Airfoil Aerodynamics & Vortex Method Reference

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Contents

1. Summary of Rocket-Model Tests at Zero Lift of the Northrop MX-775B Missile Configuration from Mach Numbers of 0.9 to 1.8
2. Summary of Section Data on Trailing-Edge High-Lift Devices
3. NACA Conference on Aerodynamic Problems of Transonic Airplane Design
4. Summary of section data on trailing-edge high-lift devices
5. NACA Conference on Aerodynamic Problems of Transonic Airplane Design
6. Vortex Flow Aerodynamics, volume 1
7. The NACA variable-density wind tunnel
8. NACA Report 824 Summary of Airfoil Data
9. Application of Circulation Control Technology to Airframe Noise Reduction
10. Experimental Studies of Low-Pressure Turbine Flows and Flow Control
11. NASA Hybrid Thermally Efficient Core (HyTEC) Phase 2 Q3’GFY25 to Q2’GFY26 Unlimited Rights Annual Report for CLIN 1 and
12. Some applications of the quasi vortex-lattice method in steady and unsteady aerodynamics
13. Extended applications of the vortex lattice method
14. CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics 1999

1. Summary of Rocket-Model Tests at Zero Lift of the Northrop MX-775B Missile Configuration from Mach Numbers of 0.9 to 1.8

Primary source: https://ntrs.nasa.gov/citations/20090026523

f the nearly two- dimensional character of the flow over the wing. Reference 4 indicates that the base drag of a body of revolution with the same base area as that of the wing would be approximately 50 percent of that due to wing-trailing- edge bluntness at Mach number 1.5. Figure 8(c) presents the drag increase of the large-body model over that of the basic small-body configuration. The increase is a maximum just below Mach number 1.0. It should be realized that this curve and also the curve of figure 8(b) could be altered appreciably in this region CONFIDENTIAL NACA RM SL53JO2 CONFIDENTIAL 7 due to a possible Mach number error of 0.01. The drag increment of fig- ure 8(c) represents an increase of 13 percent at Mach number 0.90, 24 percent at 1.03, and 17 percent at 1.4. The wing-plus-interference drag coefficient presented in figure 8(d) was obtained by subtracting the body-plus-vertic

tests of the proposed Northrop MX-775B Missile are as follows: 1. The basic small- and large-body configurations had low supersonic drag. The small-body configuration with body-to-wing area ratio of 0.0127 had a subsonic drag coefficient of 0.0080 increasing to a maximum of 0.0125 at Mach number 1.03 and decreasing to 0.010 at Mach number 1.80. Increasing the body-to-wing area ratio to 0.033 resulted in an increase in drag coefficient of 13 percent at Mach number 0.90, 24 percent at Mach number 1.03, and 17 percent at Mach number 1.40. 2. The effect of the blunt wing trailing edge, obtained by cutting off 10 percent of the basic wing chord, was to increase the zero-lift drag coefficient by approximately 20 percent at Mach number 0.95, 21 per- cent at Mach number 1.03, and 13 percent at Mach number 1.50. 3. For the basic small-body configuration, the wing-plus-interference drag accounted

dy length and equal to 1.27 percent of the total wing area. The wing of model 2 was modified by cutting off the last 10 percent of the chord resulting in a trailing-edge sweep of 25.80 and forming a blunt trailing edge with a base area equal to 0485 percent of the wing area. In addition, model 2 had a booster- coupling support strut approximately two-thirds the size of that shown on model 5 in figure 1 and similarly located. The wing of model 3 had the trailing-edge ailerons deflected to roll the model. One aileron was deflected 3.050 up and the other 2®400 down resulting in an average deflec- tion of 2.7304 Model 4 did not have a wing but had horizontal stabilizing fins. Model 5 had a large body of fineness ratio 14.9 and a maximum cross- sectional area located at approximately 50 percent of the body length and equal to 3.30 percent of the total wing area. The models were of wood and me

weight, lb x distance from nose of fuselage to any station on the fuselage, ft pb— 8 rolling-effectiveness parameter, per degree 2V s average elevon deflection, deg MODELS The five models tested are shown in figure 1, and the body and air- foil ordinates are listed in table In The basic arrow wing had an aspect ratio of 1.86, 67.50 leading-edge sweep, 150 trailing-edge sweep, and a CONFIDENTIAL Ile 4 CONFIDENTIAL NACA RM SL53JO2 modified NACA 0004 airfoil section. The model vertical tails had 00 sweep of the 50-percent-chord line and had the same exposed plan form but dif- fered slightly in airfoil section, as shown in figure lm Models 1, 2, 3, and 4 had a small body of fineness ratio 15.5 and a maximum cross-sectional area located at approximately 30 percent of the body length and equal to 1.27 percent of the total wing area. The wing of model 2 was modified by cutting off the last 10

1. The wing-plus-interference drag coefficient presented in figure 8(d) was obtained by subtracting the body-plus-vertical-tail drag coefficient from that of the basic small-body configuration and shows that the wing- plus-interference drag accounted for approximately 78 percent of the total drag at Mach number 0.9 and 70 percent at Mach number 1.5. Rolling Effectiveness Rolling-effectiveness data obtained from the flight of the roll model are shown in figure 9(a) between Mach numbers 1.0 and 1.44. and dynamic pres- sures for the test are presented in figure 9(b). The 8 used in the rolling-effectiveness parameter 2V 6 was the average aileron deflection (2.730). The rolling-effectiveness parameter varied uniformly from approx- imately 0.02 at Mach number 1.02 to 0.0065 at Mach number 1.39. There is no evidence of aileron reversal for the Mach number range covered. The rolling effectivenes

ces, an indication that the average aileron deflection of 2.730 resulted in no measurable drag increase. The curve shown for "model 4 without horizontal fins" was determined by subtracting the known drag coefficient for the horizontal fins, obtained as explained in reference 2, from that of the fin-stabilized body model. The curve shown is, therefore, the variation of drag coeffi- cient for the small body with vertical tail except for interference-drag effects which could not be accounted for. The blunt-trailing-edge model (model 2) is seen in figure 8(a) to have appreciably higher drag than does the basic small-body configuration. The incremental drag due to the blunt trailing edge is shown in figure 8(b) and represents an increase of 20 percent at Mach number 0.95, 21 percent at Mach number 1.03, and 13 percent at Mach number 1.5 over the drag of the basic small-body configuration. It

