Maximum Mean Lift Coefficient Characteristics at Low Tip Mach Numbers of a Hovering Helicopter Rotor Having an NACA 64(1)A012 Airfoil Section

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NASA MEMO 1-Z3-59L ,/ .¢' _. < , ,

NASA

MEMORANDUM

MAXIMUM MEAN LIFT COEFFICIENT CHARACTERISTICS AT LOW TIP MACH NUMBERS OF A HOVER_G HELICOPTER ROTOR HAVING AN NACA 641A012 AIRFOIL SECTION By Robert D. Powell, Jr.

Langley Research Center Langley Field, Va.

NATIONAL AERONAUTICS AND

SPACE ADMINISTRATION

WASHINGTON

February 1959 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION MEMORANDUM 1-23-59L MAXIMUM MEAN LIPT COEFFICIENT CHARACTERISTICS AT LOW TIP MACH NUMBERS OF A HOVERING HELICOPTER ROTOR HAVING AN NACA 641A012 AIRFOIL SECTION By Robert D. Powell, Jr.

SUMMARY An investigation has been conducted on the Langley helicopter test tower to determine experimentally the maximum mean lift-coefficient characteristics at low tip Mach number and a limited amount of drag- divergence data at high tip Mach number of a helicopter rotor having an NACA 641A012 airfoil section and 8 ° of linear washout. Data are presented for blade tip Mach numbers M t of 0.29 to 0.74 with corresponding values of tip Reynolds number of 2.59 X 106 and 6.58 X 106 • Comparisons are made between the data from the present rotor with results previously obtained from two other rotors: one having NACA 0012 airfoil sections and the other having an NACA 0009 airfoil tip section. At low tip Mach numbers, the maximum mean lift coefficient for the blade having the NACA 641A012 section was about 0.08 less than that obtained with the blade having the NACA 0009 tip section and 0.21 less than the value obtained with the blade having the NACA 0012 tip section. Blade maximum mean lift coefficient values were not obtained for Mach number values greater than 0.47 because of a blade failure encountered during the tests.

The effective mean lift-curve slope required for predicting rotor thrust varied from 5.8 for the tip Mach number range of 0.29 to 0.55 to a value of 6.65 for a tip Mach number of 0.71. The blade pitching- moment coefficients were small and relatively unaffected by changes in thrust coefficient and Mach number. In the instances in which stall was reached, the break in the blade pitching-moment curve was in a stable direction. The efficiency of the rotor decreased with an increase in tip speed. Expressed as figure of merit, at a tip Mach number of 0.29 the maximum value was about 0.74. Similar measurements made on another rotor having an NACA 0012 airfoil and with a rdtor having an NACA 0009 tip section, showed a value of 0.75. Synthesized section lift and profile-drag characteristics for the rotor-blade airfoil section are presented as an aid in predicting the high-tip-speed performance of rotors having similar airfoils.

INTRODUCTION

A general research program has been in progress at the Langley

Research Center (refs. i to 6) to determine the low-tip-speed stall and

high-tip-speed compressibility effects on rotors having various NACA air-

foil tip sections as the primary variable. The present investigation is

a continuation of this program, in which emphasis is placed on the low-

speed, maximum meanlift coefficient characteristics of a helicopter

rotor having an NACA 641A012airfoil section, a constant chord, and

8° of linear washout. The low-speed, maxi_n lift characteristics of

this helicopter rotor will be useful in rot)r design studies, particu-

larly in the analysis of the stall charactei_istics of the retreating

blade in forward flight.

The hovering performance of the rotor )ver a tip Mach number range

of 0.29 to 0.74 (disk loading up to 4.83 ib/sq ft) is presented. Per-

formance data obtained at Mach numbers above 0.47 are incomplete because

of blade structural failure during part of _;hetests at a tip Machnumber

of 0.74. The blade low-speed maximum mean-lift and drag-rise character-

istics are discussed and a comparison of th,_ performance of the present

rotor with that of other rotors (NACA0009 _nd NACA 0012 sections) is

presented. The experimental Machnumbers f,)r drag divergence are also

comparedwith those shown by two-dimensional_ data.

