NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED August 19lt4 as Mvance Confidential Beport Ll^O^ EBTECT ON HEUCOPTEE PEEFOEMMCE OF MDDIFICATIOHS IH PROFILE-DRAG CHAEACTERISTICS OF EOTOE-BLADE AIRFOIL SECTIONS By F. B. Gustafscm Langley M^oorlal Aeronautical Laboratory Langley Field, Va. '..^k ^m-^sur. MAC A WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L-S6 DOCUMENTS DEI^AKlMtMl Digitized by tine Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/effectonhelicoptOOIang ¥AGA ACR Fo. LI+HO5 CONFIDENTIAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE CONFIDENTIAL ^REPORT EFFECT ON HELlCOPTSR PERFORMANCE OF MODIFICATIONS IN PROFILE-DRAG CHARACTERISTICS OF R0T0R-5LADS AIRFOIL SECTIONS By F. B. Gustafson SUMMARY Perfornance calculations are presented for a typical helicopter rotor in which three types cf airfoil section were successively used. The types represented are the rough conventional, the smooth conventional, and the laminar-flow or ].ow-drag sections as developed for heli- copter use. The perform.ance items covered are rotor thrust for fixed power in hovering, range and endurance at cruising speed, and povi/er required at a relatively high forward speed. Contours showing the conditions of operation encountered by the blade section and weighting curves showing the relative importance of the various section angles of attack for specified flight conditions are Included as an aid in the interpretation of the results . The calculations indicated that the use cf a smooth conventional section will result in marked performance gains throughout the flight range. Definite, though smaller, additional gains in take-off weight and in range and endurance may be realized by the use of a lovif- drag section. At high fcrvvard spee,ds or at moderate forward speeds and high loadiiigs, however, losses are Indicated for the lov/-drag sections in contrast with the- sm-ooth conventional sections. It is deiaonstrated that, if these losses are to be avoided, the lovi/-drag sections must be designed to avoid the extremj.e rise in drag coeffi- cient at the higher angles of attack wiiich is character- istic of the low-drag sections now available for use in helicopters . CONFIDENTIAL CONFIDENTIAL NACA ACR No. li|H05 INTRODUCTION It is generally recognized that an important part of the power required to operate a helicopter is absorbed by the profile drag of the blade elements; consequently, considerable interest has been shov/n in the possibility of using laminar-flow, or low-drag, airfoil sections in helicopter rotors. A recent report (reference 1) described the characteristics of several lovif-drag sections that were developed especially for use in helicopters. Pre- vious low-drag sections had either excessive pitching- moment coefficients or low drag only at extremely low lift coefficients. The sections of reference 1 were designed to give the maxiin-um lift-drag ratio (L/d)„^^ obtainable with zero pitching-moment coefficient, over an appropriate range of Reynolds nioraber. In order to indicate the magnitude of the performance gains that might result from the use of the new sections and to provide a guide for the development of additional sections, an analysis has been made for several condi- tions of fliglit for a helicopter of assumed charactsr- Istics. The method of analysis used for hovering flight differs considerably from that used for forward flight. The results for the tv/o fligjit conditions accordingly are presented separately. Material that is not essential to the analysis but provides substantial aid in under- standing the results has been incorporated in an appendix. SITMBOLS R rotor-blade radius b niomber of blades c blade chord r radius of blade element r ^ = R 8 pitch angle of blade element e , difference between hub and tip pitch angles (posi- tive when tip angle is greater) CONFIDENTIAL NACA ACR l^To. rliJi05 CONFIDENTIAL 3 Qyc blade pitch angle at x = 0.75 Cl rotor angular velocity^ radians per second V forward speed u, tip-speed ratio V \ cm J a angle of attack of rotor disk XQR speed of axial flow through rotor disk (positive upward) ttQ section angle of attack (absolute) Cj section iDrof ile-drag coefficient ^0 c^ section lift coefficient a slope of lift coefficient against section angle of attack (radian measure) a solidity; ratio of total blade area to swept-dlsk area (bc/rrR) T rotor thrust Cm thrust coefficient ( —3 ]-] torque coefficient / Rotor torque V pQ^TTR-^ P power Cp power coefficient ('R^tor-shaf t power input N Co ^r I j-totor-snai r power input; \ \ p^ttr5 J Cl lift coefficient /Rotor lif t N^ \ ^PV^TTR^ J angle of attack of blade element from zero lift ttn angle of attack of blade element at tip UmQR velocity component at blade element perpendicular to blade span and parallel to rotor disk UpQR velocity component at blade element perpendicular to blade span and to UrpQR CONFIDENTIAL i^ CONFIDENTIAL NACA ACR ITo . lijJ-:05 T Up cp = tan -^ TT^ \{; blade azimuth angle measured Troiu dov>m wind in direction of rotation ¥if gross weight, pounds W/S rotor disk loading, pounds per square foot f parasite-drag