4: Body-fin model. m0.045 rod. D-D Horizontal-fin section U 00 0 E--- c Vertical-fin section (for models 2,3 8 4) 4780-- -+--21.70 .75-4r^^ 37 85.77 Support detail Model 5: Large-body drag model. 4.42 Figure l.- Concluded . CONFIDENTIAL NACA RM SL53JO2 CONFIDENTIAL L®71696.1 (a) Top view. L-65632®1 (b) Side view® Figure 2, Photograph of basic small-body configuration. CONFIDENTIAL NACA RM SL53JO2 CONFIDENTIAL L-781x26.1 (a) Top view® L-7842 (b) Side view. Figure 30- Photograph of large-body configuration. CONFIDENTIAL I .2 .3 .4 .5 .6 X t 0 .1 requiv 0 7 .8 .9 1.0 NACA RM SL53J02 CONFIDENTIAL .010 .008 .006 A 12 .004 •002 0 1 I Small-body model +­,j I I I I I I I I J/ V I I I `-+ Large-body model I I T°--+.,A 0 .1 .2 3 .4 .5 .6 x 1 (a) Area distribution. .1 requiv 0 1 1 Small-body model Large-body model I I I I I I I 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 x 1 (b) Equivalent radius. Figure 4.-

the small- and large-body con- figurations. The effect of a blunt wing trailing edge, obtained by cutting off 10 percent of the wing chord, was to increase the zero-lift drag by 13 to 21 percent. Wing-plus-interference drag, accounted for 78 percent of the total drag at M = 0.9 and 70 percent at M = 195 for the small-body con- figuration. The ailerons produced positive rolling effectiveness for the wing stiffness of the test models and the dynamic pressures of the testa Restriction/Classification Cancelled Restriction/Classification Cancelled 2 CONFIDENTIAL NACA RM SL53JO2 INTRODUCTION At the request of the Air Research and Development Command, the Langley Pilotless Aircraft Research Division has investigated the zero- lift drag and some rolling-effectiveness characteristics of the proposed Northrop long-range, ground-to-ground, supersonic missile designated the MX-775B. The proposed mi

1 Small-body model Large-body model I I I I I I I 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 x 1 (b) Equivalent radius. Figure 4.- Nondimensional cross-sectional area distribution and equivalent radius for the basic small- and large-body models (models 1 and 5) as a function of nondimensional body length. CONFIDENTIAL NACA RM SL53JO2 CONFIDENTIAL -tu ) 30 R 20 10 0 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 M Figure 5.- Range of Reynolds number based on the wing mean aerodynamic chord for the models tested, O Model I,basic small body Model 2, blunt trailirig edge O Model 3, rol I. A Model5, larqe body CN 0 - I i i i i i i i I I i i i i i i i 1 1 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 M Figure 6, Variation of normal-force coefficient with Mach numbers .2 CONFIDENTIAL 0 02 CD .01 CD .01 0 .02 Model 4 Reference 2 Model 5 NACA RM SL53JO2 CONFIDENTIAL 03 .02 CD .01 0 02 Model 2 CD .01 0 .02 Model 3 CD .01'

nd 13 percent at Mach number 1.50. 3. For the basic small-body configuration, the wing-plus-interference drag accounted for approximately 78 percent of the total drag at Mach num- ber 0.9 and 70 percent at Mach number 1.5. 4. The trailing-edge constant-chord ailerons resulted in positive rolling effectiveness (i.e., no aileron reversal) for the Mach number range covered and for the dynamic pressures and wing flexibility of the CONFIDENTIAL NACA RM SL53JO2 CONFIDENTIAL 9 49,' test. The rolling-effectiveness parameter 2V/8 had a value of 0.020 &so at Mach number 1.02 and 0.0065 at Mach number 1.39. goo Langley Aeronautical Laboratory, National Advisory Committee for Aeronautics, Langley Field, Va., September 22, 1953. fet, a ' Y'd, f /^Richard G. Arbic Aeronautical Research Scientist Warren Gillespie, Jr. Aeronautical Research Scientist Approved by: i Joseph A. Shortal Chief PiY,/otless Ai

2. Summary of Section Data on Trailing-Edge High-Lift Devices

Primary source: https://ntrs.nasa.gov/citations/20050080791

es because of tne very thin flaps and very smaU leading-edge radii of the flaps that can be fitted into the available space. The data shown in table T for 25-percent-chord flaps on the NACA 65-210 airfoil sectim with varlms sl7t-lip extensions shm that no increase in msxixnm lift coe Pficien:, is obtained by increasing the slot-lip extension from percenh chord to 97.3 percent chord. The most favorable shape for the pzssage through which the air must fl3w ?ran the lover suri'ace over the flap is an extremely complex problem since it invalves a combination of several variables, each of which can have a large effect on the flaw condikion produced by each of the other variables. These variables include flap shape, slot-entry shape, slot-lip shape, and flap position. Data are given in references 19, 20, and 21 on the maximum lift coefficients produced by slotted flaps of various shapes. can b

