Koooaalstiaat 10 - DELFT nr REPORT No. 56
1 JULI 1952
THE COLLEGE OF A E R O N A U T I C S
CRANFIELD
THE DETERMINATION IN FLIGHT OF THE BODY
DRAG AND THE MEAN BLADE PROFILE DRAG
COEFFICIENT OF A HELICOPTER
by
F. E. BARTHOLOMEW, D.C.Ae. and W. S. D. MARSHALL, D.Ae. (Hull), A.F.R.Ae.S.
This Report must not be reproduced without the perrnission of the Principal of the College of Aeronautics.
VUEGTülGBOUWKUNDE Kanaolsuaot 10 - DELfT Report No. ^S April,
1952-- IJULI 1952
T H E C O L L E G E O F A E R O N A U T I C S C R A N F I E L DThe Determination in Plight of the Body Drag and the Mean Blade Profile Drag Coefficient
of a Helicopter* by
-F.E. Bartholomew, D.C.Ae. and
\¥.S.D. Marshall, D.Ae. (Hull), /^.F.R.Ae.S. ooOoo
S U M M A R Y
Slight modifications have been made to the energy eq.uation which enable the results of partial climb tests to be plotted as two straight lines, the slopes of which are measures of the body drag of the helicopter and the mean profile drag coefficient of the rotor blades.
Sufficient data has been analysed to show that the method can be used to obtain an accurate measurement of the body drag.
The values of (CQ - ^ ) obtained ty the method are of the right order of magnitude, and will give a good indication of the profile drag losses of the rotor if the transmission and tail rotor power can bo assessed to an accuracy of one per cent.
YSB
This report is part of a thesis submitted by the first mentioned author in part fulfilment of the requirements of the Diploma Course at the College.
N O T A T I O N (see a l s o F i g u r e 6) T Q D' D' ^100 ^D Ö
R
o
b c pQ
V a V, t V V "T u V' iX
X
V V.4 Thrust Torque Thrust coefficient Torque coefficient Body dragBody drag at 100 ft./sec. Body drag coefficient
Mean profile drag coefficient of blade Radius of rotor
Rotor solidity Number of blades
Chord of blades (assumed constant) Density of the air
Angular velocity of rotor
Rate of clirah ( l b . ) ( l b . ft.) ( l b . ) ( l b . ) T/ip(:2R)\R^ Q/^p iQ.Rf%-^ D'/ipV'^7i;R^ ( f t . )
bcAR
(ft. ) (slugs/ft-^ ) (rads. /sec. ) (ft/min) Component of velocity normal to rotor (ft/sec.) Component of velocity tangential to rotor(ft/sec)V sin i V cos i Velocity of undisturbed flight
Induced velocity through the rotor Ideal hovering induced velocity Total velocity normal to rotor Resultant velocity at rotor disc
(ft/sec) (ft/sec) (ft/sec.) (ft/sec.) (ft/sec.) ( T / 2 P 7 C R 2 ) ^ Va + V (V, + u ) Rotor incidence relative to direction of
V. (positive when relative wind is down through the disc)
Inclination of rotor disc from the hori-zontal (positive when relative wind is down through disc)
Tip speed ratio Inflow ratio
Resultant velocity ratio
The value of v at which V is its maximum.
V^/I5R U/.QR
TECHNISCHE HOGESCHOOL
VLlEGTUiGSOUWKUNDE Kanaolsuaot 10 - DELFT
2
-1. Introduction
It has long been the practice to evaluate the drag constants for a fixed wing aircraft by plotting the results of flight tests as the drag coefficient against the square of the lift coefficient. The re-lationship is found to be linear, so that
2 ^D = % -^ ^ ^L •
Thus, the constants C-n and K can readily be obtained as the
•^z
intercept and slope of the curve respectively.
At the present time, no attempt appears to have heen made to evaluate the drag constants for a helicopter in a similar manner. In this report, use is made of the energy equation for the helicopter, and, "by making small changes to the form of the equation,
it will be shown that the results of flight tests can he plotted in such a way as to give two straight lines,
the slopes of which are measures of the drag constants of the helicopter.