area, square feet p air density Subscripts: 1 induced o profile H0V3RING FLIGHT In order to indicate the effect of variation in air- foil section drag characteristics ovx the useful load that can be carried, the rotor thrust developed by a fixed shaft power was calculated for an assumed helicopter rotor in which three different types of airfoil section vvere successively used. The calculations were, in each case, carried out for a series of blade pitch settings. Sample Helicopter Rotor The sample helicopter was assumed to be in hovering flight at sea level. The rotor characteristics were taken to be as follows: Rotor radius, feet 20 Solidity O.O7 Blade plan form Rectangular Blade twist None Power available at rotor, horsepower 2d0 COFPIDEITTIAL NAG A ACR Fo. i4h05 CONFIDENTIAL Airfoil Section Characteristics The NACA 5~'K-15.5 section vvas chosen as representa- tive of the new low-drag sections of reference 1, The NACA 25015 section, for which data are also given in reference 1, was included to permit comparison vv^ith a smooth conventional section. In order to permit compari- son with a conventional section in a condition believed to be typical of present-day rotors, a "rough'* conven- tional section was included; the drag curve for this section is a composite of data from various sources. The curves of profile-drag coefficient against angle of attack used for the three sections are shown in fig- ure 1. These curves are representative of Reynolds numbers corresponding to the outer part of the rotor disk, in which most of the profile-drag losses occur. As is shown in the appendix the Reynolds number, Mach number, and angles of yaw encountered by the rotor blade vary considerably over the rotor disk. No attempt was made to modify the curves of figure 1 to allow for these variations; the analysis is thus a comparison of drag curves representative of certain ty;pes of airfoil section rather than of specific sections. The profile-drag values available for high angles of attack were Incomplete, especially for the NACA 5-H-I5.5 section. The drag data of reference 1 reach an angle of attack of 15^ for the NACA 25OI5 section and of 10° for the NACA 3-H-15.5 section. The following relation, which is based largely on a composite cf all the data for high angles of attack of reference 1, was used to extend these data as necessary: Acdo = 0.25 (Ci> - cj) where Ac^ increment in profile-drag coefficient above value at upper end of s traight-llne portion of lift cux've C7' lift coefficient as given bv extension of stralsjit- line portion of lift curve This method gives results that agree with the available values for high angles of attack for the low-drag sections of reference 1 v/ithln about ±20 percent. It is also in CONFIDENTIAL lOIIPIDSNTmL NACA ACR No. lij.H05 approximate agreement with drag data for other airfoils at angles of attack beyond the stall. The slope of the airfoil section lift curve was taken as 3*35 throughout the analysis. Method of Calculation of Thrust for Fixed Horsepovi-er Thrust .- The rotor thrust T is T = Crpp-nR^tQ or, for the assumed rotor, T = 1195C^r/ (1) The value of Crp for a given blade pitch setting may be obtained from eQ_^uation (Iq.) of reference 2, which m^ay be written Tm - o'^a J ^ + 1 a _ Om — u a \ p — H" F I 60 ■^ 5-^(1) L O ^ P-P 2 a T" ^ 15 8 v/here //•aN2 ^=\m , 1 a e In order to obtain an expression for ^, the pov/e:; required and the power available may be equated as ~Rr^? Q P = 260 hp = prrR^fl- Cq. Sr + PTtr5q^ Co .^,. M 5!?^ '^o 550 hence. Q 5/ '1/ 260 U5.46(c^. + C.J (2) Induced torque coefficient.- The value of Cr-. ^1 for a given pitch setting miay be obtained by using the CONFIDENTIAL NACA ACR rTo. Li|Ii05 COnPIDlilTIAL 7 figure-of-merit equation of reference 2, written wnicn iTiay oe 5/2 K = Oc70 |'U(. 'Q hence , 0„,5/2 JL Values of 11^. for any specified value of pitch may be obtained froin figure I7 of reference 2. The factor in the above equation is O.7O7 instead of 1/2 as in refer- ence and Since p/2 was used In the definition of Grr C^, in reference 2, v/hereas p is used in the definitfions thrt the ri^ii^ cr o BQi'iTj report... Profile torque coeffic ient," In order to obtain the desired values of C^. for a drag curve of arbitrary forrri., it is necessary/ first to calculate the induced angle of flovj at a series of radii for each of the specified pitch angles. This calculation was "xnade by means of equa- tion (11) of reference 2, which may be .written CD rr ^ x8 VVe) + Ij-- a where an upv/ard inclination of the flov/ is associated with positive values of "?j hence. .8ex) 'Hie an';:les of atback are then obtained from the relation a^ = e + 9 Sariple curves of angle of attack against fraction of radius are shown in fis;ure 2. coi:fidei:tiai 8 CONFIDENTIAL NAG A AGR No. liLH05 The torque coefficient per foot of radius can then be CrT y2 o he obtained from the expression . The torque 2ttR^ coefficient for the entire rotor is then readily obtained by graphical Integration, After both Cq and Cq are obtained, equation (2) may be solved for r2 and equation (1) may then be solved for T. Results of