Profile-drag-coefficient and lift-coefficient curves as a function

of airfoil-section angle of attack and Mach number, which were synthesized

from the rotor experimental results by use )f two-dimensional data on the

NACA641-012 airfoil (ref. 7) as an initial guide, are also presented.

SYMBOLS

a straight-line slope of section lilt coefficient with section angle of attack (assumed to be ').73 in calculations for incompressible flow curve), per radian, c_/_ r effective mean lift-curve slope, 5.73 CT_measured CT,calculated b number of blades c blade chord, ft airfoil-section profile-drag coefficient Cd,o airfoil-section lift coefficient c_ rotor-blade mean lift coefficient, 6CT/d

My

C m rotor-blade pitching-moment coefficient, rotor torque coefficient, Q CQ _R2p (_R )2R Qo rotor profile-drag torque coefficient, CQ, o

R2 ( R)2R

rotor thrust coefficient, T C T _R2p(,O.R) 2 M Mach number rotor blade tip Mach number

My rotor-blade pitching moment about 0.25 chord, ib-ft

pfaRc

NRe

Reynolds number at blade tip, Q rotor torque, ib-ft Qo rotor profile-drag torque, ib-ft R rotor-blade radius, ft T rotor thrust, lb airfoil-section angle of attack, deg blade-section angle of attack, deg or radians aT blade-section pitch angle at 0.75R measured from line of zero e .75 lift, radians difference between hub and tip pitch angles: positive when e I tip angle is larger, deg coefficient of viscosity, slugs/ft-sec

mass density of air, slugs/cu ft

rotor solidity, bc/_R

rotor angular velocity, radians/s_c

Figure of merit is equal to

o.7oTcT3/2/cQ

APPARATUS The rotor used for this investigation vas a fully articulated, two- blade rotor with the flapping hinge located on the center of rotation and the drag hinge 12 inches outboard of th,_ center. The distance from the ground to the rotor hub is 42 feet.

A sketch of a rotor blade with pertine_t dimensions is shown in figure i. The rotor blades used in the investigation were constructed of Fiberglas and incorporated a steel spar in the leading edge. The center of gravity of the rotor blades was located at the 25 percent chord.

The radius of the blades from the cent_m of rotation was 17.24 feet and the rotor solidity was 0.046. The blade,s had a constant chord of 1.25 feet. The rotor blades were smooth an([ fair over the entire chord with finished contour tolerances, back to _out 30 percent chord, of +0.000 to -0.005 inch. The rotor blades hacL 8.0 ° of linear washout (about 0.47 ° of twist per foot).

TEST METHODS AND ACCI_ACY The tests were run by setting given ro,or-blade collective pitch angles and varying the rotor speed through _ range of tip Mach numbers until either the blade limiting stress was reached or until a further increase in blade pitch did not increase th_ rotor thrust. The maximum disk loading obtained was 4.83 pounds per sc_are foot. The blade tip Mach numbers varied from 0.29 to 0.74 with _:orresponding Reynolds numbers of 2.59 × 106 to 6.58 × 106 , respectively. At each pitch setting, data were recorded from visual dial readings and by an oscillograph. Quan- tities measured were rotor thrust, rotor torque, blade pitch angle, blade drag angle, blade flapping angle, bla(.e pitching moment, and rotor- shaft rotational speed. The range of test c:onditions was chosen to determine the low-tip-speed rotor-blade maximum mean lift coefficient and the high-tip-speed compressibility drag rise.

The estimated accuracies of the basic quantities measured during the test are as follows: Rotor thrust, ib .......................... _20 Rotor torque, ib-ft ....................... _50 Rotor rotational speed, rpm ................... _i All angular measurements, deg .................. ±0.2 The overall accuracy of the plotted results is believed to be within ±3 percent. For example, at a rotor-blade mean lift coefficient _ of 0.46 (C T = 0.00348) and an M t = 0.47, the accuracy of the plotted data based on repeatability was about 3 percent for the thrust value of 2,700 pounds, 3 percent for the torque value of 2,196 pound-feet, and 0.2 percent for a rotational speed of 288 revolutions per minute. All data have been corrected to zero wind speed by the method of reference 8.

