root.) They paid some obvious atten-tion to interference drag at Grumman.Somebody knew something.

The F4U Corsair has the canopy innearly the right place, but I didn't findany other low wing airplanes that keptthe fuselage sides parallel. There areabundant examples of expanding radiusfillets, though. I think they're mostly at-tempts to cure the results of contractingthe fuselage too early. Spitfires, P-40s

and Zeros had nice ones.It wasn't until after the AR-5 had flown,

when the Sukhoi 26 and 29 aerobatic air-planes appeared, that I found anothersimilarly designed, low wing airplane. Andit wasn't really even a low wing. It's a sortof low/mid-wing configuration. But, never-theless, it's all there: the radial enginecowl, wider than the fuselage, fairs into thefuselage sides and completely by the timeit is directly above the thick part of thewing, and the fuselage sides remain paral-lel from that point back to the trailing edge,just like the AR-5. The beautiful, blowncanopy starts at the same point, over thethickest part of the wing, and it peaks overthe wing's trailing edge, on the single seatSu26. The Su29, a two-place airplane,shows that even two and four seat airplanescan have this kind of wing body configura-tion, although the canopy peaks a little toofar forward on this airplane. Both airplaneshave expanding radius fairings, like mine.Someone over there in Russia must havethought interference drag was pretty im-portant. But I really have no idea if theydid all this for the same reasons I did, orwhether it just worked out that the pilot'shead was directly over the wing's trailing

edge, so that's where they put the canopy.And, maybe it was just easier to keep thefuselage sides parallel. But the airplane isknown for its exceptional rate of climb andunusually good vertical performance(where you have to pull up really hard andhope you don't scrub off too much speedin the high G pull up). Could they havedone some tunnel testing over there anddiscovered the perfect placement for thecanopy to reduce interference drag? And itturns out to be right where I thought itshould be all along? And the people withbags of money are going over there, now?

Anyway, I was just working on a stronghunch when I first laid the AR-5 out. Thewing aspect ratio is 8:1, which brings thespan loading down to 31-1/2 Ibs. per foot,so I knew the induced drag would be low.That's the one that's easy to calculate.And, as I've been saying, I believed thewing root interference drag would be verylow, too. I just didn't know how importantit was. I have no way of finding out, forsure, that it actually has very low interfer-ence drag, but Peter Lert was surprised athow hard he had to pull in a vertical bankto get the airspeed to start bleeding off1'.And the airplane does climb at 1100 fpmon what I figure to be not more than 50 hp(at 5600 rpm). And it also turns out to haveastonishingly low drag numbers for asmall, fixed gear airplane: CD wing area =.016, CD wet = .0037, total Drag Area =.88 sq. ft. Aerodynamicists say these areamong the lowest numbers they've everseen for a propeller driven airplane, retractgear or not.12

THE AR-6: AN AIRPLANETHAT NEVER WAS

When I sat down to design the AR-6in 1993,1 was as convinced as ever thatit should be designed around the wingroot, as the AR-5 was. Everything pos-sible had to be done to reduceinterference drag, as well as induceddrag, on the AR-6, because it was to bea Formula One air racer and, as StanHall pointed out, it would spend a lot ofits time pull ing fairly high G loads inturns. If the interference drag werehigh, it would not only be slower on thestraightaways, but it would bog downas the drag built up in the turns. I'd de-signed the AR-5 back in 1981, and Iintended to use everything I'd learnedsince, on the AR-6. It was to be my "in-terference drag tour de force." I startedby reviewing what I knew.

Hoerner says that most of the dragwe're worrying about (the kind that goes

rrrSukhoi 29 (Su 26 canopy in dashed lines), showingengine cowl fairing in to fuselage sides over point ofmaximum thickness on wing, fuselage sides parallelback to wing trailing edge, and expanding radius wingroot fairings.

26 canopy in correct position. Su 29 canopy isa little too far forward, but still pretty good.

up at that dizzying rate as the lift coeffi-cient goes up) is generated over the aftsection of the top of the wing, where itjoins the side of the fuselage. It's easy tosee that the steep, positive pressure gradi-ent (decelerating air, increasing inpressure) that already exists over that por-tion of the wing's airfoil, is made evensteeper by the presence of the fuselage. Ican see two ways, right off:

1. Even if the fuselage sides are straightand parallel (like the tunnel walls Ho-erner13 uses as an example), skin frictionwill slow the air as it flows along the side,adding to the deceleration over the wing,and steepening the drag-producing positivepressure gradient.

2. If the fuselage sides start coming to-gether before they've reached the trailingedges of the wing (as they do on almost allthe low wing designs I've looked at), thereduction in fuselage cross sectional areaover the aft portion of the wing will furtherslow the flow, again steepening thedreaded positive pressure gradient. This iswhy that other airplane wouldn't get offthe ground until Irv used an expanding ra-dius fairing to fill in the space left by thecontracting fuselage. Without the fairings,when the nose was brought up to developmaximum lift for takeoff the already-highinterference drag skyrocketed.