Hovering Analysis Rotor thrust vi/as calculated for a range of pitch angle from 7° to 21°. The results are shown in figure J. Curves for zero profile drag and for the still more Ideal case of zero profile drag together with uniform induced velocity have been included for comparison. The maximum section angle of attack, that is, at the blade tip, is Indicated in figure '-) along v;ith the blade pitch. At the higher pitch angles, the slope of the airfoil lift curves falls off and the calculated thrust values are optimistic These portions of the curves have been drawn as dashed lines. Discussion of Fiesults of Hovering Analysis It Is apparent from figure 3 that, within the range of tip speed corresponding to present practice, the rela- tive merit of the three sectioxis being considered remains virtually fixed. A change from the rough conventional section to the sm^ooth NACA 25015 section results In an Increase in rotor thrust of more than JOO pounds. Changing from the smooth NACA 25015 section to the smooth NACA 3"H-13.5 section results in a further increase of approximately 200 pounds. It is noteworthy that only about 300 pounds mere could be gained if the profile drag could be made zero. The calculated values of maximum available thrust shown in figure 5 ai"© greater than the gross weight assumed in the forward-flight analysis. The lower gross weight was assumed because, in a practicable irj.achlne, the ability to hover at altitude and the ability to take off with an overload are considered desirable features, CONFIDENTIAL FACA ACR Y.o, LljJT05 . COIJFIDSNTIAL POroVARD FLICtKT Of the various performancs characteristics associated with forward flight, range and endurance seem of greatest interest at the present time. Calculations of range and endur'ance at a particular airspeed (approxi- Kiately that for rninimum. power) consequently Vi^ere made for a sample helicopter in which the three airfoil sec- tions previously described were used successively. A fuel load of 10 percent of the gross weight was assumed in each case. The power absorbed bj?" all items other than the rotor, including cooling fans and torque - compensating devices, was allov»'ed for by assuming a specific fuel consumption of 0.55 pound per rotor horsepower-hour, which is approximately I5 to 20 percent higher than the normal value for ci'uising power. Because of the irregular shape of the drag curve for the lo¥/-drag airfoil, analytical treatments of the rotor profile-drag losses, such as that of reference 5, were not feasible and graphical methods were used. Sample Helicopter and Assijaned Conditions The sample helicopter v/as assumed to be in level flight at sea level and to be operating under the fol- lov.'lng conditions: Forward speed Feet per second 80 Miles per hour - 55 Rotor tip speed, feet per second J4_00 Tip-speed ratio 0.2 The geometric characteristics assumied Vvere as follows : Rotor radius, feet 20 Disk loading, pounds per square foot 2.5 Gross vi/eight, pounds Jl^O Blade plan form Rectangular Blade twist None Solidity 0.07 Para site -drag area, square feet .... 15 CONFin32TTIAL 10 CONFIDENTIAL NAG A ACR No. li;K05 Except where otherwise indicated, the foregoing asstmiptions apply to all results presented for forVi,'ard flight. It v/ill be noted that the geometric character- istics e.ss^amed for the rotor are the sair^e as those used in the hovering analysis. Method of Analysis The power absorbed by the rotor may be considered as the sum of the power required to overcome the parasite drag, the induced drag, and the rotor-blade profile drag. The power required to overcome the para-Site drag is 6 horsepower which is considered to be constant. The horsepowej required to overcome the induced drag is P i = ©. '550 As explained in reference 5^ the Induced d/L is sim.ply Cl/Ii, Because the change in v/eight is small, the use of the average weight is considered permissible, and the average induced pov/er is then Or) P. = 0.0753 X 29SO X -^^ - 55-9 horsepower The calculation of profile-drag losses is much more complex and is described in some detail. Calculation of angles of attack.- Anv erarhical treatm.ent of profile-drag losses requires knowledge of blade section angle of attack at various points on the rotor disk. In order to calculate the angle of attack of a blade elem.ent at any given point, it is necessary first to calculate the required blade pitch, the inflow velocity, and the blade flapping coefficients. The pitch and the irif low velocity were determ.ined by means of the analysis described in reference [j.. This analysis GO^JPIDEI^TTIAL -\\CA ACR No. 1.11-305 CONFIDENTIAL 11 extends the analysis of reference 3 by the addition of a parameter that represents the shaft power supplied to the rotor. The flapping coefficients v;ere then deter- mined bj" equctions (1) to (5) of reference J* In determining the pitch and inflow velocity, it was necessary to estimate the rotor profile-drag losses. This estimation was accomplished by use of a specific air'foil drag curve as represented b^r a power series. The drag curve used corresponds to that employed in the example of