Document
TECHNICAL NOTE 3586
IMPINGEMENT O F WATER DROPLETS ON NACA 65A004 AIRFOIL AT Oo ANGLE O F ATTACK By Rinaldo J. B r u n and Dorothea E. Vogt Lewis Flight Propulsion Laboratory Cleveland, Ohio , Washington
November 1955
J X A T I O N A L ADVISORY COMMITTEE FOR AERONA'UTICS TECHMICAL NOTE 3586 IMPINGEMENT O F WATER DROPLETS ON NACA 65A004 AIRFOIL AT Oo ANGLE O F ATTACK By Rinaldo J. Brun and Dorothea E. V o g t S U M M A R Y The t r a j e c t o r i e s of w a t e r droplets i n t h e air flowing past an NACA The amount 6511004 a i r f o i l at a n angle of attack of Oo w e r e determined.
of water i n droplet form impinging on t h e a i r f o i l , t h e area of droplet impingement, and t h e rate of droplet impingement per u n i t area on t h e a i r f o i l surface were calculated from t h e t r a j e c t o r i e s and presented t o cover a large range of f l i g h t and atmospheric conditions. These i m - pingement c h a r a c t e r i s t i c s are compared b r i e f l y with those previously reported f o r t h e same a i r f o i l at angles of attack of 4' and 8'.
INTRODUCTION The d a t a presented herein are a continuation of t h e study reported i n references 1 and 2 on t h e impingement of cloud droplets on a low-drag, t h i n a i r f o i l . The a i r f o i l studied i n both t h e references c i t e d and i n t h i s report i s a 4-percent-thick symmetrical NACA 65A004 a i r f o i l . I n references 1 and 2 t h e impingement characteristics of t h e a i r f o i l w e r e reported with t h e a i r f o i l set at angles of attack o f 4' and 8 O , respec- tively; whereas, t h e data herein apply f o r an angle of attack of Oo.
The range o f angle of attack studied i n t h e three reports permits t h e
evaluation OF t h e impingement characteristics f o r most f l i g h t plans of
interceptor, fighter, and other high-speed aircraft.
The t r a j e c t o r i e s of atmospheric w a t e r droplets about an NACA 65A004 a i r f o i l at Oo angle of a t t a c k at subsonic velocities were calculated with t h e aid of a d i f f e r e n t i a l analyzer at t h e NACA L e w i s laboratory.
From t h e computed t r a j e c t o r i e s , the rate, distribution, and surface ex- t e n t of impinging water w e r e obtained and summarized i n t h i s report.
The r e s u l t s are applicable unaer t h e following conditions: chord lengths from 2 t o 20 f e e t ; a l t i t u d e s from 1000 t o 35,000 feet; airplane speeds from 150 m i l e s per hour t o t h e f l i g h t c r i t i c a l Mach number; and droplet diameters from 5 t o 100 microns.
