Document
NA TIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
TECHNICAL NOTE 1922 w (n TWO-DII'v'IENSIONAL INVESTIGATION OF FIVE RELATED NACA AIRFOIL " I SECTIONS DESIGNED FOR ROTATING - WING AIRCRAFT By Raymond F. Schaefer, Laur e nce K. Loftin, Jr., an d Elme r A. Ho r ton .
Langley Aer on a utica l La bor a tory Langley Air Force Ba se, Va.
/ Washington July 1949
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TECH L.IBRARY KAFB, NM 11 11 111 11 11 1 11 11 11 11 1 1111 11 1111 11 1 111 1 1111 11 1 NATIONAL ADVISORY COMMITTEE FO R AERONAUT lvo 00 6 5390 TECHNICAL NOTE 1922 TWO-DIMENSIONAL INVESTIGATION OF FIVE RELATED NACA AIR FO IL SECTIONS D E SIGNED FOR ROTATING-WING AIRCRAFT By Raymond F. Schaefer, Laurence K. L ofti n, J r ., and Elmer A. H orto n SUMMARY Five NACA ai rfoil sections int e nd ed for use in ro to r blades hav e bee n designed an d tested in the Langley two-dimensional lo w -turbul e nc e tunnel. The airfoils have thicknesses that vary from 9 percent to 15 pe rcent of t he chord and the o retical design lift coefficients t ha t vary fr om 0.3 t o 0.7. Theoretical-pressure-distribution dat a and the measured two-dimensional aerodynamic characteristics at Reyno lds numbers from 0.9 x 10 to 2 . 6 x 10 ar e pr e s e nt ed fo r eac h airfoil. The effe cts
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of surf ace cond itio n wer e inv e sti gate d at a Re ynolds numb er of 2.1 x 10 . The r e sults ar e analyzed to show the e ff e cts of vari- ations in thickne ss and camber upon the pertin e nt s ectio n aero dynamic characteristics. Theoretical calcul ati ons for diff er ent flight condi- tions are also inc lud ed t o indica te the r el at ive pe rformanc e of sampl e rotors employing the different a irfoils. These ca lcula t ions show that the 9-percent - thick s ec ti on of 0.5 de sign lift coefficient is, in general , the best of the airfoils of the pr e s e nt inv e sti gati on for t he flight conditions conSidered, but, as compared with the NACA 8-H-12 airfoil s ection designed in a pr e vious NACA inv e sti gat ion, this s e ction does no t appea r to offer any hope of gains in performanc e fo r most of the f li ght conditions.
INTRODUCTION Studie s of rotating-wing ai rcraf t have indicat ed that siza bl e reductions in the profile-drag power should be r ea li ze d through the us e of airfoil s ect ions d esigne d to ta ke a dvant age of the low p rofil e -dra g coefficients a ss ociate d with the atta inme nt of r el at iv ely large e xt en ts of laminar f low. For ro to r-blad e applic atio ns, low valu es of dra g ar e desirable not only at low and mod e rat e lif t co e ffici e nts but also at high lift coeff ici ent s and, therefore, the low dra g corr e spondin g to extensive laminar flow sho uld be obtained at relativ e ly high lift coefficients. Of primary importance in all cases, howeve r, is the 2 NACA TN 1922 maintenance of near-zero pitching moments throughout the useful lift- coefficient range. These requirements indicate the desirability of employing cambered airfoils for rotor blades but, at the same time, preclude the use of NACA 6-series, or low-drag, airfoils (reference 1) cambered with conventional mean lines such as the a = 1.0.
Several investigations have therefore been made for the purpose of obtaining laminar-flow airfoils that have the previously mentioned desirable characteristics. The drag at high lift coefficients, the sensitivity of the airfoil to surface roughness, and the critical Mach number were other characteristics considered in the design of the airfoils. In all cases, the airfoils designed consisted of NACA 6-series basic thickness forms cambered with various specially designed mean lines.
The purpose of the initial investigation, described in reference 2, was to explore the possibility of designing sections with zero pitching moments and high maximum lift-drag ratios corresponding to the attain- ment of extensive laminar flow at relatively high lift coefficients.
Near-zero pitching moments were obtained with the new airfoils and, in comparison with other airfoils considered for use in rotor blades, considerable improvement in the values of maximum lift-drag ratio was obtained. The new airfoils (reference 2), however, seemed to be unduly sensitive to surface roughness and were characterized by undesirable variations in the drag, lift, and moment at high lift coefficients.
In an attempt to minimize the undesirable characteristics of the airfoils discussed in reference 2, four new experimental sections were derived and tested (reference 3). Some of the airfoils described in reference 3 have highly desirable over-all characteristics and at the present time one of these airfOils, the NACA 8-H-12, is being considered for application in numerous helicopter designs. In order to allow the designer more latitude in the selection of airfoils for rotor blades, however, the evaluation of the effects of airfoil thickness and camber upon the characteristics of airfoils generally similar in design to the best of those discussed in reference 3 seemed desirable. Five airfoil sections have accordingly been derived and tested in an effort to show the effects on the aerodynamic characteristics of systematically varying the thickness and camber. The purpose of the present paper is to present pertinent design information and experimental aerodynamic characteristics of these airfoils.
The airfoils considered varied in thickness from 9 to 15 percent of the chord and in camber from 0.3 to 0.7 design lift coefficient.
The NACA 64-·series basic thickness form was employed for all the airfoils. The two-dimensional lift, drag, and pitching-moment charac- teristics were obtained for each Bmooth airfoil at Reynolds numbers of 6 6 approximately 0.9 X 10 , 2.1 X 10 , and 2.6 X 10 . The effects upon NACA TN 19 the aero~amic characteristics of roughening the leading edges of the models were determined at a Reynolds number of 2.1 X 10 . In conjunc- • tion with the analysiB of the airfoil characteriBtics obtained, an evaluation has been made according to the methods of reference 4 of the performance characteriBtics under various flight conditions to be expected from rotorB employing the different airfoils.
SYMBOLS Airfoil-Section Symbols a mean-line deSignation, fraction of chord from leading edge over which design load is uniform ~o section angle of attack c chord cd section drag coefficient Cdwin minimum section drag coefficient c2 section lift coefficient c1 maximum section lift coefficient max c2 design section lift coefficient i (C2/Cd)ma:x maximum 11ft-drag ratio r_ s ecti on moment coefficient about aerodynamic center -mac
Cmc/4 section moment coefficient about quarter-chord point
Mcr critical Mach number R Reynolds number t airfoil thickness V free-stream velocity v local velocity x distance along chord ~rom leading edge NACA TN 1922 distance perpendicular to chord y Rotating-Wing-Aircraft Symbo ls . t (Rotor-Shaft power input) f Cp power coef lcien pn31ffi5 angle of attack of blade el em ent from zero lift rotor angle of attack; angl e between projection in plane of symm et ry of axis of no feathering and lin e perpen- dicular to flight path~ positive when axis is pointin g r e arward, radians rotor-bl~de radius R forward speed v rotor disk loading, pounds per squar e foot W/s parasite drag area, square feet f
(V sin a. - v"
inflow ratio \ QR :J
v' induced inflow velocity at rotor
V cos a. )
tip - speed ratio nR ( rotor solidity; ratio of total blade area to sw ept - di sk are a (re c tangular blade s ) pitch angle of blade element
e
difference between hub and tip pitch angles, degrees (po s itive when tip angle is great e r) rotor angular velocity, radians per second p air den s ity ; .
NACA TN 1922 THEORETICAL AIRFOIL CHARACTERISTICS The five airfoil sections that were derived and tested are designated as follows: NACA l2-H-12 NACA ll-H-09 NACA l3-H-12 NACA l 5 -H-15 NACA l4-li-12 The first number in the designation is a serial number, the H indi- cates that the airfoil section has been designed for use on rotating- wing aircraft, and the last two ~ig1ts represent the magnitude of the maximum thickness in percent of the chord. The NACA l2-H-12, l3-H-12, and 14-H-12 sections are 12-perc ent -thick airfoil sections with the amount of camber varied to give theor et ical design lift coefficients of 0.3, 0.5, and 0.7, respectively. The NACA Il-H-09, 13-H-12, and 15 -H-15 airfoil s ection s have the same design lift coefficient (0.5) but have maximum thicknesses of 9, 12, and 15 percent of the chord, respectively. The thickness forms of all the airfoils were of the NACA 64-series (reference 1).