2. Evaluation of the Drag Constants for the Helicopter 2.1 The energy equation
(^ )
An energy equation has been derived^ ' from a consideration that the power supplied to the rotor is used
(a) to overcome the drag of the fuselage, (b) to overcome the profile drag of the rotor
blades,
(c) to provide an induced velocity through the rotor disc,
and (d) to climb.
In a non-dimensional form the energy equation
hecomes
C? V^.Cn
Co. = C ' . v^ + ^ ( 1 + 3v^)+é ^-&^ (2.1)
In the derivation of equation (2.1) a componentof velocity along the blades has been neglected. Glauert (2^ has shown the effect of this velocity
com-ponent to change the term (1 + 3'^ ) into a terra (1 +Z|. 5v ). Equation (2.1) thus becomes
2
• ° Q = - ^ * T 7 ^ T r (^ -^•5v = ) + Oiv5 (2.2)
and it is this energy equation which will be used inthe subsequent analysis.
The two drag constants in this equation are 5, the mean profile drag coefficient of the rotor blades, and C-Q, the drag coefficient of the fuselage.
2. 2 Evaluation of the body drag coefficient
Inspection of equation (2.2) reveals that, for a constant value of the torque coefficient C Q and increasing velocity v, values for the rate of climb VQ are given which rise to a maximum and then fall with further increase in v.
The value for v for the maximum "VQ will be designated v ^ It is found that for values of v well in excess of v^ the variation in the terms
C 2
T ^ , ^ 0 5 2
is negligible compared with the variation in the terra C v . This is to be expected, since at the high forward speed
more power is used to translate the fuselage. Therefore, over the range v >> v.
V . C m -2
— O R — ~ ® constant - C ' v-^ (2. 3)
from which it is seen that, for a constant thrust , coefficient, the rate of climb varies linearly with v . Hence, by plotting Y^ against v3 the body drag coef-ficient^ C-p. , can be evaluated from
^ ^c ^T
2.3 Evaluation of the mean profile drag coefficient If equation (2.2) is multiplied throughout by V and re-arranged, there results an expression for
the rate of climb as follows -2
^c'^T ,, .„ Ö0 X , ^T U. 5 0 5 3 p » 4
(2.5)
In this case, only values of v well below v, are considered, and over this range the variation in the terms involving v^ and v^ is negligible in com-parison with the term in v on the left-hand side of the equation.
Thus, for the range v <:< v^ , the expression for the rate of climb becomes
V C
-. c l T ^ ^ 3, (c ^ ^ ) V - a constant (2. 6) and the value of the mean profile drag coefficient, 5, for the blades can be evaluated from
k
-2.4 The application of the method
The method of analysis described in the preceding paragraph is seen to be readily applicable
to the resiilts of flight tests. If measurements of the rate of climb are made at various forward speeds, the results of these partial climb tests can be
re-duced to curves of V Q against v3 (over the range v > v.) and YQ . V against v (over the range v. > v ) .
In the evaluation of the body and mean profile drag coefficients, it is necessary to assume that the thrust is constant and equal to the weight. It is also necessary to assume that the angle of tilt, X , of the rotor axis is small, so that the forward speed, as
measured by the airspeed indicator, equals the velocity, V-t, tangential to the rotor disc, and that the rate of climb Vc is equal to the velocity Vg, normal to the disc.
It is also necessary to estimate the induced velocity through the disc. A chart has been prepared
(Figure 1) which gives the induced velocity v for various values of the velocity normal and parallel to the disc. This chart^ ' is based on ,Experimental values obtained by Brotherhood and Stewart'^'^).
3. Results and Discussion
Flight test results were available for the following aircraft.
Sikorsky S. 5I (ref. 5)
Hoverfly Mk.I (ref.6) Bristol 171 (ref. 7)
The leading particulars of these aircraft are given in Table I.
In each case V Q was plotted against v and YQ.V against v. The graphs v/ere found to be straight lines, thus supporting the predictions of the energy equation. The only departure from the linear relation-ship was in the region where the forward speed was close to the forward speed for maximum rate of climb. A specimen reduction is given for the S.5I in Table II and the graphs in Figures 2 and 3.
3.1 The body drag
The results obtained from the analysis are tabulated below -S.51 Hoverfly Mk.I Bristol 171 ^^c dv3 -3i4.,800 -8i+,000 -57.100
D^oodb.)
