Document
REPORT No. 416 ‘
THE N. A. C. A. VARIABLE-DENSITY WIND TUNNEL By EASTMAN N. JACOES and IaA H. ABBOm SUMMARY balance was built. The balance was installed in January, 1929, and several investigations were made This report dkwibe3 the redwigwd variuble-&n@ on airfoil and airship models.
wind tunnel of the Nationul Adtiory Committee for Owing to several difficulties, some of whioh had Aeronuutim; it superseaks a prti report th.d de- existed in the earlier form of the tunnel, the open- soribedth original i%nn+d. The oper~ion of the balunce throat tunnel was not considered satisfactory in the and the methodof testing are arplaind and the methodof light of later developmem% in the art of wind-tunnel correcting and presenting ai~oi.1 &a h dwribed. A design. The diiiiculties, which included excessive summary of tlwjormulu.sfor predicting the characiwiatica vibration, unsteady velocity at the test section, a of jinite wings from i% airfoil seetion data as they are rather Iarge pressure gradient along the axis of the usually presenied is also @en.
teat section, and excessive effects of extraneous air INTRODUCTION currents on the bakmoe, were overcome by rebuilding parts of the tunnel. The whole interior structure was The variabledensity wind tunnel was constructed altered to give greater rigidity and the method of by the National Advisory Committee for Aeronautics supporting the structure and the balance from the to provide equipment for testing models wherein the tank wall waa improved. The test section was error resulting horn the comparatively low dynamic changed to the closed-throat type. A new exit cone scales common to most other model tests could be having a smaller divergence angle and a new entrance eliminated. The necessity of recognizing this source cone having a better form were built. The synchro- of error and the practicability of eliminating it by the nous-drive motor was replaced by a direct-current use of this type of wind tunnel have been demonstrate.d motor. These changes were completed in December, by investigations which have been made in the variable- 1930. This report describes in some detail the me- density wind tunnel and in flight. A discussion of the chanical features and the method of operation of the theory of this @e of wind tunnel is given in reference redesigned tunnel.
1. The Reynolds Number ‘Y is a measure of the (?
DESCRIPTION OF TUNNEL dynamic scale, and large values of the Reynolds The variable-density wind tunnel is similar to other Number are obtained in this tunnel by increasing the density (p) while the other factors kunain sensibly tunnels except that it is inclosed wit$i.n a tank to constant. allow the use of ccmpreased air as the working fluid.
The variabledensity wind tunnel was proposed in The novel features arise horn the restricted space 1921 (referenca 2), and the construction of the tunnel inside the tank, the exterior controls for the balance “ was completed in March, 1923. A d~cription of the’ and other apparatus, and the large range of forces on tunnel as it then existed is given in reference 1. The the model.
closed-throat test section was 5 feet in diameter, and Tank and arrangement,-The general arrangement the tunnel was of wooden construction inclosed within is shown in Figures 1 and 2. Entrance to the tunnel, a steel tank. A number of investigations were made which is constructed tide the tank, is gained by in this tunnel, and the results showed the theory to be means of an elliptical door in one end. The propeller correct. drive shaft passea through a suitable stuiiing box in the The tunnel was destroyed by tire in August, 1927, opposite end of the tank. Small glass windows are but the tank in which it was inclosed was not seriously provided for read.@ the balances and observing the damaged. The tunnel was rebuilt, using tieproof model. The tank, which is designed to withstand a construction, and the balance was made more acces- working pressure of 21 atmospheres, is built of heavy sible by building the test section of the open-throat steel plate lapped and riveted according to the usual type. After the reconstruction of the tunnel was com- practice in steam-boiler cmstruction. A conorete pleted in April, 1928, the tunnel was employed for foundation supports the tank, which, together with pressure-distribution investigations until the new its contents, weighs about 100 tons.