My solution to these two problems —just to get things back to where they werebefore the fuselage was added to the wing— is to keep the fuselage sides parallelfrom the thickest part of the wing, back tothe trailing edge; and to make up for thedeceleration caused by skin friction along

the sides, to add the expanding radius fair-ings. That might get the positive pressuregradient on the aft portion of the wing backdown to normal, providing there is nothingelse around adding to it. But Irv's tantaliz-ing suggestion that interference drag canbe made negative ("You can make thewing think it's skinnier at the root") mademe look for more.

I drew an approximate curve over a sideview of the old AR-5 that plotted what Ithought was the pressure distribution overthe top of the fuselage. I "eyeballed" it bylooking at other similarly-shaped airplane'spressure distributions, and by rememberingthat pressure is low on outside curves, highon inside curves and, finally, that it rises onthe aft portions of streamlined bodies wherethey contract. Then I drew the pressure dis-tribution of the wing at its root as I thoughtit would look in a climb.

When I put the canopy and wing pressuredistributions together, I looked to see howthey lined up and, behold!... the high pres-sure area at the front of the canopy is directlyover the low pressure area on top of the wing,and the low pressure area over the top of thecanopy is directly over that bad old highpressure gradient over the aft section of thewing. They work to cancel each other outwhen they're lined up like this — to reducethe steep angle of the positive pressure gradi-ent on the aft section of the wing.

But, notice what moving the canopyforward or back even a little from this po-sition does. Instead of canceling, thepressure fields add to each other wherethey overlap on the fuselage side, steepen-ing the positive pressure gradient over the

SPORT AVIATION 65

. Kawasaki Ki 100, showing engine cowl fairing in tofuselage sides over point of maximum thickness onwing. Fuselage sides parallel back to trailing edge.

Nice expanding radius wing root fairings.

trailing edge. I think getting this alignmentright helps explain why the exhaust streakthat forms on the AR-5's fuselage side isso straight when compared with exhauststreaks I see on other low wing airplanes.The others all take a dive over the aft por-tion of the wing, but on the AR-5, thesooty flow stays up high and runs smackinto the horizontal tail (I didn't expect

that). I believe matching the pressure gra-dients inversely by putting the canopy inthe right place (and not contracting thefuselage too early) prevents drag produc-ing separation, reduces cross flow on thefuselage, as well as drag caused by need-less expansion and contraction of the flow(pressure drag). But, I'm still just guessing.

The AR-6 has that big wide Continental

TlArnold AR-5, showing parallel fuselage sides overwing, back to trailing edge.

" mExpanding radius wing root fairings.

, i i ( i r ; -

Canopy in correct position over wing.

UJ ,,„:„

O-200 in it. While keeping the cowl assmall as possible, I also tried to make it asfull and round as I could to minimize thevariations in velocity near the propeller,and to avoid the drag caused by the inter-sections of "blister" cowls. I used its fullshape to create another high pressure areaover the front part of the wing (over thewing's low pressure area) by fairing it intothe fuselage sides over the airfoil's point ofmaximum thickness (inside curve = highpressure). The big cowl also allowed theuse of a tuned exhaust system under theengine. To avoid problems caused by thehigh pressure peak at the stagnation pointof the wing's leading edge colliding withthe high pressure caused by the contractingcowl, I kept the sides of the cowl straightand parallel at the bottom and made a littleleading edge fairing out of it to soften theimpact at the wing root. Bruce points outthat it's important to keep the bottom cor-ners of the fuselage rounded near theleading edge to avoid tripping the flow ofhigh pressure air that comes from underthe fuselage when the nose comes up. Irvcautions that there isn't as much to gainplaying with the area forward of the pointof peak velocity (over the thick point onthe wing) because things kind of take careof themselves up there. The air makes itsown fairing, so to speak. But, I think ifthere's a bump that has to be somewherearound there anyway, like a cowl or acanopy, why not put it where it'll help,rather than hurt?

The canopy, of course, is shaped andpositioned to provide high pressure overthe low pressure area of the wing, and lowpressure over the positive pressure gradientthat peaks at the wing's trailing edge.

You'll notice that the tail surfaces on theAR-6 are rather large for a Formula One airracer. I found that the pitched and yaw sta-bility margins of the AR-5, even though Iused large tail surfaces and the tail arm wasa normal length were less than I thoughtthey would be. I knew that the long nosewas going to be destabilizing, but there'smore. Hoerner explains that expanding ra-dius fillets at the wing roots are destabilizingin that they move the aerodynamic center ofthe wing back at the root14.1 would expectthat this is also true for the rest of the stuffwe've done at the wing root. Nothing'sfree! If you're going to use inverse pressuregradient matching on your design, be pre-pared to use somewhat larger tail powercoefficients (I'm guessing, maybe 5%higher) than you would ordinarily. I thinkthis is a more-than-fair trade though, con-sidering that tail drag doesn't go up the way

66 MAY 1997

interference drag and induced drag do (withincreases in lift).