NACA TE 3586 SYMBOLS The following symbols are used i n t h i s report: d droplet diameter, microns (micron = 3.28X10’6 f t ) K i n e r t i a parameter, 1. 7O4X10-l2 dimensionless (density of ric’ w a t e r , 1.94 slugs/cu ft, included i n constant) N 0, co M L a i r f o i l chord length, f t free-stream Reynolds number with respect t o droplet, 4. 813X10’6 Re0 dPaU
- , dimensionless
I.r distance on surface of a i r f o i l measured from leading-edge chord S point, r a t i o t o chord length f l i g h t speed, mph U l o c a l air velocity, r a t i o t o free-stream velocity U W r a t e of water impingement per u n i t span of a i r f o i l , ~ b / ( h . r ) ( f t span) rate of t o t a l water impingement per u n i t span of a i r f o i l , lb/(hr) Wm ( f t span) l o c a l rate of water impingement, ~ / ( h r ) ( s q f t ] wP W liquid-water content i n cloud, g/cu m rectangular coordinates, r a t i o t o chord length X , Y dYO
l o c a l impingement efficiency, - aimensionless
P
d s ’ viscosity of air, s l u g s / ( f t ) (sec)
w
density of air, slugs/cu f t P a Subscripts : I lower a i r f o i l surf ace NACA TN 3586 3 S a i r f o i l surface u upper a i r f o i l surface 0 f r e e stream RESULTS AND DISCUSSION In order t o obtain t h e extent of impingement and the r a t e of drop- l e t impingement per u n i t area on the a i r f o i l , the cloud-droplet t r a j e c - t o r i e s with respect t o the a i r f o i l were determined. The method f o r cal- culating t h e droplet t r a j e c t o r i e s is described i n reference 3. A solution of the d i f f e r e n t i a l equations t h a t describe t h e droplet motion w a s obtained with the use of the mechanical analog (described i n ref. 4) based on t h e principle of a d i f f e r e n t i a l analyzer. The air-flow f i e l d around the a i r f o i l w a s obtained as discussed i n references 2 and 3. The values of t h e surface velocities f o r the 65A004 a i r f o i l , which are r e - quired i n t h e flow-f i e l d determination, were calculated by the Douglas Lewis laboratory (see f i g . 1). Although Aircraft Corporation f o r the the droplet t r a j e c t o r i e s were calculated f o r an incompressible flow field, t h e r e s u l t s of the calculations can be applied up t o the f l i g h t c r i t i c a l Mach number (ref. 5).
The geometric chord l i n e of the a i r f o i l is oriented at an angle of Oo with t h e x-axis of t h e rectangular coordinate system, and t h e leading as shown i n figure 2.
edge i s placed at the origin of the coordinates, The a i r f o i l orientation presented i n references 1 and 2 i s retained here- except f o r the magnitude of the angle of attack. A t an i n f i n i t e dis- in, tance ahead of the a i r f o i l , t h e uniform air flow carrying t h e cloud droplets is assumed t o be approaching t h e a i r f o i l f r d m t h e negative x-direction and para.llel t o the x-axis. All distances are given as dimensionless ratios, because they are r a t i o s of t h e respective a c t u a l distance t o the a i r f o i l chord length L.
Rate of Total Water Interception The rate of t o t a l water interception, i n pounds per hour per foot of wing span, i s determined by the tangent droplet t r a j e c t o r i e s ( f i g . 2 ) , by the speed of the a i r c r a f t , and by t h e liquid-water content i n t h e The f l i g h t speed and s i z e of t h e a i r f o i l , as well as the droplet cloud.
s i z e i n t h e cloud, are t h e principal variables t h a t a f f e c t the spacing between t h e two tangent t r a j e c t o r i e s . The amount of water t h a t s t r i k e s
t h e a i r f o i l is proportional t o the spacing - yo,z, and the rate of
yo,u t o t a l w a t e r interception per u n i t span of t h e a i r f o i l on t h a t portion of t h e a i r f o i l surface bounded by t h e upper and lower tangent t r a j e c - t o r i e s can be calculated from t h e r e l a t i o n we given i n figure 3 i n terms of t h e r e - The va,lues of y
0,u - yo,2
ciprocal of t h e i n e r t i a parameter 1/K and the free-stream Reynolds nuniber Reo. The i n e r t i a parameter K is a measure of t h e droplet size, t h e f l i g h t speed and s i z e of t h e a i r f o i l , and t h e viscosity of t h e air through t h e r e l a t i o n The density of w a t e r and t h e acceleration of gravity, which are ex- pressed as p a r t of t h e conversion factor, are 62.4 pounds per cubic foot and 32.17 feet per second per second, respectively. The free-stream Reynolds number is defined with respect t o t h e droplet as
Reo = 4.813x10"6 - 'PaU
(3) P A graphical procedure f o r determining values of t h e dimensionless pasam- eters K and Reo i n terms of airplane speed, chord length, a l t i t u d e , and droplet s i z e is presented i n appendix B of reference 3.