series sections. of maxFmumlift coefficients with position of minimum pressure for l'?ACA 6-series sections is sham in figure 18. indicate a small decrease in maximum lift coefficients of both the plain and flapped airfoils regardless of thickness ratio as the position of minimum pressure is moved to the rear. The fact that all of the flap data shown in figures 17 and 18 were obtained wlth 0.20~ flaps der3ected 60° prevents a cmplete indicatlon of the effects of airfoil section on maximum lift coef- ficient since both the optim flap size and optimum deflection change with changes in airfoil thicknesses as sham in figure 15. is parthularlx true of the data shown in figure 17 since both the flap-chord ratio and flap deflection for highest maximum lift coefficient increase as the airfoil thickness ratio is Increased. The optimum maximum lift coefficients should, therefore, increase even mor

mrurimum lift position. the data were obtained are also given in the table. ficients of airfoils with slotted flaps are shown to be considerably higher than those of the smne airfoils equipped with plain or split flaps of comparable size. The advantage of the higher maximum lift coefficients nust be balanced, however, against the added complication of providing external brackets to hold the flap6 or of more crPnplicated mechanlsma required to operate the flap. References frm which Maximum lift coef- Maximum lift coefficients are shown in figure 25 plotted against flap deflection for the ISACA 23012 airfoil section with various sizes of slotted flaps and in figure 26 for two NACA 6-series airfoils with slotted flaps. These data show that the flap deflections for maximum lift coefficients of airfoils with slotted flaps vary over a range of frm about 30' to over 60°. deflection with flap s

lift coefficients of airfoils with slotted flaps vary over a range of frm about 30' to over 60°. deflection with flap size cx slot-lip extension can be shown, it E.EJ be seen from the deta in table I that flaps with the slot Up extended to the trailing edge seem to show their highest meximum lift coefficients at lower flap deflections than with shorter slot-lip extensions- Although no rigid variation of optimum The effect on maximum lift coefficient of increasing the effective chord of the airfoil-iflap combination is shown in figure 27 for various flap cambinations on the NACA 23012 airfoil sectim. The meximum lift coefficients are all based on the chord of the airfoil with flap ccmpletely retracted. Naximum lift coefficients are shown to increase as the total chord is increased either by increesing the flap chord or the slot-lip extension. Increases in flap size above about 25 percent

s increased either by increesing the flap chord or the slot-lip extension. Increases in flap size above about 25 percent of the airfoil chord are shown to have much smaller effects on maximum lift coefficients than increases in the lower rqe of flep size. Increases in slot-lip extension, however, seem to be more efyective as the slot lip is extended toward the trailing e%e. of maximtun lift coefficient shown in figure 27 cannot be expected to hold strictly for different types of airfoil section, the variations shown are probably indicative of the results to be expected frm conventianal Although the variations 20 NACA RM No. LeD09 airfoils of 110,rml thicknesses. The use of thinner airfoils, however, and particularly 2hin NACA 6-series sections, presents added difficulties because of tne very thin flaps and very smaU leading-edge radii of the flaps that can be fitted into the available sp

of the best flap location for airfoil-flap cambinations similar to those for which data are available. Generally, it may be said that the best location of a flap of a given shape vill be a location which, when ccanbined with the slot lip and slot entry, will pro;ride EL con.rerging passage and allow the flow to be directed down over the flap. figure 30, for ipstance, show lift characteristics of an airfoil-Tlap combination for which the slot does not form e converging passage. A caparison of these data with those in table I for airfoils of similar thickness share the low maxFmum lift coefficients obtained with a flap configuration of this type. lift coefficient are shoun in figure 31 for two airfoil sections equipped with various configurations of slotted flaps. the sensitivity of the mimum lift coefficient to small changes in flap position and the accuracy with which the flap must be bu

characteristics for a 0.20~ sflit flap on the HACA 23021 airfoil are shown in reference 15- Pressure dlstributions and flap force Extensible Split Flap Pa extensible sflit flap 18 a epllt- flap pnvi&rf Vr+& 8 ~~mmble The purpose hinge which is moved to the rear as the flap is deflected. of displacing the hinge is to provide a larger area and, therefore, greater lifts. Maximum lift coefficients taken from reference 16 are shown in figure 22 for a Clark1 Y of 0-2Oc, O-~OC, and 0.40~ hinged at various positions from the normal hinge position to the trailing edge. coefficient (&s high as 0.3 for the 0.40~ flap) are produced by the extension of the chord in this way, increases being noted for the 0.20~ flap for each ex%ension of the flap hiage from the normal hinge axis to the trailiw edge although the larger flaps produced increases for extensions of the flap hinge only to 0.90~. airfoil equ

case for plain flaps. design parameters which will affect the aerodynamic characteristics of a wing section with a split flap are, therefore, the flap-chord ratio and the flap deflection. The important Maximum Lift The effect of flap deflection on the maximum lift coefficients of NACA 23012, 23021, and 23030 airfoil sections with split flaps ranging in size from 0.10~ to 0.40~ are sham in figure 14 (data from reference 13) and op’~imum increments in maxhm lift coefficient are shown plotted against flap-chord ratio in figure 15. Although the increments of maximum lift coefficient me considerably higher for thick than €or thin sections, the values of maximum lift coefficient vary in a different manner with thickness because of the decrease in maxkxm lift coefficient of the airfoil with flap undeflected as the thickness is increased. These data show that as the airfoil thickness is increase

nce 7). show that alt,hoq$ the max3m-m lift coefficients of the plain airfoil secticxm decrease as the thickness ratio is increased abo-re about 0.12, the maximum lift coefficients of the flapped airfoils continue to increase to thickness ratios of at least 0.18. Increases in design lift coefficient ark shown to increase maximum lift coefficients nf b3th the glhh anti the fiapped airfoils by 811 equal amount for airfoils of low and moderate thicknesses. the effect of increasing camber is smaller and for the 21-percent- thick airfoils is actually to decrease the maximum lift coefficients with flaps deflected. EACA 23015 airfoil sections are also shown in this figure. maximum lift coefficients for the RACA 230-series sections me sham to follw the same trend 88 the NACX 6-series sections. of maxFmumlift coefficients with position of minimum pressure for l'?ACA 6-series sections is sham in f

