xperixnental Towing Tank
Sbevens Institute of Technology
Hoboken, New Jersey
THE EFFECT 0F SPEED AND SIZE
ON THE PERFORLiANCE 0F A MODEL SHIP PROPELLER AT OPTTh1UM FFICIENCY
B, V. Korvin-Kroukovsky
Presented at the March
16, 1951Meeting
of the
Section of Mathematicsand
Engineeringof the New York Acaderr of Sciences
Prepared under
Contract No. N6orir-2L7O7
U.S. Navy
Office of
Naval Research
(E.T.T. Project No
DF1321)TABLE OF CONTENTS PAGE Summary i Introduction i Experimental Daba 2 Iiethod of Analysis
Analysis of the Blade Section Drag .. 8
Lift of the Blade Sections IO
Concluding Remarks 11
References 12
Table I: Model Propeller ?erforniance at V/nD of
Maximum Efficiency .. .
i1
Table II Ordinates of the Propeller Section at
OThR
...
15Figures . ... .... 16
UMIAhY
The torque and thrust coefficients of three model propellers of the
motorship SAN FR.NCISCO, tested independently in open water in three tow-ing tanks) are analyzed by the methods of circulation theory of propellers
to obtain the lift and drag characteristics of a typical blade section.
The drag coefficients are found to vary with Reynolds number in a manner
indicating that a turbulent boundary layer condition edsts even at low
Rrnolds numbers This may be attributed to the turbulence stimulation
caused by the vibration connected with the high rotational speed of small
propellers. The lift coefficient is lower than can be expected from the
propeller and airfoil theories, This can be attributed to the reduction
in absolute value of zero lifte angle, and corresponds to a similar
reduc-tion in the case of wind-tunnel tests of airfoils at very low Rrnolds
numbers.
The analysis and some of the tests were conducted at the ßxperinen't
Towing Tank of Stevens Institute cf Technolor) under the auspices of the
Office of Nava].. Research,
INTRODUCTION
A naval architect is forced to depend on test results obtained on
rrdel ships and model propellers for the prediction of ship speed, for the
specification of the power to be provided, and for the specification of
speed of rotation of the propeller shafts of the full-s:ze vessel, In
this connection) he is always confronted with the question as to how accurately full-scale performance can be predicted from model data, or more specifically) as to what kind of data and methods can be used to make an accurate full-scale prediction, A part of this problem will be
examined in this paper --- that of the performance of the propeller itself)
not considering the propeller-hull interaction, the so-called
free-water performance of propellers0 The problem will be further limited to
a study of one particular propeller design, tested independently in three
difL'erent laboratories,,
Kempf1 and van Lammeren2 conducted tests on model propellers of dif
f erent sizes and at different speeds, and presented data on the effect of
TM-102
TM-102
-2-.
these parameters on the propeller thrust torque and efficiency. However,
an examination of the changes in the over-all characteristics of the tested propellers often results in a confusing pictire, and sheds little
light on the methods of extrapolation to full size, and on the limitation
of such methods. In particular, it often leads to an arbitrary and
errone-ous statement of the minimum practical size of the model, as well as to
the unwarranted assumption that a model of a certain larger size will well
represent the characteristics of the full-size prototype. A more useful
and reliable guide can be obtained .t'rom an analysis of the model propeller
performance by applying the methods of existing well-developed propeller
theory to assist in reducing the test data to the lift and drag
character-istics of an isolated blade section. This procedure can vary in scope and complexity, depending on the nature of the experimental data, and on the
completeness of the results desired. In this paper', a simple method is used to obtain the lift and drag characteristics of a single section
located at 7i% of the maximum blade radius, and at an advance ratio V/nD
at which the maximum propeller efficiency is obtained.
The work is part of the research on self-propulsion tests of ship
models done at the Experimental Towing Tank of Stevens Institute of
Tech-nolor, Hoboken, N.J., under contract with the Office of Naval Research,
Task Order VII.
