Mccloud, John L , III

Rogallo, Vernon L

English

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~ 
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co 1 ~ 
J ~ NATIONAL ADVISORY COMMITIEE 
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~ FOR AERONAUTICS 
TECHNICAL NOTE 2894 
CALCULA TrONS OF UPWASH IN THE REGION ABOVE OR 
BELOW THE WING-CHORD PLANES OF SWEPT-BACK 
WING-FUSELAGE-NACELLE COMBINATIONS 
By Vernon L. Rogallo and John L. McCloud, III 
Ames Aeronautical Laboratory 
Moffett Field, Calif. 
Washington 
February 1953 
https://ntrs.nasa.gov/search.jsp?R=19930083824 2020-06-17T19:51:55+00:00Z
lQ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE 2894 
CALCULATIONS DF UPWASH I N THE REGION ABOVE OR 
BELOW THE WING - CHORD PLANES OF SWEPT-BACK 
WING - FUSELAGE - NACELLE COMBINATIONS 
By Vernon L. Rogal lo and John L. McCloud, III 
SUMMARY 
A procedure has been deve l oped for predicting the upwash compo-
nents of the upflow angles in t he r egion above or below the wing-chord 
planes of swept -back wing- fuse l age - nacel le combinations. This procedure 
entails modifications to the methods given in NACA TN's 2528 and 2795, 
for predicting induced upwash angles . 
Comparisons of predicted and measured upflow angles are shown for 
Six semispan models with 400 swept -back wings . The models differ mainly 
in nacell e location (spanwise, chordwise, and vertical relative to the 
Wing) . For all model s , the agreement between the measured and predicted 
upflow angles was found to be good for all points along the horizontal 
center l ine of the pr opeller disks . 
The accuracy of the upflow angle s obtained by this procedure is 
considered satisfactory for use in estimating propeller vibratory 
stresses . 
INTRODUCTION 
It has been shown in refer ence 1 that the oscillating aerodynamic 
loadings on propellers, which contribute to the vibratory stresses , are 
di r ectl y dependent upon the upflow angles l at the horizontal center line 
of the propeller disk. A method for predicting the upwash angle contri -
butions to t he upflow angl es, including the effects of wing , nacelle, 
and fus elage , for a twin- engine airplane having an unswept wing is 
given in r eference 2 . The method of reference 2 has been extended in 
reference 3 to show the effects of wing sweep on the upwash . 
l Angl e between the thrust axis and the direction of local flow measured 
in a plane parallel to the model ver tical plane of symmetry. 
2 NACA TN 2894 
The methods as developed in references 2 an~ 3 have the following 
limitations : The fuselage induction effects are limited to the extended 
horizontal plane of symmetry; and the wing upwash of reference 3 is only 
applicable in the region of the extended wing-chord plane. 
It is the purpose of this report to present modifications to the 
existing methods to remove the above-mentioned limitations, and to pre-
sent experimental evidence by whi ch to assess the accuracy of the modi-
fied methods. 
NOTATION 
A total upflow angle (aw + Ew + En + Eb + ,) 
b wing span 
c wing chord at inboard nacelle 
CL wing lift coefficient (l~~t) 
q dynamic pressure 
R radius of body 
S wing area 
U longitudinal component of free-stream velocity (Vo cos ab) 
6U increase in longitudinal velocity 
Vo free-stream velocity 
W cross component of free-s tream velocity (Vo sin ab) 