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THE N. A. C. A. VMUAJ3LJi+DENSITY WIND TUNNEL Air passages and structme.-The tunnel cotita matic voltage regulator. Fine speed control is obtained essentially of a central air passage (*. 2) consisting of by means of rheostats in the field circuit of the the entrance cone, the test section, and the exit cone, drive motor. The propeller shaft pasaes through a and an annular return passage surrounding the central loosely packed stufling box in the tank walL Air air passage but separated tim it by a dead-air space Ieakage is reduced by oil which slowly leaks through containing the balance. In each circuit of the passage-s the stuffing box and is returned to a reservoir by a small pump.
The air is compressed by a 2-stage primary com- pressor and a boostar compressor which fill the tank with air at 20 atmospheres pressure in about 70 minutes. The booster compressor can also be used to ewkuate the tank to preasurasbelow atmospheric.
TUNNEL CHARACTERISTICS VelociW and pressure distribution.-l?igure 3 indi- cates the velocity distribution over a dktanm across the test section equfkl to the span of the largest model used in this tunnel. The veloci@ is slightly low at the tunnel axis, but the variation is within +0.5 per cent. The variation in direction of the air flow as indicated by a yaw head passed across the test “ section is less than + %O. Figure 4 indicat8s the Distanceininchesfrom funnel axis, horizonid dia.
smfdl static-pressure variation along the tunnel axis.
~aua!s 3.—Ratfoof dynamlopmssme at thamedalpmitionto the pmssmw MPAP auzm thastatb~ adflas Energyratio.-The energjratio E. R=uPOWW~put
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-the air is twice turned through an angle of 180°, one of the tunnel at atmospheric pressure without any -turnbeing made in the entrance cone, which is designed screims in the air passages is about 2.3 if the power to prevent the air horn separating tim the walls.
input is taken as the power supplied to the propeller by The test section is 5 feet in diametar and 6 feet long, and it is made slightly divergent to reduce I To& pr!sssure the horizontal static-pressure gradient. Four O I A fmoqohere — A 2% .
holes are cut in the wall of the test section q 15 - downstream from the model position to main- + 10 “ x 20 “ tain the pressure in the dead-air space very nearly the same as the static pressure in the .10 teat section, and accordingly to reduce the - P flow of air into the test section through the I%p Vf holes for the model-support struts. The in- L7— — . — — — — y - — ~ * cluded angle between the walls of the exit cone .
A ~ is a little less than 6°, and the portion tapered I at this angle is 14 feet lo~; The return pas- A40delposiiian I‘ aage has a constant cross-sectional area about -.10 , t~ee times that of the teat section. A screen, I to provide a certain amount of damping and 10 20 30 40 50 to equalize the flow, is located in the return D!siancefrom entrance cone,inches msmwe at the Dosition shown in I&zure 2. and n- L—W or stati to d-o msmre an the M Of the variabkhnsity wind tnn- d. Thar&IoPls rafarrdtoth eprmmrafmath e8tatio~ -htheanmllca i safe-i screen “not shown, ie locateil in th~ exit me cone in front of the propeller. Twisting of the the drive motor. The energy ratio of the tunnel as it is air stream is prevented by 12 antkirl vanes located actually operated at 20 atmospheres tank prcmnre &mediately behind the propeller and extending for with both screens in place is 1.o9 if the power input is some distance into the r@mrnpassage and by 6 vanca taken as the electrical power supplied to the drive fastened to the deflector doors in the entrance cone.
motor.
Propeller, drive motor, and compressors.—The air DESCRPITON OF BALANCE is circulated by a 3-bladed metal propeller 6.5 feet in diameter which is driven by a shun~wound &rec& General.-The balance must measure the large range mrrent motor. The current is provided by a 200- of force9 resdting from the large variation of air Icilowatt motor generator set equipped with an auto- densities at which tests are made, and it must be oper- . . .. . __ ,.
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.
