v393 - dome
TRANSCRIPT
V393.R46
jr
z :j
F :,j I -
Dr
THE RADIAL DISTRIBUTION OF PROPELLER THRUST
FROM MODEL WAKE MEASUREMENTS
by
John L. Beveridge
November 1958 Report 1136
NS715-102
II
TABLE OF CONTENTS
ABSTRACT ............................................................ ............... . . . . ........... ....
INTRODUCTION .........................................................................................................
EXPERIMENTAL WAKE DISTRIBUTIONS .............................................................
RADIAL THRUST DISTRIBUTIONS ........................................................................
TOTAL THRUST ........................................................................................................
CONCLUSIONS ..........................................................................................................
ACKNOWDLEGMENTS ..........................................................................................
REFERENCES ...........................................................................................................
Figure 1 -
Figure
Figure
Figure
Figure
LIST OF ILLUSTRATIONS
Radial Distribution of Wake Fraction with and without aPropeller as Determined from Tests on a Submerged Bodyof R evolution ........................................................................................
View of Wake Survey Rakes ...............................................................
Radial Distribution of (1 - Vx) and Axial Velocity Changefrom Towed and Self-Propelled Tests ..............................................
Thrust-Load Coefficients for Propeller 3273 ..................................
Plans and Open-Water Characteristic Curves for Propeller 3273 ......
Page
1
1
1
2
5
5
8
8
--nrCks*, ~__~_______ -ca~,-- ~n*r*~*r --r~-Pr~,~radCllarerlh~-r- I I I Is II
NOTATION
Dimensions
. Dimensions inSymbol Description DiMass-Lensgth-Timeons in
d Propeller Diameter L
n Propeller rate of revolution T- 1
R Propeller tip radius L
R' Radius of slip stream in Lplane of wake measurement
r Local radius L
T Propeller thrust MLT "2
v Axial velocity of propeller orpitot tube through the water LT 1
at radius fraction x
v8 Ship speed LT" 1
Av Axial velocity change at LT-1radius fraction z
p Mass density ML- 3
Coefficients and Ratios
Symbol Formula Description
T Propeller thrust-loadCTST% p 7 2 coefficient
_ Propeller advanceJnd coefficient
Ja V Propeller apparent
nd advance coefficient
TK Propeller thrustT p 2d4 coefficient
1 - Taylor wake fraction atWx 1- Sradius fraction as
r rSor -Radius fractionR R'
- -- 'l HIM
1111 1~~ ~---IIYI Lii i MUM, l
ABSTRACT
The radial distribution of propeller thrust-load coefficient is calculated
from experimental wake data obtained from towed and self-propulsion tests on a
submerged body of revolution. The experimentally obtained thrust distribution
is in excellent agreement with a theoretically calculated distribution. Numer-
ical integration yields a total thrust-load coefficient which is in good agreement
with propulsion test results.
INTRODUCTION
Past efforts to determine the radial distribution of propeller thrust have been mostly
by theoretical means. Information is especially needed for a propeller operating behind a
submerged body rather than for the open-water propeller condition.
In this report, a radial distribution of propeller thrust obtained theoretically is com-
pared with one obtained experimentally. The experimentally determined radial wake distri-
butions were obtained from tests on a submerged body of revolution. The radial distribution
of propeller thrust, or more conveniently the propeller thrust-load coefficient, CTS is easily
obtained from such wake data. The results are presented as curves of wake fraction and thrust
coefficients. The calculated total thrust-load coefficient is compared to the thrust-load
coefficient obtained from propulsion tests.