The mean camber line of each section was obtained by
c ombinin g a = 0, a = 0.4 (modifi ed) , and a = 1.0 mean lines. These
mean lines were combined to give first-approximation-zero, theoretical, quarter-chord pitching moments and extensive favorable pressure gradients along the lower surface. The design lift coefficients of the airfoil s e ctions in the group representative of varying amounts of camber wer e obtained by linearly scaling the mean-line ordinates. The airfoils that have the same amount of camber but different thickness ratiOS, however, have mean lines that are slightly different for each thickness ratio. These differences arise as a result of an attempt to make the pressure distribution of the resultant cambered airfoil more desirable for eac h thickness ratio than could have been obtained by USing exactly the same mean line in all cases. The loading typical of the mean lines employed is given in figure 1 for the mean line used in the NACA l3-H-12 section. Ordinates for the five airfoil sections are given in tables I to V and the s ection profiles can be seen in figures 2 to 6.
Calculated pressure distributions at the theoretical deSign lift coefficient for each airfoil are presented in figures 2 to 6.
Increasing the airfoil thickness from 9 to 15 percent of the chord while maintaining a constant design lift coefficient of 0.5 increases the peak negative pressure somewhat and makes the pressure gradient on the forward part of the upper surface more favorable for laminar flow (figs. 2, 4, and 6). Increasing the design lift coefficient from 0.3 to 0.7 while maintaining a constant thickness of 12 percent of the chord
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NACA TN 1922 c au ses large increas e s in the pe ak negative pressure coefficient and makes the pr e ssur e gradient over the forward part of th e upper surface progressively more unfavorable to the maint e nance of laminar flow (figs. 3, 4, and 5). The pr e ssure gradi e nt on the lower surface may be seen to be favorable over the ent ire chord for all the airfoils and to become progressively more favorabl e as the camber is increased.
Although experimental pressure distributions are not a vail able for t he airfoils under consid e ration, previous experience wi th airfoils de sign ed to produce appreciable lo a ds near the trailing edge (r efe r- e nc e 5 ) indicates that the effects of viscosity are such that the theoretical loading is n ot com pl ete ly reali ze d near the t railin g edge.
As a cons e~ u enc e , som e of the exper im e ntally det e rmin ed charac teri stics of the NACA R -s e ri e s airfoils would be expe ct ed to b e s o mewh at diff erent from those predicted on the basis of a th eo retical inviscid flow. In the de sign of th e airfoils, however, the amount of loss in lo ad n e ar the t r aili ng e dg e was e stimated and allowed for in such a way that the e xp e rim ent ally d ete rmin ed pitching moments would be expected to be near ze ro.
The critical Mach num be r Mer for eac h airfoil s ec t ion was e s timate d by emp loyin g the Von K~-Tsien r el ati onship in which the t h eoretica l low-speed peak negative pressure co eff icients at the theo - retical design lift coefficient are us e d; the valu e s of Mcr are given in table VI. In o rd er to g iv e som e indication of the lar ge r educt ion in the theo r eti cal valu e s of Mcr pr odu ced by the a dditio n of camber to the symmetrical s ectio ns, comparative theo r eti cal valu es of the critical Mach number for the symm et rical th ickn es s forms ar e als o included in tab l e VI. As would be expected , de cr ea s e s in the cri t ical speed accompany increases in camber and thickne ss. In view of the expected departure of the theoretical and expe rim en tal low-sp eed pr es sur e distributions and the differences that usually e xist between the theoret i ca l critical an d force-break Mach num be rs, the prac tical value of the critical Mach numb e rs presented s eems ~ ue stion ab l e .
MODELS AND TESTS Each of the two -d imensional models that was tested in this investi - gation had a 24 - inch chord and a 3 5 ~-1nCh span and was constructed of chordwise , mahogany laminations. The models were prepared for J testing by applying a thin coat of glazing compound to the surf ace s and sanding in a chordwise direction with No. 400 carb orundum paper until the surfaces were aerodynamically smooth. For te sts with t ransi tio n fixed forward at the leading edge, standard r oughne ss was applied on the top and bottom sur faces spanwise along the leading edge of each NACA TN 1922 model over a surface length of 8 percent of the chord measured from the leading edge. A more detailed description of the standard roughness selected for 24-inch-chord models is given in reference 1.
The models were tested in the Langley two-dimensional low- turbulence tunnel. This tunnel was designed to test models completely spanning the width of the tunnel in two-dimensional flow. The rectangular test section of this closed-throat, continuous tunnel is 3 feet wide and 7"2 feet high. The turbulence level amounts to only a few hundredths of 1 percent and is achieved by the large contraction ratio (19.6 to 1) and by the use of seven layers of fine-wire, emall- mesh, turbulence-reducing screens in the widest part of the entrance cone. The maximum velocity of this wind tunnel is approximately 6 155 miles per hour which gives a Reynolds number of about 1.4 X 10 per foot of model chord.
Lift forces and pitching moments were measured on balances and drag forces lIere obtained with a wake-survey apparatus. The wake-survey method was used because it had been proved to yield greater accuracy in the range of low and moderate drags than the tunnel drag balance.
The models were supported in the tunnel at the chordwise quarter- chord position, but, for structural reasons, different vertical distances were necessary between the chord line and the pitch axis of rotation for each model. All pitching moments were measured about the axis of rotation but were corrected to the true quarter-chord axis before pre- sentation. When the models were mounted for lift and moment tests, a small gap (approx. 0.020 in.) was, of neceSSity, allowed between the ends of the model and the tunnel walls in order to insure freedom of the balance. Comparative low-turbulence-tunnel te-sts of various air- foils with and without gaps indicated that error due to leakage through these gaps is substantially within the experimental accuracy of the test methods at Reynolds numbers corresponding to the present tests. A more complete description of the tunnel and the methods of obtaining and reducing the data are given in reference 6.
Lift, drag, and pitching moments were obtained at Reynold8 numbers 6 6 of approximately 0.9 x 10 , 2.1 x 10 , and 2.6 X 10 for each airfoil in ~ smooth condition and at a Reynolds number of 2.1 X 10 for each airfoil with standard leading-edge roughness.
RESULTS The results of the tests are presented (figs. 7 to 11) in the form of standard coefficients representing the lift, drag, and pitching NACA TN 1922 moment (about both the Quarter chord and the aerodynamic center) at the Reynolds numbers covered for the mnooth and rough surface condi tions.
The aerodynamic-center locations that were calculated for both surface conditions at the corresponding Reynolds numbers of the tests are also gi ven in these figures. All the data have been corrected for the finite size of the tunnel test section. The relative magnitude of each correction is given for the NACA ll-H-09 airfoil section by the following eQuations (see reference 6) in which the primed symbols are the measured Quantities: Corrections for the other airfoil sections are of a similar order of magnitude.
A summary of the more important aerodynamic characteristics of the five airfoils is given in table VI for both smooth and rough surface conditions and two Reynolds numbers. Included for comparison are values for the NACA 23012 and 8-H-12 airfoil sections taken from references 1 and 3, respectively.
DISCUSSION The discussion is concerned with an analysis of the effects of variations in airfoil design upon the aerodynamic characteristics of the airfoil sections and, of perhaps greater practical importance, with the performance of helicopter rotors employing the different airfoil sections tested. The section aerodynamic characteristics considered are: pitching moment, 11ft, and drag.
Pi tch1ng Moment The val'1es of pitching moment about the aerodynamic center for all the airfoil sections are essentially constant and nearly zero throughout the useful range of lift (figs. 7 to 11). Only small changes in the aerodynamic-center pitching moments in the useful range of lift occur as a result of variations in the Reynolds number and surface NACA TN 192 2 condition. No consistent variation of the chordw1se position of the aerodynamic center with camber and thic kn e ss apl'ears to exist. The range in which the values of the aerodynamic-center pitching momenta remain almost constant and the positions of the aerodynamic center are summarized in table VI.
Lift Maximum lift.- A comparison of maximum lift coefficients at . 6 6 Reynolds numbers of 2.1 X 10 and 2.6 X 10 for both airfoil surface conditions is given in the table of aerodynamic characteristics (table VI). The data for both Reynolds numbers indicate that the maximum section l~ft coefficients for all the airfoil sections in the smooth condition, including the NACA 8-H-12 section, are of the order of 1.3, except for a value nearly one-tenth higher attained by the highest-cambered airfoil, the NACA 14-H-12. The values of the maximum lift obtained at a Reynolds number of 0.9 X 10 (figs. 7 to 11) are somewhat lower than those corresponding to the higher Reynolds numbers, but the magnitude of this scale effect is relatively insignificant.