FOR AERONAUTICS REPORT NATIONAL ADTISORY COMMITTEE TEE N. A. C. A. VMU.M3LE-DENSITY WIND TUNNEL moment. The rear vertical linkage is therefore called ated compIetdy from outside the tank. The balance the moment balance, and the model is usually mounted measures the lift and drag forces and the pitching the pitching so that this balance measurea directly moments by means of three beams bakumd by moving weights. The essential parts of the balance are a rigid steel frame called the balance cradle, the balance beams, and the linkages necessary to transmit the forces to the balance beams horn the cradle to which the model is rigidly fastened.
Linkages.-Figure 5 is a diagrammatic drawing of the balance showing the main parts. The bakmce cradle, which is a rigid structure extending across the tunnel under the test section, is suspended by rods from two of the balance beams, which in turn are e.sternaUy supported through knife-edges. The rods thus serve to transmit vertical forces from the cradle to the beams and also to form parallelograms, of which ~e~-gmfiktiage Ta17fi beam l%- , ~\.
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moment. The forward vertical linkage is called the lift balahce because it measures most of the lift, although the tital lift is the sum of the forces measured by the-lift and moment beams.
c, Knife-edge FIGURE 13.-Dkwammatla drawingof the Int.%mxtlon of theIlk anddms llnkaw the sides of the cradle are the lower horizontal membem, on each side of the test section. The bakmce cradle would thus be free to move along the tunnel d if it were not restrained in this movement by the drag Iinkagcs, which are attached to the balance cradle, as shown diagrammatically in Figure 6. Cross-tunnel movement and rotation of the balance cradle are prevented by the torque tubes and the restrainkrg arch shown in Figure 5.
The drag linkage transmits the horizontal or drag forces horn the balance cradle to the drag beam -.
through bell cranks, one of which is shown photo- graphically in Figure 7. The horizontal members of I “-) -%. .
this linkage lie in the plane of the tunnel axis. There- fore, if pitching moments are taken about a point on ~GUEE 8.—Pho~ph of OUO Oftfw I@II SUPPO*K f~ Ofthe dragMnrim the axis of the tunnel in the pkne of the forward verti- cal linkages, i. e., about a point on the line of inter- Knife-edges,-All linkages are connected by means sections of the lift and drag linkages (@. 6), neither of lmife-edges and seata carefully made of hardened the forces from the drag linkage nor the forces from high carbon steel. In all casea the We-edges are the forward verticsl linkage contribute to the pitching fixed in the members in which the lever arms must be ,— . . —.?— .. . . .-..-— . — —. .
310 REPORT NATIONAII ADVISORY COMMITTEE FOR AERONAUTICS maintained exactly. The knife-edge seata are arranged balanced by a moving counterpoise, the position of so that they may align themselves with the Imife-edges. which is controlled by a motor-driven lead screw and indicatid by a revolution counter. The beams swing In some parts of the balance it is necessary to iix accurately the position of the seat as well as that of between motor-operated adjustable stops that contain the knife-edge. Seats of this type are called main platinum contact points, which are connected in the supporting seats. A photograph of one is ahown in circuits of the beam motors so that the beams may be Figure 8. They have a V-shaped groove in which the balanced either automatically or by hand switchas.
knife-edge rests. The bottom of the V is sharp and The beams are calibrated so that one unit on the drag the included angle between the sides is 120°. The or moment beams indicates 1 gram, and on the lift main supporting seats are carried by secondwy lmife- beam 10 grams. & the forces to be measured on the edges at rights angles to the main ones so that the balance are greatez than the capacities of the beams, seats are free to rock in such a way that the bearing iE each beam is provided with a set of 10 counterweights equalized along the resin Imi&edge. The positions (&. 5), which may be applied aa needed by means of of these seats are adjustable along the secondary lm.ife- motor-driven camshafts.
edge in the direction of the tunnel sxis by means of Model support.-The models are held in the tunnel the thumbscrews shown in Figure 8, and the whole by the partly shielded support struts shown in Figures unit, including the secondary lmife-edge and thumb- 5 and 9. The two forward or main support struts, which carry most of the air load on the model, are rigidly attached to the balance cradle. The model is attached to the upper ends of these support struts by pins about which the model rotates in changing angle of attack. The pins are located with reference to the balance in line with the intersections of the lift and drag balanca linkages. If possible, the pins are fsstened in the model on the line about which momenta are desired; for airfoils, on the chord line one-quarter of the chord behind the leading edge. The moment balance then reads directly the pitching moment.