6W increase in cross velocity 
iw angle of wing with respect to fuselage center line2 
Xw longitudinal distance ahead of wing quarter-chord line 
Yb lateral distance from body center line 
Yw lateral distance from longitudinal center line of wing 
2 Measured in a plane parallel to the model plane of symmetry. 
NACA TN 2894 
Zb vertical distance from body center line 
Zw vertical distance fromwing-chord plane 
~ effective angle of attack of the longitudinal axis of a body2 
(a.w + Ew - iw) 
~ wing angle of attack2 with respect to free~tream direction 
compressibility parameter 
3 
nacelle-longitudinal-axis inclination as measured from the local 
chord2 (negative below wing-chord line) 
E angle of upwash2 measured from free~tream direction 
vertical coordinate 
lateral coordinate 
(~) semi spans bj2 ' 
( yw) semi spans b/2 . , 
T longitudinal coordinate (~) semi spans bj2 ' 
A sweep angle of quarter-chord line, positive for sweepback 
Subscripts 
w wing 
n nacelle 
b body 
2 See footnote 2, p. 2. 
3 
4 NACA TN 2894 
PROCEDURE 
The basic procedure used in computing the upwash in this r~port is 
the same as that used in existing methods of references 2 and 3; namely, 
the total upwash angle at a point is assumed equal to the sum of the 
upwash angles induced by the wing, nacelle, and fuselage. The wing 
upwash is due to the wing lift and is calculated using lifting-line or 
lifting-6urface theory and the fuselage and nacelle upwash are calcu-
lated from potential flow equations for an infinite cylinder and semi-
infinite body, respectively. 
Wing-Induced Upwash 
Although the lifting-line theory used in reference 2 is applicable 
in regions above or below the wing-chord plane, it is not directly 
applicable to swept wings. The simplified lifting-6urface method of 
reference 3 enables calculation of the upwash ahead of wings of arbi-
trary plan form, but only in the wing-chord plane. Thus to determine 
the upwash in regions other than the wing-chord plane for wings of 
arbitrary plan form, it is necessary to extend or modif1 the existing 
methods. 
For simplicity, the lifting-6urface method of reference 3 has been 
modified. The modification i s based on the assumption that the vertical 
variation of upwash from a wing is similar to the vertical variation of 
upwash from a horseshoe vortex. For low Mach nunibers, the bound vortex 
has the same sweep as the wing quarter-chord line, and lies in the wing-
chord plane.3 For a value of ~ and T/~, the vertical variation of 
upwash due to the horseshoe vortex is readily found from the following 
equation which corresponds to equation (34) of reference 4. 
For high Mach numbers, the horseshoe vortex s hould have a sweep 
angle 1\3 given by tan.ti3 = (tan A)/~ in ac'cordance 1-1ith the 
Prandtl-Glauert rule. 
[ 1----'f) J [1+T\ ] - S 2+(1----'f) )2 - ~2+(1+T\ )2 + E 1 . peL = 41t'l3b2 js 
LT/~ ).: ~ /cos"A~J [(T /~ tan Ap + C~;A~ ) ] + [t 2 ~~-<])2 ] { [T /P+(l-!]) tan ApJ } 
j [T/~ + (1----'f) tan 11.13) 2 + (1-fl)2 + S2 
[ 
21) tan lj,--r/f3 ] 
(21) tan Ar3-~/rp)2 + ~2/COS2A~ [( T/13 tan 11.13 + 1~1))+ 2T\] - [ 2
1
+T\ 2J{ [ 'T/I3+(l----'f) tanA13 J} 
cos 1\.13 S +(1+1) 
j[rr/13 + (1-fj) tan ~ 12 + (1+T\)2 + ~ 2 
[_~T/f3_J (rlf3 tan~ - T\ ) - [ 21') tan .11.13 -T/I3 J Ifrlf3 tan A - T\ )+ 21)J (T/f3'f+~2/cos2 A~ \. COS2~ (21)tan~-T/f3)2+ ~<JCOS2 Arp L\' f3 cos 2Arp 
~1) tan 11.13 - '''/13)2 + 1)2 + ~2 
~ 
f; 
~ 
~ 
I\) 
()) 
\0 
+=-
\Jl 
6 NACA TN 2894 
If the upwash at a point above or below the wing-chord plane is expressed 
as a percentage of the upwash in the wing-chord plane, this percentage 
may be used to determine the wing upwash at a corresponding ~, T/~, 
and distance above or below the wing-chord plane. To show a typical 
example, the upwash expressed in this manner is presented in figure 1 
for a 40 0 swept-back horseshoe vortex system. 