The variation of t o t a l rate of w a t e r interception with a i r f o i l speed is summarized f o r an a l t i t u d e of 20,000 feet i n f i g u r e 4, i n which t h e ordinate W d w is t h e t o t a l r a t e of water impingement per f o o t span of a i r f o i l per u n i t liquid-water content (g/cu m) i n t h e cloud. Several chord lengths ranging i n value from 2 t o 20 f e e t are considered. The values i n figure 4 are f o r f l i g h t through clouds composed of uniform droplets 15, 20, 30, and 40 microns i n diameter. The values of W d w given i n figure 4 are based on t h e most probable i c i n g temperature as a f i n e t i o n of a l t i t u d e presented i n figure 15 of reference 3. (The most probable i c i n g temperature w a s obtained from approximately 300 i c i n g observations i n f l i g h t s . ) A s shown i n reference 3, a change i n a l t i t u d e of 10,000 feet w i l l change t h e r a t e of water impingement by approximately 7 percent. The droplet s i z e and the liquid-water content of clouds are seldom known with s u f f i c i e n t accuracy (ref. 4) t o permit t h e r a t e of water impingement t o be calculated within 10 percent; therefore, within can be used p r a c t i c a l limits of application, the r e s u l t s of figure 4 over a wide range of a l t i t u d e s (approx. jJ0,OOO ft, see r e f . 3 ) , A TN 3586 5 The e f f e c t of wing taper can also be obtained from figure 4 , pro- vided t h a t f o r each section of span considered the taper is small enough t h a t two-dimensional flow over the section is approximated, as is men- tioned i n reference 3.
Extent of Impingement The l i m i t of impingement i s determined by the point of tangency on the a i r f o i l surface of t h e two tangent t r a j e c t o r i e s . The reasward l i m - its of impingement on t h e upper and lower surface are shown i n figure 5.
Because the a i r f o i l i s symmetrical at an angle of attack of Oo, t h e l i m - it of impingement on t h e lower surface is equal t o t h a t on the upper surface. The distances S, and. SI are measured on the a i r f o i l sur- face from t h e point of intersection of the geometric chord l i n e with t h e leading edge (fig. 2) i n terms of the chord length. The l i m i t s of i m - pingement are given i n figure 5 i n terms of the reciprocal of the i n e r t i a parameter and free-stream Reynolds number.
Uncertainties i n t h e location of t h e tangency point, and therefore i n the magnitude of the l i m i t of impingement, were discussed i n r e f e r - ences 1 and 2 f o r the a i r f o i l placed at angles of attack of 4' and 8 O , respectively. The uncertainties at Oo angle of attack a r e not as large as reported i n t h e two references cited, because, generally, the tangent t r a j e c t o r i e s do not approach the a i r f o i l surface as gradually at Oo as the lower surface i s approached at e i t h e r 4 O or 8'. Also, Oo angle o f attack permitted the use of a much larger scale factor i n the y-ordinate of the calculating machine; thus, the point of tangency became more certain, The uncertainty i n the location o f the point of tangency i s estimated t o be l e s s than st3 percent f o r t h e a i r f o i l reported herein, The surface limits are .summasized i n figure 6 f o r the same speeds, chord lengths, droplet sizes, and a l t i t u d e given i n figure 4.
Impingement Distribution on Surface
Trajectory s t a r t i n g ordinate as f'unction of point of impact. - The
manner i n which water is distributed on the surface of an a i r f o i l can be obtained if t h e s t a r t i n g point of a droplet t r a j e c t o r y i s known with respect t o the point of impingement on t h e surface. The s t a r t i n g ordi- nate yo at i n f i n i t y of any impinging trajectory, including t r a j e c t o r i e s bounded by t h e upper and lower tangent t r a j e c t o r i e s (fig. 2), can be found i n figure 7 with respect t o t h e point of impingement on the surface. The values f o r t h e s t a r t i n g and ending positions of the t r a j e c t o r i e s are shown i n figure 7 f o r four values of free-stream Reynolds number. For each value of Reo, curves f o r several values of 1 / K are given.