equipped with deflected plain flaps is caused by the fact that the flow over the :lap separates at relatively low deflections (of the order of 15' or 20'). The higher drags of the larger flaps are therefore probably a result of a larger separated area and a larger wake. Envelope polars of Drag data on an NACA 23012 airfoil fitted with a 0.20~ flap are shown in figure 10 at two values of the Reynolds number. These data show that the favorable effect of increasing Reynolds numbers extends throughout the entire range of lift coefficient. It should be noted that the effective Reynolds number of 8.4 X 106 corresponds to a test Reynolds number of approximately Any conclusion concerning the effect of Reynolds number based on these data is subject to the limitations of the concept of effective Reynolds number. given 'in figure 10 3 X 106. Drag polws for several low-drag airfoils equipped with pl

3. NACA Conference on Aerodynamic Problems of Transonic Airplane Design

Primary source: https://ntrs.nasa.gov/citations/19790079919

2XXnA=9,CL-0.2 NACA 65-0XX,A=7.6,CL=0 Figure 2.- Effect of wing thickness ratio on Mach number of the drag rise. FREE FALL (NACA 65-009) WIND TUNNEL 30°0-9-0 (NACA 65-110) m ------ (NACA 65 - I 10) (NACA 0012) Figure 3.- Effects of aspect Patio and sweep of wings on the Mach number of the drag rise; a = oO. NACA 65-OXX, M = 1.15 Mgure 4. - Variation of drag coefficient of unswept wings with thickness ratio. M = 1.15; CL = 0. 0 i L/ j:~) ROCKET A FREE FALL Figure 5. - Variation of wing drag coefficient with aspect ratio and sweepback. M = 1.15; CL = 0. Figure 6.- Comparison of drag of sweptfomard and sweptback wings through the -- transonic range. CL = 0; = 0.12. 0 0" 45" (L.E.) 35" (L.E.) ----fl . Figure 7.- Effects of various combinations of taper and sweep on the drag of wings at Mach number 1.15. CL = 0. Figure 8. - Comparison of drag of wings with sharp -leading-edge and conventional

of wings at Mach number 1.15. CL = 0. Figure 8. - Comparison of drag of wings with sharp -leading-edge and conventional NACA airfoil sections through the transonic range. CL = 0. L .04 - co .02 - 0 CIRCULAR ARC - D NACA 65-006 I I I 1 .8 .9 1 -0 1 .I 1.2 M Figure 9.- Effects of fineness ratio and thickness distribution on the drag of bodies of revolution at transonic speeds. Figure 10.- Logarithmic plot of variation of pressure drag with inverse of fineness ratio for four bodies of revolution. P_ ,q 'A\ FREE Figure 11. - Pressure distributions from wing-flow tests through the speed of sound on a fineness ratio 6 body of revolution, and com- parison of the corresponding pressure drag with the total drag measured in free-fall tests of a similar body. NACA 65,-208 NACA 6 5,-210 NACA 65,-212 .O6, 1 1 I Figure 12. - Comparison of initial drag rise of wing alone and wing- fuselage combinati

: st reasonable distance. Consider, for example, the case of a repesentative modern jet air2lane having a wing loading of about 50 pounds por square foot and operatin: at an altitude of 30,000 feet. . . , In figure 1 the up-pr solid cum6 shows the variation of drag coefficient with speed or Mach nwnber (reference 1) and the lower cwve, the corresponding variation in range (base3 on assqtion of conetant specific fuel cons~unption 3n terms of tlnmrst). For an increase in speed of about 100 miles per hour or in Mach n~mber of 0.25 above the spsed at which the drag rise starts, the range would decrease about 75 percent and would be too small to be ~~seful. The dashed curves show that if the drag rise could be delayed sufficiently, or eliminated, the speed could be ihcreesed 100 milss acr hour with only a 10-percent lose in range or 200 miles per hour with about 20gpercent decreme In range. h

6 5,-210 NACA 65,-212 .O6, 1 1 I Figure 12. - Comparison of initial drag rise of wing alone and wing- fuselage combination for three wings of different thickness ratio. - Figure 13.- Effect on drag of wing-body -tail combination through transonic range due to fore-and-aft position of 45' swept wing. Figure 14.- Comparison of drag rise of three wing-body-tail combinations varying in wing sweep and thickness and of representative, modern turbo jet airplane. Thrust available from turbojet engine at 30,000 to 40,000 feet altitude shown h~ form corresponding to drag coefficient for comparison. - tr(-C) I AIRFOIL SECTION CEARAC'PERISTICS . -. AT HIGH StlBSOmC SPEEDS . . By Louis S. Stivers, Jr. '_. . . Amee AercxButical ~aborrttory . '.. . . The design of airplane ' lifting surkace e' and the of thelr aerodynamic characteristics have always depended, to a pest,. extent, on ai.rfoil section dat

he maxim value of the Uft-curve slope for the airfoil with a 6-percent thickness is nearly three time as large as the value at 1~ speeds. The effect of a change in the extent of favorable pressure gradient Prom 0.4 chord to 0.6 chord for'lQ-percant thick MCA keries airfoils is indicat~d in the lowor group of curves in this figure. me data show taat the maxim values df liftcurve alope decrease ae the region of favorable ' pressure gradient becomes -re exteuive or ae the poeition of - ~i- thickness moves rearward. he poeitions of entun thick- nees for the mCA 64-, 65-, aa 66-eeries airfoils are at epproxi- mately 38-, 41-, and 45-percent chord, respectively.) The Mach - numb%& at which the lift-curve slopeb begin to decrease seem to be the bast for the airfoil having the greatest extent of favorable pressure gradient. The preceding rernarks can be expected to apply only to airfoils with sm