RESULTS AND DISCUSSION The measured hovering performance and rotor-blade pitching-moment curves are presented. A detailed analysis of the effects of stall and compressibility shown by these data is presented for tip Mach numbers ranging from 0.29 to 0.47. Data obtained for M t of 0.51 to 0.74 are incomplete for the high angles of attack due to blade failure at M t = 0.74. Synthesized airfoil-section data deduced from the measured rotor performance are also shown.

Rotor Hovering Performance The effect of Mach number on rotor performance is shown in figure 2 as the variation of thrust coefficient with torque coefficient for blade tip Mach numbers from 0.29 to 0.74. An incompressible-flow rotor- performance curve calculated by using conventional strip analyses (ref. 9) and incompressible drag coefficients is plotted for comparison with the experimental data. The calculated rotor-performance curve is based on the linear lift-coefficient slope (c Z = a_r, where a = 5.73) and the commonly used drag polar (Cd, o = 0.0087 - 0.0216_ r + 0.400_r 2) of reference i0.

Since reference 9 does not allow for any tip loss, a 3-percent tip-loss factor (the outer 3 percent of the blade is considered to produce no lift but to have profile drag) was used in the calculations.

In the low range of CT (0 to 0.0025) the experimental data showed less power required at all tip Mach numbers than that indicated by the incompressible (no stall) flow curve. This result indicates that the

rotor actually has less profile drag than that predicted by the assumed

profile-drag polar. Above a value of C T o__0.0025 the experimental

data are in fair agreement at tip Machnumbers of 0.29 to 0.60 up to a

C T value of 0.0040 (_ = 0.52). Past this value of CT, the experimental

data (limited to M t = 0.29 to 0.47) showa large increase in torque coef-

ficient as the blade approaches maximum lift Increasing tip speed caused

the experimental rotor performance to deteriorate progressively. The

point at which the experimental data separated from the calculated curve

indicates the critical value at which stall and compressibility losses

begin.

Rotor mean lift coefficients.- The maxii_um value of _ obtained with the present rotor was 0.92 which is som_what less than that obtained with other rotors having similarly smooth a_ fair surfaces but different airfoil sections. For example, the maximum _alue of cz given in ref- erence 6 for the rotor having NACA 0012 sections and a constant chord was 1.13. A somewhat higher maximum _Z might be expected from the rotor with NACA 0012 sections than from the rotor having NACA 641A012 sec- tions because of a more favorable section le_ing-edge radius.

The maximum _Z for the rotor having an NACA 0009 tip section was 0.995 (ref. 4). However, this rotor had an 18-percent-thick root section. It is probable that the thicker in)oard sections of this rotor were an important factor in its having a slightly higher maximum _ than was obtained from the rotor having an _CA 641A012 section. At _Z of 0.85 (CT = 0.0065), the increase in p,)wer from M t = 0.29 to M t = 0.47 for the test blades with the NACA 641A012 section was about 35 percent compared with values of 21 and 12 percent (obtained at the same operating condition) for the blades witll the NACA 0009 tip-section blades and NACA 0012 section, respectively.

Data recorded at tip Mach numbers above 0.47 were incomplete inasmuch as the data were obtained only up to thrust _oefficients Just prior to or at the point where drag divergence might _e expected. Maximum values of C T that were obtained are indicated in figure 2 by leaders with identifying Mach number values.

Rotor efficiency.- The efficiency of th_ rotor at various tip Mach numbers up to 0.47, expressed in terms of fixture of merit, is shown in figure 3. The maximum figure of merit obtained at tip Mach numbers of 0.29 and 0.38 was about 0.74 compared wit_ a value of 0.75 obtained with blades having NACA 0009 airfoil tip sections (ref. 4) and blades having NACA 0012 airfoil sections !ref. 6). As the tip Mach number increases, the maximum value of the figure of merit decreases.