6 NACA TN 3586 A t an angle of attack of Oo the a i r f o i l and t h e impingement are symmetrical with respect t o t h e chord l i n e (also x-axis) e For t h i s reason, t h e data are presented i n figure 7 f o r the upper surface only, whereas i n references 1 and 2 the corresponding data at 4 ' and % ' , .
respectively, are presented f o r both t h e upper and lower surfaces. The values of yo obtained from t h e end points of each curve i n f i g u r e 7 a r e the same as one-half t h e values given i n figure 3. The tangent- were used f o r figures 3 and 5, f a l l on t h e t r a j e c t o r y values, which \ 7.
dashed termini curves of f i g u r e The amount of water impinging between any two given points on t h e a i r f o i l surface my be found by applying t h e r e s u l t s of figure 7 i n t h e following relation:
Local r a t e of droplet impingement. - The local r a t e of d.roplet i m -
pingement per u n i t area of a i r f o i l surface can be determined from t h e expression
wp = 0.33Uw dY0 - - 0.33TJwp
which i s r e l a t e d t o equation (4). The values o f t h e l o c a l impingement efficiency f 3 as a function of the a i r f o i l distance S are given i n figure 8. These values w e r e obtained from the slopes of t h e curves i n figure 7.
A s i s discussed i n reference 1, the values of fl (fig. 8) are very sensitive t o t h e shape of t h e yo against S curves (fig. 7 ) . Because of the geometry of the sharp-nosed NACA 65A004 a i r f o i l and the manner i n which t h e t r a j e c t o r i e s approach t h e a i r f o i l surface, s m a l l e r r o r s i n t h e calculated t r a j e c t o r i e s result i n considerable error i n the slopes of the curves of figure 7. The possible error i n t h e values of j 3 , due t o computational procedxre, f o r surface positions other than near the stagnation point, i s estimated i n reference 1 t o be somewhat l e s s than a 0 percent f o r the values reported therein. Because of improved tech- niques i n t h e computational procedure, t h e values of f3 given i n figure 8 herein are i n error by somewhat less than fz percent f o r surface posi- t i o n s other than within 1 percent of t h e surface distance where t h e peak values of j 3 occur. Since t h e t o t a l water impinging is d i r e c t l y r e l a t e d t o NACA TM 3586 7 a check on t h e computational accuracy of t h e values of j 3 i n figure 8 w a s a l s o obtained by comparing the area under each j 3 curve with the values of y given i n figure 3. The area values checked
0,u - Y0,Z
within &l percent of the corresponding values for t o t a l water interception.
The m a x i m u m values of $ at the stagnation point (S = 0) are very uncertain. A t Oo angle of attack the maximum values of f3 can be ex- pected t o be high (approx. equal t o 1) f o r a t h i n sharp-nosed a i r f o i l 6 ' such as the 65A004 studied. The area check used i n figure 8 also indi- cates high values f o r f3 a t S = 0.
Variation of Impingement with Angle of Attack The e f f e c t of varying t h e angle of attack from 0 ' t o 8 ' on impinge- ment can be found by comparing the r e s u l t s of references 1 and 2 with t h e present study. Because a complete comparison t h a t covers a wide range of f l i g h t and atmospheric conditions i s beyond t h e scope of t h i s report, the following limited comparison is made f o r a set of conditions t h a t occur rather frequently. However, the choice of only a few sets of conditions f o r comparison i s dangerous, because the r e l a t i v e importance of the different factors involved may change with other conditions not discussed.