Location of the 45' Sweztback Wing. NACA RM NO L7IO1, 1947 20. Wright, John B . , and Lovin~, Donald L. : Xi:$-Sped WLnd-Tunnel Tests of a 1/16-~cale Model of the 339 Researcli Airplane Lift and Drag Characteristics of the D-588-1 and Various Wing and Tail Configurations. RACA PJI No. ~6J09, 1946. 21. Alexander, Sidney: Flight Tests to Deterninc tho Aerodyaamic Characteristics of a I-scale Model of the ;le?ublic D-91 Airplane 9 (MX-809) with Controls VnEeflected end Short Tail Length. MA RII No. ~7~16, Army Air Forces, 1947 . -- -- ---- ----- ALTITUDE 30,000 FT. RANGE 0; I I I I 400 500 600 700 000 SPEED, M.P.H. I I I I I I .6 .7 .8 .9 1 .O 1.1 MACH NUMBER Figure 1.- Effect of drag rise on range of representative modern turbojet airplane. WIND TUNNEL FREE FALL NACA 65-2XXnA=9,CL-0.2 NACA 65-0XX,A=7.6,CL=0 Figure 2.- Effect of wing thickness ratio on Mach number of the drag rise. FREE FA

in t;hs immediate future in terms of a representative wing area and dynamic ;>resoure for comparison with the drag coefficients. The a-eed of the conventional. aimlane, with unswept wings, 13-percent thick, is llmlted by the intersection of the thrust and drag curves to a Mxh number of 0.80 with the Ilighest speed for reasonably efficient cruising gmbably not greater than 0.70 in Mach nmrber. It was found that the drags of mgdels of three projected high-speed aiqlanos with wings or" arotlni! 37 sweep and 10- to 12 -percent thickness (references 16, 20, en8- 21) fell ~enerally bettreen the two drag curves fo;. the 35O configurations shown here. It appears therefore that maw speeds uj! to Yach nunber of 0.9 to 0.95 and reasonable range ~tp to blech numbers of almost 0.3 can be realized with the moderate sweep an$ thiclmese that are be-- incor*>orated in a number of new high-spesd jet airp

t coefficient of 0.h~ tested in the high- speed tunnel (reference 2); and in the right-hand figure for a straight, symmetrical wing at zero lift from the results of free-fall tests (referanee 3). It is indicated that in both cases the Mach number of the drag rise increaseo by 0.015 to 0.02 or 'oetween 10 and 15 miles -,' per hour for each percent reduction in thiclmeso ratio. The effects of ewee2back mi!! aspect ratio on the Mach number of the drag rise, dof ined as before, are illustrated in f igme 3. In this .f iwe, the Mach ntpnber of. the drat rise is ahown plotted against - the Lnverse of the aspect ratio from the resvlts of high-speed tunnel teats of' two series of unswe-t wi~s of diffsrent airfoil section, and a series of lings of 30° weep (references 4 and 5), and from the resats of free-fall tests of two wines of 43O avee; (reference 6). The indicated values of the ?zag-rise Mac

s are also shown i~ the sketch. The pressure distributions along ths body are shown for four Mach numbers from 0.92 to 1-05 in th3 left hand figure and tho variation of ~reseure-drag coefficient wlth Mach nurriber determined from these data is plotted in the right hanh figure. The preeeure distribution fm. Mach rmmber' 0.92 Iff typical of the resulta obtai-md at lower M~ch nuribere and gave no appreciable preeeure Breg. 'With increasw Mach m?mber, the suction peak moves back of the &ixbitm- diat&ter of the body and the preeeure . . drag rises accordingly. The gceateet rearward mowment of the suction peak in relation to chawse of Mach number occurs between Mach nmber 0.96 and 1.00 and tho drag rise Is also most abrupt over this ran@. At Mach numbers frorn 1.00 to' 1.05, ths chase in presstwe distribution and in drag coefficient is relatively mall. Although the preseuros over the forebop3

100 milss acr hour with only a 10-percent lose in range or 200 miles per hour with about 20gpercent decreme In range. his -11 losa in rango ~oaults from the condition of constant altitude assumed here: tho effect of decreasing L/D, resulting from the decreas- lift coefficient with increasing speed, somewhat more than offsets the effect of the increasing aped.) With the development of more concentrated fuels end efficjent power plants to utilize them, the effect of tho dzag rise will no doubt be less critical fram this standpoint, but for the present, at least, it seem clear that fi%thc;r increase in $15 s2eail.s at which airplanes may operate efficiently will be accm~lishcd by changes in aerodynamic design required to avoid any substantial drag rioe up to these speedrJ. . . . qe purpme of this payer fa to point out briefly the Information relating to drag in the transonic range which is