EXPERIMENTAL WAKE DISTRIBUTIONS
The wake curves of Figure 1 were obtained from measurements made a short distance
(0.227 d) abaft the propeller rotational plane on both a towed and self-propelled model. The
wake survey was made on both the port and starboard sides of the model by means of pitot
rakes. The method of mounting the wake survey rakes in the upper quadrants and the general
arrangement of the port and starboard wake survey assemblies on the model are shown in
Figure 2. The axes of the pitot static tubes of the rakes were set parallel to the average
slope (tan 14 deg) of the afterbody and lie in a 45-deg meridian plane. For the purpose of
computing thrust, a cosine correction was applied to the measured velocities. The effect
of slip stream rotation on the experimentally derived thrust distribution as obtained by the
pitot survey was mathematically investigated. For this case, the correction as calculated
by the method of Pankhurst 1 was found to be negligibly small.
1References are listed on page 8.
'14 111 i,11,10 IN ffilih
U.bNote: Plane of Measurement 0.227d Behind
_Propeller Rotational Plane
0.4 - _
_Port RakeTowed (Without Propeller)
0.2 Rn --= 2.34 ox I 9
0.0 "
-Propelled, da = 0.924
-0.2
0.2 0.4 0.6 0.8 1.0 1.2
Radius Fraction x
1.6 I.8
Figure 1 - Radial Distribution of Wake Fraction With and Without a Propelleras Determined from Tests on a Submerged Body of Revolution
RADIAL THRUST DISTRIBUTIONS
The axial momentum equation functionally relates the wake fraction curves from towedand self-propulsion tests (Figure 1) to the incremental thrust as follows:
Av)dT = 2nrp ( v +- A vrdr
\ 2 )
where A v represents the velocity change between the towed (without propeller) and the pro-
pelled condition. A v and v are expressed nondimensionally (Figure 3) as A v/v s and (1 -Wx) ,
respectively. The curves shown in Figure 3 were derived from the curves of Figure 1 byapplying the appropriate cosine corrections (mentioned previously) and by correcting for the
contraction of the propeller slip stream. In computing z for the propelled condition, R'-was
estimated to be equal to 0.968 R based on data derived by Theodorsen. 2
Equation [1] can also be conveniently written in nondimensional terms. Let z = r/R
and divide by (% p v 27 R2) then the thrust distribution is given by
dCrS
dx
-- -- II --r - ~---------- --------- -
Av*+ 1 "-As"
V2 2 v.'
Figure 2a - Plan View
Figure 2b - Elevation
Figure 2 - View of Wake Survey Rakes
-- II .
0.6
C
0.4-OA
0.2
0
Figure 3 -
0.2 0.4 0.6 0.8 1.0Radius Fraction x
Radial Distribution of (1-IVx) and Axial Velocity Change fromTowed and Self-Propelled Tests
1.9
1.2 - -__ _ _ __ __
1.0 Experimental
0. Theo retical
0.6 0
0.4
0.QZ
Radius Fraction U.Radius Fraction x
Figure 4 - Thrust-Load Coefficients for Propeller 3273
4
I-
0
to.
I-
--~-- s I-- --~- ------------r~ s~sl---rYI--lrP---luu*r. Ili~ LW--
-- --
U. C.4 U 0.8
Elm11 lb _
The experimental thrust distribution dCTs/do obtained from Equation [2] and a theoretically
obtained distribution are plotted in Figure 4. The agreement between the experimental curve
and the theoretical curve is excellent. Recent developments in the circulation theory 3,4,5
and the manner in which the experimental distribution was obtained, both make necessary an
explanation of the curves shown in Figure 4. The shape of the distributions towards the pro-
peller hub and propeller tip is of particular interest. At the propeller tip, the experimental
curve exhibits a finite value of dCTs/dx (solid line) which fairs into real experimental distri-
bution at x= 0.9. Why the diameter of the slipstream is larger than the propeller diameter i
not completely understood. A number of factors such as flow separation on the appendages;
interaction between the hull, appendages, and propeller; or the appendage arrangement itself
could be contributing factors. This virtual Av does not, however, produce any additional pro-
peller thrust due to the lack of a point of application beyond the propeller disk. Equation [21
does not consider this fact; therefore, the real experimental distribution is faired to zero at
x = 1.0. In contrast to the experimental curve just discussed, the theoretical thrust distribu-
tion falls to zero at both the propeller hub and propeller tip. The accuracy of theoretical thrust
distributions was greatly increased by Tachmindji's formulation and solution of the potential
problem for the circulation distribution of a propeller with a finite hub. Prior to the publi-
cation of the data contained in References 4 and 5, theoretical thrust distributions were less
accurate near the extremities. The circulation distribution as calculated assuming zero hub
diameter would yield a finite value for dCTs/dx at the propeller hub. This is caused by the
extention of the vortex sheets to the propeller axis.