Variations in thickness are seen to have little effect on the maximum lift coefficients of these airfoils and only the highest amount of camber produced an increase in the maximum lift. The effect of adding the type of camber employed in these airfoils to the symmetrical NACA 64-series sections (data for which are presented in reference 1) resulted in reductions in maximum lift coefficient for the 12-percent- thick and 15-percent-thick airfoil sections in contrast to an increase obtained with the 9-percent-thick airfoil. The maximum lift coeffi- cients of all the airfoils considered in the present investigation and that of the NACA 8-H-12 section at a Reynolds number of 2.6 X 10 are lower than the value of 1.6 obtained for the NACA 23012 section at a Reynolds number of 3 X 10 (references 1 and 3). The type of stall shown by the NACA 23012 section is, however, much more abrupt than that which is characteristic of the H-series helicopter-rotor-blade sections.
The effect of standard leading-edge roughness is to decrease the maximum lift of all the airfoils. The magnitude of the decrement, however, varies from a value of approximately 0.1 for the NACA Il-H-09, 12-H-12, and l3-H-12 airfoil sections to 0.3 for the NACA l4-H-12 and 15-H-15 sections. The resultant maximum lift coefficients vary fram 1.19 for the 9-percent-thick section to 1.04 for the 15-percent- thick section. The maximum lift coefficient of the NACA 8-H-12 section in the rough condition is also of the order of 1.1. Unpublished data show that the maximum lift of the NACA 23012 section under similar conditions is about 1.15 and that the stall is still abrupt; whereas the H-series sections in the rough condition have a more gradual type of stall just as occurred in the amooth condition.
NACA TN 1922 Lift-curve slope.- The experimental data (figs. 7 to 11) for the NACA H-series sections indicate the variation of the lift curves from a straight line to be such that the lift-curve slopes are quite difficult to define adequately in many cases. In order to give some indication of their order of magnitude, however, values of the lift-curve slope were measured for a short range of lift coefficient surrounding the experimental design values for a Reynolds number of 2.6 X 10 . For the smooth surface condition, the lift-curve slopes so determined showed a wide variation from values of the order of 0.100 for the 9-percent- thick section to 0.l20 for the thicker, more highly cambered airfoils.
In comparison, the theoretical value of the lift-curve slope, as shown by thin-airfoil theory, is 2~ per radian or 0.110 per degree.
Reductions in the Reynolds number generally caused some decrease in the lift-curve slope, and, in all cases, large decreases occurred when the leading edges of the airfoils were roughened.
Angle of zero lift.- As would be expected from theory, the angles of zero lift are seen to become progressively more negative as the amount of camber is increased. A small negative shift in the angle of zero lift also occurs as the thickness ratio is increased. This small shift may possibly be explained by the fact that as the thickness is increased, the pressure-recovery gradients over the rear of the airfoil become pro~'esBively more severe. Hence, because of viscous effects, a smaller proportion of the theoretical design negative load is realized near the trailing edge so that the amount of effective positive camber is increased and thus the angle of zero lift becomes more negative.
Drag In order to show more clearly the effects of airfoil design on the drag, the drag polars for the different airfoils are plotted tObether in figures 12 and 13 for the ff.mooth surface condition at a Reynolds number of 2.6 X 10 and in figures 14 and 15 for the rough surface condition at a Reynolds number of 2.1 X 10 . Figures 12 and 14 show the effects of varying camber on the drag characteristics of the airfoils of 12-percent thickness , and figures 13 and 15 show the effects of varying thickness ratio on the airfoils with deSign lift coefficient of 0.5. The characteristics of the NACA 8-H -1 2 airfoil section, taken from reference 3, are shown in the figures for comparison. The drag characteristics that are discussed are: the minimum drag, the low-drag range, the drag outside the lOW-drag range, and the maximum value of the lift-drag ratio.
~inimum drag ~gefficient.- An examination of the data of figures 12 and 13 indicates that the values of the minimum drag coefficient for the
r- ------~----------~~~~------~----~--~ ~ ---------~------~---------- - .- -~-- - -- --
NACA TN 192 11 smooth condition at a Reynolds number of 2.6 X 10 range between 0.0045 and 0.0053 for the NACA 8-H-12 airfoil and ali the airfoils of the pre- sent investigation except for the highest-cambered section which had a minimum drag coefficient of 0.0072. By way of comparison, the minimum \ drags of the NACA 641-012 and NACA 23012 airfoil sections at a Reynolds number of 3.0 x 10 are 0.0050 and 0.0064, respectively (reference 1).
The data of figures 12 and 13 clearly show that the value of the minimum drag coefficient of the helicopter-rotor-blade sections is little affected by the airfoil thickness but increases significantly with camber. This significant effect of camber is contrary to previously reported resultB (reference 1) that show that the magnitude of the minimum drag coefficient is relatively insensitive to variations in the amount of camber for NACA 6-series airfoil sections with the a = 1.0 type of mean line. The increase of minimum drag with camber shown by the H-series sections probably can be explained by the fact that the pressure gradient over the forward part of the upper surface becomes increaSingly unfavorable to laminar flow as the camber increases (figs. 3, 4, and 5).
The effect of Reynolds number on the minimum drag can be seen in figures 7 to 11. In general, increasing the Reynolds number from 0.9 x 10 to 2.1 x 10 appears to have a rather important favorable effect upon the minimum drag. This trend is particularly pronounced for the thicker, more highly cambered sections. The existence at the lower Reynolds number of a large separation bubble on the upper surface that decreases rapidly in size as the Reynolds number is increased to 2.1 X 10 may possibly account for the large favorable scale effect.
Further increases in the Reynolds number to 2.6 X 10 appear to have a relatively unimportant and seemingly inconsistent effect upon the minimum drag. The small amount of adverse scale effect shown by some of the airfoils as compared with the favorable effect shown by others can, however, be explained by the relation between the pressure gradient on the upper surface of the airfoil and the critical boundary-layer Reynolds number for transition. (See, for example, reference 7.)
The effect of leading-edge roughness is to increase greatly the minimum drag of all the airfoils (figs. 14 and 15). Variations in the airfoil thickness from 9 to 12 percent of the chord and in the amount of camber from theoretical design 11ft coefficients of 0.3 to 0.5 had 11 ttle effect on the minimum drag that was of the order of 0.012. For the 15-percent-thick airfoil and the airfoil with 0.7 design lift coeffiCient, however, the value of the minimum drag is of the order of 0.015. The minimum drag coefficient of the NACA 8-H-12 airfoil section (with roughness) at a Reynolds number of 2.1 x 10 is approxi- mately 0.0104. Unpublished data indicate that NACA 6-serie8 NACA TN 192 2 and 230-series airfoils of 12-percent to 15 -percent thickness have minimum drag for the rough condition of about 0.012 at a corresponding Reynolds number.
I Low-drag range.- Because of the similar pressure gradients on the upper and lower surfaces of co nventional NACA 6 -s eries airfoils at the design condition, the theoretical design lift coefficients for th e se airfoils usually occur near the experimentally determined center of that range of lift coefficient through which low drag is obtain e d. At the theoretical design lift coefficient, the pressure gradients on the upper and lower surfaces of the NACA H-series airfoils, how eve r, are usually dissimilar, and therefore the theoretical value of the design lift co e fficient would not occur in the center of the low-dr ag rang e .
An examination of the pressure-distribution data of figures 2 to 6 indicates that, at the design lift co ef ficient, the pressure gradi e nts on the upper surf a ce are generally much l e ss favorable for th e mainte- nanc e of laminar flow than are those on the lower surfac e . A con- sid er atio n of this fact, together with a knowledg e of the type of load distribution due to angl e of at tack shown by the NACA 64-s e ri es basic thickness form (r efe r e nc e 1), suggests that th e theor et ical de sign lift co ef ficient of th e NACA H -s eries airfoils should occur nearer the high rather than the low e nd of th e lift-co e fficient range for low drag.
On the contrary, however, the theoretical value of the design lift co e fficient occurs closer to the low er end of the low-drag rang e (figs. 12 and 13). This r e sult can be explained in th e followin g qualitative manne r: As was pointed out in the discussion of the theoretical character- istics of the H-series airfoils, the theoretical load distribution n e ar the trailing edge is probably not fully r e aliz ed experimentally becaus e of the effects of viscosity. If Buch is th e case, the pr e ssure gradi - e nts on the forward portions of the upper and lower surfaces of the H-series sections at the theoretical design lift coefficient actually occur at a higher e xperim e ntal lift coefficien t because the load near the trailing edge of the s e airfoils acts in a n egat iv e dir e ction.