4. Summary of section data on trailing-edge high-lift devices

Primary source: https://ntrs.nasa.gov/citations/19930092003

flap-chord ratio to remain unstalled up to higher flap deflections and highSr and the flap deflection, flap-chord ratios for split flaps than for plain flaps. Maximum- lift data from reference 16 are shown in figure 16 for MAX|MUMLIFT three NACA 6-series airfoil sections equipped with 0.20c The effect of flap deflection on the maximum lift coefficients split flaps. These data indicate the same tendency towai'd of NACA 23012, 23021, and 23030 airfoil sections with split higher optimum deflections for thicker airfoils as was shown flaps ranging in size from 0.10c to 0.40c are shown in figure 14 by the NACA 230-series sections. (data from reference 15) and optimum increments in In order to provide a simple means for showing the effect maximum lift coefficient are shown plotted against flap- of flaps on airfoil section characteristics, all the airfoils chord ratio in figure 15. Although the

th optimum cnange w enanges flap-ehordratio. NACA230-seriesairfoilsequipped with spiitflaps. R=3.5X10< nesses as shown in figure 15. This fact is particularly tru, :: SUMMARY OF SECTION DATA ON TRAILING-EDGE HIGH-LIFT DEVICES 11 /._ for each of the airfoils for which data are shown. A com- parison of the data for smooth and rough airfoils in figure 19 shows that the decrease in maximum lift coefficients of air- --____ -- foils with split flaps increases as the Reynolds number is in- f-- creased and that tile effect of roughness on the maximum lift _ coefficients of NACA 230-series sections is greater than that _ -- _ _--------5 on NACA 6-series sections but not enough to make the actual 1 values of the maximum lift coefficients lower. DRAG Envelope drag polars for an NACA 23012 airfoil equipped t/c with various sizes of split flaps are shown in figure 20. Theseo 0.09 [] /: data indicat

the flapped airfoils continue to L/ I I I A/rfo/I increase to thickness ratios of at least 0.18. Increases in /_ o NAOA 651-212 design lift coefficient are shown to increase maximum lift 2.4 /f_- u NACA 66,/-2/2 __ /2_ 0 NACA 66[215)-2/6 coefficients of both the plain and the flapped airfoils by an _ ,, _, _ Iequal amount for airfoils of low and moderate thicknesses. " !o // " At the higher thicknesses, however, the effect of increasing ._ / j camber is smaller and for the 21-percent-thick airfoils is _ actually to decrease the maximum lift coefficients with flaps _ .G ¢ _-deflected. Maximum lift coefficients for NACA 23012 and NACA 23015 airfoil sections are also shown in this figure. The maximum lift coefficients for the NACA 230-series >g '.Z sections _re shown to follow the same trend as the NACA ; 6-series sections. The variation of maximum lift coeffÉcients _ .8 with position o

n flaps on(d) several airfoil sections in figure 5 (data from references 7 to 12). Generally, the maximum lift coefficient is shown to increase with flap deflection to a maximum at a flap de- flection of about 60 ° or 70 ° except for the largest flap (0.60c) ,cm' _ which increases the maximum lift coefficient only for very Ac, small deflections. • A comparison of the increments in maximum lift coefficient for the NACA 23012 airfoil with 0.20c flaps at Reynolds (e) numbers of 0.609X106 and 3.5X106 shown in figure 6 (a) Normal-fdrcc distribution for airfoil with flapneutral, indicates that, in this range of Reynolds number at least, (b) Normal-force distribution for airfoilwith flap deflected, the maximum-lift-coefficient increment is essentially in- (c)Distribution shownin (a) with flap normal4orce distribution plotted normal to dependent of scale. Optimum maximum-lift-coefficient in- f

ift coefficients to the rear as it is deflected, the effective area of the wing taken from reference 18 are shown in figure 22 for a Clark Y behind the normal quarter-chord point is increased and the airfoil equipped with split flaps of 0.20c, 0.30c, and 0.40c negative pitching moments become larger. Data are shown hinged at various positions from the normal hinge position in figure 23 (from reference 18) oil the effect of split-flap ex- to the trailing edge. Sizable increases in maximum lift co- tension on the pitching-moment-coefficient increments causec_ efficient (as high as 0.3 for the 0.40c flap) are produced by the extension of the chord in this way, increases being noted for the 0.20c flap for each extension of the flap hinge from the normal hinge axis to the trailing edge although the larger __ Abroi/ flaps produced increases for extensions of the flap hinge only o NACA23012 []

xplained by the flaps, ct,=0.2;R=6.0X100.(Flagged symbols _re for60° simulatedsplit flap.) fact that the rear part of an airfoil with a split flap deflected presents a very thick, blunt body rather than the thin mean of the data shown in figure 17 since both the flap-chord line which is assumed in the theory and which is at least ratio and flap d6flection for highest maximum lift coefficient approximated by plain flaps. increase as the airfoil thickness ratio is increased. The FLAP LOADS AND MOMENTS optimum maximum lift coefficients should, therefore, in- crease even nmre rapidly with thickness ratio than the The methods for predicting flap loads and moments which maximum lift coefficients shown, are based on the thin-airfoil theory could not be expected to Data are shown in figure 19 on the effects of Reynolds provide a good indication of split-flap loads since the pressure number varia

IONAL ADVISORY COMMITTEE FOR AERONAUTICS 2.2 \ These incremental coefficients are then converted to coeffi \ cients corresponding to the distribution shown in figure 4 (el by means of the following equations: \ /(_m t : TmAC m /.8 AVn t = ACn'd- 7nAcre The factors r,, and r,, are given in tables V _nd VI of ref erence 6. The incremental basic normal-force distribution i /.6 responsible for tlle entire incremental pitehing-momen_ coefficient Acre' and the magnitude of the incremental bast( normal-force coefficient is therefore determined from the /.4 equation ACr_t " Cribs= G /' _ where G is equal to the distance of the centroid of the incremental basic normal-force distribution from the quarter " - chord axis and is given for various flap-chord ratios and flat ' 1.0 deflections in table IV of reference 6. Ttie incrementa / additional normal-force coefficient is then equal to: •8 /