reference 5j tut the resulting values of rotor profile drag were decreased about 10 percent to provide a better approximation to the characteristics of the smiooth sections being considered in the present s"oudy. In a strict sense, a different com.bln&tion of pitch and inflow velocity should be determined for each section, particularly for the rough conventional section, because of the difference in required power input; how- ever, the effects of such changes in the combination of pitch and inflow velocity are negligible except in cases in which the retreating tip-section angles becomie high enough to produce excessive drag. The effect of an extreme change in power input and in the resulting combi- nation of "oitch and inflov/ velocity maj be noted by referring to the example given in the appendix; this example compares the rotor profile-drag losses v;hen 15 square feet of parasite-drag area and zero parasite- drag area are successively assumed at a relatively high forwai-'d speed. The normal and tangential components of velocity relative to a blade element were obtained from the fol- lo".''lng expressions, v.liich a-i.^e modifications of equa- tions (8) and (9) of reference 5° U.-n = K]_ + X Up = K2 + KvX where Kj_ = [J, sin \]/ K2 = A. + — [ia-]_ + f -[la^^ + 5-(j,a2 ) cos \1/ + jpb2 sin Uf + ^^a-^ cos 2it + — [j.b-]_ sin 2^1/ '^ ^'t^^2 ^°^ ^'4^ '^ p^^Z ^■^^' 5^-^ CONFIDENTIAL 12 CONFIDENTIAL NAG A ACR No. lI^II05 Kz = b-, cos ^ - a-[_ sin ij/ + 2b2 cos Z^i - 2ap sin 2\\f and a^, a-]_, &2} bj , and b2 represent coefficients in the Fourier series expressing the blade flapping motion. In reference 6 the angle of attack of an element a^ is shown to be equal to 9 + tan"-*- — ^. In the present Urn analysis, the tangent was assum.ed equal to the angle in radians; hence, the angle in degrees is °- = ".3(e.ji^ Values of a^ were calculated at every 10° azimuth and at intervals of O.IR over the blade radius, so that values were provided at a total of 3^0 points on the rotor disk. Pr ofil e-dr ag power loss .- The rate of profile-drag energy dissipation for a blade element of unit length is the product of the drag and the relative velocity, or OS cp 1 f'Ur^UH \- u '^ \cos cp/ '-^ c For the conditions of operation covered by the present analysis, a negligible error is introduced by the omis- sion of cos cp and the profile-drag pov/er loss per foot of radius becomes Pq - 2p(^T^^)^ ^°° *^dc By using the assumed values of solidity, blade radius, and tip speed, there is obtained in foot-pounds per second per foot of radius Pq = 55U/oocuT5cd^ (5) In order to obtain the total power for a given airfoil, the drag coefficient corresponding to the calculated angle of attack at each point in the disk is used succes- sively in equation (5). The details of the integration of the 360 values are omitted. CONFIDENTIAL NACA AC'^. No. Llj.H05 CQN^irEITTIAL 13 In against loss wer The resu for the for coiTip order to figure 1 an angle example increase for surf describe increase order to obtain curves of profile-drag p weight, calculations of angle of attack e carried out for five values of gross w Iting curves are shovi'n in figure l\.. The rough airfoil obtained analytically are arisen with the values obtained granhica peiTnit such calculations;, the drag curv for the rough airfoil was made to have, of attack of 10°, the satne form as that given in reference J; the crdinates v/ere d 28 percent in order to m.ake the desire ace roughness. Values of d/L obtained d in reference 3 could thus be used afte d 23 percent. ower loss and energy eight. values included liy. In e of up to of the , however, d allowance as r being Calculation oJ Range and Endurance By using the average profile-drag loss in horsepower, as given by figure k, for the range of weight from 5l[j.O pounds to 2850 pounds, the average total rotor drag losses for each airfoil section may be evaluated as follows : ^\^^^ Air-f oil lo3ses^\ ih-p) Rough conventional Sm.ooth NACA 23015 Smooth 'NACA 5-H-15-5 Parasite Induced Profile 16.6 55.9 r+7.5 16.6 55.9 27.5 16.6 55.9 20.0 Total 1 97.8 77.6 70.5 By assuming a specific fuel consumption of 0.55 pound per rotor horsepower-hour, the values of range and endurance are as follows: "^"^^^rfoil Rough conventional Smooth NACA 25015 Smooth liACA 3-B-I3.5 Range, miles Endurance, hours 520 5.8 7.5 U;0 S.l Ik CONFIDENTIAL NACA ACR No. li4iT05 High-Speed Condition As an indication of the effect of tip-speed ratio on the relative merit of the airfoil sections, calcula- tions were made for the sample helicopter at a tip-speed ratio of O.3. The corresponding forward speed becomes 120 feet per second, or about 80 miles per hour; all other assumptions are as previously given. The drag losses then are as follows: \. Airfoil Drag\. lo3ses^\^ (hp) \ Rough conventional Smooth NACA 25015 Smooth NACA 5-H-I5.5 parasite Induced Profile 56.0 25.0 67.5 56.0 25.0 53.5 56.0 25.0 5^.5 Total ■ f ia.8.5 i 11U.5 135.5 The high profile-drag loss for the low-drag section results from the high drag values above the low-drag notch; this point demonstrated in the appendix, Discussion of Results of