The angle of attti. of the model is controlled by a vertical motor-driven screw which can+s the lower end of the angle-of-attack strut and is geared to a revolution countar. A sting attached to the lower surface of the airfoil model, as shown photographically in Figure 9, cm.nects the angle-of-attack strut and the model.
For special trots other types of support are used, but the main support struts are usually employed.
For some special teats, such as airship-model tests, an auxiliary drag balance may be used instead of the main balance. The auxili~ balance iE described in reference 3.
OPERATING PROCEDURE Velocity determination.-To guard against errors, atapdtiva lhotm. 9.—Photczmph of an afrfdl modalmountedfnthetmmal two independent sets of static-pressure orificeEIand =mda of atb.ck manometers are used h measure the air velocity.
screw assembly is he h rotate about a vertical Each manometar is connected between a set of four axis to align the seat with the main knife-edge. The orifices spared around the inner wall of the return passage and a set of four orifices spaced around the less important seats, such as those shown in Figure entrance cone near the test section. These manom- 6, also have a V+ihaped groove in which the We-edge eters, which are simiku in principle to the one deacfibed rests, but the angle between the sides is 150° and a in reference 4, have stationary index tubes and movable bottom radius is provided b lessen the fiction. This reservoirs carried on motor-driven lead screws. Revo- type of seat is not fastened rigidly to the member that lution counters geared to the motors indicate the heads carries it but rests on a curved base, so that the seat ta 0.1 millimeter. The temperature of the manometer can take up positions such that the knife-edge will liquid is measured im 1° C. by a &stan&reading ther- bear evenly on the seat throughout its bngth.
mometer. Pure ethyI alcohol with a known variation Balanoe beama,-The balance beams are fastened of specilic gravity with temperature is used for the to torque tubes which extend across the tunrd above manometer liquid. The manometer are calibrated the teat section m-d move in arcs about the supporting by balancing the head of alcohol in the manometers fulcrums as the beams swing. Each balance beam is against a head of distilled water.
T1333 N. A. C. A. VARIA13LE1-DFINSITY m TUNNEL 311 The static-pressure oriiices am calibrated at ill tank windage. The interference of the supports on the premurea at which tests are to be made by making model is usually neglected.
The distribution of the weight of the model and sting velocib surveys (with a calibrated Pitot, tube) along the horizontal diameter of the tunnel. The ratio of between the lift and moment beams varies as the model the dynamic pressure to the pressure across the static- pivots with changing angle of attack. A correction, pressure orifices is then plotted (&g.3) and the calibrw which is evaluated by observing moment balance zero tion factor is taken as the mean value of this ratio.
readings at two angles of attack, is applied to the Balance alignrnent.-The lift, drag, and pitching measured momenta to allow for ti change of weight moments measured by the balance are actually vertical distribution. ~ and horizontal forces applied at, and the moment A typical airfoil test.—The standard airfoil models, about, the line joining the points of intemection of @e 30-inch span and 5-inch chord, used in this tunnel are It is essenti+ that any one lift and drag linkages.
made of hea&treated duralumin. A special -airfoil- force or moment does not allect the value of any other, generating mactie is employed that works from a 6- and that the measured valuea be the true ones. To fold templet of the section. The templets are carefully satisfy these conditions the theoretically vertical and laid out on a table that permits the plotting of the horizontal portions of the balance linkages must be Stations and ordinatm to an accuracy of 0.001 inch.
exactly vertical and horizontal.