Hence, wh en the th€oretical design lift coefficient is reached expe ri- me ntally, the pr e ssure gr adie nt on the low er surface would be much l e ss favorable to laminar flow than is indicated theoretically and a peak would be expected to form n ear the l eadi ng edge as the li ft co eff ici ent is r educ ed much be low the theoretical design v a lu e . As a resul t , turbulent flow would beg i n near the l ea ding edge on the low er surface an d therefore the drag would ris e rapidly. If this e xplan at ion of the observed behavior of the de sign lif t coefficient is corr e ct, increasing the d es ign lift coefficient of the H-series s ect ions would be expe ct ed to · cause the theoretical design lift co effi cient to occur closer to the low er e nd of the range of lift coefficient for low dr ag . The data of figure 12 show that such is the case; in fact , for the high e st- camber ed s ection , the theo r et ical design li ft coefficient oc curs below t he lo we r NACA TN 1922 limit of the low-drag range. The experimentally observed shift of the design lift coefficient to higher values was expected because of the manner in which the estimated loss in load near the trailing edge was accounted for so that the experimental pitching moments would be zero.
\ In spite of the fact that the lift coefficient corresponding to the center of .the low-drag range beara little relation to the theoretical design lift coefficient, the designer is probably most interested in the lift coefficient at the center of the low-drag range. The value of this lift coefficient increases from approximately 0.4 to 1.0 as the theo- retical design lift coefficient is increased from 0.3 to 0.7 (fig. 12).
The width of the low-drag range does not appear to vary appreciably with the amount of camber, but as might be expected, it increases somewhat with airfoil thickness (fig. 13). The data of figures 12 and 13 show the NACA 8-H-12 section to have a more extensive low-drag range than any of the airfoils of the present investigation. Because of the manner in which the low-drag range increases with thickness, the value of the lift coefficient corresponding to the center of this range also increases somewhat with thickness. The values of the lift coefficient corresponding to the center of the low-drag range for all the airfoils are 'summarized in table VI.
Variations in the Reynolds number between 2.1 X 10 and 2.6 X 10 appear to have a relatively unimportant effect upon the low-drag range (figs. 7 to 11). Lowering the Reynolds number to 0.9 X 10 , however, results in the almost complete disappearance of the low-drag nbucket" for all the airfoils except the one of lowest camber. This disappear- ance is believed to be associated with the existence of rather extensive regions of laminar separation on the upper surfaces of the airfoils.
With standard leading-edge roughness no low-drag range exists, of course, that corresponds to the attainment of extensive laminar layers on either surface. The drag polars for the different airfoils in the rough condition (figs. 14 and 15), however, do have a range of lift coefficient through which the drag coefficient varies only slightly from the minimum value. The data of figures 14 and 15 show that this range decreases markedly with both increaSing thickness and increasing camber and that the center of this range gen e rally bears little relation to the center of the low-drag range obtain ed for the airfoils in the s.mooth condition. These results can possibly be explained by the f a ct that th e pressure-recovery gradients on the upper surfaces of the airfoils become increasingly more severe as the thickness and camber are increased and, hence, separation of the turbulent boundary layer is promoted. In comparieon with the airfoils of the pres e nt investigation, th e NACA 8-H-12 airfoil appear s to have drag near th e minimum value in the rough condition over an extremely wide range of lift coefficient (figs. 14 and 15 ).
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NACA TN 1922 Drag outside the low-drag range.- As the lift coefficient is decreased below those values corresponding to the lower end of the low- drag range, the drag of all the smooth airfoils first rises abruptly, then rather slowly, then very abruptly again (figs. 12 and 13). The I same type of "jog" appears in the polars for some of the airfoils following the upper end of the low-drag range, and in all cases, the drag finally rises abruptly. The exact extent and the nature .of these jogs vary somewhat with the airfoil design parameters. The net effect is that the lift-coefficient range between the final abrupt rise in drag on the two sides of the polar increases with airfoil thickness and decreases somewhat with camber. The NACA 8-H-12 airfoil appears to have a wider range of lift coefficient between the two abrupt increases in drag than do any of the airfoils of the present investigation (figs. 12 and 13).
In the rough condition, the rate of drag rise above the flat portion of the polar is very steep and in general does not appear to vary with airfoil thickness and camber (figs. 14 and 15).
Maximum lift-drag ratios.- The values of the maximum section lift- drag ratio axe included in table VI for the airfoils of the present ' investigation and for the NACA 8-H-12 and 23012 sections. For the smooth surface condition, the maximum values of the lift-drag ratio at a Reynolds number of 2.6 X 10 vary between 147 and 153 for all the air- foils of the present investigation except for the 12-percent-thick section with the smallest design lift coefficient, 0.3. The maximum value of the lift-drag ratio for both this airfOil and the NACA 8-H-12 airfoil was of the order of 135. In comparison with the value of 111 obtained for the NACA 23012 section (reference 1), the lift-drag ratios of the newer sections seem ~uite high. Variations in the Reynolds number betWeen 2.6 x 10 and 2.1 x 10 had a somewhat inconsistent effect upon the value of the lift-drag ratio for the different airfoils (tahle VI), whereas decreaSing the Reynolds number to 0.9 x 10 caused red~ctions in the lift-drag ratios in all cases.
The addition of standard leading-edge roughness caused large decreases in the value of the lift-drag ratio for all the airfoils, the amount of the decrement increasing with both airfoil thickness and camber. In the rough condition, the NACA 8-H-12 section has a value of the lift-drag ratio higher than that of any of the airfoils of the pre- sent investigation. Unpublished data show that at a Reynolds number of 2.0 X 10 the value of the maximum lift-drag ratio for the NACA 23012 section in the rough condition is 45, which is higher than that of many of the newer airfoils ..
-~
NACA TN 1922 HELICOPl'ER PERF ORMANCE CALCULATIONS Although the preceding discussi on of the effect of , airfoil design upon the section aerodynamic characteristics of the airfoils IDSY be of interest, their merits may be adequately judge d only thro~gh a con - sideration of the relative performance of helicopter rotors employing the different sections. A method of eva . luatin g the relative perform- ance that can be expected for various flight conditions as a result of employing different airfoil sections in a rotor consists of predicting the power that will be expended in overcoming the rotor-blade profile drag. This method of analysis was dealt with in reference 4 and the nondimensional weightin g curves developed in that paper have been ~sed for cal culatin g and comparing the p rofile-dra g power 103ses that result when the airfoils of the present investigatio~ are incorporated in sample rotors. The calculations have been made for the various con- figurations and flight conditions covered in the original analysis (reference 4) .
A list of the flight conditi ons and assumed characteristics of the sample ~elicopter is given in table VII. The results of the calculations are presented in table VIII for smooth and rough airf o il surface co~ditions, and values taken fron referenc e 3 are included for the NACA 8-H-12 and 23012 airfoil sections.
It should be noted that the method of analysis employed makes the simplifying assumption that secti on characteristics correspondin g to a single Reynolds number apply for the entire r oto r disk; whereas in t he case of the assumed rotor, the variation of the Reynolds number is between zero and approximately 4 x 10 for a tip-speed ratio of 0 .2 (reference 4). Good agreement between predictions made by the theory discussed in reference 4 and experiment is indicated, however, in reference 8. In the present calculations, section data corresp on din g to a Reynolds number of 2.6 X 10 were employed in all cases. This mean v.alue is the same as that employed in reference 4 for r otors having the same maximum Reynolds n~be r at the tip as do those con - sidered in the present calculations.
A comp arison of the results in tab le VIII indicates that, for tee smooth surface condition, the NACA ll-H- 09 airfoil is · the best of the five airfoils tested in the presen ~ investigatio~ for nearly all the f li ght conditions investigated. The gains to be expected by using the NACA ll- H- 09 section in preference to one of t he others varie s , however , to a large extent with the flight conditi ')n . The results also indicate thst the NACA Il-H-09 sectio~ is ab o ut equally as good as the NACA 8-H-12 section at the conditions of tigh disk loadin3 a~d hl&h tip -spe e d ratio. For the other conditi ons conSi d ered , however, the 16 NACA TN 1922 NACA 8-H-12 section shows smaller losses than were calculated for the NAOA ll-H-09 section. The NACA 8-H-12 and ll-H-09 airfoils both show net power savings for most of the flight conditions When considered in relation to the NACA 23012 airfoil. The NACA 23012 airfoil, however, f appears to be better than the other airfoils of the present investi- gation for many individual flight conditions. Variations in airfoil thickness and camber have an appreciable effect upon the drag power; however, the amount and direction of the effect seem t:> va ry markedly with the flight condition being considered.
As an aid in understanding the reason that different airfoils may be preferred for applicati o ns emphasizing different flight conditions, a few sample weighting curves (taken from reference 4) showing the relative distribution of profile-drag power for different helicopter operating conditions are presented in figure 16. The weighting curves are presented for tip-speed ratios of 0 (hovering), 0.2, and 0.3.