TOTAL THRUST
Using Simpson's rule, the total thrust-load coefficient was calculated from the experi-
mental distribution shown in Figure 4. A CTS value of 0.595 results from the integration.
The total thrust obtained from a model self-propulsion test is estimated from Figure 5. The
characteristic curves for Propeller 3273 are entered on the abscissa at a J of 0.605 as deter-
mined from a model self-propulsion test. The corresponding KT/J 2 value is found, by inter-
polation, to be 0.545. By calculation KT/Ja 2 = 0.545 (1 - W)2 is found to be equal to 0.2163.
Therefore, the value of CTS obtained from the propulsion test is 8/rr - 0.2163 = 0.551. The
agreement between the CTS values obtained by the two methods is very good.
CONCLUSIONS
1. For the hull-propeller combination considered, the experimental and theoretical thrust
distributions are in excellent agreement.
2. An integration of the experimental thrust distribution yields a total thrust which is in
good agreement with the results obtained from submerged model propulsion tests.
Propeller 3273
TMB Drawing C-3273
Number of BladesExp. Area RatioMWR
BTFp/dDiameterPitchRotationTest RPMTest Vo
50.6110.242Var.0.9519.900 in.9.415 in.RH858
2.5 -7.0 knots
Reynolds Number,
Thrust Coefficient,
Torque Coefficient,
Speed Coefficient,
Efficiency.
b0 .7 VV2 + (0.7nd)2
Re=Y
TKt= pn2d 4
QKq -Kq pn 2d5
VoJ
nd
TVoe =
27TQn
t J= -X-
Kq 27
ThrustTorqueRevolutions per Unit TimeSpeed of AdvanceKin.ematic ViscosityDiameterPitchDensity of Water
I-YI I i
0,7 iiii .]l i t.tix I,I. I : : ::11 1 1 1 1 1 1 1 1 , [ . , : I I ; I I I l l l I I I l II
iI IlI : : ; 1:1 1 I I ! I F ] 1
i i iI l I L i*l /1lz
, 0.60
0K....Re 5.4 x I0s
i-. 1 17 ;4; 1 1 1 1 t 1 10.5z'LiJ0
I~It
0.4 -- -0Kt
0.3
LL.T I
w
I-
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
SPEED COEFFICIENT J
Figure 5 - Plans and Open-Water Characteristic Curves for Propeller 3273
-- _ _ it
ACKNOWLEDGMENTS
The author wishes to express his appreciation to Mr. A.J. Tachmindji whose critical
review and suggestions have greatly enhanced the value of the report, and to Mr. W.B. Morgan
for his contribution to the programming of the propeller design on the Univac.
REFERENCES
1. Pankhrust, R.C., "Airscrew Thrust Grading by Pitot Traverse: Allowance for Rotation
of Slipstream at High Rates of Advance," R&M 2049 (1945).
2. Theodorsen, Theodore, "Theory of Propellers," First Edition, McGraw-Hill, New York,
(1948).
3. Tachmindji, A.J., "The Potential Problem of the Optimum Propeller with Finite Hub,"
David Taylor Model Basin Report 1051 (Aug 1956) and I.S.P. (Nov 1956).