Effect of tip Mach number on blade lift.- Figure 4 shows the varia- tion in rotor thrust coefficient as a function of the blade pitch angle at the 0.75 radius over a range of tip Mach numbers from 0.29 to 0.74.

In general the thrust coefficient was little affected by M t up to a value of M t = 0.51 except for M t = 0.47 where data indicate higher values of CT over the intermediate range of blade-sectlon pitch angles.

As would be expected, a substantial increase in rotor thrust coefficient for a given blade-pitch angle was obtained as the tip Mach number was increased past 0.60.

Values of effective mean lift-curve slope a were deduced from figure 4 for the various tip Mach numbers and are plotted in figure 5 as a function of blade tip Mach number. These values of _ were obtained by taking the value of C T obtained from measured data at a particular pitch angle and Mach number, dividing it by the value of C T obtained from two-dimensional incompressible-flow calculations at the same pitch angle, and multiplying this ratio of thrust coefficients (measured over calculated) times the value 5.73. An average curve is shown for blade-pitch angles of 6 ° , 8 ° , and 12 ° at the 0.75 radius.

The figure shows that the mean lift-curve slope had an average value of 5.8 at tip Mach numbers rangin_ from 0.29 to 0.55. As tip Mach num- ber is increased, higher lift-curve-slope values are obtained. For example, at M t = 0.74 and @.75 = 60, a value of a _ 6.6 will be required to predict the rotor thrust when the strip analysis method outlined in reference 9 is used.

Rotor-Blade Pitching Moments Rotor-blade pitching-moment data are necessary to determine the rotor control forces and are important in blade vibration and stability analysis. A comparison of the blade pitching-moment characteristics for representative tip Mach numbers of 0.29 to 0.74 for the rotor blade tested as a function of rotor thrust coefficient is shown in figure 6.

The pitching-moment data represent the measured rotor-blade moments about the blade pitch axis (0.25 chord) and include aerodynamic and blade mass forces.

Changes in blade pitching-moment coefficient as thrust coefficient is increased are probably largely due to the displacement of the blade center of pressure from the blade center of gravity. Since the position of the blade center of pressure is not precisely known and since the actual blade pitching moments were reasonably small (from -79 to 65 lb-ft), no attempt was made to separate the mass moments from the aerodynamic moments. The most important factor is the presence or absence of abrupt changes in pitching-moment slopes rather than the actual values.

The pitching-moment coefficients that were obtained through the tip

Mach number range of 0.56 to 0.74 remained slightly positive, that is,

nose up, with very little variation in the momentswith increases in

thrust. At the lower tip Machnumbers (0.29 to 0.47) the pitching-

momentcoefficients were almost entirely negative and becamemore nega-

tive gradually as thrust coefficients were increased until the rotor

approached its maximum thrust coefficient and a portion of the blade

stalled. As would be expected from the stall characteristics of the

NACA 6_IA012 airfoil section, a rearward shift of the center of pressure

occurs on the blade at stall and tends to cacse nose-down pitching

moment s.

Rotor Profile-Drag Torque

The principal effect of stall or compressiblity on the rotor per-

formance has been shownto be a rapid increase in the rotor profile-

drag torque. (See refs 1 to 6.) Figure 7(a) presents the rate of growth

of profile-drag torque as a function of the ratio of (CQ,o)measured to

CQ,o)calculated plotted against the calculated rotor-blade-tip angle

of attack. Values of ar for drag divergence are represented by the

point at which the curves faired through the experimental data exceed

a profile-torque coefficient ratio of unity. At tip Machnumbers ranging

from 0.29 to 0.47, the ratio of profile-drag torque coefficients did

not exceed unity up to a calculated blade-tip angle of attack of 4° .