These curves show, for example, that both the small range of angle of attack over which the largest power losses occur and the entire range of angle of attack which need be considered vary with the operating condition. The application of two of the weighting curves in calcu- lating the distribution of profile-drag power' loss for the NACA 8-H-12 and Il-H-09 airfoil sections is shown in figure 17. The curves of figure 17 were obtained by multiplying the drag polars of the two airfoils by the weighting curves of figure 16 for tip-speed ratios of 0.2 and 0.3. Since the area under each curve of figure 17 represents the total profile-drag power loss, the influence of different regions of the drag palars for these airfoils on the magnitude of the total power loss is indicated for the operat~ng conditions considered.
In the rough leading-edge condition, the data of table VIII again show the NACA ll-H-09 section to be the best of the airfoils considered in the present investigation for most flight conditions, although in many cases the results for this airfoil do not differ much from those for the 12-percent-thick section of smallest camber. In general, the results for the NACA 8-H-12 section are similar to those for the NACA ll-H-09 section. The data for the airfoils in the rough conQitlon are rather consistent in that they show the profile-drag power loss to increase in all cases with increasing airfoil thickness and camber.
The am o unt of the increase, however, depends markedly on the flight condition, although in general, increasing the camber of the 12-percent- thick section has a les8 adverse effect than increasing the thicknes~ from 9 to 15 percent with constant camber of 0·5 design lift coefficient.
NACA TN 1922 CONCLUSIONS A two-dimensional wind-tunnel investigation has been made of five NACA airfoils of varying thickness and camber designed for use in rotor blades. For the range of values of thickness and camber covered, the following conclusions can be drawn from the results of the investigation: 1. Near-zero pitching moments about the aerodynamic center were obtained for all the airfoils in the useful range of lift coefficient.
The position of the ae rodynamic center did not vary appreciably with airfoil thickness and camber.
2. The values of the maximum lift c oef ficient for the smooth condi- tion in most cases showed little variation with airfoil thickness and camber and were in ge~eral lower than those for symmetrical NACA 64-series airfoils of corresponding thickness. In the rough surface condition, the maximum lift decreased, although in a not entirely consistent manner, with both increaSing thickness and camber· 3· The value of the minimum drag coefficient for the smooth surface condition increased significantly with camber but was little affected by variations in the airfoil thickness. With roughened leading edges, the value of the minimum drag seemed to be relatively insensitive to variations in thickness and camber in most cases.
4. In the sm oo th surface condition, the value of the lift coeffi- cient corresp on din g to the center of that ra ng e of lift c oe fficient throu gh which l ow drag prevails increased wit h increasin g camber and, in all cases, was larger than the theoretical design lift c oe fficient.
Increasin g th e airfoil thickness caused some increase in the low-dr a g range. In the rough surface condition, increases in b oth camber and thickness had a very adverse effect upon the dra g polar in all cas es.
5· For vari ous flight conditions, comparis ons of the predicted relative performance of sample helicopter r oto rs employing the diffe rent airfoil sections indicate that , in gene ral, the NACA ll-H- 09 airfoil is the best airfoil of the group investi g ated for bo th smooth and rough surface conditions. The effect of increasing airfoil t hick - ness and camber upon the relativ e performance varied with the flight conditi on for the sm o oth airf oi ls, but in all cases, increases in thickness and camber had an adv erse effect upon performance when the airfoil surfaces were r ough .
6 . In com p arison with the NACA 8-H-12 airfoil (d esigne d in a previous NACA in7estigation), th e NACA Il-H-09 airfoil d oes not appe ar to offer any hope of gains in pe rform9nce for most of the flight 18 NACA TN 1922 cond itions c onsidere d. Both the NACA 8- H- 12 and ll-H -09 airfoil se c tions show net powe r s a vinga in comparison with the NA CA 23012 air- foil for nlost of the flight conditions , whereas t he NA CA 2301.2 airfoil appears to be better than the other ai r foi l s· of the present investiga- tion in most cases .
Langl ey A eronautical Labor a tory Nation a l Advisory Committee fo r Aer onautics La ngley Air For ce Base , Va ., J une 1, 1949 REFERENCES 1 . A bbott, Ira H ., V::JU D oenhoff , Albert E . , and St ~ vers , Louis S ., J r . : Summary of Ai rfoil D ata . NAC A Rep . 824 , 1945 · 2 . Tetervin, Neal : Tests in the NACA Tw o -D imensiona l Low - Turbulence Tunnel of Air foil Sections D esigned t o Have Sma l l P itchin g Moments an d High Li ft -Dr ag R atios . NAC A CB 31 13, 1943· 3 . Stivers , Louis S " Jr ., and R ice , Fred J., Jr . : A erodynamic Characteristics of Four NA CA Airfoil Se c tions D esigne d for Helicopter Rotor B l ~des . NA CA RB L5K02 , 1946 .
4 . Gustafson , F . B . : Effect on H elicopter Per formance of Modifications in P rofile- Dr ag Cha r acter i stics of Roto r- Bl ade Ai rfoil Sectiona .
NA CA ACR L4 H05 , 1944 .
5 . Von Doenhof f , Al ' bert E., Sti v ers , Louis S ., J r ., and 0 'Connor, James M. : L ow - Speed Tests of Five NACA 66 - Series Air foils Having Mean Lines D eSigned to G ive High Critic al Mach Nmnbe r s . NAC A TN 1276, 1947 .
6 . Von DoeILhoff, A lbert E ., and A bbott , Fr ank T ., J r. : The Langley Two - D imensional Low- Turb:llen ce Press m: e Turmel . NACA TN 1283 , 1947 .
7 . Loftin , La urence K., Jr., and Cohen, K enneth S .: A erodynamic Char acterist i cs of a Nmnbe r of Mo d ifie d NA CA Fo ur-D ig i t - Ser i es Air foi l Sect i ons . NACA TN 159 1, 1943 .
8 . Gust af son , F . B ., and Gessow, A lf r e d: Ef f ect of Blad e Stalling on the Ef fi c iency of a H eli c opter R oto r a s Me a sure d in Flight.