EXPERIUENTAL DATA
The propeller design chosen for this analysis is that of the
motor-ship SAN FRéNCISCO which was initially investigated by Kempf1 in Hamburg.
Recently, a model of the same size was made from Kexnpf's drawings, and was
tested at the David Taylor Model Basin in Carderock, Md. Also, a small
model of this same propeller was made and tested at the Experimental Towing
Tank of Stevens Institute of Technolor. The E.T.T. model was copied' from the DTMB model by a pantograph attachment to a lathe. The geometric
di-mensions, test speeds, and resulting performance of the tested propellers
are given in Table I. A typical plot of the data is given on Figure 1.
* This paper, illustrated with slides, was prepared for presentation at
the meeting of the section of h&athematics and Engineering of the New York
T-l02
-3-This customary way of presenting the data consists of plotting the measured
thrust T and torque Q in the form of nondirnensional thrust and torque
Kq coefficients (as defined on the chart) against the ratio of the
veloc-ity V through undisturbed water to the product of the revolution per
second n and the propeller diameter D (Le0, J V/nD). Each series of
tests was conducted at approximately the same RPI, with J varying with
the velocity of advance V from zero to the speed at whioh the thrust
vanishes. As can be observed from Figure 1, there is a certain scatter
of the data, and it is difficult to distinguish by eye the relatively
small effect of the speed of rotation as shown by different coding of
the four series of tests shown0 In order to make the comparison as
re-liable as possible, a definite method of fairing by calculation. was
adopted, and was applied to all test data, without any regard to the
visual fairing performed by the original investigators. In the case of
the thrust coefficient Kt, it is observed that the curve is practically a
straight line in the range from J
= o55
to J at which Kt becomes zero. Furthermore, it is noted that in this range of J, the slope dK/dJ of theline is about uniform in all cases, and that any error in the estimation of the slope would not be important in vier of the location of the finally
desired points at J 0.80, which is abou: in the middle of the range
chosen0 The equation of this part of the thrust line then becomes:
Kt = A - C'5O J (1)
The values of the coefficient A were computed for all observed test values
of in the range
0.55
< J < max, and were averaged separately for eachseries of tests0 The final f aired value of for J of maximum efficiency
(0,75
oro,8o)
was then computed by Equation (1), using the averagedval-ues of A, and is given in the fifth column of Table I.
A similar process was used for the torque coefficient K; except
in this case, the plot of Figure 1 is represented by the parabolic arc
Kq
= c - o
j2The constant C was computed for each test value of Kq averaged for
each series, and the value of Kq for J of madmum efficiency was computed
on the basis of this average, and is given in the sixth column of Table I.
TM-102
-b--of Lairing were eliminated, and each value -b--of Kt or Kq at J -b--of maximum
ef-ficiency was found as an average of a number of test points. In the
seventh and eighth columns of Table I, these data are converted to another form of nondimensional coefficients, and which are more convenient
for use in the contemplated analysis. The efficiency n
= TIP
is givenin the last column. In view of the process of fairing used, these
effi-ciencies do not always correspond to bhe ones reported by the original
in-vestigators.
LETHOD OF ANkLYSIS
An analysis of the data will be made utilizing the modern theory of
propellers, known as the circulation theoxy Although this theory is
dif-ficult in its original derivation, it is ectremely simple in its
applica-tion. Figure 2 shows a four-bladed propeller with a helicoidal vortex
sheet trailing from the edge of each blade. Betz3 has shown that the
opti-mum efficiency of a propeller is obtained when the velocity distribution
in the wake is such that these helicoidal vortex sheets trail aft without change of form, Le., as if they were rigid-material sheets. Prandtl3
made the first approximate calculation of the velocity distribution needed
to satisfy this condition, and Goldstein developed the final rigorous
solution.