-fluid theory. only on flap-chord ratio. Experimental data indicate that Hinge moments for plain flaps are subject to the same this linear relation of pitching moment to lift. is actually differences between the ideal conditions and those normally obtained. Figure 11 shows a curve of the theoretical encountered in practice. The same sort of comparison could slope Ac_/Acz plotted against flap-chord ratio along with therefore be expected between the theory and experiment. several experimental values. The agreement is shown to be Data are shown in figure 13 for the 0.20c flap on the NACA 23012 airfoil and again show good agreement with predic- reasonably good. Lions based on Alien's empirical method. FLAP LOADS AND MOMENTS SUMMARY OF PLAIN-FLAP DATA Tile method derived by Allen for predicting flap loads and moments has been summarized in the section on flap theory. Maximum lift coefficients

lap lowm corresponding to the distribution of figure 4 (c) are not surface. The analysis reported in reference 6 showed thai significantly different from those of figure 4 (a). Then "tbove a flap deflection of about 40 ° the load distributions (fig. 4 (d)): for plain and split flaps were identical. Ac,=c,,,2--cm _ The incremental flap normal force and hinge moment caused by flap deflection are equal to the sums of the contri- Ac=c_2--c_ buttons to each from the incremental basic and incremental SUMMARY OF SECTION DATA ON TRAILING-EDGE HIGH-LIFT DEVICES 5 x The values of the factors _/ and _ are given in reference 6- Comparisons of experimental data with loads and distri-Crn! e butions calculated by this method show that excellent agree- ' ment is obtained for plain flaps when the proper assumption is made as to whether the flap is stalled. Sinfilar compari- (a) sons made for split fl

foil-flap combination. The airfoil thickness is increased increments of maximum lift systematic split-flap data should be useful, however, for coefficients, flap deflections for maximum lift, and the size showing the manner in which airfoil parameters alone affect of flap that provides the highest increment of maximum lift the characteristics of airfoils with flaps. coefficient also increase. For any given airfoil section the The effects of thickness ratio and camber on maximum flap deflection at which the highest maximum lift coefficient lift coefficients of NACA 64-series airfoil sections with and was measured decreased as the size of flap was increased, without 60 ° split flaps are shown in figure 17 (data from A comparison of the data in figure 14 v_ith the data shown reference 7). These data show that, although the maximum previously for plain flaps (fig. 5) of similar size shows th

5. NACA Conference on Aerodynamic Problems of Transonic Airplane Design

Primary source: https://ntrs.nasa.gov/citations/19650074048

rmined for leading-edge radii of 1.10, 0.70, and 0.27 percent of the airfoil chord. The nose shapes investigated are illustrated in figure 6. The leading-edge-radius variation was accomplished without altering the profile aft of the maximum thickness position. The effect of the variation in leading-edge radius on the lift- curve slope of the airfoil section is shown in figure 7 to be unim- portant. Figure 8 demonstrates a small favorable effect of reduction in leading-edge radius on the maximum section lift coefficient at Mach numbers above 0.69. _ results shown in figure 9 indicate that Mach numbers of drag divergence were decreased somewhat at low lift ,mmmmb 18 coefficients With decreasing radius. The effects on all these charac- teristics were considerably smaller than those noted previously for the variation in trailing-edge angle. The pitching-moment character- istics were not sign

ening influence of trailing-edge angle with decreasing thickness-chord ratio. In figure 3, an improvement in the maximum section lift coeffi- cient C_ma x at Mach numbers above about 0.7 is seen to accompany a reduction in the trailing-edge angle. Reduction of the trailing-edge angle adversely affected the drag-divergence Mach number Md of the airfoil section at lift coefficients near zero as is evidenced in figure . The difference at zero lift coefficient over the range of angles investigated amoanted to approximately O.O& Mach number. At lift coefficients above 0.2 3 the difference disappeared. The effects of changes in trailing-edge angle on the variation with Mach number of the lift effectiveness of a plain flap are shown in figure }. In this figure, the rate of change of section lift coefficient with flap deflection dc/d5 for deflections from -2° to 6° is shown as a function of Ma

ustrated in figure 1. The only appreciable effects of the trailing-edge-angle variation on the characteristics of the airfoil without a flap were observed in the lift-curve slope, maximumllft-coefficient variation with Machnumber, and the drag-divergence Machnumberat low'lift coefficients. In figure 2, the lift-curve slope dc/dm at 0° angle of attack is shownas a function of Machnumber M for the three trailing-edge angles. The differences are small and of no particular importance in that the variation with Machnumberwas not significantly changed. This result is nothing llke that of G_thert in reference l, where a pronounced effect of traillng-edge angle was observed on the lift- curve slope of a 15-percent-chord-thick airfoil section. This would seemto indicate a lessening influence of trailing-edge angle with decreasing thickness-chord ratio. In figure 3, an improvement in the maximum

incorporated in this discussion, but it did not appear appropriate to make the subject of correlation as am isolated subject a major item on the program. Rather, numerous detailed comparisons of results from different sources have been incorporated at appropriate points in the many papers to be presented subsequently. P .- .- .. . ..- .. . . ~ . .. - -- . .. ... 0 TRANSONIC TUNNEL ROCKET WING FLOW AND BUMP FALLING BODY - CLOSE 0-THROAT TUNNEL I M PROVED TECHNIQUE CONVENTIONAL CLOSED-THROAT WIND TUNNEL c 9 a I1 -T@zij7 .6 .8 1.0 1.2 1.4 1.6 MACH NUMBER Figure 1.- Speed ranges covered by various transonic research techniques. Figure 2.- Semispan moaei mounted on wind-tunnel bump. I-Precedi_pageblank,_ 11 0 • w,NG_LOW_"\,__ STING ---7 J_/ "_ \ SEMISPAN ' ' .e ' ,io Figure 3.- Variation of Cm5 with Mach number as obtained by three techniques. CL i1 °°°° FLIGHT 000_00 O, 0 0 = 0 nO \ UP 12