This result indicates that there was no drag increase over that repre-

sented by the assumeddrag polar. In fact, _.t the lower angles of

attack, the blade has less profile drag than that predicted by the

assumeddrag polar, as indicated by the data points below the profile-

drag torque-coefficient ratio of unity. At _,lade-tip angles of attack

greater than 4°, the profile-drag torque-coefficient ratios became

greater than unity, which indicates that the assumeddrag polar under-

estimated the actual profile drag. As the al_le of attack was increased

past the drag divergence point at the variou:_ tip Machnumbers, the

increase in the profile-drag torque coefficic_nt was, for the most part,

gradual. In the low tip Machnumber range o:" 0.29 to 0.42 there is no

orderly progression of the tip angle for pro:_ile-drag increase as a

function of M_. At a Machnumber of 0.47, _he principal factor influ-

encing the point of drag rise is the tip Mach number. In this instance,

the curve showsthat the profile-drag torque was approximately doubled

for tip angles of attack 3° beyond the initilL1 drag-rise point.

Figure 7(b) shows the sameexperimental data that were shown in

figure 7(a) except that the drag-divergence ralues in figure 7(b) for

ar at the various Machnumbers were obtaine,[ by a straight-line fairing

of the data points. Considerable scatter in these plotted points exists

at someMach numbers (especially M t = 0.47). In view of this scatter

a linear (or straight-line) fairing of the data points as shown in

figure 7(b) might be considered more appropriate. More data points than

are presently available will be required before the most accurate fairing

of figure 7(a) can be determined; however_ the failure of the rotor

blades madethis impossible in the present investigation.

Figure 8 shows the rotor profile-drag-torque ratio rise as a func-

tion of rotor-blade meanlift coefficient. At the low tip Mach numbers

(0.29 and 0.33), the maximum meanlift coefficient before drag rise

(defined as the point at which the profile-drag-torque ratio becomes

greater than unity) was about 0.58. This value of _ is about 35 per-

cent lower than that reported in reference 6 for a rotor having an NACA

0012 airfoil section and about 29 percent lower than that reported in

reference 4 for a rotor having an NACA 0009 tip airfoil. As the tip

Mach numberwas increased, the values of _Z for drag rise were in

somewhatbetter agreement with values for the blades reported in refer-

ences 4 and 6. For example, at a tip Machnumber of 0.47 the _Z value

for drag rise for the NACA 641A012airfoil was 0.52 which was 18 percent

and 15 percent lower than that obtained with the NACA 0012 and NACA

0009 blades, respectively. At a tip _ch number of 0.69 the values

for the NACA 641A012and NACA 0012 were the same(_ = 0.45), whereas

the value of _Z for the NACA 0009 blade was 0.41.

Comparison of Drag-Divergence Data with Results

From Two-Dimensional-Airfoil Tests

A comparison of the rotor drag-divergence Mach numbers with those

predicted from two-dimensional-airfoil data is presented in figure 9.

The measureddrag-divergence data were obtained from figures 7(a) and

7(b). The point of drag divergence was defined as the point at which

the profile-drag torque-coefficient ratio exceeds a value of unity.

The two-dimensional-airfoil drag-divergence data for the NACA

641-012 airfoil (ref. 7) are presented in two ways. In one case the

Mach number for drag divergence was selected as the point at which

was

_Cd/f_M= 0.i. In the other case the drag-divergence Mach number

taken as the point at which the profile-drag coefficient begins to increase.

The rather abrupt decrease in the experimental Mach number for drag divergence in the tip angle-of-attack range of 4 ° to 5 ° (shown in fig. 9 by the points plotted as circles) is of interest. Although experience with the rotor of reference 4 has shown that a decrease

lO

in the experimentally defined drag-divergencc_ Math number occurs at

moderately high angles of attack because of inboard stalling, this ten-

dency is not found for the rotor with the NA(_ 641A012 airfoil. Calcu- lations of the inboard blade angles of attach show the maximum values to be only 6 ° or 7 ° at tip angles of attack in "_he region of 4 ° to 5 ° .

