File 629.13/Un 3 as/ No. 688 AIR CORPS TECHNICAL REPORT No.38?2
AIR CORPS INFORMATION CIRCULAR
Vol. VII
PUBLISHED BY THE CHIEF OF THE AIR CORPS, WASHINGTON, D.C.
July 10, 1934
COMPARISON OF VARIOUS METHODS
OF PREDICTING EFFECT OF PROPELLER ON
DIVING SPEED
(AIRCRAFT BRANCH REPORT )
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON: 1934
No. 688 '
•'
,--·--
COMPARISON OF VARIOUS METHODS OF PREDICTING
EFFECT OF PROPELLER ON DIVING SPEED
(Prepared by R. E. Middleton, Materiel Division, Air Corps, Wright Field, Dayton Ohio, August 3, 1933)
SUMMARY
The method of calculating propeller drag in a dive
as outlined by the Handbook of Instructions for Airplane
Designers in section II, part V, paragraph 12 (b)
(3), pages 180- 182, was compared with the same method
modified by use of the method for finding the dynamic
pitch of the propeller as proposed in Report No. 5085 of
the Curtiss Aeroplane & Motor Co.
The results show little difference in accurac~ between
the two methods. A variation of about 15 percent
in the value of (V/nD)0 can be expected with either
method. A corresponding variation in terminal
diving velocity of approximately 8.5 percent for highspeed
airplanes will result.
OBJECT
A comparison of two different methods of obtaining
propeller drag in dives.
DESCRIPTION, METHOD, AND PROCEDURE
Glide tests were available on two airplanes, in which
the revolutions per minute and velocity at zero thrust
were obtained by use of a zero-thrust indicator.
The V/nD for zero thrust for both airplanes was
calculated by both methods and compared with that
obtained from the tests.
An example was then worked out in which the terminal
velocity of the Y 1 P-25 airplane was calculated:
(a) by the handbook method neglecting propeller drag;
(b) by the handbook method, including propeller drag;
(c) same as (b) except for a change of zero-lift angle of
the blade from 4° to 2°; (d) same as (b) with a zero lift
angle of 6°; and (e) by the handbook method revised
to include the Curtiss method of calculating the V/nD
for zero thrust. The detailed calculations for these
examples follow:
1. V/nD for zero thrust= (V/nD) 0 for BT-2B, Air
Corps No. 31- 35.
(a) Handbook method:
Data:
Propeller diamet er= 9 feet 6 inches.
Blade setting= 15° at 42-inch radius.
Calculations:
T1. p rad r"n s=-11z4= 5 7 ·m· ches.
Y. radius=%X 57 = 42.8 inches.
Use 42-inch radius.
Blade angle= 15°. Zero-lift angle=4°.
Helix angle= 15+4= 19°='1t.
(~nD) 0 =2:xr tDa n '1t =2xX421X14ta n 19° =0. 796
62692-34 (1)
(b) Curtiss method:
Data:
High speed= 134.2 m.p.h. R.p.m.=2085.
Engine: Pratt & Whitney R- 1340-D,
450 hp. at 2,100 r.p.m.
Brake hp. at 2,085 r.p.m. = 445 (p. 104,
handbook).
Propeller diameter= 9 feet 6 inches= 9.5
feet.
Calculations: . (V) 134.2X 88
Design V/nD= nD D = 2085X 9.5• 0.596
'Im= .805 (from p. 102, handbook).
Thr us t = 375X ,,Vm X Hp.
375 x 0.805 x 445 - 1 008 d
134.2 - ' poun s
T
CTD=- pn2D•
1,008
= - (2085)2 _ = -0.0430
0.002378X 60 X 9.5 4
M =- 0.140 (from Curtiss Report No.
5085) .
( v) o.043o
nD.
0
=0.596+ 0_140 =0.596 + 0.307
=0.903.
(c) From glide tests at zero thrust:
See figure 1, page 3.
( V) 170X 88
Average nD o=l830 Xfil=0.859 .
Using this value as a basis, the error of the
handbook method i.s 0.859 - 0.796 7 33 0_859 = . per-cent.
The error of the Curtiss method is
0.903-0.859 5.13 percent.
0.859
2. (V/nD) 0 for XC0- 6C airplane.
(a) Handbook method:
Data:
Propeller diameter= 13 feet 0 inch.
Blade drawing no.= X55553.
Blade setting= 27° at 42-inch radius.
Calculations:
Radius= 6.5 feet = 78 inches.
%R= Y.X 78= 58.5 inches.
Pitch distribution from blade drawing
shown in figure 2, page 4.
Difference in pitch between 42-inch radius
and % R = 25.8-20.1 = 5.7°.
Blade angle at Y. R = 27- 5.7 = 21.3°.
Helix angle= 21.3 + 4= 25.3°.
(~) =2xn tan '1t 2x X 58.5X tan 25.3°
nD 0 D 156
=1.110.
... (b) Curtiss method:
Data:
High speed= 133.5 m.p .h. Engine r.p.m.
= 1,865.
Engine: ·Allison VG- 1410.
Brake hp. at 1,865 r.p.m. = 412.
Gear ratio: 5:3 . . Propeller r .p.m.= 1,120.
Calculations:
( V) 133.5X 88
nD D - 1120X 13=0.307.
'lm = 0.836 (handbook, p . 102).
Thrust 375 X ~38{~ X4 12=969 lb.
969
CrD= - ( 1120) 2 _ =-0.0404.
0.002378X 5 0- Xl3 4
M= - 0.140.
(; v:15) o.0404 0
= 0.801 + 0_140= i.o96.
(c) From glide tests at zero thrust:
See figure 1, page 3.
( V) 80X 88
Average nD o=458 X l 3=1.184.
