In the present paper I shall not consider the problem of the best arrangement of airplane and propeller, but only a simple method for designing a propeller for a given arrangement of airplane parts. The inflow to the propeller and hence the efficiency of the propeller is affected most by the fuselage

Troller, Theodor

English

NASA Technical Reports Server

---- . .
.. . .
~#-
. .
,, TEOHN-1CAL MEMORANDUMS ...----
/’
L’
-.
INI’LUELTCEOF FUSELAGE
By Theodor
.
.,
ON PROPELLERDESIGN
Troller
From Zeitschrift fk I’lugtechnik und ll~torl~~ftscbiffallrt
July 28, 1928
?.’ .:
Washington
December, 1928
https://ntrs.nasa.gov/search.jsp?R=19930090819 2020-06-17T03:54:48+00:00Z
! 1111111111111111’iimnfllllllll!
31176014402169
]~ATIONAL A.DVISORy CONU1TTEE
TEoHNICAL MEMORANDUM
.
FOR AERONAUTICS .
NO. 492.
INFLUENCE OF FUSELAGE
By Theodor
ON PROPELLER DESIGN. *
Troller.
The works of Eienen, Von Karman and Helmtioldt have given
a simple and sufficiently a~curate i~~thod for designing detached
propellers. ** Previous proposals for the.design of propellers
for actual working conditions and the imethod for the deterinina–
tion of the best pcssible efficiency of propulsion of an assern–
blage of screw-propelled bodies weze not so thoroughly worked
out . The best treatise on this subject is probably the one by
Helmboldt. ***
In the present paper I shall not consider the problem of
the best arrangei~ent of airplane and propeller, but only a sii’n–
ple method for designing a propeller for s.given arrangei~eiltof
the airplme parts. The inflow to the propeller and hence the
efficiency of the propeller is affected most by the fuselage.
-.-—
*“Zur Berficksichtigung des Rumpfes beim Luftschraubenentl~Jurf,“
a coinmunica’~ionfrom the Aerodynamic,,Institute of the Aachen
Technical High School, Zeitschrift fur Flugtechnik und Motorluft-
schiffahrt, July 28, 1928.
‘k*Bienen ad Von Karma, V.D.I. (Zeitschrift des Vereines deut-
scher In.genieure),1924;,,Helmboldt, ‘tZurAer~dynamik der .Treib-
schraube, ” Zeitschrift fur Flu.gtechnik und Motorluftschiffahrt,
1924.
***Helmboldt, l’Nachstromschrauben,“ Werft, Reederei, Hafen, 1927,
and l’Ueberden Vortriebswirkungsgrad, IIWerft, Reederei, Hafen,
April, 1928. See also A. Betz, ‘fConsiderations on Propeller
Efficiency” (N.A.c.A. Technical Memorandum No. 481, 1928), and
“Propeller Problems” (N.A.C.A. Technical MemoradumNo. 491,
1928).
.
--
N.A.C.A. Technical Memorandum No. 492 2
The effect of the wings and of the otheT parts lying in the pro-
peller-slip stream’is much less and is also more difficult to
determine.
In order to determine the influence of the fuselage on the
propeller design, we must first ascertain the flow conditions
in the plane of the propeller, which are affected by the shape
of the fuselage. Instea,dof the troublesome experimental inves-
tigation of the flow about the fuselage, a mathematical method
can be used with good approximation. The fuselage is approxi-
mately represented by a body of revolution and the latter in
turn by a system of sources ad sinks corresponding to the illethod
employed by Von Karman for calculating the pressure distribution
on the hull of an airship.* The sources and sinks are.shown in
constant strength over a stretch a along the axis.
It follows that the stream function of the resultant flow
is
in which
,
U = air speed,in horizontal flight,
Qi = strength of source in section i,
Pi]~’j ~i~f =, distance of reference point from front
or rear end of a source stretch,
rk . distance of reference point from axis,
a= length of source stretch.
*Von Karman, ‘lBerechnungder Druckverteilung an Luftschiffkbr–
pern,” Abh. ad. Aerodyn. Inst. d. T. H. Aachen,’No. 6.
ii.A.C.A. Technical Memorandum No. 492 3
The source strengths are calculated from the streamline
~~~*,= ~;...,ihich. ......
must yield the axi”sand the surface curve -of the
fuselage. Fhr determining the
tion of the streainline ~ = O,
n points of the surface qurve
put
Qi = ~i and 1 +
2Una2
we thus cktain
n source strengths the equa–
yields n equations by taking
for reference points. If we
cik?
.2
. . . l l
l . . . .
. . . . .
Since we are here interested cnly in the flow irithe plane
of the propeller, i.e., at the nose of the fuselage, it is only
necessary to replace the b~w by the system of sources and si-nks.
A small number (3-5) of constant source stretches will furnish
a close enough approximation for our present purpose. Since,
however, a systematic solution of the system of equation~ with
sufficient mathematical accuracy would require too extensive
calculations, it is preferable to solve the equations by estimati-
ng the roots and by verifications. After the values zi, and
hence the source strengths, are thus found, the velocities in
the plane of the propeller become
N.A.G.A. Technical Memorandum No. 492 4
; i~l(P*, - -J-’ux=u-u — pikl,zi,
. ,. n“
(
Xill xi!)