269 250^5k
The values for the body drags follow the expected trend, the Bristol I7I being obviously the cleanest of these three aircraft. In the case of the Hoverfly a rough check on the value of 1)!^^^ is possible, Stewart having made an estimate^ ' of the component drags. In this reference the body drag at 100 f.p.s. is quoted as 21+0 lb. , which is seen to be close to the value derived'from the flight test
results.
3. 2 The value of (C^ - •^)
Q iL„
The results obtained from the flight tests are given in the following table
-S.51 Hoverfly Mk,I B r i s t o l 171
i'^-o-")
1860 17i|0 1130 P 5 0 ^Q " T .000666 .000370 .000li|6With the existing available data it is not possible to make a conclusive independent check of these values. However, Stewaru8)gives information concerning the collective pitch angles,* and with the
^^^ of rotor characteristics,
00
additional aid of Tables
an estimate of the quantity (C -^Q - , •) is possible. The follov;ing table gives the estimated values.
S.51 Hoverfly Mk.I i P 05 .00060 . OOOL1.2
These two estimated values verify the order of the results obtained from the flight measurements.
The usefulness of the parameter (Cg - ^ ) is limited, as in itself it does not give an indication of the profile drag of the rotor blades. Separation of the profile drag coefficient, 6, by the evaluation of *-'Q requires an accurate assessment of the power
ex-pended in overcoming transmission losses and in driving the tail rotor. For the three helicopters considered here, this information regarding wasted power was not readily available. However, if firstly'ten per cent and then fifteen per cent of the total engine power is
6
-ass-umed for the povi^er losses, the following values for 5 are obtained. S.51 Bristol 171 Hoverfly Mk.I Ó 10 per cent Waste power .0134 .0184 .0208 15 per cent Waste power .0106 .0160 .0181
These values for 5 are all of the expected order of magnitude, but the differences with each power loss are such that they are of little value in assessing the profile drag losses of the rotor. Consequently, an assessment of the waste power to an accuracy of one per cent of the total engine power is required before a satisfactory value of 5 can be determined.
3.3 The ap-plication of the method to the auto-rotative glide
The energy equation (2. 2), without alteration, is applicable to the helicopter in an autorotative
descent. It must be noted in this case that C Q is
small and negative. It is based on the torque required to overcome the transmission losses and to drive the r tail rotor.
Flight test results for the Bristol I7I have been plotted in Figures 4 and 5. The predictions con-cerning the linearity of the curves are again verified. Analysis of the results leads to the following results.
^100 141 lb. Ö 0
"^Q - 4
-.00016 M 10 per cent Waste power .00955 15 per cent Waste pov/er .00795The value for the body drag gives further support for the method since the ten per cent variation from the value quoted in paragraph 3. "i can easily be accounted to the change in direction of the resultant velocity over the body.
The values for the mean profile drag coefficient for the blade are considerably less than those for powered flight quoted in paragraph 3.2. But at high forward
speeds the degree of stalling of the retreating blade is greater .in powered flight than in auto-rotation, and this blade stalling would account for the increase in the mean profile drag coefficient of the rotor blades.
4' Conclusions
(a) Sufficient data has been analysed to show that the method can be used to obtain an accurate measurement of the body drag.
(b) The values of (Cg - ^ ) obtained by the use of the method are of the right order, and will give a good indication of the profile drag losses of the rotor if the transmission and tail rotor pov/er can be assessed to an accuracy of one per cent.
(c) The value of ö obtained from flight test results by this analysis represents a mean of the values over the
range v « v., and cannot be assigned to any particular forvmrd speed. Further, the value of 5 thus obtained will
8 -R E F E -R E N C E S A u t h o r S q u i r e , H.B. G l a u e r t , H. Brotherhood, P. Brotherhood, P. and Stewart, W. Glass, J. S. and Mailer, H.A. Stewart, W. Stewart, V7. Squire, H.B. and Sibbald Hafner, R. Title, etc.
The Plight of a Helicopter. A.R.C. R. and M. 1730,
1935-A General Theory of the 1935-Autogiro. A.R.C. R, and M.1111, 1927.
Flov/ through a Helicopter Rotor in Vertical Descent.
R.A.E. Report No. Aero. 2272, July 1948.'
An Experimental Investigation of the Flow through a Helicopter Rotor in Forward Flight.