Using this value as basis, the error of the hand-k
h
. 1. 184-1.110
boo met od lS 1.184 =6.25 percent.
'flw erroi: of. t i1 e c ur t"1 ss me th ocl l. s u 314.- l.096
184
--
= 7.43 percent. .
3. Terminal velocity of the YlP- 25 airplane.
Data:
Wing area = 296 square feet. Design g1·oss
weight = 4,834 po"unds.
Engine: Gl V- 1570 geared 7:5, 600 hp.
at 2,450 r .p.m.
Propeller no. 31- 1978. Diameter = 9 feet,
10 inches.
Three blades, mean blade width ratio=
7.41
59 = 0.1255.
Blade setting = 30° at 42-inch radius.
Cv (Airplane, from dive analysis) = 0.0267
at terminal velocity.
For diving velocity diagram see figure 3,
page 4.
(a) Handbook method: •
Raclius = 59 inches. %R = %X 59 = 43.5 inches.
Use blade angle at 42 inches, or 30°.
Helix angle = 30 + 4= 34°. (n1;;)
0
_2x X 421~~an 34° - 1.508.
Normal engine r.p.m.= 2,450.
Maximum safe r.p.m. = l.3 X 2,450 = 3,190.
First approximation of t ermi nal vclocity = 450
m.p.h.
~Q=3190 X 9.843 X 5 O 566 V 450 X 88 X 7 . .
Cr= - 0.0130 (handbook, p . 181) .
c b 3 1• (Three blades'w=0.1255)=-0.0130 X2
x 00.1.12555 = - 0.0163.
2
C, (Tl . t)_2CTD2 2 X 0.0163 X(9.84)2
D HUS - - S- 296
= - 0.01055.
CD (Airpla ne) ~ 0.0267 + 0.0106 = 0.0373.
V (Terminal) = . / VI~
V cD2s
I 4834
= -y 0.001189X 0.0373X 296= 4l 4 m.p.h.
Second approximation of terminal velocity=
450+414
- 2- -=432 m.p.h.
n;; = 0.589 C1·= - 0.0105.
C1, (Three blades) = - 0.0132 CD= 0.00862
+ 0.0267=0.0353.
I 4834
V= Vo.001189 X 0.0353 X 296=425 m.p.h.
Third approxim!ttion of t erminal velocity
425+432
= --2--=428 m.p.h.
nD
--v= 0.593 Cr= - 0.0102 Cr (3 blades)
= - 0.01285.
CD= 0.00835 + 0.0267= 0.0350.
,_ J 4834
l - -y 0.001189X 0.0350X 296 428 m.p.h.
(b) Curtiss method:
High speecl = 247.2 rn .p.h. at 2,385 r.p.m.
Altitude = 14,900 feet (use 15,000 feet).
Assume brake horsepower = 90 percent sea level
hp.
( V) 247.2 X 88 X 7
nD· D =2385X 9.84X 5 i. 3o.
'7m = 86.0 (Handbook, p. 102) .
Brake horsepower at 15,000 feet= 591 X O.!JO
= 532.
375X0.86 X 532 _
Thrust= 247 _2 690 lb.
c 695
TD 0.002378X 0.629 X (
23
6
8; ;\
52
) X 9.84'
= 0.0615
(~) = l.30 + 0.0615
nD o · 0.140 L 74o.
·Third approximation of terminal velocity = 463
m.p.h. R.p.m. = 3, 190.
nD
v=0.550 Cr= 0.0030 Cr (3 blades) = 0.00376
Co = 0.0267+ (2 X O.OO~~g x 9.842) = 0.02976.
· ; 4834
V = \ 0.0011 89 X 0.02976 X 29tl= 463 m.p.h.
(c) Handbook method using zero lift angle of 2° :
Helix angle=30 + 2= 32°, (n~) 0= 1.393.
Second approximation of terminal velocity= 407
m.p. h., '!!:_$=0.625.
Cr= 0.0182 Co= 0.0119+ 0.0267 = 0.0386.
J 4834
V=vo.0011 89X O.o386 X 296. 4o7 m.p.h.
(d) Using zero lift angle of 6°:
Helix angle=30+6=36°, (n~\ =l.623.
Second approximation of terminal velocity=447
m.p.h.
nD
v=0.570 Cr= 0.0066 Cr (3 blades)
= .00821?.
Co= 0.0267 + 0.0054 = 0.0321.
V /, 4834 446 h
=, 0.00ll89 X 296X0.0321 m.p. ·
DISCUSSION
The value of any of the methods used for calculatingpropeller
drag in dives hinges, first, on the reliability
of the data used in calculating the dynamic pitch of
the propeller, and, second, on the reliability of the
data on variation of the thrust coefficient with n(} ·
The Curtiss method of calculating the dynamic
pitch is based on full-scale wind tunnel tests made by
the N.A.C.A. and is a logical development. However,
. ++
H
3
..
when compared with actual flight tests made with a ·~
zero thrust in.dic;ator, the Handbook method seems to
answer the purpose, with about the same accuracy as
the Curtiss method.
The labor involved in using either method and the
availability of the required data are about the same,
although probably the data for the Curtiss method
will be somewhat easier to obtain for new designs.
Since both methods require use. of the same data on
variation of thrust coefficient with n(}, this data
should be checked before ultra-refinement in calcu-
1ating dynamic pitch is resorted to.
CONCLUSIONS AND RECOM;MENDATIONS
It can be concluded that present data is insufficient
to form a reliable opinion as to which method is '
superior.
It is recommended that further data be accumulated
from actual flight tests with a zero thrust in-dicator
or otherwise before making changes in the - ~ _. >I'- - present Handbook method .
·;
FIGURE 1.
4
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