PART I

Drag Analysis Of 1 IkyhopperBy J. V. Walsh, EAA 2351

INTRODUCTIONThe membership of the EAA is made up of amateurs

with a sprinkling of trained aeronautical engineers. Thisarticle is written by a non-professional for the use of non-professionals. For this reason, each step is detailed, sothat no doubt of the method used may exist.

The professional manufacturer can improve the per-formance of his design by increasing engine power, theuse of a constant-speed propeller, etc. The homebuilderis limited in the performance of his aircraft by weightand finances. Relatively few engines are priced withinthe range of his pocketbook. He differs from the pro-fessional in that he works with a minimum of skills, aminimum of means, and a minimum budget. The per-formance of his aircraft is, therefore, governed by thethrust he can afford to purchase and the total drag of theproduct of his labors.

Relatively little has appeared in SPORT AVIATIONin the past five years on drag analysis. This article ispresented in the hope that professional aeronautical en-gineers will criticize it in a constructive manner, andoffer refinements or better methods of analysis.

The net result hoped for is a system of drag analysisthat any homebuilder can apply to any project, in orderto obtain maximum performance from limited sources.

Since we are interested in efficient cruise, thisanalysis was made at the engine manufacturer's recom-mended cruising rpm. If the performance figures seemrather low, it is because they are honest. Many individ-uals have been disappointed when the performance oftheir aircraft fell short of published figures, even thoughtheir workmanship was beyond reproach. In some cases,this discrepancy has been due to the publishing of inac-curate data.

Part of the reason for this inaccuracy lies in faultyinstrumentation. In his article, "How to Improve the Per-formance of Small Biplanes," EAA member Silas Well-man pointed out how the addition of a small ring just

ahead of the static vent can make 115 TAS read as highas 140 IAS. He also pointed out the fallacy of usingwar surplus rate of climb instruments. In this particularaircraft, we discovered that by shortening the pilot tube12 in., the IAS increased 10 mph.

The remainder of the answer lies in what we shallpolitely call "Oriental Hyperbolae." For example, in onedesign formerly advertised in SPORT AVIATION, how doyou make a 170 Ib. pilot, a parachute, 28 gals, of gas, 6qts. of oil, and 40 Ibs. of baggage come out to a totalof 300 Ib. payload? To cite another case, how do youland a ship at 70 mph IAS, when pilots who have flownit say it falls out of the air at 85-90 IAS? That such dis-crepancies should escape the notice of the amateur isunderstandable. That those who quote such inconsisten-cies for their designs should fail to appreciate the dis-service they are doing to EAA is difficult to understand.

In this analysis, you will note that in many casesfigures are worked out to three decimal points. Honestyand accuracy are essential for a successful analysis. Thisis particularly true of airspeed. True airspeed is essen-tial; indicated airspeed will only compound error.

Principal Dimensions and DataTotal Wing Area SWing Span bAspect Ratio AOverall Length LGross Weight WCruise Speed VPower BMPProp Efficiency PeAltitude

100 sq. ft.25 ft.

6.25 ft.18 ft.

1,230 Ibs.161.37 (110 mph)

92.5%86%

3,000 ft.

SourcesReference 1: Fluid Dynamic Drag—S. F. Hoerner, 1958

Edition

The Salvay "Skyhopper," CF-RDG, is thesubject of this article on drag analysis.

The installation of this Beech-Roby propeller has highdrag and should include a spinner. However, it is verydifficult to mount the backing plates for a spinner. Thecowl openings are much too large, increasing coolingdrag greatly.

14 JULY 1964

Reference 2: Aircraft Mechanics Pocket Manual, 5th Edi-tion

Reference 3: Homebuilders Handbook—S. Urshan, 1955

Formula:The formula for drag is Cd x S x q. "Cd" is the par-

ticular coefficient of drag; "S" is the particular drag areain square feet; "q" is the dynamic pressure corrected foraltitude. Dynamic pressure at 3,000 ft. is only 92 percentof sea level pressure, i.e., .92 x .00238 = .00219 — QUES-TION: Should the dynamic pressure be corrected for tem-perature also, and if so, how?