R.A.E. Report No. Aero-2330, May 1949.
Sikoraki S.5I. W.' 209,
Performance and Handling Tests. AFEE Report No. Rotor 3.
Brief Performance Tests on the Hoverfly Mk.I by the Aneroid Method and Flight Path Recorder. R.A.E. Tech. Note No. Aero. 1889, May
1947-Sycamore Mk.I. VL. 958.
Performance and Handling Trials. 1st part of A. and A.E.E./874, October 1950.
Helicopter Control to Trim in Forvmrd Plight.
R.A.E. Report No. Aero.2358, March 1950.
Tables of Rotor Characteristics. R.A.E. Tech. Note No. Aero. 1883, April 1947.
Rotor Systems and Control Problems in the Helicopter.
Aeronautical Conference, London, 1947» pp. 579-632. (Roy.Aero.Soc. ).
T A B L E I
Leading Particulars of the Aircraft Considered in this Report. Weight lb. i Rotor diameter 2 Disc loading lb/ft. Solidity
Tip speed (under power)ft/sec. Tip speed (autorotation)" "
S.51 4985 48' 2.756 0.073 486 Bristol 171 4850 47'-5" 2.746 0.050 669 640 1 Hoverfly I 2650 38' 2.335 0.058 449
1
10
-T A B L E II
Specimen Reduction of Flight Test Results
Sikorsky S.51 •
ft/rain. 765 875 960 1030 1070 1090 1075 1045 985 910 815 690 • 540 370 185 ^i knots 20 25 30 35 40 45 50 55 60 65 70 ^5 80 85 90 'X .073 .091 .109 .127 .145 .163 .182 .199 .218 .236 .254 .272 .291 .309 .327 i ^ t / % 1.43 1.78 2. 14 2.48 2.84 3.19 3.57 3.90 4.264.64
i 4.99
5.34
j 5.71 i 6.06 6.41 \ / U T • 514 .587 .645 .691 .719 .732 .722 .702 .661 .611 .547.464
.362 .249 j .124 v/U^ .46 .50.43
.39 •34 .30 .28 .26 .24 .22 .20 I .19 .19 .19 j .19X
.057 .055 .055 .055 . 0 5 4 .053 .051 .049 .046 .043 .038 .033 .028 .022 1 .016 V .093' .106 .122 .138 .155 .171 .189 .204 .223 .240 .256 .274 .292 1 i .310 i1 .327
\ 1Height = 3»000 ft.
Q.R
= 486 ft./sec.
c^. = .0105.
I
a.
o u. o o > > 3i.>i
Ul > III < J>CHART FOR DETERMINATION OF INDUCED VELOCITY IN FORWARD FLIGHT
COLLEGE OF AERONAUTICS REPORT No. 56. FIG. 2 .
tpoo
FT/MIN 7 SO 5 0 0 2 SO ,-^ X \ \ ,s
^ ^ \ V \ \ XHZÜIZI I I I ~~~~
OOIPARTIAL CLIMBS AT ipOO FT.
0 0 2 O 03
\3 .
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REPORT No. S6. 2 0 0 * FT/MJ l I : r ^ 1 0 0 SO 0 '
y
/ / / / / / / / / / / / / / • , / // " / / /r
1 1 1 { 0 1 0PARTIAL CLIMBS AT ipOO FT.
O-IS 0 - 2 0
V c V - V FOR V,>>i)
COLLEGE OF AERONAUTICS FIG. 4. REPORT No. 56.
V'
-1600 • I 7 0 0 FT/MIN. •I BOO - I 9 0 0 0 ' 0 0 2 0 ' 0 0 4 0 0 0 6 O 0 0 8 OOIO \ \ A A i \ \ \ ^ \ •** , \ \ AUTOROTATIVE DESCENTS AT lOOOFT.V c - V FOR V > V, BRISTOL 171
REPORT No. 56. - 2 0 0 - 2 5 0 Vc.V FTTMIN. - 3 0 0 - 3 5 0 \ OMO
V
\ k \ \ \ \ V vo-Os,
V
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— ' S NV
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V V - V FOR \>, > S)
COLLEGE OF AERONAUTICS
REPORT No. 56.
FIG. 6 .
U = Vg •
U-Vt« Vcosi L V r (V,' * U f
= Viin i + w