, a preliminary 16 _ ........ experimental investigation was undertaken in the Amesi- by -foot high-speed wind tunnel. The aerodynamiccharacteristics of a lO-percent-chord-thick airfoil section, both alone and with a 2-percent-chord plain flap, were determined for trailing-edge angles of 6°, 12°, and approxi- mately 18°. The characteristics for the profile without a flap are reported in reference 5. The airfoil thickness distribution was chosen as that of the modified NACAfour-digit series. (See reference 6._) This thickness distribution is expressed by a fourth-power equation which permits the traillng-edge portion of the profile to be varied without essentially changing the shape forward of the maximumthickness position. The trailing-edge shapes investigated are illustrated in figure 1. The only appreciable effects of the trailing-edge-angle variation on the characteristics of the ai

han those noted previously for the variation in trailing-edge angle. The pitching-moment character- istics were not significantly affected by the changes in leading-edge radius. The effects of similar variations of leading-edge radius on 4- and 6-percent-chord-thick sections were not sufficiently important to warrant discussion. CAMBER The effects of large camber variation on the characteristic_ of a 10-percent-chord-thick airfoil section at high Mach numbers have recently been determined from tests of am NACA 64A-series profile cambered for design lift coefficients ranging from 0 to 0.9. In figure lO, the lift-divergence Mach number M_ is plotted as a function of lift coefficient for the various design llft coefficients czi. It is obvious that, for applications calling for operating lift coeffi- cients up to 0.5, the symmetrical section would be the most desirable. For lift coefficients

is that it is in this critical range where forces change abruptly at a critical Mach number that discrepancies are likely to be greatest. In figure 4 is shown a comparison of the elevator engle required to trim an airplane configuration as deduced from wing-flow results for three different lift coefficients, 0, 0.1, and 0.2. The zero case required some extrapolation of data. It will be observed that the elevator angle required to trim according to these results is changed enormously by variations in the lift coefficient. Also shown are points obtained from flight tests for the full--size airplane. At the top of the figure is shown a variation in lift coefficient from 0.1 to 0 experienced by the airplane in passing through the range of Mach numbers shown. This figure illustrates some of the difficulties involved in correlating data frem one source with those from another. In this particu

ts with different techniques is shown in figure 3. The techniques used involved: (a) a stin_-supported full-pan model in the Langley high-speed 7--by lO-foot tunnel, (b) a semispan model attached to the wall of the same tunnel, and (c) a wir- flow model. The figure shows the effectiveness of the flap in producing pitching moment (Cm5) at various Mach numbers for the airplane configuration illustrated. The discrepancies noted for the critical range near Mach number 1.0 are about as large as are likely to be encountered. It may be noted in this case that the semispan model referred to is one-half of the same model that was used on the sting --4 7 support. The wing-flow model is somewhat smaller than the }-inch-eemispan model shown in figure 2. The chief point to be made is that it is in this critical range where forces change abruptly at a critical Mach number that discrepancies are like

Mach number. Satisfactory effective- hess cannot be assured at all lift coefficients merely by holding the trailing-edge augle to a value less than, say, lO ° or 12°, which has been tacitly accepted in some quarters as an upper limit for satis- factory characteristics. LEADING-EDGE RADIUS An analysis of the characteristics at high Mach numbers of a large number of airfoil sections has indicated the shape of the forward portion of-an airfoil to be an important parameter governing these characteristics. To a first order this shape is expressed by the leading-edge radius. In the course of a preliminary investigation (reference 9) of the influence of this parameter, the characteristics of a lO-percent-chord-thick airfoil of the modified NACA four-digit series have been determined for leading-edge radii of 1.10, 0.70, and 0.27 percent of the airfoil chord. The nose shapes investigated are ill

ary layer is only a fraction of an inch thick but the model is small, and even that may be sufficient to affect the flow over the model fuselage appreciably. It is probable that the effect on the wing--bod,v combination or on the wing alone without fuselage is of little consequence, but one would view with caution data that might be deduced for the fuselage alone. Another point to observe concerns the velocity gradients in the field of flow over the model. In the spanw se direction the gradient is generally of the order of 0.007 to 0.01 M per inch or a total of 3 to 5 percent for a 5-inch span. In the chordwise direction the gradients, particularly at the highest Mach numbers, are fairly large and amount to as much as 2 percent for a typical case. Some effects of such variations in velocity would be expected but any quantitative evaluation of such effects have eluded us. The least that o

6. Vortex Flow Aerodynamics, volume 1

Primary source: https://ntrs.nasa.gov/citations/19860017718

gram are illustrated in figure 9. On the left is an example from the theoret and experimental study performed by Boyden (ref. 27) in which he investigated both the steady-state and oscillatory roll damping of slender wings. He developed a method of extending the an e roll case and, as shown, his theory accurately predicte ed damping. The overall 1 ongi tudi nal 1 oad di stri buti on, which is re1 ated to the 1 ongi tudi nal stability and pitch damping, is shown on the right of figure 9. Snyder and Lamar (ref. 28) have shown that a1 though the analogy does not provide detailed surface pressures it does provide an accurate prediction of the longitudinal distribution of 1 ift which can be translate i 11 ustrated the strong trai f 1 ow theori es . Other stabil i ty-relate by Davenport and Huffman (r supersonic speed regimes and the investigation of vortex asymmetry by Fox and Lamar (ref. 25)

y Davenport and Huffman (r supersonic speed regimes and the investigation of vortex asymmetry by Fox and Lamar (ref. 25). - By the early 19701s, the suction analogy had been ctions of the vortex flow charaateri stics of sf ender sharp-edge delta wings for a wide variety of aerodynamic performance and stability parameters and was being routinely app4 i ed throughout much of the aeronautical communi ty . The Langl ey research program was then extended to i ncl ude arbitrary planforms and round leading edges as illustrated in figure 10. In addition to t...