The comparisons i n t h i s section at different angles of attack f o r t h e NACA 65A004 a i r f o i l are a l l made f o r conditions established at 300 miles per hour, a chord length of 9.4 feet, and an a l t i t u d e of 1 0 , 0 0 0 f e e t . Tbe comparisons are made f o r three droplet diameters, 80, 25, and 8 microns, which r e s u l t i n values of of 1, 10, and 100, respec- l / K t ively .
Rate of t o t a l water impingement. - The variation of the difference
with between t h e upper and lower tangent t r a j e c t o r i e s
' y0,u - y 0 , v
change i n angle of attack i s shown i n figure 9. The rate of t o t a l water impingement, which i s proportional t o y increases rapidly
0,u - Y0,Z'
with increase i n angle of attack, especially f o r the large droplet. With t h e s m a l l droplets (8 microns), the area o f impingement remains on t h e rounded portion of the leading edge while t h e a i r f o i l angle of attack i s changed from 0 ' t o 4'. The influence of changes i n t h e air-flow f i e l d on the t r a j e c t o r i e s t h a t impinge i s not appreciable with changes i n angle between 0 ' and 4O, because t h e impinging t r a j e c t o r i e s a r e confined t o a region near t h e stagnation l i n e for those angles. Along t h e stagnation l i n e the v e r t i c a l components of air velocity are not large between Oo and 4 ' . With t h e large droplets (80 microns), because of the larger droplet i n e r t i a , t h e influence of the air-flow f i e l d on t h e t r a j e c t o r i e s 8 RACA TN 3586 i n changing t h e a i r f o i l from Oo t o 4O is even l e s s than with the small b u t t h e a i r f o i l shape and t h e amount of area presented t o t h e impinging t r a j e c t o r i e s are considerably different, because the impinge- ment occurs much f a r t h e r back on the a i r f o i l .
Between 4O and 8 O t h e influence of change i n flow f i e l d on t h e t r a j e c t o r i e s of smll droplets is probably of the same order of import- ance as t h e change of physical geometry. Even f o r s m a l l droplets t h e impingement no longer occurs principally around the leading edge when the a i r f o i l is raised t o angles greater than 4 ' . The combined influ- ences of change i n air-flow f i e l d and physical geometry on the t r a j e c - t o r i e s t h a t impinge r e s u l t i n a greater increasing slope of the curve (in f i g . 9 ) for small droplets when angle of attack i s increasing between 4 O and 8O. The slope of t h e curve f o r large droplets (80 microns) a l s o increases with increasing angles of attack between 4' and 8'; however, I because of t h e higher i n e r t i a of the droplets and because of the large i n i t i a l slope of the curve, t h e increase i n slope is not as large as f o r t h e s m a l l droplets.
Extent of impingement. - Because of t h e shape of t h e 65A004 a i r f o i l
(principally, because t h e a i r f o i l i s t h i n and the maxim thickness occurs n e w t h e midpoint), t h e impingement on t h e upper surface i s of consequence only at very small angles of attack. As was discussed i n reference 2, t h e extent of irnpingement on t h e upper surface i s very s m a l l
f o r both 4' and 8'. A t 4 ' angle of attack, % i s always l e s s than 0.02
f o r values of 1 / K > 1 ; and, at 8 O angle of attack, S, i s always l e s s
than 0.01 f o r values of 1 / K =- 1 . A t 0 ' angle of attack, S, = S 2
and, as i s seen i n figure 5, ranges from 0.26 t o 0,004 f o r I c l / K < l O O .
The lower-surface l i m i t i s summarized i n figure 10 f o r the same f l i g h t m d atmospheric conditions given i n figure 9. The change i n shape of the curves as the droplet s i z e is increased is explained i n t h e follow- ing manner: A s t h e angle of attack of the t h i n a i r f o i l i s increased, the a i r f o i l presents i t s e l f t o t h e droplets i n the cloud ahead more as a flat p l a t e without thickness than as a streamlined 4-percent-thick a i r f o i l .