4. A.J. Tachmindji and A.B. Milam, "The Calculation of the Circulation Distribution for
Propellers with Finite Hub Having Three, Four, Five and Six Blades," David Taylor Model
Basin Report 1141 (Jun 1957).
5. CDR J.W. Shultz, Jr., USN, "The Ideal Efficiency of Optimum Propellers having Finite
Hubs and Finite Numbers of Blades," David Taylor Model Basin Report 1148 (Jul 1957).
1 " ~"IR --.- --nrm nrrc~~x. - - -- - - 0001n*a"Rw-n..n karr _ I
INITIAL DISTRIBUTION
Copies
10 CHBUSHIPS, Library (Code 312)5 Tech Library1 Tech Asst to Chief (Code 106)1 Prelim Des (Code 420)1 Mech Sci Perf (Code 436)1 Submarines (Code 525)1 Prop & Shafting (Code 654)
2 CHBUORD1 Research (ReU-1)1 Research (Re-1c) Attn: Mr. H. Eggers
1 CHONR, Fluid Mech Br (Code 438)
1 Dir, USNRL
2 CDR,USNOL
1 CO, USNOTS, Pasadena, Calif.
1 Dir, ORL, Penn State Univ, Univ Park, Pa.
1 Dir of Aero Res, NASA
1 Electric Boat Div, Genl Dynamics Corp,Groton, Conn. Via SUPSHIPINSORD,Groton, Conn.
1 ETT, SIT, Hoboken, N.J. Attn: Prof. Korvin.Kroukovsky
1 Head, Dept, NAME, MIT, Cambridge, Mass.
1 Dr. H.A. Schade, Dir of Engin Res, Col ofEngin, Univ of Calif., Berkeley, Calif.
1 Supt, AEW, Haslar, Gosport, Hants, England
1 Supt, Ship Div, NPL, Teddington, Middlesex,England
1 Dir, Netherlands ScheepsbouwkundigProefstation, Wageningen, Holland
1 Dir, Statens Skippsmodeltaken, Tyholdt,Trondheim, Norway
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Copies
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1 Dir, Vasca Nazionale Perle Experienze, RomeItaly
1 Dir, Hamburg Model Basin, Hamburg, Germany
1 Dir, Inst fur Schiffbau, Hamburg, Germany
1 BSRA, London, England
1 Karlstads Mekaniska Werkstad, Kristinehamm,Sweden
1 Prof. Dr. F. Horn, Laehr St. 28, Berlin-Zelendorf, Germany
1 Prof. Dr. H. Amtsberg, Tech Univ, Berlin-Charlottenburg, Germany
1 Prof. L.C. Burrill, Dept of rlav Arch, KingsCollege, Univ of Durham, Newcastle uponTyne, England
-- - ---- s-i ili 11Wi
wm mlollll
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
O
F P
RO
PE
LL
ER
T
HR
UST
FRO
M M
OD
EL
WA
KE
ME
ASU
RE
ME
NT
S,
by J
ohn
L.
Bev
erid
ge.
Nov
embe
r 19
58.
9p.
phot
os.,
diag
rs.,
grap
hs,
refs
.U
NC
LA
SSIF
IED
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed
from
exp
erim
enta
l w
ake
data
obt
aine
d fr
om
tow
ed a
ndse
lf-p
ropu
lsio
n te
sts
on a
sub
mer
ged
body
of
revo
luti
on.
The
expe
rim
enta
lly
obta
ined
thr
ust
dist
ribu
tion
is
in e
xcel
lent
agr
ee-
men
t w
ith
a th
eore
tica
lly
calc
ulat
ed d
istr
ibut
ion.
N
umer
ical
inte
grat
ion
yiel
ds a
tot
al t
hrus
t-lo
ad c
oeff
icie
nt w
hich
is
in g
ood
agre
emen
t w
ith p
ropu
lsio
n te
st r
esu
lts.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on -
Ana
lysi
s2.