l^'orward-Plight tiy SIJ It is apparent from f ignore [1. that the relative merit of the airfoils depends on the loading used. Certain aspects of the com.parison are brought out mxore clearly by plotting the profile drag-lift ratio (d/L)q instead of power loss. Figure 5 stiOY/s this factor plotted against the loading factor 2Crn/oa, v;hich is mere general than but is proportional to weight or loading. It is evident that the optimuin (d/l)^ occurs at a considerably lower loading for the NACA 3-N-13.5 sec- tion than for the NACA 25OI5 section. Although a relatively sm.all portion of the rotor disk is affected, it should be pointed out that the assuTiiption of constant lift-curve slope is not strictly valid at the high loadings and at [^ = O.J. The calcu- lations for the NACA 5-H-15.5 section, in particular, are increasingly optimistic as these conditions are reached. CONFIDENTIAL NACA ACR No. LI4JIO5 CONFIDENTIAL I5 CONCLUSIONS The effect of modifications in the airfoil section drag characteristics, as indicated by the theoretical performance analysis made for the sample helicopter, m.ay be summarized as follows: 1. The use of the section characteristics taken as representative of a smooth conventional section instead of those taken as representative of a rough conventional section resulted in an increase of approximately 9 percent in the rotor thrust available with fixed shaft power in hovering, an increase of 25 percent in range and endurance (with equal fuel load) at cruising speed, and a reduction of 23 percent in the power required at a relatively high forward speed (80 mph; tip-speed ratio, O.J) . 2. The use of the section characteristics taken as representative of the low-drag airfoils of NACA CB No. 5115 Instead of those for the smooth conventional section resulted in a further Increase of approximately 5 percent in the rotor thrust available with fixed shaft power in hovering and an additional increase of 10 per- cent in range and endurance at cruising speed; hovvever, at the high-speed condition, an increase of approximately 18 percent In the power required v\ras indicated. 3. If the losses shown for the low-drag section at high speeds and at m.oderate speeds and high loadings are to be avoided, the low-drag section must be designed to prevent the extreme rise in drag coefficient at the higher angles of attack exhibited by the low-drag sections of NACA CB No. 3115. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Lang-ley Field, Va . CONFIDENTIAL l6 CONFIDENTIAL MCA ACR ¥.0 . L)j1I05 APPENDIX CONDITIONS OF OPERATION ENCOUNTERED BY THE BLADE SECTION AND EFFECT OP VARIATIONS IN ASSUMPTIONS Contours of angle of attack and power loss.- In order to make the reason for the results obtained in the forv;ard- flight analysis mors evident, contours of angle of attack and power loss were prepared. The source of the values of section angle of attack has already been sufficiently explained. In order to shov/ the relative importance of a given increment in drag coefficient in the different parts of the rotor disk, the expression previously given for power loss per foot of radius \\as m.odified by dividing by the area of the annulus at the appropriate radius; the resulting expression for the power loss in foot-pounds per second per square foot of disk area for a profile-drag coefficient of 0.01 is u 5 . p = 26.60 ^ Contours for the set of conditions initially assumed are shovvn in figure 6(ai. Figure 6(b) shows the effect on the contours of increasing the ass^umed value of solidity. Changes in loading produce similar effects, since the higher solidity is comparable with lower loading. Contours for the original solidity but for ti = 0.5 (V = 60 mph) instead of ^ = 0,2 (v'= 55 mph) are shown in figiare 7- We ight ing curve s . - The contours in figures 6 and 7 indicate that a given increment of profile -drag coeffi- cient is more important at low than at high section angles of attack. It is difficulty however, to judge the significance of certain factors - for example, the abrupt rise in drag coefficient at high angles of attack shown for tiie NACA 5'-fi-15'5 section (fig. 1). In order to permit more rapid quantitative judgem.ent of such factors, the data may be combined for the two sets of contours into a single curve showing the relative impor- tance of different parts of the curve of airfoil section profile-drag coefficient against section angle of attack. This weighting curve is designed to show the amount by GONPIDSNTIAL NAG A ACR No. lIj.H05 CONFIDENTIAL 1? which the povirer consumed in overcoming the profile drag of all the hlade elements operating at any particular angle of attack is increased if the airfoil section drag coefficient corresponding to that angle of attack is increased hy some convenient increment, for example, 0.01. Such a curve has the further m^erit of permitting rapid calculation of total power for any airfoil section; it is necessary only to miiltiply the ordinates of the curve of profile-drag coefficient against angle of attack charac- teristic of the airfoil section "by the ordinates of the weighting curve and ootain the area under the resulting curve . In order to obtain such a vii'eighting curve, the range (or ranges) of azimuth angle (■''2_ to i|/2) through which a given range of angle of attack (o^r-, to ^-rn\ ^^^^ maintained was determined for a given radius hy using a plot of angle of attack against azimuth angle for that radius. The process was repeated for successive ranges of angle of attack imtil the entire circumference was accounted for. The appropriate average value of Uiji^ for each range of azimuth angle was then read from a plot of VirjP against azimuth angle. Ordinates for the weighting curve for the specified radius were then obtained hy m^eans of the expression for the energy per second per degree angle of attack per foot of radius 1 , — 5n^p3 .