"q" equals one-half the dynamic pressure times thevelocity in feet squared. For the test specified, "q" equals(110 x 1.467)2 times J/i(.00219) = (161.37)2 x .0011 =28.64

SECTION ONECalculation of Thrust

In the first test, a metal prop 70 in. in diameter witha 56 in. pitch was used. Applying the method described

Another source ofinterference dragis this little blis-ter to cover thelanding gear leg.

in "Amateur Builder's Manual," (Vol. 2, page 30), theeffective pitch was determined to be 88 percent. RPMused was 2350. The Lycoming Corp. power curve for the0-235-C engine (No. 8210) indicates this to be 90 hp.

The total thrust at 110 mph, (TAS) using the formulapresented in Ref. 2, is—

90 x .88 x 375

110A Beech-Roby variable pitch propeller was installed,

after a bit of engineering and a great deal of 17th cen-tury English to make it fit a Lycoming engine. At thesame altitude, 110 mph was obtained with 2400 rpm.Using the same power graph, this worked out to 92.5brake hp.

Since the speed was the same, thrust (and drag) werethe same. Therefore, the "Pe" of the Beech-Roby was—

90 x .88 x 375 92.5 x Pe x 375————————— equals —————————

110 110The Beech-Reby at 2400 rpm was .856 or 86 percent

efficient. While it did not improve the cruise, it did make

Such protuberances as tie-down rings, aileron controlfairings and inspection plates, while contributing to drag,are located where the drag is lower.

The "coke-bottle" tuselage effect on this "Skyhopper" iscaused by the '"Super Cub" cowl which is too wide andhas high drag.

an appreciable difference in take-off time and distance,as well as rate of climb. The installation remained, andall future calculations were made with it.

Incidentally, if anyone can tell me how to fit a spin-ner on a Beech-Roby—Lycoming installation, I will bemost grateful. This installation was once FAA approved,but Univair, who made the modifications to the prop,were unable to supply drawings on how it was done.

SECTION TWOInduced Drag

We have seen that the thrust of the airplane (at alti-tude, power setting and speed specified) was

92.5 x .86 x 375

110which equals 271.2 Ibs. In steady horizontal flight, thetotal drag is equal to the thrust. Therefore, the totaldrag under the conditions specified is 271.2 Ibs.

For any flight condition, lift coefficient equals W/S.

When computing W/S, don't forget to add the down-loadon the tail for the given flight condition, for the wingmust also Hit this load. In my case, W/S worked out to12.5 Ibs. per sq. ft.

For the given flight condition, Cl equalsW/S 12.5

= .4428.5

(Continued on next page)

This type of traf-fic - tread p a i n tused for a wing-walk has a veryhigh interferencedrag.

SPORT AVIATION 15

DRAG ANALYSIS . . .(Continued from page 15)

Because of tip shape, the effective aspect ratio isreduced from the geometric 6.25 by an estimated minus.13 to 6.12.

The wing planform has a taper of 2 to 1. This in-creases the induced drag by an estimated 2 percent. Thewing twist of 3 deg. increases it by another estimated 2percent. The coefficient of induced drag bears the follow-ing relationship to the coefficient of lift and aspect ratio:

Cdi equals C12AA—this now becomesCdi equals 1.04 (CPAA)

Dihedral also has a bearing on induced drag, sinceit lessens the span and therefore the aspect ratio. For the3 deg. of dihedral in this ship, the results are so smallthey can be ignored. However, if your project has a pro-nounced dihedral in relation to span, such as found in agull-wing, you might be well advised to investigate thispoint.

Cd in-iuced = l.C4(C12AA)= 1.04C.442/3.1416 x 6.12)= .011

Induced drag equals Cdi x S x Q — equals .011 x100 x 28.64. For the speed, weight and altitude specified,the induced drag of the aircraft is 31.5 Ibs.Conclusions:

The basic formula for induced drag coefficient isC12/«rA. The larger we make "A," the greater the denomi-nator of the fraction becomes, and the smaller the re-sultant drag coefficient.

The wing control gaps are anoth-er factor adding to parasite drag.

"A" is determined by b2/S. Therefore, to lessen in-duced drag, increase the span—never the wing area. Re-member, though, you can only go so far with this. Asyou increase span, you also increase weight, which willraise your Cl and nullify your efforts. Take some paperand work on it. Somewhere along the line, you will hit aratio of CP/irA that will give you the smallest Cdifor your design.