These values are too low for stall to occur for the test condition repre- sented. It will be recalled that the drag-d:.vergence Mach numbers plotted as circles in figure 9 were defined by the p_int at which the faired curves first exceeded the incompressible value of i_CQ2o#measured (CQ,o)calculated The values for the drag-divergence Mach numbers defined by a straight- line fairing of the data points, (triangular symbol) are shown to fall approximately on the curve given in figure 9 for the two-dlmensional air- foil data where drag-divergence Mach numbers were defined as the point where drag begins to increase. ExperimentaL-data points noted by the flagged symbols are for tip Mach numbers abo te 0.47. Although data above this Mach number were incomplete, thes_ values of M t are believed to be the points that represent either the d_ag-divergence value or a value very close to this point. This fact w:_s further borne out by visual data readings made during the test.

At an angle of attack of about 2 ° and _ = 0.74 the blades show some tip relief; that is, the drag-dlvergenc_ Mach number for the rotor data is greater than the drag-divergence Mac_ number for the two- dimensional data. At higher tip angles of attack and lower tip Maeh numbers the points of drag divergence become less than the values indi- cated by the two-dimenslonal data (as much as a 0.25 difference in tip Mach number for the same angle of attack) wh_re drag-divergence points were defined as the point of initial drag iocrease.

Synthesized Characteristics of the E&CA 641A012 Airfoil Section for Rotor Performance Calculations The section lift and drag characteristics shown in figures i0 and ii were synthesized by the method outlined in _etail in reference 6. These data, when used with an established method cf performance analysis, might be used as an aid in calculating the forward-flight performance of rotors having similar airfoil sections and operatirg at high tip speeds. The original assumptions used for synthesizing _he drag and lift curves herein are based, to a large extent, on wine-tunnel data (ref. 7) for the two-dimensional NACA 641-012 airfoil section. Drag and lift curves are presented for Mach numbers ranging from 0.29 to 0.74, but below or beyond these values the curves are dashed to, indicate their provisional nature.

ii

Figure I0 showsthe synthesized drag coefficients for the NACA

641AO12 airfoil section plotted as a function of Mach number for blade

angles of attack from 0° to 12°. The resulting curves retain the general

shape of the variation of drag with Mach number as that for the two-

dimensional NACA 641-012 airfoil section (ref. 7) up to angles of attack of 8 ° or 9 ° . The rate of increase in section profile drag at angles of attack above 6 ° was somewhat greater than that indicated by the two- dimensional data.

The synthesized lift coefficients for the NACA 641A012 airfoil sec- tion are plotted in figure ii as a function of Mach number for angles of attack from 0 ° to 12 °. The section-lift-coefficient curves are almost identical to the two-dimensional lift-coefficient data for the NACA 641-012 airfoil section except that the maximum lift-coefficient values for M = 0.iO, 0.20, 0.30, 0.35 were decreased to predict more accurately the actual experimental rotor performance. Above M = 0.35, the slopes of the two-dimensional-data curves were also decreased slightly for better correlation between the two-dimensional and experimental data.

CONCLUSIONS The low-speed maximum mean lift coefficients _ on a rotor having a constant-chord NACA 641A012 airfoil section and 8 ° of linear washout have been determined over a range of blade-tip Mach number M t of 0.29 to 0.47. Maximum rotor-blade mean lift coefficients for the range of tip Mach numbers from 0.51 to 0.74 were not obtained and only a limited amount of drag-divergence data was obtained for this range. As a result Of this investigation the following conclusions can be made: i. At low tip Mach numbers the blade maximum mean lift coefficient for the NACA 641A012 section was about 0.08 less than was obtained with a blade having an NACA 0009 tip airfoil section and 0.21 less than was obtained with a blade having NACA 0012 sections.

2. The power increase from M t = 0.29 to M t = 0.47 for the NACA 641A012 blades at a value of _ of 0.85 was about 35 percent compared with the 12- and 21-percent increases measured for NACA 0012 and NACA 0009 blades, respectively.