,Fuselage-Induced Upwash 
In the previous applications of the methods of references 2 and 3, 
the horizontal center lines of the propeller planes were coincident with 
the median plane of the fuselage. In order to calculate upwash at the 
horizontal center line of propeller planes which are not coincident with 
the fuselage median plane, the method used in references 2 and 3 must be 
extended. The velocity components (in a vertical plane parallel to the 
body longitudinal axis) of the flow about an inclined body are shown in 
the following sketch. 
From the geometry of the velocity components 
therefore, since wju = tan ~, 
= ~Q + ~) 
U l + m 
U 
1 + !:M 
W 
=--~ 
1 + m 
U 
(1) 
(2 ) 
NACA TN 2894 
which for small angles (ab and Eb) may be written 
1 + !§l 
1 + Eb ~ W 
% 1 + m 
u 
7 
If f:M and m can be found for any point in space, Eb is known 
for that point. Although it is difficult to find these quantities for 
a finite body, they are readily obtained for the infinite cylinder in 
incompressible flow. 
For a fuselage which has a large fineness ratio and extends well 
forward of the propeller plane (at least three maximum mean diameters), 
it may be assumed that the fuselage can be represented by an infinite 
cylinder equal in diameter to that of the cross section of the fuselage 
in the extenied propeller plane (see reference 2).4 In the case of an 
infinite cylinder, m is equal to zero, hence equation 3 becomes 
Eb AU 1 + - ~ 1 + ort_ or 
a.b W (4) 
To determine the increase in cross-flow velocity, the well-known 
source-sink or doublet equations found in most texts on hydrodynamics 
are used. For an infinite circular cylinder in an incompressible flow 
f'Stl= 
w 
The lateral distribution of E b/a.b at constant distances above or 
below the median plane of an infinite circular cylinder is presented 
in figure 2. 
4The validity of this assumption has not been checked for the case of 
compressible flow. 
8 NACA TN 2894 
RESULTS 
To provide experimental data for evaluation of the modified 
methods, surveys were made of the upflow angles at the horizontal center 
line of the propeller disks for six semispan models with 400 swept-back 
Wings. The surveys were made i n the Ames 40- by SO-foot wind tunnel at 
a Mach number of 0 . 13. One of the models is shown mounted in the wind 
tunnel in figure 3. All six models are shown in figUre 4. The survey 
rake shown in fi"gure 3 consisted of six directional-pi tot--£tatic tubes 
mounted at various intervals along a steel tube. The method of refer-
ence 3, together with the modifications included herein, has been used 
to predict the upwash angles, which are combined with the geometric 
angles to obtain the upflow angles for the six models. Comparison of 
the measured and predicted upflow angles at several locations along the 
horizontal center line of each propeller disk is shown in figure 5. 
Upflow angles are shown for angles of attack of -40 , 00 , 40 , So, 
and 100 • Although not evident from figure 5, the agreement between the 
measured and predicted upflow angles was found to be of the same order 
at various points along the horizontal center line of the propeller 
disks and for the different nacelle locations at a given angle of attack. 
CONCLUDING REMARKS 
A procedure for predicting the upwash component of the upflow 
angles in the region above or below the wing-chord planes of swept-back 
wing-fuselage-uacelle combinations has been developed and evaluated. 
The accuracy of the upflow angles obtained by this procedure is 
considered satisfactory for use in estimating propeller Vibratory 
stresses. 
Ames Aeronautical Laboratory 
National Advisory Committee for Aeronautics 
Moffett Field, Calif . , Nov. 14,1952 
REFERENCES 
1. Roberts, John C., and Yaggy, Paul F. : A Survey of the Flow at the 
Plane of the Propeller of a Twin-Engine Airplane. NACA TN 2192, 
1950. 
2. Yaggy, Paul F.: A Method for Predicting the Upwash Angles Induced 
at the Propeller ~lane of a Combination of Bodies With an Unswept 
Wing. NACA TN 252S, 1951 . 
2Q NACA TN 2894 
3. Rogallo, Vernon L.: Effects of Wing Sweep on the Upwash at the 
Propeller Planes of Multiengine Airplanes. NACA TN 2795, 1952. 