Thus, the e f f e c t of a convex lower surface on impingement is minimized as the angle of attack i s increased. For a flat p l a t e of zero thickness, t h e impingement extends t o t h e t r a i l i n g edge ( S 2 = 1) f o r all values of K and Reo at a l l angles other than zero. When t h e convexity of t h e lower surface of t h e a i r f o i l is no longer an important geometrical factor i n determining t h e limit, t h e impingement extends t o t h e t r a i l i n g edge For s m a l l angles of attack t h e l i m - (Sz 1) f o r all sizes of droplets.
it is very sensitive t o t h e a i r f o i l shape on the surface l o c a l i t y where t h e l i m i t occurs. If, for example, t h e l i m i t for t h e 8-micron droplet occurs at S 2 = 0.04 at 4 O angle of attack, a very small change i n shape ( o r r a t e of change of curvature) of t h e a i r f o i l surface i n t h a t neighbor- hood w i l l change t h e l i m i t considerably. A t the same angle of attack the NACA TN 3586 9 l i m i t f o r t h e 80-micron droplets i s 0 - 5 3 , The difference i n the shape of t h e a i r f o i l i n the neighborhood of S2 = 0.53 compared with t h e shape i n t h e neighborhood of S l = 0-04, along with t h e difference i n angle of approach of the t r a j e c t o r i e s t o t h e surface at the two posi- tions, accounts f o r the difference i n t h e shape of t h e two curves.
The preceding discussion on the difference i n t h e shape of t h e three curves i n figure 10 m a y be summarized as follows: The l i m i t of impingement is very sensitive t o the physical geometry t h a t the a i r f o i l w m presents t o t h e impinging trajectories, as well as t o t h e pattern of the co N For t h i s reason, limits of impinge- air streamlines around the a i r f o i l .
ment determined f o r one a i r f o i l shape should be used f o r another a i r f o i l shape only with extreme caution.
Local rate of droplet impingement. - The m a x i m u m l o c a l r a t e of i m -
pingement occurs very nearly at S = 0 f o r all angles of attack up t o The manner of distribution varies considerably with angle of attack. 8 O .
A t 0 ' the water is evenly divided on t h e upper and lower surface. A t 4 ' the amount of w a t e r impinging on t h e upper surface i s a very s m a l l cu I portion o f t h e t o t a l , and at 8 ' the amount is n i l . I n t h e design of ice-
B
protective systems, t h e upper surface protection should be designed f o r low angles of attack and t h e lower surface protection f o r t h e higher angles of attack encountered. A t a l l angles of attack, t h e higher r a t e s of local impingement w e near the leading edge.
CONCLUDING REMARKS The calculated data presented herein apply d i r e c t l y t o f l i g h t s i n clouds composed of droplets t h a t are all uniform i n s i z e and t o nonswept wings of high aspect r a t i o . A detailed procedure f o r weighting t h e i m - pingement of droplets f o r f l i g h t s i n nonuniform clouds i s presented i n reference 4 . A method f o r extending t h e impingement calculations f o r nonswept wings t o svept wings is presented i n reference 6. As i s d i s - cussed i n reference 5, t h e impingement r e s u l t s should be applicable f o r most engineering uses throughout the subsonic. region, because the sub- sonic compressibility of air does not a f f e c t the droplet t r a j e c t o r i e s appr ec iably .
Lewis Flight Propulsion Laboratory National Advisory Committee f o r Aeronautics Cleveland, Ohio, September 23, 1955 10 NACA TN 3586 REFERENCES 1 . Brun, Rinaldo J . , Gallagher, Helen M., and Vogt, Dorothea E. : Im- pingement of Water Droplets on NACA 65A004 A i r f o i l and Effect of Change i n A i r f o i l Thickness from 12 t o 4 Percent at 4 O Angle D f Attack. NACA TN 3047, 1953.