^^-J^l 1 where Urp^ is the average value of urp^ for the range from ^|/] to \i;p. It was found bhat increments of angle of attack of 0.2° provided ample detail in the final curve . The process was repeated at intervals of O.IR over the blade radius. The resulting weighting curves for representative radii and the over-all v/eighting curve obtained by a summation of the curves at the various radii are shown in figure 8 for ij. = 0.2. Values of power obtained by use of the curve of figure 8 and other values obtained from each of a number of other weighting curves were checked against corresponding values obtained by the more laborious point-by-point m.ethod already described, and the answers agree v/ithin ±0.3 horsepower. nONi^TDE\^TIAL l8 CONFIDENTIAL NACA ACR No. lh,EO'^ In order to permit ready application of the v^reighting curves to rotors differing from the sample rotor in chord, radius, or airfoil section and likewise to rotors oper- ating at different tip speeds and altitudes, the curves have been piotted in nondimenslonal form. The use of the curves for calculation of the profile -drag loss for a particular x^otor and a particular airfoil section involves the follov/ing steps: (1) Multiply the ordinate s of the weighting curve by the ordinates of the curve for airfoil section profile- drag coefficient. 2) Multiply the resulting,...ordinates hj 100 to allow e fact that the given for Cq^ = 0.01 for the fact that the v:eigiiting- curve ordinates were (5) Obtain the area under the resulting curve and thus obtain the total value of Cp/a aPOlU (k) Multiply the value of Cp/a by the factor 5 _S ' ' 550 Steps (2) and (I).) may of course be combined; the factor for the sample rotor is then 100 X 0.07 X 0.002378 X (20)'^ X -r X (20)5 ^ . ^ ^^ = 2 . a.9 X 10 affect of variations in helicopter characteristics and flight conditions .- The weighting curves provide a convenient means for indicating the effect of changes in assumptions on the airfoil requirevnents . Tiie effects of tip-speed ratio, loading, solidity, blade twist, and power input are thus Indicated in figure 9« Corresponding profile-drag losses for the drag curves ujider considera- tion are given in table I. Source of losses indicated for low-drag airfoil . - Comparison of the weighting cur-ves of figure 9 with the profile-drag curves of figure 1 shovvs that, for the conditions in which the low-drag airfoil shows losses instead of gains, these losses result from, the extremely high values of profile-drag coefficient at the high angles CONPIDSNTML- FACA AGR No. Ll4Jl05 COKFIDEMTIAL 19 of attack. The point is brought cut more clearly in fig- ure 10, which shows the curves that result from multi- plying the drag curves of figure 1 by the corresponding v/eighting curves of figure ^{a.) for |j. = 0.5. preliminary results (unpublished) of additional lov^r- drag airfoils intended to reduce these losses at high angles of attack indicate that considerable progress may be expected. Conditions of operation ignored in analysis. - Simplifying assumptions or procedui^es^ which have been used in the analysis but have not been discussed and may be suspected of endangering the validity of the compari- sons made, include: (1) Use of statically measui'ed section character- istics ivith no allowance for effects due to rotation (2) Assumption of uniform Inflow velocity (forward- flight analysis only) (3> Use of section characteristics corresponding to a single Reynolds number and a single Mach number 8.s applying at all points on the rotor disk ([[.) Neglect of effect of angles of yaw on section characteristics Past experience indicates that airfoil sections used in rotating blades exhibit characteristics similar to their statically measured section characteristics. Pos- sible effects on the characteristics of the low-drag sections are conjectural. The effect of nonunif ormity of inflow velocity v^as examined in reference 6, and it was concluded that the net effect on the rotor forces was secondary. The m.ethod of analysis used would permit study of items (5) and {h) > or even inclusion of the effects in the analysis if such were deemed desirable and if suffi- cient section data were available. Although the data at hand are insufficient to perialt complete calculations, it is of Interest to note the magnitude of the variations of Reynolds niamber. Ma oh number, and