B
odie
s of
rev
olut
ion
Wak
e -
Mod
el
test
I. B
ever
idge
, Jo
hn L
.II
. N
S715
-102
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
OF
PR
OP
EL
LE
R T
HR
UST
FRO
M M
OD
EL W
AK
E M
EASU
REM
ENTS
, by
Joh
n L.
Bev
erid
ge.
Nov
embe
r 19
58.
9p.
phot
os.,
diag
rs.,
grap
hs,
refs
.U
NC
LA
SSIF
IED
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed f
rom
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on i
s in
exc
elle
nt a
gree
-m
ent
with
a t
heor
etic
ally
ca
lcul
ated
dis
trib
utio
n.
Num
eric
alin
tegr
atio
n yi
elds
a t
otal
thr
ust-
load
coe
ffic
ient
whi
ch i
s in
goo
dag
reem
ent
with
pro
puls
ion
test
res
ults
.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on -
Ana
lysi
s2.
B
odie
s of
rev
olut
ion
-W
ake
-M
odel
tes
tI.
Bev
erid
ge,
John
L.
II.
NS7
15-1
02
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
O
F P
RO
PE
LL
ER
T
HR
UST
FRO
M M
OD
EL
WA
KE
ME
ASU
RE
ME
NT
S,
by J
ohn
L.
Bev
erid
ge.
Nov
embe
r 19
58.
9p.
phot
os.,
diag
rs.,
grap
hs,
refs
.U
NC
LA
SSIF
IED
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed f
rom
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on i
s in
exc
elle
nt a
gree
-m
ent
with
a t
heor
etic
ally
cal
cula
ted
dist
ribu
tion
. N
umer
ical
inte
grat
ion
yiel
ds a
tot
al t
hrus
t-lo
ad c
oeff
icie
nt w
hich
is
in g
ood
agre
emen
t w
ith p
ropu
lsio
n te
st r
esult
s.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on
-A
naly
sis
2.
Bod
ies
of r
evol
utio
n -
Wak
e -
Mod
el t
est
I. B
ever
idge
, Jo
hn L
.II
. N
S 71
5-10
2
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
O
F P
RO
PE
LL
ER
T
HR
UST
FRO
M M
OD
EL W
AK
E M
EASU
REM
ENTS
, by
Joh
n L.
B
ever
idge
.N
ovem
ber
1958
. 9p
. ph
otos
., di
agrs
., gr
aphs
, re
fs.
UN
CL
ASS
IFIE
D
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed
from
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on
is i
n ex
cell
ent
agre
e-m
ent
with
a t
heor
etic
ally
ca
lcul
ated
dis
trib
utio
n.
Num
eric
alin
tegr
atio
n yi
elds
a t
otal
thr
ust-
load
coe
ffic
ient
whi
ch i
s in
goo
dag
reem
ent
with
pro
puls
ion
test
res
ults
.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on
-A
naly
sis
2.
Bod
ies
of r
evol
utio
nW
ake
-M
odel
tes
tI.
B
ever
idge
, Jo
hn L
.II
. N
S 71
5-10
2
1
1 __
L--
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
OF
PR
OP
EL
LE
R T
HR
UST
FRO
M M
OD
EL W
AK
E M
EA
SUR
EM
EN
TS,
by
Joh
n L.
B
ever
idge
.N
ovem
ber
1958
. 9p
. ph
otos
., di
agrs
., gr
aphs
, re
fs.
UN
CL
ASS
IFIE
D
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed f
rom
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on i
s in
exc
elle
nt a
gree
-m
ent
wit
h a
theo
reti
call
y ca
lcul
ated
di
stri
buti
on.
Num
eric
alin
tegr
atio
n yi
elds
a t
otal
thr
ust-
load
coe
ffic
ient
w
hich
is
in g
ood
agre
emen
t w
ith p
ropu
lsio
n te
st r
esult
s.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on -
Ana
lysi
s2.