N ACA TN 1250 , 194 7· NACA TN 1922 TABLE 1. - ORD I NATES FOR TABLE 11. - ORDIllATES FOR NACA 11-H - 09 AIR} ' OIL SE CTION N A CA 12 -H - 12 AIRFOIL SECTION (Stations and ordinates given i n !Stations and ordinates given in perce nt of airfo i l chor~ percant of airfoil cho r d] Upper surfac e Lowe r surface Uppe r surface Lower surfac e Station Ordinate Sta t ion Ordinate Sta t ion Ordinate Stat i on Ordinate 0 0 0 0 0 0 0 0 · 983 . 866 .1 83 1.123 -· 3 01 . IJlJ
- '11/
1.267 1.162 1.10 : ;~ -. }15 03 . ~92 l 'a 1. 715 0 1. 62 1. 650 -1: 009 ·7 5 5 - · 311
1.Zt . 2
2. 000 2. 0 } . OOO - .2}8 2. 0 1 2 · 723 2 . ~39 - 1.~1 - .090 4 . 521 - 1. 8 3· 996 ~ . 525 ~.990 t : tJ~ . 012
5. 0 18 . 036 i: J~ 7· 012
. ~ 75 - 1'$~3 10.1 ,80 5. 8 51 5. 00 - 1. 2 ·~~5 10.~8t ~J~O
J: ga
7· 112 . 250 15 · 385 J . I02 15.4 - 2 . ~6 20 . 272
.278 t 0 20.3 0 - 2. 6
g. t4
. 07~ $ : 9g~
~ : $~ 25 . 2 71
25 . ~6 8 · 77
' J29 -2 'E 0
:~ 8 . 890 30 . 3 29·957 9. 246 30 .171 2, ' 29 -2 . ~8 .019 ~ · 925 9. 472 - 2 . 44 ,5 .0 75 8'A7~
4 .9§l
35 : gttg 8. 2 - . 1.42 0. 217 83 0.1 - 2· 525 9 : ~~ Gl 'Z 45 . 331 8 . 387 .' 69 - · 315 Gl.697 45 . 303 - 2· 532 0 - . 513 O A. 412 91 ~.606 4, . 60 9 - 2 . ~20 5 ' [..94 lJ2§
5 'E
9O - 2. 85 g5 . ,10 ~5 . 25 5 . 57~
-' JlO L~9 1
't -2.422
0·392 0· 422 ~ . 9~7 - . ,3 lZ ' 08 . 963 .648 - L O 7 ~ : ~I1 65.352 65 . 389 - 2· 327 -2 . 202
1 - 1.173 t4~ 670
3.g 5 70·}30 70.29~ 6' .7 0~ 2. 62 - 1. 252
t ~5 . 252 3· 333
~5 . 22 -2. 0R
7 'J4
7 'U
-1. 2 71 0.1 66 1. 843 2. 230 - 1.8 0.1 ,M ~.34 Jt926 - 1.2 16 · 916 1.219 . 91 85 .0 - 1. 5§9 85 . ~ g - 1. 052 90 . 024 .1 70 89 · 976 90. 0 . 387 89.97 - 1.1 ~ -. 1 50 95.006 -. 271 95 · 005 -· 725 94 . 994 - ·72 94 . 995 0 100.000 0 1 00 . 000 100 . 000 0 0 100 . 000 -- L. E. ra di U.9 : 1 .040 L.E• .r a di us : 0· 579 Sl op e of r ad i us through L. E .: Sl ope of r adius th r ough L.E. : 0. 569 0. 343 TAB LE III . - ORDINATES FOR NA CA 13-H - 12 AIRFOI L SECTION ~ ta t i ons an d or dina te s gi v en in perc e nt of a irf o il chord] Upp er sur f ac e Low e r su r fa ce
St at i on 1 0rdi n at e S tat ion I Ord inate
o 0 0 0 . 02 5 1.183 . 975 I -. 52 7 .2 13 1. 5 11 1. 287 -.5 89 . 642 2. 05 7 1. 858 -. 663 1. 82 0 3. 11 0 3.1 80 - .7 26 u.268 4 .674 5 . 7 ~ -. 752 6.772 5.883 8.228 -. 74 7 9. 299 6. 882 10 .7 01 -. 7 32 14 .410 8 . 426 15. 59 - ·7 38 19 . . 55 3 9 · 535 20 · 44 7 -· 773 24 708 10.296 25 . 292 - . 840 29 . 86 7 10.7 57 30. 13 3 -· 92 7 g5 . ~5 10. 92, 34 . 95~ -1 . 02 7 4~ : ~5~ i g : ~$4 Gl : ~~5 :i : ~ ft 50 . 555 9. 50 1 49 . 44 5 -1 .4 03 55 . 588 8 . 521 54 . 412 -1.5 23 60.5 74 7. 395 59 . 1;26 - 1. 629 65 . 5~3 6.1 72 64 .477 -1 .7 06 70.440 4 . 889 69 . 56 0 -1. 75 3 75. 335 3. 596 74 . 665 - 1·752 80 . 220 2. 350 79 .7 80 - 1 . ~8 4 85 .11h 1. 220 84 . 886 -1. 'i?/t 90.034 . 306 89 . 966 I -1. 264
94 . 993 - . 25 7 95 . 007 I -. 8 33
100 . 000 0 1 00 . 000 a f-.
L. E. radius : 1 . ~40 Sl ope of r ad i us th r ough L. E .: 0. 556 NACA TN 1922 TABLE IV. - ORDINATES FOR NACA llt-H -12 AIRF 'O I L SEC'l'ION [ Stations and ordinates g iven in percen t of airfoil chord ) Upper surface Lower surface Station Or dina te Station Ordinate 0 0 0 0 - . 096 1.233 1.0 96 -· 319 1. 606 1.429 -·32 2 . 0Zl 2. 031 -· 301 2 . 23~ l:~OS 3 .L ~ 7 3· 392 - .180 .062 5. 338 ~ , or ~ ' G6 7 . 262 6.774 • 57 · 5 3 7. 9 10 ·9 11 . . ~28 ~ . O 9 9. 7 6 . 26 4 2cl 5.7
1 4R
10.~94 20 · 53 ~ : ~t : lO~ • 86 11 . 12 25 . 314 29 · 905 30 . 095 12. 234
' 4~3
12· 3 34 · 867 . 30 ,5 . 1 33 12 .152 1 .218 o· t°9.
El · 9
45 . 06 11. 515 -. 017 . 3~4 50 · 717 -. 281 4;: .2 3 10'4£4 5 . 250 ~5 . 750 -. ~56 ~ :1 50 -. ~O 0 'Z 2 ~4 : 274 O 6.7 58 - 1.0 2 70 . 9 7 03
6 'M
64 · ~1 5' "$0 -1'E
~5 • . 16 3. 57 -1. 69 7 · 5 ~ 0. 27 L f 2. 470 0 -1. 55 ~ ' A2 1. 223 85 · 11f3 . 57 -1.527 90 . ol~3 . 225 89• 95 - 1.345 A 94 . 99 -. 363 95 · 00 -· 939 100.000 0 100.000 0 L. B. r adius : 1.040 S lope of radius through L.E.: 0· 768 -- , TABLE V. - ORDINATES FOR NACA 15 -H-15 AIRFOIL SECTION [ sta · tions and ord i nates given in p erce nt of ai rf oil chord] Uppe r surface Lower surface S ta ti on Ordinate Station Ordinate 0 0 0 1.062 1.3 82 -. 062 - . ~56 1. 386 - . 70 .1llt 1.750 1.985 -1.024- 15 2.3 54 -1. 213
't 1. 33 3·537 ~ . 367
OOO . 000 l·33~ -1.~ -1 .
i'
45 ·77 • l 8.~~ 0 .l1.0 -1. 1+7 8 ·97 7. 99 -1. 50 1 15 · 94 9 . 9 1 ~ 14 . ~4 11.34 20 · 753 -1. 5~ ~ . 7 2 2 -1.
5. 5 7 12.3~4 . 4~
t
t 30 . 27 -1. 47
12. 9 1 29 ·7 OO1 13.~1 -1.~ 23
R . 34Ji4
86 -1. 37 13·0 9 0'6 -1.
12.451 ~ . 33 1 9 5 45. 69 -2.0 6 G 11.472 4, . 167 50.8 "$3 -2.1 56 8 10.2 50
5 . M4
l5. l
- 2. 25 2 8. 856 0.8l -2· 31 7 7 . 3~3 l4:2~3 65 ·Z 7 70 . 3 - 2,33,
~.7 9 6,.3 l
G .230 - 2.2l
5 47 7 ' l2 A • -2.1 5 0·310 2·739 ~4:~~ 1.391 -1. 9~7 85 . ~ 89 · 956 -1. 5 7 90 . · 3 11 -1. 031 94 . 9 7 -·33 9 95 ·013 0 100.000 100.000 0. 382 L. E. radiu s : Slope of radius through L.E.: 0. 525 ) ~ rD f-' rD rD
~ :t> 1-3 ~ f-'
\0 on c- 103 087 . .020 .
.08:> . .081 ti y/c 0 .056 poe!
M rod,yna1u1 .259 .264 ·278 .241 .2 .
x/c center .112 .112 .140 .117 .U8 .111 tic .t 0.250 0 .083 p .280 ~ - airfoil.
0t basic .744 .7 .744 ·704 Mer 8 -R-12 ----- -.--- for 0 .784 symmetrical A aeet1en, NAC ·518 · at .625 ·573 ·547 .60 (tt the 0·580 6) for .
6x10 99 57 ·39 .68 · · 01 6 cl i 0.68 ---- ---- (exp.)
(J;,,2. of X 10 .53 .85 .91 2.6 ---- l06) 1.08 value 6X ------ toO.79 to t o to to - - - -dreg - R .
Tango 50 go .26 · . .25 Lo,,' ~.
( 0 ·58 ---- .--- end 0~7 experimentsl (e) .007 . .006 .005 _c X 10 - .013 0 .005 0 .8 the (~.6xlO6) at R _ .- and - CS at 01,1 0J.04 .oU8 .0118 .0148 . .
--- 0 .0113 1l, o (RJ~~06) !UBrI CTE airf A results AR the CI! 0051< 007 0053 0046 .00 .0053 . . . .0064 cdmin 23012 0 .
at (R:::2.6xJ.Q6) NACA SECTION Smooth the IL polAtion .0050 .0063 .0055 .0057 .
r ------ and.
0 .0047 .
(R::2.1x106) AIRFO inte 6 · - 10 by VI 17 3 x ~ito6) 1. 1.13 1 .07 1.11 ---- 1.19 1.
of TABLE (l1o:~ investigation i
I I
obtained s 6) hi t 9 beBn 6x10 61 msx .
of Cl 1 .28 1.2 1·38 1.27 1.26 1.
1.30 ave h (J<::2 specified. 6 Smooth airfo1ls e Reyno ld.e number X 10 -- 39 31 .1x106) 1.25 -- erwise the for 1.32 1.26 1.25 1. 1.