A specified velocity distribution in the wake implies a specified distribution of the thrust along the blade; this is referred to as
Goldstein's (or Betz') thrust distribution, Strictly speaking, the
cir-culation theory applies only to propellers designed to provide this thrust
distribution, and only to their performance at the speed of maximum eff
i-ciency. In practice, it is found, however, that the maximum efficiency
is affected very little by a certain amount of deviation of thrust
distri-bution from the optimum, which thus implies a certain range of deviation
of the ratio V/riD from the optimum Little error will be involved,
there-fore, in the inverted application of the theory to the analysis of a given
propeller, in assuming that the propeller operating at maximum efficiency
conforms to the ideal thrust distribution. With this assumption, the
analysis can proceed following the elementary Rarikine-Froude momentum
the mean velocity r a computed by Goldstein0
First, reference is made to Figure 3, which gives the velocity and
force vector diagrams at the propeller blade, and also the velocity vector
diagram at the surface of the helicoidal sheet at an infinite distance aft
of the propeller, where the flow in the wake becomes steady0 The
hori-zontal vector C*Jr is the tangential velocity of a blade element due to the
velocity of' rotation; the vector V is the velocity of advance; and U is
the resultant velocity of a blade element with respect to the undisturbed
fluid. The reaction to the lift force L is an induced velocity vector
w/2 produced at the blade, so that the actual velocity of the water with
respect to the blade is shown by the vector U. The angles of the vectors
U' and U with the plane of the propeller are designated by and
,
re-spectively0 At the propeller blade, the vector U is tangent to the
heli-coidal vortex sheet, which by definition floats with the fluid, Le0, moves normal to itself with the induced velocity
w/20
At an infinite distance aft of the propeller, the induced velocity increases to w, and, since its axial and tangential components u and u0 increase in thesame proportion, the helicoid rotates as it moves aft without change of
shape0 In making this statement it is assumed that the diameter of the
helicoid remains equal to the propeller diameter, or in other words, that
the contraction of the wake is neglected0 This assumption is permissible
for moderately loaded propellers used in common practice.
The movement of the helicoidal surfaces is caused by the induced
fluid velocity w, and conversely it can be said that movement of the helicoid causes the velocity w0 Since a perfect fluid is considered,
and the forces of friction do not exist, the velocity of the helicoidal
sheet along its surface will cause no motion in the fluid This being
the case, it is convenient to replace the vortex sheet velocity w in a
direction normal to itself by the velocity of' displacement W along the
direction z parallel to the propeller axis0 In either case, the fluid
will have the velocity w with components u and u0, but now these are
expressed in terms of W as
= w
u
= Wcos
sinÇ..
(2)
TM-l02
--r1-1o2
-6-Furthermore, the velocity in the wake is not uniform, and it was shown by Prandtl3 and Go1dstein that the fluid velocity is smaller in the space
between the helicoidal sheets than at the surface, The mean axial
com-ponent Uzm of the fluid velocity is, therefore,
u
=Ku
where the constant K was Origiflally computed by Goldstein, and then the
computations were ecended by Lock5 and Kramer6; they are used here as
reproduced by Theodorsen7.
Now the Rankine-Froude axial momentum relations can be rritten,
Consider the area contained between radii r and r + dr:
2,irdr
(3)
The fluid mass flowing through the above area is:
2iP (V
+u)rdr
,()
where P is the mass density of the
fluid.
Thechange of momentum of the
fluid mass which is equal to the
thrust increment dT is:dT =
2tP (V
+-u)urdr
(s)
Expressing mean velocity u in terms of displacement V of helicoids gives
U a KW
cas2
.(6)
The thrust increment in terms of' W is:
dT =
2p
[VwK co21$.
(WKcos2.)2]rdr
. (7)Let r
xR
arid divide bydT = li
[(K
+(K
2
)2
]x
dx . (8)The thrust can be obtained now by integrating dT (x) from x O to
x a
1, Le., over the length cf the blade. A short cut is available, how-ever, in that, in practice, the distribution of the thrust along the bladeis found to be suí'ficiently uniform for different propellers so that the
integral can be evaluated on the assumption that
(dT/dx) atx= a
T = I dT(x)
c (9)
C. i constant
I
On this basis, the performance of a propeller is often judged by
the performance of a single section at x = O7 or x = O75 In the present
case, the analysis is based on x = 07li, since a section was shown on
Kempfts drawing at r = 100 mm, or r = 0071R0 The interpolation of the
8 9 10
data given for this type of analysis by Lock , Driggs', Hartman , and
11
Lerbs leads, in the present case, to an estimate of the constant as
being
l63,
so that:T
l63
[(K cos2ç.) + (K
cos2i
The ideal efficiency of a propeller l is defined as
i tank
- i+w/2v
tan.
and the power disk loading coefficient is
P
=T /77.