2, Brun, Rinaldo J., Gallagher, Helen M., and Vogt, Dorothea E.: I m - pingement of Water Droplets on NACA 65A004 A i r f o i l at 8O Angle of Attack. NACA TN 3155, 1954.
3. B m , Rinaldo J . , Gallagher, Helen M., and Vogt, Dorothea E.: Im- pingement of Water Droplets on NACA 651-208 and 651-212 Airfoils at 4 O Angle of Attack. NACA TM 2952, 1953.
4. Brun, Rinaldo J., and Mergler, Harry W.: Impingement of Water Drop- l e t s on a Cylinder i n an Incompressible Flow Field and Evaluation of Rotating Multicylinder Method f o r Measurement of Droplet-Size Distribution, Volume-Median Droplet Size, and Liquid-Water Content i n Clouds. NACA TN 2904, 1953.
5. Brun, Rinaldo J., Serafini, John S., and Gallagher, Helen M. : I m - pingement of Cloud Droplets on Aerodynamic Bodies as Affected by Compressibility of Air Flow Around the Body. NACA TN 2903, 1953.
6. Dorsch, Robert G., and Brun, Rinddo J. : A Method f o r Determining Cloud-Droplet Impingement on Swept Wings. NACA TN 2931, 1953.
.* e .
.!i a -Q N .Q cd k a , ri bo r i rl k k d 12 NACA Tm 3586 I (u x NACA TEJ 3586 14 NACA TE 3586 c a C C 15 NACA TN 3586 i l D D Q 100 200 300 400 500 Flight speed, mph ( e ) Droplet size, 30 microns. (d) Droplet size, 40 microns.
Figure 4. - Concluded. Total rate of water impingement on 65A004 airfoil. Angle of attack, 0'; altitude, 20,000 feet; most probable icing temperature, - 1 1 ' F.
NACA TN 5586 CA TN 3586 17 c \ 3 c n W M (c) Droplet size, 30 microns.
(a) Droplet size, 40 microns.
Figure 6. - Concluded.
L i m i t of impingement on upper or lower surface of 65A004 a i r f o i l .
Altitude, 20,000 f e e t ; angle of attack, Oo; most probable icing temperature, -1l0 F.
NACA TN 3586 NACA TN 3586 .36 .40 . 4 4 Figure 7. - Continued. Trajectory s t a r t i n g ordinates as function of point of impingement on surface of 658004 a i r f o i l . Angle of a t t a c k , 0 ' .
NACA TN 3586 22 NACA TN 3586 (d) Free-stream Reynolds number, 1024.
Figure 7. - Concluded. Trajectory starting ordinates as function of point of impingement on surface of 658004 a i r f o i l . Angle of attack, 0'.
NACA TN 3586 m (a) Free-stream Reynolds number, 16.
Figure 8. - Local Impingement efficiency of NACA 65A004 airfoil. Angle of attack, Oo.
24 NACA TN 5586 ( b ) Free-stream Reynolds number, 64.
Figure 8 . - Continued. Local impingement efficiency of NACA 65A004 a i r f o i l . Angle of attack, 0 ' .
NACA TN 3586 U r) D BACA T E J 3586 a ( d ) Free-stream Reynolds number, 1024 Angle of a t t a c k , 0 ' .
Local impingement e f f i c i e n c y of NACA 65A004 a i r f o i l .
Figure 8. - Concluded.
NACA TN 3586 27 0 2 4 6 Angle of attack, deg Figure 9. - Difference between tangent trajectories as function of angle of attack. Flight speed, 300 mph; chord length, 9.4 feet; altitude, 10,000 feet, 2% NACA TN 3586 I 0 2 4 6 Angle of attack, deg
Figure 10. - Lower-surface impingement a8 function
of angle of attack. Flight speed, 300 mph; chord length, 9.4 feet; a l t i t u d e , 10,000 f e e t .
NACA - Langley Field, vd