The templets are then cut out and checked for pre- The balance is assembled w nearly aligned as possible cision of contour. A section of the airfoil model is also by measurement and all balance beazqs are balanced.
checked after the cut has started. and any necessary Weights are then placed successively on eaoh of the corrections are made on the templet. As the cut counterweight bridges, and adjustments are made until progresses, the masimum thickness is checked from a weight placed on the bridge of any balance beam does time to time to guard against errom resultiug horn not tiect the balance of any other beam. The pivot excessive tool were. The models are hand iinished to points of the model support struts are aligned with the remove small tool marks and then buffed to produce a pointa of intersection of the lift and drag linkages by a polished surface. To insure accuracy of alignment in similar method. The balance dignrnent is checked the tunnel, a special hilling jig is employed to drill the and changed if necessary from time to time.
airfoil models for mounting.
As the balance is aligned, the measured lift and drag A sting is fastened to the lower surface of the model forces are respectively vertical and horizontal; but parallel to the chord, after which the model& mounted since the air-flow direction is not exactly horizontal, in the tunnel, as shown in Figure 9. The model is the measured forces are not the tie lift and drag.
fastened to the support struts by lugs which are ab The deviation of the direction of the air flow from the tached to the struts by pins and which lie completely horizontal is determined by the well-known method of within the model. A sensitive inclinometer is used to testing an airfoil in the erect and inverted positions.
set the chord of the model successively paralkl to the The deviation is so small that the corrections to the air flow and at a large angle of attack. From the data lift and moment are not appreciable if the zero angle of so obtained, the proper calibration table for the angle- attack is set with reference to the air-flow direction.
of-attack counter is selected &m a previously calcu- The measured drag is corrected by adding to it a small lated set.
The air-flow alignment is component of the lift.
After the air in the tank is compressed to the de- checked periodically.
sired pre9sure, the drive motor is run until the temper- Balance calibration.—The balance is calibrated by atures inside the tank are equalized. Two observers means of standard weights checked by the Bureau of ~d one recorder stationed as shown in Yigure 1 are Standards. The counterweights used on the balance required for the test. The, recorder reads the tank bridges are checked against these weights, and the bal- prwsure on a 12-inch bourdon-type pressure gauge ance beams are calibrated by weighing the standard and the temperature of the mmometer liquid on a weights which are placed on the counterweight bridges diattmt-reading thermometer., From the thermometer for this purpose. The weight of the moving cmmter- reading he calculaks the manometer setting for the poise is adjusted until the beam counter reads the desired air speed, which is selected so that the counters weights correctly.
on the balance beams read directly the force coel3i- Determination of tare forces.—The tare forces are cients, or simple multiples of them.
evaluated by measuring the air forces on the suppork The iirst observer sets the rnauometere, regulates ing members while they are connected inside a hollow the air speed, and balanc= the drag beam. He also dummy airfoil mounted independently of the b&mce.
operates a signal systam which lights lamps visible to These meaeuremenk, which are made with the dummy the three operators when the air speed is correct.
model at several angles of attack, include the interfer- The second observer balances the lift and moment ence of the model on the supports and the balance 149900—33—21 COMMITTEE FOR AERONAUTICS 312 REPORT NA’ITONAL ADVISORY beams. The swing of the lift beam affects the balance The formulas for correcting the data from the closed- of the moment beam, so the lift beam is held in the bal- throat tunnel conditions to free air are as follows: anced position by the contact points while the moment (Y& beam is being balanced. The final balance of all beams a= a=+2TPx 67.3 is obtained ordy when the signal lamps are lighted.
Another signal lamp warns the recorder if the balance (Angles of attack are measured in degrees.)
fouls during the test.
The recorder makea all necessary calculations and 0.= c.,+~~ corrections to obtain the final force and moment coeiiicients of the airfoil as corrected to inflnita aspect Since the redu@ion to infinite aspect ratio is made ratio, and plots these coefficients as the test progresses.
from the uncorrected tunnel data, the e.tlective aspeot These cilculationa are greatly simplified by the selec- ratio (R,) of the airfoil is used.
tion of the air speed and by previously calculated tables.