3. At M t = 0.69 the rotor-blade mean lift coefficient for drag rise for the NACA 641A012 blade was 0.45 compared with values of 0.45 and 0.41 for the NACA 0012 and NACA 0009 airfoil blades, respectively.

4. The effective meanlift-curve slope r_quired for an analytical

prediction of the rotor thrust varied from an average of 5.8 at

M t = 0.29 to a value of 6.6 at M t = 0.74.

5. The blade pitching-moment coefficients were small and relatively

unaffected by changes in thrust coefficient and Machnumber. In the

instances in which stall was reached the momentbreak in the blade

pitching-moment curves was in a stable direction.

6. The NACA641A012blades showedsometip relief as regards drag

divergence at the higher Machnumbers in comparison with two-dimensional

data. At the lower Mach numbers more data were needed to define accu-

rately the exact point for drag divergence.

7. The efficiency of the rotor, expressed as figure of merit,

decreased with an increase in tip Machnumber. At M t = 0.29, the maxi-

mumfigure of merit was about 0.74. Similar measurementsmadeon rotors

having NACA 0009 and NACA 0012 airfoil secticns showedvalues of 0.75.

Langley Research Center, National Aeronautics and Space Administzation, Langley Field, Va., October 17, 19_8.

REFERENCES i. Carpenter, Paul J.: Effects of Compressibility on the Performance of Two Full-Scale Helicopter Rotors. NACA Rep. 1078, 1952.

(Supersedes NACA TN 2277.)

2. Shivers, James P., and Carpenter, Paul J.: Experimental Investigation on the Langley Helicopter Test Tower of Compressibility Effects on a Rotor Having NACA 632-015 Airfoil Sections. NACA TN 3850, 1956.

3. Powell, Robert D., Jr.: Compressibility Effects on a Hovering Heli- copter Rotor Having an NACA 0018 Root Airfoil Tapering to an NACA 0012 Tip Airfoil. NACA RM L57F26, 1957.

4. Powell, Robert D., Jr., and Carpenter, Paul J.: Low Tip Mach Number Stall Characteristics and High Tip Mach Number Compressibility Effects on a Helicopter Rotor Having an NACA 0009 Tip Airfoil Section. NACA TN 4355, 1958.

5. Shivers, James P., and Carpenter, Paul J.: Effects of Compressibility on Rotor Hovering Performance and Synthesized Blade-Section Charac- teristics Derived From Measured Rotor Performance of Blades Having NACA 0015 Airfoil Tip Sections. NACA TN 4356, 1958.

6. Carpenter, Paul J.: Lift and Profile Drag Characteristics of an NACA 0012 Airfoil Section as Derived From Measured Helicopter- Rotor Hovering Performance. NACA TN 4357, 1958.

7. Wilson, Homer B., Jr., and Horton, Elmer A.: Aerodynamic Character- istics at High and Low Subsonic Mach Numbers of Four NACA 6-Serles Airfoil Sections at Angles of Attack From -2 ° to 51 °. NACA RM L55C20, 1955.

8. Carpenter, Paul J.: Effect of Wind Velocity on Performance of Heli- copter Rotors as Investigated with the Langley Helicopter Apparatus.

NACA TN 1698, 1948.

9. Gessow, Alfred: Effect of Rotor-Blade Twist and Plan-form Taper on Helicopter Hovering Performance. NACA TN 1542, 1948.

i0. Bailey, F. J., Jr.: A Simplified Theoretical Method of Determining the Characteristics of a Lifting Rotor in Forward Flight. NACA Rep. 716, 1941.

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0 0 0 0 0o • • • • e0ue&_eAlp _'e_p _0,_ _eq_'tu q0'el_ .18 .16 O .14 _2 o .12 _D .I0 e.-.t o % .08 G) .06 .O4 .O2 4 ,3 0 .i .2 .3 .4 ._; .6 .7 .8 Uach number, U Figure i0.- Synthesized section profile-drag co,efficient plotted against Mach number for the NACA 641A0_2 airfoil.

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Overview