C.
i
C.i
In the Rankine-Froude linear momentum theozy, the velocity W in
Equation (li) above was understood to be the true axial velocity of the
uniform wake, and the only energy loss was considered to be in connection
with the increment of the axial velocity0
In the circulation theory, W is understood to be the fictitious
9displacement velocity" of helicoids, greater than the mean axial velocity
Uzm and as such, it includes the effects of energy losses of velocity in
tangential and radial components, as well as in the axial component0
The subscript i in the above designates the ideal efficiency, i.e., the efficiency obtained by neglecting the profile drag of blade sections.
The values of Tc, Pc19 and
r.
are uniquely determined by the displace-ment velocity ratiow/v.
On Figures L and5,
the upper curves designatedE = O represent plots of the ideal efficiency 77 vs thnist disk loading
coefficient T0 or power disk loading coefficient co The displacement
velocity ratio
w/v
is indicated by the dotted parametric lines0 This curveof ideal efficiency agrees closely with similar (and greater in slope)
curves published by Kramer6 and Lerbs12.
)2J
TM-102
-7-(10)
Ti-1O2
-8-.
As shown on Figure
3,
the effect of the profile drag D is to reduce the thrust and to increase the torque of a blade element. Bienen andl3
von LarInan have shown that the integrated effect for the entire blade
length can be put into the forni of a correction to the ideal thnist and
torque coefficients, so that the actual coefficients become:
T = T
(1- 2C tanp)
C C. (13)i
P =P (1+.a)
(Th)
C C. i owhere = CU/CL, i.e., the ratio of drag coefficient to lift coefficient,
and tan = tan
.
at r = R (which means at the tip of the blade)
The blade efficiency
b is:
i - 26tan
71b 2 £
,
+ 3 tan and the total efficiency t is
= b
(16)
Parametric curves of the total efficiency T are plotted on Figures
L and 5 for a number of values of the drag/lift ratio E
Finally, the lift coefficient of a blade element is given asfllS:
C - - li sink. tan('.
-L0
ir1
(17)where
K = a coefficient related to K, and is tabulated by Lock in
Refer-ence
5,
O = the solidity defined as Nb/2 n r, where N = the number of blades, and b = the chord of a blade at radius r.
ANALYSIS OF T1 BLADE SECTION DEG
The analysis of the propeller performance now becomes very simple
The observed efficiency taken from Table I is plotted vs. T and on
CD/CL for the blade element are read directly from the relation of
the plotted point to the parametric lines w/v = const and L = conste
With w/v known, tan
.
is determined as
tan.
(i+ tan
Tank is known, since tan= \1/cr. With and known, the lift
coef-ficient is computed by Equation (17) and the drag coefcoef-ficient C is comrn.
puted as £CL.
The drag coefficients CD found in this way are plotted vs Reynolds
number on Figure 6 for the three tested propellers All ten test condi tions are plotted and compared with three standard friction resistance
curves. Although there is a considerable scatter of data, there is a c1ear
ly defined tendency to follow an average line, essential]y parallel t'o the
lines expressing the frictional drag for the turbulent condition of the
boundary layer. The mean profile drag of the section at OThR of the
propeller design under consideration is found to be equal to two tes the
friction drag of a flat plate having the same projected area-j Since thi
factor of 2 is unexpected] high, the wir:d=tunnel test data of an old design
airfoil RAF6, tested in a very turbulent type wind tunnel at low Reynolds
number, are plotted on Figure 6 for comparison. The two sets of data agree
as to the order of magnitude, and, in fact, the direction of: the plotted
curve indicates a turbulent condition of the boundary 1ayer. This
eondi-tion for an airfoil is probably brought about j the turbulent condition
of the wind tunnel, and by the type of airfoil section possessing a harsh
curvature
at the leading edge.