Ur=Ui&i~z
—–~,Pi”
in which
Ux = axial velocity ccmponent,
Ur = radial “ II
Xil , Xill= distance of front or,rear end of source
stretch from the propeller plane”.
Herewith the necessary values for the design are obtained.
We must first determine the best thrust distribution bef~re
undertaking the constructive calculation of the propeller. This
is determined on the prir.ciple that the efficiency must be made
as great as possible, i.e., that the losses in the energy trans-
formation must be as small as possible. We here disregard the
friction losses, which are of slight importance from this view-
point. We must then regarflthe kinetic energy in the slip stream
as small. In c~nsidering the energy in the slip stream far be-
hind. the fuselage, we disregard. the cmtractien due to the ac-
tion of the propeller and the disturbances in the flew caused
by the tail group, etc. Let Wx t ~r~ rx
ties ail.dradii in the propeller plane; w!
corresponding values (located on the same
represent the v.elcc,i-
red@lred rred~ the
streamline) in,the flow
behind the fuselage. As in the case of the detached propeller,
we then have the condition
N.A.C.A. Technical Memorandum Ifo. 492 5
Rred --
Oj (u+ “p) (W’:r’d-t‘2red2“=red) r
1 red d rred = Min. ,
,.
whereby Rred
21-rl.r u+
(
‘tred) wired
2/ rred d rredgo
is given. wtred is the axial velocity to’be added and
r~red, ~“}~e~ is the resulting peripheral velocity on the
r in the slip
condition that
stream. We can best determine Rred frOm
radius
the
R
2~Jux Xxdrx=UR2red n
o
in which
and
We then have
R = propeller “radius;
U = air speed
Ux = axia’l”-velocityin the propeller plane.
.,..
—.—-
The integral,is easy to determine graphically. Again it follows
from the minimum coudition that
Ti=- UdS
dQ w~~ed ~ dQ rl~edu?~ed “
UdS -t- 2 2
is to be kept constant along the radiuq dS being a’thrust el-
ement and dQ being the mass of air flowing through a circular
element p’erunit of time. On further introducing dS = dQ Wr,
we obtain
N.A.C.A. Technical Memorandum N;. 492 6
Ti = ‘1 = const. ,
“red + rzred ~l$eds,, ,.,. ,,,,, l+=
2 U w!~ed .
or, finally, as the condition for the best thrust distribution,
with the subordinate condition
Rred
= C U [C = const.]
*
wired) Wtred ??redY[ u+ 2 ;2Tr-:
(
d rred = S.
g(-)
The simple relation
‘red “red = wtr.d A’red,
which exists for the detached propeller, no longer obtains here,
but we have the following relations in which A = effeotive
pitch angle and Al = Ilinducedlfpitch angle.
rx @xl = wxl hxl = wxl L
~ (analogous to detached propeller),
x Ti
Ux
Wx1 = Wfred ~,
Ax=%= u Ux ‘red— —.
rx w rred @ U rx ‘
(l’red”~!~ed)= (rx ‘x’ ) ~~ (from the constamcy of the spiral).
It then follows t,hat
Ux 2()rred ~:red = W~red ~, Lred’& = wtred x~
x being variable along the radius and dependent on the shape
i,
7’N.A.C.A. Technical Memorandum No. 492
of the fuselage and on the pitch angle of the propeller. The
condition for the best thrust distribution now reads
wired (1 + X2) = C u.
The constant c is found from the equation for
thrust Rred
the total
(s=211zJ TJ—l—— c- ) c-u130 ‘red d ‘red*2 (1 + x )~1 -1-X2)
The values of WI can be calculated for any value of c,
but most conveniently for c = 1. (Ti is estimated at first.
A small error in estimating does rrotappreciably affect the
subsequent calculation. ) We determine graphically the inte–
grals Rred
an?’ U*J
(
-1 ) rred d rred = a
Eo 1 -1-xz~
and Rred
lf
~ ; U20J (1 + xz~ rred d rred = b.
We then have
a c + b C2 = S, .,.
whence r
C=-.-.E. +
2b (-).1
$+f
We now have all the requisite data
of the thrust distribution. and also the
the propeller
qi= 1
1+;
for the determination
induced efficiency of
N.A.C.A. Technical Memorandum No. 492 8
The allowance for the finite number of blades can now be
“made’i-nthe’“same way as for the detached propeller. The propell-
er thrust SCU, which would be attained with an infinite num--
ber of blades, is”made the basis of the calculation. It de-
pends on the desired thrust according to the well-known fomula
Sm=”s[ 1 ‘1’
_13gsinP/’1.