B “-1 – %($)9 REDUCTION AND PRESENTATION OF DATA then Method of cokecting data.-The formulas used in &~= &T –~c (1 +7) x 57.3 correcting the data”to infinite aspect ratio and for the influence of the tunnel walls are from the works of Munk, Glauert, and Prandtl, and are summarized in –~(l+u) “ CDO= CDT reference 5. The notation and formulw used are as follows: ‘TABLE I CL, absolute lift coefficient.
AIRFOIL: CLARK Y D, diameter of wind-tunnel throat.
IleynoldY Nmnbec 3JE@YX1.
b, span of airfoiL i%%%wlel: 5 b 30ink ~ sMerlatmm@erex m.7.
8; area of airfoil.
T* No. 625 %riebklem?ky wind tunnel. Date: Mar& 19,1% a, angle of attack in free air.
a ~, angle of attack as me~ed in the tunnel. c% % %/4 ai, induced angle of attaok.
-am :&o -a 076 CYo, angle of attack at which an airfoil of il&- –. m -. (km nite span would give the same-lift coeffi- .075 .Cm9 -. M7 .aw -. C&l cient as the airfoil tested in the tunnel.
:% .Ix$7a -.033 .M7 .0111 -. cm R, actual aspect ratio of airfoil. .982 .0134 -. m .Olm -. ma R,, effective aspect ratio of the airfoil; the :% .mlo -. C33 L6M .0443 -. on aspect ratio of an airfoil which would L 518 . llW -. m .!XW -. 13a give the same characteristics in bee air i%% .44W -.170 aa the airfoil tested.in the tunnel.
c =Cli$ moment coefficient about a point one- . .
Method of presenting data.-The results of a test quarter of the chord behind the lead- of the Clark Y-airfoil ar~given in Table I and Figure 10 @@e.
to show the method of presenting airfoil data. It will (?., absolute drag cceiiicient for an airfoil in be noticed that the characteristics of airfoils are pre- free air.
mnted by means of two independent sets of curves.
O.., proiile drag coefficient.
The fit is the conventional plot UL, U~, L/D, and C& absolute drag coefbient obtained horn c. p.. against angle of attack, but differs from most the tunnel teats.
premous plots in that the results are corrected for C~,, induced drag coefficient.
tunnel wall effects to aspect ratio 6. The second set r, a faotor correcting the induced angle of attack to of curves gives the deduced characteristics of an air- allow for the change &m elliptical span loading foil of Mllite span.
The protie drag COt3ffiCht UDO, resulting from the use of an airfoil of rect~~ular the angle of attack ao, and the moment coefficient plan form.
about the quarter-chord point (7m&A are plotted against u, a factor correcting the induced drag to allow for the the lift coefficient. 11%.istype of plot, which has been change from elliptical span loading remdting from used in England, has three important advantage over the use of an airfoil of rectangular plan form.
the more familiar type. X’irst, the charaoteristica are dCL —~ increase in lift coefficient per degree for an plotted againat the lift coefficient as abscissa because a= da the lift coefficient is usually treated as the independent airfoil of aspect ratio B.
d05 . variable. Second, the eficiency and pitching char- ao == increase in lift coefficient per degree for an acteristics of dii7erent airfoils may be compared much airfoil of i.&inite spa more readily by oomparing profile drag and moment ‘I’H@ N. A. C. A. VARLADIilkD13NSITY WIND TUNNEL 313 where a. is the slope for the w-uqgof “mbits span.
coefficient curves rather than the familiar L/D and The drag coefficient is This is particukmly true if the moment c. ‘p. Ourvea.
coefficient about a point, one-quarter of the chord
c.=c.o+~(l+u)
behind the leading edge is used, because its value for a given airfoil is approximately constant over the The values of ~ and u depend on the shape of the working range. Third, in applying the reaulta of air- span-loading diagram of the airfoil. For an elliptical foil teats, it is almost always necessary to correct them wing without effective twist they are zero and for a to another aapect ratio, and it is more convenient to cor- rectanguhw wing their vriluea are given in Figure 11.
rect from an irdinite than horn some finite aspect ratio.