2.1 (J<::2 oth - for R _ given - 011 at .. 33 62 -- unless ere 51< 47 40 26 ~~106) il of o (~
I
) airfoil a~ue eirf v condition 33 50 35 6xlOO 147 1 148 1 153 1 111 this ca l th1s tor t or (Cl/Cd)""" (R0<2. amooth reti ) theo Smooth the given 147 149 148 169 147 130 --- for the l'esultB at (~.1xJ.0 given 3) 1) given il on are o nce -I!-12 chareoterlsticB ex:pel'1Inental HACA seetl 11-l!oC9 12 13-1!-12 14-1!-12 airf 15-H-15 ~3012 c8_R_12 (refere (reference ~elu"B ~r CAll dAll
•
NACA TN 19 22 TABLE VII FLIGHT CONDITIONS AND ASSUMED CHARACTERISTICS OF THE SAMPLE HELICOPl'ER OF REFERENCE 4 ~otor diam., 40 ft; tip speed, 400 fps; gross weight for W /S of 2.5, 3140 1~ r---- - ).
(J el e
Condition f W/S ~ ------- 1 0 0.07 0 15 1·55 7 2 ------- 0 .07 0 15 3·33 13 ------- 0 .07 15 3 5·42 0 19 ------- 4 0 .07 15 2·5 0 10·3 .2 .07 0 -0.0385 15 5 2·5 9 6 .07 II - .0695 15 2·5 0 ·3 .2 .07 - .0319 15 1·9 0 7 8 .2 .07 II - .0469 3·1 0 15 .2 .10 2·5 0 - .0350 15 9 7 -8 -.0680 10 2·5 .07 a10·5 15 ·3 aMeasured at 0.75 R.
, I\) I\)
~ :x> 8 ~ f-'
\0 I\) w n g g of of of of of o lidity adin loading (hoveri ( o fi~~~)d so f ect blade twist Remarks flight) tip-speed rati Effect Effect Effect Effect Ef ~ ~ } l J
l J }
I}
~
.7 (a) 42.6 31.0 ---- 24.1 21.7 25.7 23.5 25.7 29. 2 23012 .7 1 31.0 ---- 39.0 35.3 41.4 65.7 37.7 41.4 57·3 41.4 \ 25 65 112.1 1 32.3 1 20.1 (a) 8-H-12 36.7 18.5 56.8 16.3 21.2 17.5 21.2 28.6 25.2 27.7 .3 1 21.2 6.1 6.6 50'5 1, 14.4 248.5 483.5 181.2 194.2 11 181.2 24 181 159·5 170.6 !
I
. .2 hp 15-H-15 VARIOUS 18.7 17.9 1153.8 63.8 36 46·5 25 26.3 25.3 26·3 51.7 FOR OPl'ER '7 1 loss, 5 3.3 ! 26·3 4 64·9 73.3 337·0 155.6 101·9 120·7 LOSS 126.1 103.3 134.2 103· 3 146.4 10 HELIC ! !134.2 ! 63·8 1194.2 ! 36.7
I
section .
14-H-12 30 60.4 57.7 36.7 38.0 54.3 54·9 22·3 25.2 29.5 29·5 SAMPLE profile-drag airfoil VIII THE 37.3 1 72.6 45.6 74.6 49·8 74.6 74.6 1 29.5 69·3 86.6 101.9 :rnOFILE-DRAG 287·0 1ll·5 !101.9 ! 57.7
I
OF NACA T.ABU: 13-H-12 30.1 32.4 19·3 16.2 30.1 66·5 22.8 62.5 50.~ Rotor-blade ·9 35.81 22·3 59·3 40.6 60·9 81 45·3 60·9 85·4 60. 91 30.1 63.4 81.9 ! 66.5 71.0 CONDl'1'IONS ROTOR-BLADE 199·0215.6
I
OF .
12-H-12 13 32.1 18·3 32.1 61.1 32.1 25·8 58·7 44·5 FLIGRI' 23.3
1 ,195.6 I 1 17.7 ! 1 58·7 I
.8 .5 44.8 60.5 44.8 53·8 58.1 60 53.7 COMPARISON
~ 1
I 1 136 11-H-09 16.6 . 43.8 40.0 186.4 32.0 25·5 23.1 144.8 32.3 29·2 21.8 \ 34.4 22·7 23·1 SmoothIRough /Smooth IRoughISmoothIRough IBmoothIRough ISmoothIRough /Smooth IRough 1Smooth .2 .2 .2 · 3 2.5 1 16·7 2·5 1 23·1 2·5 0.2 0.2 0.3 1 32.0 0 0 0 = = '" 3.
I.l I.l I.l VII) I.l t I \ ' W!S", tions 55 .33 .2 .3 .10 0 0 3 5.42 1.9 3·1 0.07 0 table 1. 0 2·5 ~ -8 '" '" = = = ~ condi reference Helicopter a I.l (see ..-.
e
W!S w/s
.- l \ 2 3 4' 5' 6, 51 51 9 6 lO ~rom
-
i L
1 I ------'-'
~-- - ~ ---...- 24 NACA TN 1922
1.6
r'-..
~
~
1.2
~
f\
\
1\
\
~
\
\
~
o
'\
~
-.1+
\
r\
~ "\
-.8
o .2 .4 .6 .8 1.0
x/c
Figur e 1.- Theor eti cal load dis t ribution of the NACA l 3-li -1 2 airfoil
section at the de sign lif t coefficient , cl = 0 .5 ·
i
---- -~"~
• NACA TN 1922 r--- 2.0
r---
~
~
~
1.6
V--Upper aurt'ace ["- Lower surt'ace
IY
't?(
'\ i.--"-'
V-
J ~
--
V
L-----'l-i-
~
'"
.8
---
~
V ---
V-
"'-
"(
I i
.4
-
~ t---
r--
V r----
t---- ~
o
1.0
.B
o .6
.2 .4
x/c
? igur e 2 .- The or e tical pressure distribution of the NACA Il-H-09 airfoil s e ction at the design lift coefficient, c~i = 0· 5 · \ .
26 • NACA TN 1922 2.0 ~ .
L------
/
~
1. 6
surface v-Upper Burfa.ce fLower
I
~
'K
2 1.
'\
'\.
!
'\ I-- L---
"\
L------
I / f"\
'\
l
!
~
I " '"
,
-
V--
:----.-.
-----
I----
V
r----..
:--- ~ .6 .8 1.0
o .2 .4
xJc
Figure 3 .- Theoretical pressure d i stribution of the NACA 12- H-12 airfoil
s e ction at th e de sign lift coefficient, cl = 0· 3 ·
i , . ~ NACA TN 1922 o ,/' r-..
2.
----
(
1\
\ surface
v--Upper wwer surface
V r
6 1.
1/
\
2 ·
\
/
(~) 1.
'\
v-----
L..----
...---- .
/ ~
~
'\
~ ~
------
'"
V
~
~ /'
(
~
~
r----
IV
v--I
I---
i t--
i
j ~
i
o .2 .6 .8 1.0
·4
x/c Figure 4.- Theoretical - pr e ssure distribution of the NACA l 3 -H-12 airfoil section at the design 11ft coefficient, c = 0·5· Li 28 NACA TN 1922 2.8 ~
. (
--- ~N
~ )
\
2.0
\
I
I
~Upper surface !
jwwer surface J.
~
1.6
I J
\
J
i/ \ /
1.2
/
Y /
/
\
~
,/' '\ .8 ~
/
\
~ v
V
I--
/ ~
-
v
------
---
j/
-----
~
-----
~ I ,
o
.8 1.0
o .2 .6
·4
x/c
Figure 5 .- Theoretical pressure distribution of the NACA 14-H-12 airfoil section at the design lift coefficient, c~i = 0·7.
NACA TN 1922
V
/ i\
2.0
\
I
J ~Upper surface surface ,-wwer
~
1.6
\
~J
l\
-- \
~
V ~
~
L-------
L-------
\
.8
--
-----
\
/'
\
(
!----
r-- ~
-
.4
~
-
t---.
"
V
t---.
r--
~~
o
.2 .6 .8 1.0
o .4
x/c Figure 6.- Theoretical pr e ssure distribution of th e NACA 15 -li-1 5 airfoil s ectio n at the design lift co e fficient, eli = 0.5.
o
w ~ ~ t-3 ~ I\) I\)
t--' \0 o chord.
24-inch .27g .2M .276 0.2 roughness section, 6 X .1 X R 2 0.9 2.1 2·7 Standard airfoil :.f::r']'::t:·'!t:r"n;m; ~ nJ: t: ll-H-09 l ·J'~T:T NACA I Ik the .
Y .
of ..
.
.