Although interference drag isn't as highon tail sections because these intersectionsare operating in the much slower movingair of the fuselage's thick boundary layer, Isaw an opportunity to use some more "in-verse pressure gradient matching" (I'veasked others what I should call this thing. . . this seems to describe it as well as any-thing) here too, by placing the highpressure area of the horizontal stabilizer inthe low pressure area of the vertical stabi-lizer. Can't hurt. And I tried to position thewheel pants so their point of maximumthickness was directly below that highpressure peak that forms at the leadingedge of the wing, just as I did on the AR-5.Harry Riblett thinks this is a good idea,too. He's the only one who's noticed it.We think using inverse pressure gradientmatching here softens the impact of thewing's leading edge (or it could just reducethe drag of the wheel pants — either wayis O.K. with me).

I was inspired to design the AR-6 byFormula One pilot, Troy Charming, whomI'd met at Oshkosh in 1993.1 was juststarting detail design when Troy was killedin a Mustang II near Livermore, CA and Inever got enthused enough again to finishit. But, I refer back to the model to remindmyself what inverse pressure gradientmatching looks like, if taken seriously. Ioffer it here for the same purpose.

IT SOUNDS LIKEAREA RULE

In my January 1993 article in SportAviation (Getting the Most Out of 65 HP) Isaid that I had arranged the wing, canopy,fuselage and wheel pants so they formed asort of "poor man's area rule." I had readsomewhere that John Thorp had said thatabout his T-18 design.

Aerodynamicists quickly pointed outthat "Area Rule," strictly speaking, wasonly valid for the transonic speed range,and that it was misleading to say that I hadapplied it to reduce drag in the subsonicregime. Area rule says that airplanes de-signed for transonic or supersonic flightshould have their total cross sectional ar-eas expand and contract smoothly alongtheir lengths in order to delay and reducethe dramatic drag rise that occurs just asthe airplane nears the speed of sound. Iffollowed as a "rule" it would have me sub-tract the total cross sectional area of thewing (for example), from tip to tip fromthe cross sectional area of the fuselage inorder to keep the total cross section of the

Grumman F8F Bearcat, showing parallel fuselagesides over wing, from leading edge to trailing edge. Nowing root fairings. This airplane climbs well, though.

airplane from suddenly increasing in thepresence of the wing. If 1 subtracted thewhole cross sectional area of the 6" thickwing on the AR-5 from its fuselage, 1wouldn't have any fuselage left! This iswhy supersonic airplanes have such thinwings (and coke-bottle shaped fuselages).

But, I didn't have to compensate for thewhole wing on the AR-5, because in sub-sonic flight things work differently. Belowtransonic speeds (under, say, 350 mph),the fuselage doesn't feel the presence ofthe wing out toward the tips because pres-sure, at that speed, dissipates rapidly in alldirections as it moves away from itssource; unlike what happens in the flat,compressed, disc-like form pressure as-sumes at transonic speeds. At slowerspeeds I only have to consider that portionof the wing that is in the near vicinity ofthe fuselage. It's not altogether different,but different enough.

So, discouraged from referring to it as"area rule" any longer, 1 now call it "in-verse pressure gradient matching," andeverybody's happy. It more closely de-scribes what I'm doing anyway.

REFERENCES

1. Why it goes so fast." Jan. 1993, TheArnold Company, 5960 So Land Park Dr.,#361, Sacramento, CA 95822.

2. Hoerner, Sighard F., "Fluid DynamicDrag," 1965, Hoerner Fluid Dynamics,P.O. Box 65283, Vancouver, WA 98665.

3. Carmichael, Bruce, noted aerody-namicist specializing in laminar flow,

34795 Camino Capistrano, CapistranoBeach, CA 92624.

3a. Carmichael, Bruce. "BruceCarmichaeFs Personal Aircraft Drag Re-duction," Fall 1995. (Self published —seeaddress above) page 152. This wonderfullyinformative book is the only one I've everseen that spells out the advantage of paral-lel fuselage sides. It's about time!

4. On August 30,1992, the AR-5 set a 3km straight line speed record of 213.18mph in F.A.I. Class ClaO, near Davis, CA.

5. Riblett, Harry C., author and pub-lisher of "G A Airfoils," June 1990, 416Riblett Lane, Wilmington, DE 19808.

6. Culver, Irv H., noted aerodynamicistspecializing in interference drag, propellersand lots of other stuff, 225 Redlands St.,Playa Del Rey CA 90293.

7. Arnold, Mike S., "The AR-5 — Get-ting the Most Out of 65 HP," SportAviation, Jan. 1993, pg. 35.

8. "Fluid Dynamic Drag," pg. 14-79. Ditto, pg. 8-1110. Hall, Stan., "High Aspect Ratio

Wings for Formula One Racers," SportAviation, Sept. 1988, pg. 33

11. Lert, Peter, "Crockett Rockett"(AR-5 pilot report), Air Progress Maga-zine, July 1995, pg. 38

12. Carmichael, Bruce, "Drag Analysisof the Arnold AR-5 Airplane," CON-TACT Magazine, Jan-Feb. 1994,pg. 15

13. "Fluid Dynamic Drag," pgs. 8-10and 8-12

14. "Fluid Dynamic Lift" (Hoerner),pg. 11-19 *

SPORT AVIATION 67