The moment coefficient at a given value of the lift Application of section data to the predictions of coefficient may be taken as the same for any aspect & ~haraoteristios.-The formulas for predicting the I 1 8 ? 80 IC o .-70 chard 1.8 .36 1.6 ..32 a .4 .&l .2 .04 r 3-/9-.57 177/see. ..2 D. Z 525 Yeffecf.
5!
.
-8-4 0 4 8 /.216202. 4 28 Z-”4 Lif( coeft7a”enf, C’ Angle of affackin degrees,ct F-mum Io.-okuk Y A’fon ratio. The center of pressure, measured as a frac- characteristics of iinite winga flom the airfoil section tion of the ohord bm the leading edge, is given by data as they are usu~y presented (CL, CDO, CW4) will also be summarized here for convenience.
c
~d4 The angle of attack in degrees for the lift coefficient c. p. =0.25 — OL COS a+CD sin a o. (the independent vmiable) is where 0md4is the moment coefficient about a point ~-ao+$(l+T)x67.3 one-qum%er of the ohord behind the leading edge.
or The use of the foregoing formuk may be more easily understood horn the following example. Sup- ~m~.+~%L(l+r) pose it is desired to find the aerodynmnic oharacter- istios of a rectangular Clark Y wing of aspect ratio 8.
The lift curve slope when angle of attaok is measured Since the lift eoeffieiant is considered the independent in degrees is variable, we shall seleot a value for this coefficient and aO a= calculate the other characteristics. For the sample 1+% (1+7)57.3 calculation a lift coefficient of 0.7 will be taken.
FOB AERONAUTICS RDPORT NATIONAL ADVISORY COMMITPEE From Figure 11, for an aspect ratio of 8, u-0.074.
Then c== C.O+ 0.04270Lg From Figge 10, wh~ CL= 0.7, UDOE0.0112 cD=0.0112 + 0.0209 ‘ 0==0.0321 L 0.7 D“ixim=21”8 The moment coefficient about the quarter-chord – 0.063 for a lift cceficient point, from Figure 10, is of 0.7. The position of the center of pressure moaa- ured as a fraction of the chord horn the leading edge is cm~, c. p.=o.26– (?LC08 a+c= & a C. P.‘o.25 – (o.7) COS4.1~+”&j321) Sk 4.1° C. p.=0.25+0.090 c. p.= 0.34 of the chord from the leading edge.
Flaw= 11.-oarwnall hcbns forrect=wd= ~~ This w-ill be the position of the center of pressure for The angle of attack for a given value of CLis an angle of attack of 4.1°.
a=%+af L.KPWLEY MEaIom-m AERONA~CAL LABORATORY, NATIONAL ADVISORY CowrrIWE FOR AERONAUTICS, Of 8, r= O.22.
From Figure 11, for an aspect ratio LKPTGLBY I?=D, VA., ~ovemlw M, 19$?1.
Then REFERENCES a=~+2.780CL 1. Munk, Max M., and Miller, Elton W.: The Variabl*Density From Figure 10, when Wind Tunnel of the National Advisory Committee for Aeronautics. T. IL No. 227, N. A. C. A., 1926.
CL=-O.7, %=2.2° 2. Mnnk, Max M.: On a New Type of Wind Tunnel. T. N.
No. 80, N. A. C. A., 1921.
a=2.2°+1.90 3. Higgine, George J.: Tds of the N. P. L. AirEMp Models in a-u” , the Variable Density Wind Tunnel. T. N. No. 264, N. A. C. A, 1927.
The drag coefficient is 4. Baoq D. L.: Langley Field Wind-Tunnel Apparatus.
T. N. No. 81, N. A. C. A., 1922.
Jacobs, Ewtman N., and Andereon, Raymond F.: Largo- 5.
Soale Acrodynamio Charaoterktkm of Airfoils Tested in the Variable Density Wind Tu.nneJ. T. IL No. 362,
@%o+~ (1+ U)
N. A. C! A., 1929.