SECTION THREEParasite Drag of the Wing

1. Basic Skin FrictionFrom Ref. 1, p. 2-5, the following formula is extracted

as adequate to approximate the friction-drag-coefficientof a smooth and plane surface within the Reynolds Num-ber range associated with aircraft, i.e., between RN 106

and RN 10?Cd friction = K/(RN)'/6

where "K" is considered a constant of .036, and RN is theReynolds Number of the surface under consideration.

This frontal view of the "Skyhopper" easilypoints up the high-drag items on the airplane.

Reynolds Number at sea level may be computed byRN = V x c x 6380

with "V" as velocity in feet per second and "c" as thechord in feet. However, since density of air and tempera-ture decrease, with altitude, the RN for constant speedalso decreases with altitude. At 3,000 ft., RN wouldbe V x c x .92(6380), i.e., 92 percent of RN at sea level.This means RN becomes smaller as we ascend higher,and Cdf becomes larger. Now you know why manufac-turers engaged in the cut-throat game of selling airplanesalways quote performance figures at sea level, and oneof the main reasons why the performance of your air-craft decreases with altitude.

The aircraft in question has a mean geometric chordof four feet. RN of the wing at sea level would be4,118,290. But RN at sea level is of no value to us, un-less we want to use the wing as a surf-board. RN at flightlevel 3,000 ft. is what we need — and that is

V x c x .92(6380) = 3,788,826.The Cd friction is, therefore,

Cdf = .036 - .036/12.48 = .0029(3,788,826)'/6

Now, you can't have a smooth and plane surface,such as a wing, without having two sides — top and bot-tom. Therefore, Cd section equals 2Cdf.

If our smooth and plane surface were such a thinsection, its thickness would be negligible, we could leavethe formula "like that and Cds/2Cdf would equal one.But we have a section that is 15 percent thick at theroot and 12 percent thick at the tip—and average thick-ness of .15 plus .12 equals .135 — this will add to the

profile drag.Our formula for the wing now becomes (Ref. 1,

p. 6-6)Cds equals 1 plus 2(T/C) plus 100(T/C)<

2CdfIf the wing surfaces were identically smooth on

both sides, friction drag would be the same on both sides,and the above formula would be adequate to give us ourparasite drag. But such is never the case in actual con-struction. We always roughen the top and bottom sur-faces by adding such things as skin joints, inspectionpanels, rivets, etc. All these increase our friction drag,and since we hardly ever add these things in equalamounts to top and bottom surfaces, the increased fric-

16 JULY 1964

tion-drag-coefficient is never the same for both top andbottom.

Then, too. the dynamic pressure will only remain thesame for top and bottom if we use an elliptical sectionat a constant zero angle of attack. Now, if we so desire,we can do this — but it poses a slight difficulty — thewing will never generate any lift and the airplane willnever get off the ground. To make the wing lift, we mustintroduce angle of attack and/or camber. Actually, we doboth with an airfoil section — increasing the pressure onthe bottom side and decreasing the pressure on the topside. This results in an increase of drag on the top sideand a decrease of drag on the bottom side. Now you cansee why if you must add barnacles, such as inspectionpanels or struts, the best place for them is the bottom ofthe wing — the side where the drag is lower.

Professor Hoerner says this increase due to angle ofattack and camber can be added to our equation by plusor minus CI/5. Our equation for section drag now be-comes

a) upper surface:Cds = 1 + 2OVC + Cl/5) + 100(T/C + Cl/5)"

Cdfb) lower surface:

Cds = 1 + 2(T/C — Cl/5) — 100 T/C — Cl/5)4

Cdf (Ref. 1, p. 6-11)On this aircraft, with T/C = .135, and Cl/5 = .088a) upper surface: Cds equals 1.693

Cdfb) lower surface: Cds equals 1.093

Cdf2. Surface Imperfections

Before we can compute the section drag of the wingby the above formulae, we must compute all the surfaceimperfections for both sides of the wing, in order to de-termine what additions we must make to our basic skinfriction-drag-coefficient of .0029.

The wings of this aircraft contain a number of im-perfections in the form of inspection panels, streamlineblisters, fasteners, etc. — all of which are necessary forservice and maintenance.