B
odie
s of
rev
olut
ion
Wak
e -
Mod
el te
stI.
B
ever
idge
, Jo
hn L
.II
. N
S 71
5-10
2
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
O
F P
RO
PE
LL
ER
TH
RU
STFR
OM
MO
DEL
WA
KE
ME
ASU
RE
ME
NT
S,
by J
ohn
L.
Bev
erid
ge.
Nov
embe
r 19
58.
9p.
phot
os.,
diag
rs.,
grap
hs,
refs
.U
NC
LA
SSIF
IED
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed
from
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on i
s in
exc
elle
nt a
gree
-m
ent
with
a t
heor
etic
ally
cal
cula
ted
dist
ribu
tion
. N
umer
ical
inte
grat
ion
yiel
ds a
tot
al t
hrus
t-lo
ad
coef
fici
ent
whi
ch i
s in
goo
dag
reem
ent
with
pro
puls
ion
test
res
ults
.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on -
Ana
lysi
s2.
B
odie
s of
rev
olut
ion
-W
ake
-M
odel
test
I. B
ever
idge
, Jo
hn L
.II
. N
S 71
5-10
2
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L
DIS
TR
IBU
TIO
N
OF
PR
OP
EL
LE
R T
HR
UST
FRO
M M
OD
EL W
AK
E M
EA
SUR
EM
EN
TS,
by
Joh
n L.
B
ever
idge
.N
ovem
ber
1958
. 9p
. ph
otos
., di
agrs
., gr
aphs
, re
fs.
UN
CL
ASS
IFIE
D
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed
from
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed
thru
st d
istr
ibut
ion
is i
n ex
cell
ent
agre
e-m
ent
with
a t
heor
etic
ally
cal
cula
ted
dist
ribu
tion
. N
umer
ical
inte
grat
ion
yiel
ds a
tot
al t
hrus
t-lo
ad c
oeff
icie
nt w
hich
is
in g
ood
agre
emen
t w
ith p
ropu
lsio
n te
st r
esul
ts.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on
-A
naly
sis
2.
Bod
ies
of r
evol
utio
n -
Wak
e -
Mod
el te
stI.
B
ever
idge
, Jo
hn L
.II
. N
S 71
5-10
2
Dav
id T
aylo
r M
odel
Bas
in.
Rep
ort
1136
.T
HE
RA
DIA
L D
IST
RIB
UT
ION
O
F P
RO
PE
LL
ER
T
HR
UST
FRO
M M
OD
EL W
AK
E M
EA
SUR
EM
EN
TS,
by
Joh
n L.
B
ever
idge
.N
ovem
ber
1958
. 9p
. ph
otos
., di
agrs
., gr
aphs
, re
fs.
UN
CL
ASS
IFIE
D
The
rad
ial
dist
ribu
tion
of
prop
elle
r th
rust
-loa
d co
effi
cien
t is
calc
ulat
ed
from
exp
erim
enta
l w
ake
data
obt
aine
d fr
om t
owed
and
self
-pro
puls
ion
test
s on
a s
ubm
erge
d bo
dy o
f re
volu
tion
. T
heex
peri
men
tall
y ob
tain
ed t
hrus
t di
stri
buti
on i
s in
exc
elle
nt a
gree
-m
ent
with
a t
heor
etic
ally
cal
cula
ted
dist
ribu
tion
. N
umer
ical
inte
grat
ion
yiel
ds a
tot
al t
hrus
t-lo
ad
coef
fici
ent
whi
ch i
s in
goo
dag
reem
ent
with
pro
puls
ion
test
res
ults
.
1.
Pro
pell
ers
(Mar
ine)
-T
hrus
t di
stri
buti
on -
Ana
lysi
s2.
B
odie
s of
rev
olut
ion
-W
ake
-M
odel
te
stI.
Bev
erid
ge,
John
L.
II.
NS7
15-1
02
I
9080 02754 259
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