'., .
cteristics , a ~ ~.r.,..
char ness rour 6 x 10 rd .1 a x 2 R .1 0.9 2 2·7 Stand Aerodynamic 7.- Figure f\)
~ :x> ~ f-> f\)
1-3 \() f-> W o chord.
24-inch section, airfoil -R-1 l 2 NACA ~ I - .. ..
the I ' fh '"" of • " , """ L I l J L \ 1 .j" " I k .1<1" racteristics & "" a ' U ch roU~hneBB x 1 0 R x 2 . 1 Aerodynamic 0.9 2 . 1 2. 6 Standard o G <> t:::. .- Figure I f\) w !:2l f.; :x> 8 ~ f\) f\) ........
\D .0 chord.
24-inch .271 .264 .271 0.265 10 section, roughness )( x 2.1 R 0.9 2.1 2.6 Standard airfoil l3-li-12 NACA the of characteristics Aerodynamic 9.- Figure :x> f-'3 ~ I\) I\)
~ l-' \0
LV LV chord.
24-inch 21': 2S5 . 266 . 259 .
0.
ess 106 section, r ou ghn )( )( 2.1 R ndard a St 0.9 2.l 2.7 airfoil -12 14-R NACA the of -~
--
characteristics rodynamic e A .- e Figur f\) ~ o ~ !-OJ ~ f-J f\) -I="" \() (..,u O ' ~ I \!; ~ i chord.
:;;;fejgl¥Cn~fl U?
~~~r~~ltll m 24-inch g .26 .264 .2g0 0.276 section, roughness 6 )( )( 2.1 R .1 airfoil 0.9 2 2·7 standard -15 l 5-H NACA the of characteristics Aerodynamic 11.- e 2.8 Figur NACA TN 1922 .028
I I
NACA l.2-H-12 / NACA iE.-H-1.2 I-NACA -H-1.2
Vr
/V /
.024
l7
V /
I
\'
\
1/
.020 \ I I 't:I () I
\
\ ..
I ~ I s:: CI)
\ I !I \
-rl .016 () \
\
-rl I \ ~ I 'H \
I \
~ r () I
If
\ I
\
tIC
\
1\ .012 Cd "I M I '0
I~ I
\ \
s::
\ \
-rl
v .... -
I I ~
\
() I
/' ~
Q)
~~ '-, / /
It r---
ell .008 ---..
[l7 ~ \
~'5f
/ ~
,/ r::- 1----
V
\~
~ , NACA g-H-12
.004
I
, I
~
o
.8 1.2 1.6
o .4
- .8 -.4
Section lift coefficient, c1 Figure 1 2.- Vari a tion of section drag coefficient with section lift coefficient for the NACA 12-H-12, 13-H-12, And 14-li-12 airfoil sections. Smooth condition; R = 2.6 X 10 • Data for NACA 8-H-12 airfoil sec ti on are from reference 3.
NACA TN 19 22 .028 ,
I I
f-NAOA 15-H-15
I I
.024
~-NACA 13-H-12 I I I I I ~NACA Il-H-Q9 I
\/
.020 'd I
"
r~\
/
" ~ I \ s::: I \/ Q) I \ -rl
V
1-- .
.016 .' .
"
I ~ \ ~ I \ Q)
\
/
" \
\ bO
/'V
oj \
\
M .012 'C I
1/'/
I
s::: Y I
\ I I
1\ I -rl ~ / "- Q)
"
/'
~
til N,
//
I r--
.008 ~
V
'\
V
I-- NACA 8-H-12
~~\
a-:
li
V- ~ ~--=
i\--
I--' .004
~
I
a
1.2
-.8 -.4 0 .4 .8
Seotion 11ft coe~flclent~ 01 Figur e 13.- Variation of section drag coefficient with section lift co e fficient for the NACA ll-H-09, 13-H-12, and 15-H-15 airfoil sections. Smooth condition; R = 2.6 X 10 . Data for NACA 8-H-12 airfoil section are from reference 3.
NACA TN 1922 .028 I 1 ~ NACA 1)-H-12
r I I
1 .1 NACA 14-H-12
!
II
.024
\
\ / II I
\ \ I
II
\ I
II
\ I
\ f
.020 T I \ I tt$ \
\
/ I I
/'
, ...
.p
I
/ I
J::: \
Q) \ / I /
\ .016 ....
\
"
.... / /
\
LJI
fH
\
\
fH / / /
Q) '\ /
0 7
/ () \ I il',
v/ 1'-..\
tID
/
.012 QS s:.. "-
--
~
-
~ f-- V
....
...,.
I C)
\
I- NACA g-H-12
Q) /
.008 til
L
I f-- NACA 12-H-12
I
.004
I
I
~
i I I
o
1.2
-.8 o .8
-.4
·4
Section lift coefficient, cl Fig ur e 1 4 .- Variati on of secti on drag c o efficient with s ec tio n lif t c ce ffi cien t f or the NAC A 1 2 -R-12 , 1 3-R-12 , and 14-R-1 2 airfoil 6.
sec tio n s w it h leading-edge r o ughness. R = 2 .1 x 1 0 Data fo r NA CA 8- H-12 airf o il secti on are f or R = 1.8 x 1 0 (reference 3) · NACA TN 19 22 .028
~N ACA l}-H-12 I
/ rNACA ll-H-09
.024
t:
I / /
I I
I
\
\ /
.020 I II \ 'd
\ \
\ c>
I
\ \ \
I I I I II
\ "'
I I
~
/ I / ~
4)
i\ \ / i / I
\
~
...+ .016 c> -// ...+
/ J / 1
4-i
'\\-
'H
\ / I I I
/
4)
/ I
c> /
\\
!
/ / I ~ bO
\/ ~
ctf .012 I M ~ I
I
'd I
'----
I
-
s::
r: I
r I
...+ I I +:> NACA
L 15-H-15 \
c> f- NACA 8-H-12
:5
.008 I .004 ~ I I
o
o 1.2.
-.8 .8
.4
-·4
Section 11ft coefficient, cL Figure 1 5 .- Variation of section drag coefficiept with section li f t co efficient for the NAC A Il-H- 09 , 1 3-H-12 , and 15-H-1 5 air foi l sec t i ons wi t h leading-edge roughness. R = 2 .1 X 10 . Data fo r NACA 8- H -1 2 airf o il sec t i on are fo r R = 1.8 X 10 (reference 3)· NACA TN 19 22 .2 0 I
I
til Q) .12 '1j ~ Q) P- ..
I
'd .10 ()
I
b
--
J'i
I I
.O s
. 06
---- - ( ' I I
I
I I " I I
I
- , W/S I H over i ng
2.7
I I"-
- -
.04
2. 5 v-lJ.= 0.2
1; \
2. 5 j lJ.= o.~ ~V
I t
il ~
~
! :
"
1/ I
I
~Ll
~
t- (-
-
I . \
r-
I-~
)
- - t'.
.. ./ I V : °4
o 4 S 12
- Seotion angle of attack from zero 11ft, ctr, deg Fi gure 16 . - Weighti n g curv e s f or t hr ee t ip-s peed r a tios of the sample he l ic op te r r oto r .
f\) f\)
+="" o ~ ~ 1-3 ~ ~ -0
angle I helicopter I section
~
of sample deg range the in the (tr' over used
~
lift, 5 · loss when ~- 2· zero
s
~ ; - g power from 0 sections =
e
attack airfoil "'=- ll-H-09 of 0 . 2 ; profile-dra ~ = of r--NACA 8-H-12 ~ angle
/ ll-H-09
\
~NACA /
~~
4 (a)
\ \ \ \
(I I I
I
:(V
I '/ / Section distributions 8-H-12 and condition.
~
of NACA irfoil the ~~~- for Comparison Smooth a 10-4 x ttack 17.- a 8 6 2 o of rotor.
gur e bO ~ Q) Po Q) reS
~lb
Fi I\) f\: ~ f; ~ 8 ~ f-' +:- ~ \0 , i I i
\
"-
j\
,./
~
--
V
-- ------- -.
.
--
deg - rl a
-
2 .5 .
= d.
10 11ft,
~
zero 11° ; Conclude
=
from
e
7.- ""=- 8-H-12 0 . 3;
---
attack
=
NACA ~
ll-H-09 Figure gf ~ I--- (b) NACA / angle '--..':: '-
/
"- ;--- ",-'- I
/ '/ ~
\
,
\
V Section
r\ I r I I 1,
,J
VV
~
o
10-4 x
o
6 2
8 4
...
til ~ r.. Q) p.
"0 ~Ib , , ~ .... '" o o o
z > C"l > t- ..., -
~ ~