z
@ is here given by the pitch angle of the blade tips, and z
is the nwmber of blades. See Bienen and Von Karman. )
With this value SCC we must now determine c. Then the
l
values of the thrust elements d S and also Wt must be multi-
plied by the k values, which are likewise given in the arti-
cle by Bienen amd Von Kar”man. The further constructional com-
putation is made in just the same way as for detached propel-
lers. From I
dS = dA”cos ~1 - dW sin~’
=
Ca ztd Zx (ux’ + rx’ Q’)
(dA = lift and dW = drag of the blade element) and
i,
,,., , .,. ,,,,, ....—--- . . —-..—
N.A.C.A. Technical Memorandum No. 492 9
we obtain
(
“tfred)W,red2rredndrre@ U+ a \
““’””caZt =’- ~~ ~~ ; K
d rx rx2 OP (kx2 + 1) 1 - c h’x) cos @!x
=K
Zlluz
[
+’
( CT
rx u2(k2x+l) (l-c &’)cospxl I:x’ ;l+xa’/ 1
(z =“ number of blades,
t = chord of blade section or profile,
Ca =
lift coefficient;
c= drag–lift ratio of prcfile for
infinite span,
B = arctan h.)
The correct pitches can also be given the blade sections
from the previously found inflow velocities. Any consideration
of the radial velocities, which necessitate a lengthening of
the effective blade chord and a reduction in the angle of attack,
is not ~er.erallynecessary. The whole process requires but
little uore time than the construction of detached propellers
in the usual ma,nner.
An exmple will illustrate the application of the method.
Let us suppose that a propeller is to be designed for an air–
plane having a fuselage with a maximum diameter of 1 m (Fig. 3).
The R.P.M. of the engine shaft is n = 1200. Th~ air speed
for nmrmal horizontal flight is estimated in advance to be
,.
N.A.C.A. Technical Memorandum No. 492 10
v = 24 m/s. The desired thrust S = 40 kg. The maximum allowa-
!.
-
~,
i
Iile”:p”i-o@ellerdiameter D ‘=““2m. Ftrst the nose of the fuselage
i.I:
ii is replaced by sources. Four source stretches are then adopted.
,$
,“ Figure ~ shows their location,
‘,
as also the location of the chosen
.,
reference points. The following table contains the values Cin)
which are’determined from the values Pikl, Piklr taken from
Figure 3.
I
II
III
IV
The values
1 2
1.0
0.65
0.475
0.275 I
Cikand
give the equations
1.0
‘1 + 0.65 Z2
1.225 !21+ 1.0 Z2
1.425 21 + 1~2 Z2I
1:
!,
,, .. 1.55 Z1 + 1.375 Z2
~1
1.225
1.0
0.75
0.575
3
-..
1.425
1*Z
1.0
0.775
4
—
1.55
1.375
1.2
1.0
rk (likewise taken from Figure 3)
i-0.,475 Za -1-00275 24 = 8.6,
+ 0.75 z~ + 0.575 Z4 = 16.0
+ 1.0 z3 i-().’775 2A = 20.6,
+ 1,2 z~ + 1.0 Z4 = 23.0.
,1~~\ By estimating and verifying we obtain, as an approximate
/!
i!
b
solution, the values
,.
I)
z~ = o, Z2 = 4, = 20, l,“ z~ Z4 = - 8.
from which we calculate thevelocity distribution as shown in
—
N.A.C,A. Technical Memorandum No. 492 11
Figure 5, anclfurther, fl?omthe continuity condition, the corre-
; ee’..-.,..,, ,..,-.
}, spending radii rr”e’d-iiiidrxo””The”v’alueof ‘~if which is re- .
J.
.$ ;. quired for the determination of x, we estimate as follows.
/., ‘, For the detached propeller, according to Bienen and Vo”n
Karman, we have
,,,,
in which o represents the load intensity of a propeller with
an infinite number of blades. Here we obtain ‘fli= 0.89. By
using the load intensity corresponding to the IJreducedpropeller
slip stream” for the determination of Ti, we get Ti = 0.88.
The coxrect value of Ti lies between these two. The
above-described calculation gives c = 0.226 ad qi = 0.884.
The accurate determination of ~i in this case is really super–
fluous. It would be sufficient to calculate x and c from
the estimated value. Figure 5 shows the thrust distribution
according to the above-described calculation method and also for
the corresponding detached propeller.
Translation by Dwight M. Niner,
j National Advisory Committee
1 for Aeronautics.
,,, ,.,.
r//f) —.
N,A.C.A, Technical Memorandum No.492
-1
T
r ,
1 .. -—. —-
4
\,
Fi,g,l
Fuselage dimensions.
t- 1 d
0.1 I0.990.2 1.000.4 0.950.6 0.750.8 0.45
V+l)j’
Figs.l,2,3j4,5
Tig,2
_;.
T /\h+- ‘— 1—.————-7
‘4*.’ !w?g–—gk T ~—-----/
~-M?z+.cl —— -, ; -f;y:kl ----—----------------
1 1;13 x.1 Fuselage.
120 I
lselam . I
Qn I
I f’ I
I I “ -1
01
I
Fig.4
bow
1.5
Fig.5
}=f(r)
F-dSdr
10 -
), 8
ed
g
6 ler
dr
4
ler
2 2
e-
—.
L-. ..,...
,,.
.-
... ,..,,
.. . . .
..:.,
1“
,.
..”
. . .
. .


Influence of fuselage on propeller design

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server