In addition, we have traffic tread on each wingwalk. A search of all available sources failed to producea drag-coefficient for such paint. Because of its compo-sition and surface roughness, its drag must be very highand therefore it should not be ignored. Perhaps somereader can supply the coefficient.

In computing "drag area" in square feet, the follow-ing methods were used:

a) inspection panels — spanwise and chordwise edgeswere multiplied by the thickness of the metal.

b) sheet metal blisters — frontal area of width timesheight.

c) screws and bolts — surface area of all sizes wastotaled and an average "Cd" struck for entry in the table.

d) all drag-coefficients were taken from Ref. 1, pp.5-7ff.

For the Top Surface:

ItemSpanwise surface gapsChordwise surface gapsTwo metal blisters14 No. 4 p.k. screws

"Drag Area'Ft.2

.042

.094

.11

.003

Cd.05.04.1.04

Cd"S".002.004.011.0001

Total .0171Referring this to the exposed top surface of 87 sq. ft.

(in drag analysis, consider only that portion of the wing

I

The left wing has a tendency to drop sharply at the stall,and it could be dangerous for an inexperienced pilot.Suspect burbling from the pitot tube tends to aggravatethis condition by speeding up the tip stall.

not covered by the fuselage), our additional skin-friction-coefficient equals .0171/87 = .0002.

Total skin friction Cd for the top surface equals.0029 + .0002 = .0031.For the bottom surface:

ItemSpanwise edgesChordwise edgesTwo metal blistersTie-down rings110 assorted screws12 inspection rings

"Drag Area'Ft.2

.016

.018

.07

.023

.024

Cd.175.01.07

.04

.334

Cd"S".0028.0002.0049.0110.0009.0080

Total .0278Referred to the exposed bottom area of 87 sq. ft., ad-

ditional skin-friction-coefficient is .0278/87 -— .00032, andthe total skin friction Cdf for this side equals .0029 +.00032 = .00322.

3. Section Drag CoefficientReturning to our previous determinations, viz.,

Cds upper surface = 1.693 x total Cdf topCds lower surface = 1.093 x total Cdf bottom

the total section drag Cds of the wing becomesCds = (1.693 x .0031) plus (1.093 x .00322)

= .0087678= .009

On an exposed wing area of 87 sq. ft.:Cd x S = .009 x 87 =, .783

4. Additional Sources of DragThe following sources of drag are common to both

sides of the wing:"Drag Area"

ItemAileron spanwise gapsAileron chordwise gapsNavigation lights

Ft.21.9.04.02

Cd.03.5.1

Pitot static tube

Cd"S".057.020.002.010

Total .089The total Parasite Drag CdS equals .783 plus .089 =

.872At "q" = 28.64, total parasite drag is:

Cd x S x q = .872 x 28.64 = 24.974 = 25 Ibs.Conclusions:

1) The total drag of the wing for speed, weight andaltitude specified is the sum of the induced and parasitedrag, i.e., 31.5 + 25 = 56.5 Ibs. This works out to 20.8percent of the total drag of the airplane.

(Continued on bottom of next page,

SPORT AVIATION 17

Flight-Flutter TestingBy John W. Thorp, EAA 1212

909 E. Magnolia, Burbank, Calif.

THE FLIGHT-FLUTTER test is intended to demon-strate that the subject airplane is free from flutter

behaviors within the specified operating limits of theairplane. This demonstration necessarily requires that theairplane be flown at high speed, which in itself introducescertain hazards. These hazards may be minimized whenthe structural part of the flight test program (see SPORTAVIATION, November, 1961) is conducted prior to theflight-flutter test.

In order to demonstrate freedom from flutter, it isthe usual practice to dive the airplane to a speed V,,which is 10 percent greater than the maximum indicatedair speed at which the airplane need ever be flown. This"never exceed" speed, VX K, is the speed which is markedwith a red line on the face of the airspeed indicator.

At Vn, an effort is made to excite flutter by shakingthe controls. It is obvious that if flutter does develop un-der these conditions, the consequence will likely be theloss of the airplane.

As in structural flight testing, the secret of longevityin flight-flutter testing is to creep up on critical speedscautiously, and to be equipped with a parachute that canbe used if someone has guessed wrong.