angle of yav^r. CONFIDENTIAL 10 CONPIDSNTIAL . KACA ACR No. i4H05 The Reynolds number, vmlch vifas taken as approxi- mately 5 X 10 in choosing the drag curves, actually , o varies from to L\..'j x 10" in a typical case. The value 2.8 X 10"-' corresponds to the mean value at x = 0.75 when the nuiaber of blades Is taken as three. Figure 11 shows the variation of Reynolds nimiber over the rotor disk for two tip-speed ratios. Radial components of velocity are ignoi-ed. Comparison with figures 6 and 7 indicates the regions in which the greatest differences might result If the drag curves were varied with Reynolds number. The contours of figure 11 may also be used in esti- m_ating Mach numbers. ?or this purpose, the values shown on the contours should be multiplied by O.OOOOll^R. For the sam-ple rotor In forward flighty QR = I|-00 ; hence, the Mach number is approximately equal to the value shown on the appropriate contour line times O.OO56. For jj, = 0.2, the maximum tip Mach number is thus 0.[\2 at \i/ - 900 and the minimum Is 0.28 at '4^ = 270°. The variation of angle of yaw over the rotor disk at a tip- speed ratio of 0.2 is shown In figure 12. The same contours can also be applied to any value of |i above 0.2 by placing a nev/ outer boundary at a radius equal to 0.2/[x times the original radius; the tip circle for |j, = 0.[|. has been drav/n in as an example. It is of interest to note that the regions which appear in figures 6 and 7 to be the most critical - that is, the region of high power loss per unit drag coefficient on the advancing side and the region in which tip stalling is approached on the retreating side - Include relatively lov/ angles of yaw. CONFIDENTIAL NACA ACR No. i4H05 CONFIDENTIAL 21 REFERENC3S 1. Tetervin, Neal: Tests in the NACA Two-Dimensional Low-Turbulence Tunnel of Airfoil Sections Designed to Have Small Pitching Moments and High Lift-Drag Ratios. NACA CB No. 3 113, 19li-5 • 2. Knight, Montgomery, and Hefner, Ralph A.: Static Thrust Analysis of the Lifting Airscrew. NACA TN No. 626, 1937. 3. Bailey, F. J., Jr.: A Simplified Theoretical Method of Determining the Characteristics of a Lifting Rotor in Forward plight. NACA Rep. No. 716, 191^1 '. I4.. Bailey, F. J., Jr., and Gustafson, F. B. : Charts for Estimation of the Characteristics of a Helicopter Rotor in Forward Flight. I - Profile Drag-Lift -Ratio for Untwisted Rectangular Blades. NilCA ACR No. Li^HOY, l^kk. 5. Wheatley, John B. : An Analytical and Experimental Study of the Effect of Periodic Blade Twist on the Thrust, Torque, and Flapping Motion of an Autogiro Rotor. NACA Rep. No. 59I, 193?. 6. Wheatley, John B. : An Aerodynamic Analysis of the Autogiro Rotor with a Comparison between Calculated and Experimental Results. NACA Rep. No. i|87, 195^« CONFIDENTIAL KAGA ACR Fo. rX^H05 CONFIDSWTIAL 22 m rj M EH C/D M K ErJ Eh O -Zt CO NA_ch 0:1 fl) 1 rH rH r-\ r\i \r\ rH CJ U-> < CO rvi i fH < CiH Iz; rP (>_■ xl Lr\ 1— 1 CO -p rH a Eh n >H b O t-r\ -H -d-c\j KN ix; <; ONCO U^ r—ixi i-ov rH e (\J ^' . . fZ . . . • • • w ,— * rH cx) r\i CO NAO-ro, Lt^O-rH f^ W < T3 ^ ■< ha 1 — ■ 0) •rH 0^ 1 ^ r-H rH -P < PlH •rH ai bO CO ;25 VH fH a ?H pq tilDi o ^ C •H (—* fn bO-H fn •X3 Eh Eh •H Ph :=; -p -H C! 4J a) > O-lTnCVJ • • • CO S 1— 1 • • • CO tOvOGO • • • S^i (D NAO-J" a g aM>- lAJ CTnCO > ^r^ i.(^ 0\ CO t^ -^-rjXO rH -:j-_d-UA fn a CO 1 Q, •Vh Ph -P -p rH TJ ■■.H erf a • nj CM CM C\J O-fO, 'h l^-O-O- !^ rH • • • -P ... ^ • • • ^ II 000 K^CXl H ro,hrMs-> Cm " H-l K-\ K~\ ^r^ N^is"MsrN hOvN'~\hO> <^ 1 i t3 • • • < • • ■ d -H rTMPN £* (M (\l rvj n • -- ^ , — c\J N-N :-l.Q 000 :iX) • • ~ — ■ C) u -— % ^-*» .- — ^ ■;> CO CO A-' bo -^— ' ■ ■ ■ ' •H CA O-N C^^ fc CO C o •H -P a m m 35 CO .-H QO •H Jh O o o O O 'd 'D •H •in •H O -P o 00 G O •P ■P •H ■d o o rP CONPIDSNTIAL IJACA ACR i4h05 COIMPIDENTTAL 25 H o a o o CO o > o Eh O W pq ■< EH 1 Lr> 1 1 1 — • 1 1 "1 N-A X; rH j::; i -P 1 o rVl rH 1 u-v^ -J-CJN O |rl .H • • • • • • C 1 -P N"AV,0 -zhoj OJ l^f-A S NA o OJ OJ LTvd- _-j-K^ m ® ■< CQ !^i O O ■=!< w 1 ■ C,Q -P rH fH o O O O CO OJ U">rH rHOO r-H O tO>.H S oi -P • « • • ro^ r-' • • rH O bO m o OJ rr\ N"MH"~N K^N-^ rf --« ON •H 0~\CO Cm ;3 JJ +J T^- 1 • • • • • • o C o •H GNC^N CD [>-— ^ M -d-rfN (^ U OJ rH _r}-LPx Ti VO U^ OJ Li-ALPN > CO O cd s f-, a m r->. o O o X:' a t-i o O <^ 1 fH O o rH 4^ o O -P -p • (D [>-rH o i-'i'M-Oi o NAi-O, f-i o •^ . . a) • • • « O II <;--,• KACO '.H CO'X) O iil w TJ O -p c-o '5 '■m U-NO j m D O rH rH a) oco Ch rH a • • OS Tj 1 cr 1 o O — ' LI •H -P -- •H CC ■— ' .-^ rQ -_ rH fcO CO C CO rON CD <|l 1 O i • i * ■TJ a o O "— - 1 NA 1 ri. • in ^ — . , — ^ .-— N o ^ H to •H ffi ■< -P a Oh !73 M K ^ > W 0:1 U< M ■< cd K l-H rH - <: ph OJ & !^ pq •H M pq bi) ti fH •H < Eh ?H fe; M S S -hJ Td r* O. M -H rH -H < a COlvPID^KTnL NACA ACR No. L4H05 CONFIDENTIAL Fig, .'*• / / / / .IS / / / / i I 1 1 1 .11 \ f / 1 1 1 1 1 1 t ■II If / /l / ) .10 / 1 1 I / 1 ( .ot / i 1 1 i / 1 1 I y - < / 1 1 1 / 1 1 t / 1 1 (5/ \ 3-f y-/"^ T ? / — *^ 1 ( I ] / ; ^0^ / 1 / \ / / / 1 1 > / 1 .03 / / / f 1 / ■<^ ^0^^ rro e/)// t/^'^- 0/ial I 1 .on. ^ -/ 1 ,-- ^,^'' / '"^ mcf \ 23 loot 015 h) ■oT -^ .