9 
4. Spreiter, John R., and. Sacks, Alvin H.: The Rolling Up of the 
Trailing Vortex Sheet and. Its Effect on the Downwash Behind. Wings. 
Jour. Aero. SCi., vol. 18, no. 1, Jan. 1951. 
10 NACA TN 2894 
NACA TN 2894 
100--=-T---~--~--~--~--~--~--~ 
80 
~ 
~ 
~ §- 60 
Cb 
c:: 
~ 
~ 
~ 
a 
.c::: 
u 
I 
b 
.~ 
~ 
't... 
a 
Cb 
b 
~ 
c:: 
Cb 
~ 
~ 
40 
20 
0 
fJ 
0.25 
---- 0.50 
- -- 0.75 -20L---------------~~--~--~--~--~ 
o .1 .2 .3 .4 
Dis/ancs above or below wing - chord plans, 
b*" , sem ;spans 1"2 
Figure I. - Variation of upwash of a 40° swept-
back horseshoe vortex with vertical position . 
11 
12 NACA TN 2894 
.5 
"\ \ 
1\ 
~I~ .3 
\ 1\ 
\ \ ""/I 
\ ~ R 0 
1\ \ / V~·$O 
.4 
... 
.-: 
~ 
.2 ..... ~ 
l) 
r" ~\ ~ VO. 7" 
II ~ ~ V 1.00 J 1"1-
.!! 
~ 
.1 ~ 
~ § 
l 
° . ~ 
I 
~ 
~ - .1 
I ~ ~ £ t'I-... 
I I ~ ~ ~ ~ - ~ II / Ih ~ I""""" S ~ 
,It ~ ~ "'-1.26 ['-. 
j I VI/' ~ I.~ ~/.76 
II( 2.00 
~ ~ 
~ 
-.2 
~ 
/ 
L/ !J 
/ ~ ~ 
-
1 2 ~ 
Lat.ral position, ~' 
Figure 2. - The upwash of an infinife cylinder in a fransvtlrs. pia".. 
NACA TN 2894 13 
Figure 3.- Mode l B mounted i n the 40- by 80- foot wind tunnel. 
,----~-. --------~---
14 NACA TN 2894 
OJ95c 
Model A Model 8 
OJ81c 
OJ95c 
Model C Model D 
0456c 
Model E Model F 
~ 
Model A B C 0 E F 
Aspect ratio 10 10 7.3 7.3 7.3 7.3 
Nacelle location, 7J 
Inboard 0.25 0.25 0.31 0.31 0.31 0.31 
Outboard 0.50 0.50 0.62 
Toper ratio 0.34 0.34 0.49 0.49 0.49 0.49 
Nacelle inclination 0° 0° 0° 0° 0° _7° 
Note : Extent of survey from nacelle center line, 0.19c to 0.61c . 
Figure 4 . - Semispan models. A,40°. 
NACA TN 2894 
t), 
~ 
~ 
~ 
~~ 
t), § 
~ 
:S? 
'.::: §-
~ 
III 
...... 
. ~ 
~ 
~ Q.. 
16 
12 
8 
4 
0 
0 
0 
0 
-4~----~----~~----~----~r-----~----~ 
Diagonals are lines 
of perfect correlation . 
-4 0 4 8 12 16 
Measured upflow angle I A, deg ~
..'Ie 
..'Ie . 1/) 
. 1/) il 
il 
'-
'-
~ 
~ -....; Ib 
-....; ~ Ib ~ ~ ~ t:l.. 
t:l.. ~ 
....... ~ I:l C) ~ C) ~ C) 
~ ~ ~ ~ C) 
A 0 [J 
B (> (::, 
C L1 
0 (7 
E "J 
F \-l 
Figure 5. - Comparison of predicted and measured upflow angles 
for six semispan models at several angles of attack . 
NACA-Langley - 2-17-53 - 1000 
15 


Calculations of Upwash in the Region Above or Below the Wing-chord Planes of Swept-back Wing-fuselage-nacelle Combinations

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