There is no point in picking a VX F for basis of theV,, test which is far above any speed that the airplanemay logically use. In correllary, the speed should not beso low as to seriously limit the usefulness of the air-plane. For most airplanes, a VNF of 15 to 20 percentabove the maximum speed that the airplane will attainin level flight is adequate. Airplanes which are not aero-dynamically clean and which are used for aerobatics mayrequire a higher ratio of VNI, to maximum level flightspeed. It doesn't seem likely that the ratio would everneed to be more than 1.33, however.

Flutter susceptibility is a function of true air speed.The red line is indicated air speed. Just because an air-plane doesn't flutter at 110 percent of VN K at sea levelis no assurance that it will not flutter at altitude at thisindicated air speed. Also, there is less aerodynamic damp-ing at altitude. These facts, plus consideration of "bailout" in the event of a flutter disintegration, point up thedesirability of running the flight-flutter test at the high-est feasible altitude.

In conducting the flight-flutter test, it is desirable toonly test one set of control surfaces at a time. Since theelevator, ailerons and rudder will each be tested up toVD, a number of dives will be required.

To minimize the risk of flutter, it is well to attemptto execute flutter first at low air speeds. A good speedfor the first attempt at producing flutter is probably inlevel flight at normal cruise power. When steady condi-tions exist and the airplane is trimmed hands-off, "slap"

the stick a sharp blow in the aft direction. This so thatif the elevator is going to flutter, the speed is in theprocess of being reduced, greatly reducing the danger ofa divergent flutter condition. If the stick oscillationshave been heavily damped, the test may be repeated ata 2 to 5 mph higher indicated air speed. This is repeatedagain and again until a speed of 10 percent over the redline (VN1.;) has been attained without any evidence of flut-ter. It is desirable to make at least three attempts atexcitation for each condition before proceeding.

The ailerons may be tested next. Again, it is well tostart at cruising speed. With the airplane trimmed, pullback slightly on the stick then "bat" the ailerons a sharpblow with the open hand. A large surface displacementis not required and can be structurally dangerous at high-er speeds. Displacement of surface should be at least 3deg., however. If the ailerons are well damped, a higherspeed may be selected a few miles per hour faster thanthe last. In every case, back pressure is exerted on thestick before exciting the ailerons. A transitory air speed,particularly diminishing, minimizes the possibility of adivergent flutter condition developing. However, if anincipient flutter condition is encountered, a few un-damped oscillations of the surface will be evidence thatthe "dragon's tail" has been "tickled" enough until cor-rective measures have been taken.

After 110 percent of VNE has been attained and theailerons have demonstrated no tendency to flutter, a simi-lar series of tests are conducted attempting to excitethe rudder. In every case after a steady trim speed isattained, the stick is pulled back slightly before kickingthe rudder, so that the air speed will be decreasing asthe rudder is excited.

All surfaces must be free from flutter up to VD.To demonstrate freedom from flutter at Vn with a tran-sient speed, it will be necessary to start the final checkon each surface at a speed slightly above Vn.

All elastic structures have critical flutter speeds.Flutter can destroy a structure in a matter of seconds.Unless measures are taken to prevent flutter, all airplaneswill experience flutter in one or more components at somespeed, possibly very high.

If the operating speeds are low enough, the flutterprevention measures may be pretty elementary. As speedsincrease, a greater degree of sophistication will be re-quired to insure against flutter. In any case, the builderof an airplane has the obligation to demonstrate that hisairplane will not flutter within the airspeed limits estab-lished for the particular airplane.

Since flutter is apt to be destructive, be cautious inall phases of the flight-flutter testing — you are takingyour life in your hands. Good luck! A

DRAG ANALYSIS . . .(Continued from poge 17)

2) Cd of the actual construction wing is D/Sq = .022.Checking with Report 824, we find this is almost twicethe section drag-coefficient listed for the airfoil sectionat RN 6 million and standard roughness. The home-builder who proportions his design around the listedsection drag-coefficient and fails to consider other sourcesof drag is going to experience reduced performance.18 JULY 1964

3) The parasite drag almost doubles the publisheddrag-coefficient. Therefore, for performance—

a) Keep those control gaps and control areas to theminimum required for adequate control and safety. Keepthe number and size of access panels to a minimum.

b) Flush mount all inspection covers and accesspanels with countersunk screws. It's a lot more work,but it should really pay off.

(To be continued) A