-'-' '—^ /_. ^ f-O =- — — — - U COMMI' nONAL ; lEEFOR DVISORY AERONAI TICS n ^ ^ € e /D iz CONFIDENTIAL Sect/on angle of aflacK Cabs), cc^ Ftyuris. I'—Profile-draq curves used in "the analysis 14- /6 deq Fig. 2 CONFIDENTIAL NACA ACR No. L4H05 f O Hi O <^ JO .Z i4- .6 3 F/xkct/on of /zt<^/a>5, oc F/gurG ^r~ ^ect/o/i ang/&3 of attaoK for tJiree p/tch ^setf'/ngs. Samp/e he //copter rotar /n hc>\^er//ig f//ght CONFIDENTIAL NACA ACR No. L4H05 CONFIDENTIAL Fig- I szoa \i:Unifcrm indoceej vehcttQ, zero 1 1 pn)fife draei r 4S00 4- L. 1 — H _^ ^Zero profile drijQ i4.r 1~~ 1 129 1 7' \i~— 4400 IJ.3 • — / ~s7 r^ ir e'.s° vr ^^:z ■ / I\ 1 / // / 7 H ^. ^ ^ - 5. dnOQ '/• '7 / — . ^ -/ / ^ - y / - ^ \. / b '1 ^h^ ■^ •^ ^ / / ^ N , /' ' NACA 3-H'l3.S 3600 /■ / k ^ X A ^^ ~Srr)oo-th NACAZ30I5 V s— — Roaoh J / 3200 CO nyen tunei PPD6 240f, 1 1 1 1 ! •to 1 1 1 2000 I6O0 I2DO ACO 4^0 NA- COMMIT ONAL A EEFOR 3VIS0RY ^RONAU FICS 300 340 360 S40 560 6Z0 4Z0 460 600 Tip speed, fps Figure 3.- Rotor thrvst -For £60 shaft horsepaver. Sample, helicopter in hovering ^'i^hi- CONFIDENTIAL Figs. 4,5 CONFIDENTIAL NACA ACR No. L4H05- 1600 MM. Method 'otgh con^tmonal Gixiph/cal •i^^-^Roijgh conventional Analytical mooth f//^A 3-H-i3.5 Graphical ^Smooth NACA 23015 Oraptncal NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS /2ft» 2A0O Zeco 3200 3600 4000 Gross weight, lb Figvrv 4-.— Retotr profile^^ra^ loss for a range of gross weight. Sample he.licopterj ^O.Z . .ozo .014 .0Z6 .03Z ZC^a-a .036 Pitch angle, W/S (Ib/s^ft) Airfoil ough conventional Rough conventional h^ho< i. Graphical Anakitical Smooth NA CA 3-H-I3.S' Graphical SmotsthmcA S.30IS Qra^ical .040 NATIONAL ADVISORV COMMITTEE FOR AERONAUTICS CONFIDENTIAL Figure 5".- Rotor pihofife. drag -lift rat/o as affected by loading- Sample hsiicop-ter rotor j^=0.&. NACA ACR No. L4H05 CONFIDENTIAL Fig. 6a, b Power loss (ft-lb/sec/sq ft/COlcdo) Angle of attack (deg) Direction of flight Direction of rotation 2Cn (a) Original solidity; X = -0.0385; 9=9°; 0"= 0.07; -~ = 0.0321 ca NATIONAL ADVISORY COMMinEE FOR AERONAUTICS (b) Increased solidity; X = -0.0350; 9=7°; 0"= 0.10; -^ = 0.0225 Figure 6,- Contours of power loss and angle of attack for sample helicopter rotor and for an alternate rotor with higher solidity and lower pitch. V = 55 miles per hour; p, = 0.^; W = 2, 5 pounds per square foot. S CONFIDENTIAL Fig NACA ACR No. L4H05 I — I O O ■Ha) ■ OH ' h ■iHVl Q O _ « d o O-H ■P OS O-P » o o o o m^ — a" U CO * o O (D (^ ID I ^< ■»» (0 o -p o a 4h o o a) •H ^ H cd 0) 3 ;c| a" 0) H U a 0) s ft CIS CD ;■< d o 3 Oh o ft M o in OS * • -p OJ H 43 CM (d II to O .J Vl »|cn • < o O 1— 1 Eh II 2; g^ • o o 6 OS CVJ " h— 1 II 6l. 2; cd t^ o o o CQ • •^ • CO ;4 o O 3 H o II h b 0) u » (D o ft • M p, o a H H o H •H II m a Ih a> :3 o o 00 +3 • M d ;8 in o o\ o 1 > o • • • o t- u o 1 II U o s. ;h «< NACA ACR No. L4H05 CONFIDENTIAL Fig. 8 I.OKl(T^ X'0.3 J^ 1.0 m-"^ \ x= ..T \ i.0^/0'^ 1 [1 X =.7. \ , — ^ 1 n n \ X =.9 V \ " — ■ — ^ 6*10'^ 5 4 3 Z 1 n 0>° <5 I of \ Bfit ire Y otor \ \ NAT ;oMMin DNAL Al I FOR / VISOBY ERONAU cs V V. A . / - 1 ■ — ' ^ J ^ I \ i. 7 4- £ ) t i /i 7 /. I /A Section angle of attackj oc^jCh^ Figure 8- Weighting curves -For rKpresentptive radn and for entire rotor. Sample, helicopter rotor; /juO. Z;e=9 °; A= -0.038S. CONFIDENTIAL Fig. 9a CONFIDENTIAL NACA ACR No. L4HC! Ohtiri^ - 16 i y" =o (hovering) i IZ n 1 j & e-- -- 7^ /v / i^\ \ / 4 / j 1 ,/ / J n J y / I u -• "K f? = 9* A= -0.0. 5(35: oib ^ I ^ \, / 1 n ^ , f) J _ . -1 \ 6it^ 1 4. \ e =11' X^ -0.06S '5 f V 2 1 \ \ u \ ^ NAT XJMMm 3NAL AI SFORfl VISORY PiONAir ICS ^ y — ■ — 0- ■^ ^ C 5 'tt > ^ u i 5 e 5 h 1 Z /' 4 /< S Section angle o-f- attacK, o). j deg (0) E.-Fiect of tip-speed ratio- \4/S=Z.5-i(r=0.07) 9,=0t CCNFIDENTIAL Figure 9.~ The effect of venous changes m the operating cond/tions <3hd geometric characteristics assumed for ihe, sample rotor, as shewn by *he corresponding weighting curves. NACA ACR No. L4HC5 CONFIDENTIAL Fig. 9b ax> 0-^ 6 fy 4- \ \ 2. i \ s. / ^ >» ->1 n ^ ' ^ 6'/ 0-* \ ^4 I \ \ la \ * 1 ^ 0- - y 1 6xi3-Jt -^ s 8 A? /e Section angle of at*acHj o^ri ^^ Cfc; effect of loadmq. yU-O.Z; cr-ao^j &,=0''. figureQ.- Continue. CONFIDENTIAL Fig. 9c CONFIDENTIAL NACA-ACR No. L.4HC5 5V Pn I fi / \ ! A 0-^0.07 L e= a' \ = -0.0365' 1 1 O , V 1 ^ ^^ n J " \ O^'' i 6 r\ 4^ \ 7' / vo .03t \ 9^ -0 Z / \ / 'V NAT XMMm ONAL A IFOR/ VISORY ERONAlf ICS ru y \ ' Z 4- 6 6 10 IZ Section angle of aitpck, cc^^ deg (c) ^-F-fect of sohditii- ^'-O.Z; Hf^=2.S;B, = 0°. F/^ure.9.- Continued- 14- 16 CONFIDENTIAL NACA ACR No. L4H05 CONFIDENTIAL Fig. 9d,e o^ b^h T* - 1 — "1 /■ A- I v © = II' \? -0.0695 2. \ \, J / \ ^^ y 1 ^^ — — - ^ fim, ^ AkJ^* 1 J 1 e,--8* 2. r ' \ &rs-- ■•/as* X'-aoean 1 1 1 \ 1 "^ ^-~ \ °c ) i 5_ ^ f- i K > t 5 l IZ 14 16 Section angle of ottackjic^, dey (d) £ffeot of bladm -twist. ^/u^.3j W/S-Z.Sj efCOV- ^ -fx/ 0-* NATIONAL ADVISORY COMMITTEE FOR AERONAITTICS Rfn \stt9-draq area ^ ISs i?ft Z r ■ ' * V 1 r \ s^ 1 1 ^ 0- Olb 4'' OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY P.O. BOX 117011 GAINESVILLE, FL 32611-7011 USA