The propeller blade section is described
by the ordinates given in Table II, and appears to be of the Joukows1r type
with circular arc median
line.
Then tested in the towing tanks, each bladeencountered undisturbed water as free of turbulence as could be expect-edo
It was surprising, as well as gr&tïfying, therefore, to find the turbulent
boundary layer type of resistance curve, gratifying because it permits a
convenient extrapolation to air value of the Rrncids number,
including
full sizeIn looking for reasons to explain the occurrence of a turbulent
T-I32
- lo -.
vanced that the turbulence is probably stimulated by the vibration of' the
rapidly rotating propeller model.
A test was made in the cundition corresponding to Test
L,
in which the model propeller was made to operate in the turbulent wake of a suries of round rods towed in front of the propeller. The relation of T andin this test remained the same as in Test ), indicating that added
turbu-lence had no effect on the drag. This fact can be taken as supporting
evidence that the boundary layer was already turbulent.
LIFT OF TF BLADE SECTIONS
The lift coefficient was computed by 'quation (17), and was corrected
to represent the section as it would be tested in the wind tunnel by
apply-ing ttcurvature correction" as developed by HiliTh. No wind-tunnel data
for the section in question were available, but the lift characteristics
to be expected can be estimated by the computational methods known from
the theory of airfoils. The lift coefficient as tested was found to be
very much lower than indicated by this estimate. Again a comparison was
made with the low Reynolds number tests of an PLAF airfoil, and it became
apparent that the low value of the lift coefficient is due to the decrease
in the absolute value of the angle of zero lift at small Reynolds numbers.
The angles of zero lift as computed from the test data are shown on Figure
7, where the asymptotic value for the larger Reynolds number is also shown. The mode of approach to this asymptotic value is, however, not known. It
appears that smaller, more rapidly rotating propellers have a smaller
de-ficiency in the angle of zero lift than larger propellers compared at the
2
sanie Reynolds numbers. This checks with the data of van Lanimeren , where
at a given Reynolds number, smaller propellers showed higher efficiency
than the 1argcr ones.
The propeller used for Tests 9 and 10 shows an abnormally large de-ficiency in the angle of zero lift. It also shows the best efficiency
V/nD at a value of J =
0.75
instead of at J = 0.60 which was common forthe other tested propellers, indicating a reduced strength of circulation.
The finish of the blades appeared to be unusually rough, but no data are
resulting change in the angle of zero lift.
CONCLUDING REMAEKS
The analysis of the test dat.a for model propellers on the basis of
the circulation theory explains their performance in terms of the lift
and drag characteristics of the blade sections.
The drag characteristics
follow the turbulent boundary layer law of skin frictions so that
ex-trapolation of drag coefficients from model to full scale should present
no difficulty. This conclusion refers only to the specific blade section
analyzed in this paper.
There is evidence in the van Lamineren
tests
(not yet analyzed in detail) that a mixed laminar-turbulent flow exists
in small propeller models with the low drag type of blade sections of a
more modern design.
The attempts
the
T.T. and van Lammeren to use
an artificial turbulence stimulation are inconclusive since the models
tested were already (unknowingly) in a developed tu bulent condition.
The most. serious dïscrepancy is found in the values of the angle
of zero lift., which will require further investigation.
Tentatively
it appears that in order to give the saine performance
smaller model
propellers should be made with a degree or two larger pitch angle than
the full-size prototypes. Again this appears to apply to the particular
propeller analyzed.
In an example given by
Lerbs11,
a good agreement
of lift coefficient was obtained or a very thin ogival section at
some-what greater Reynolds number.
The range of Reynolds numbers between the 'sxnall' and fllargett
models is rather narrow, and even the 'large't models cannot be assumed
to represent directly the full-size performance.
If this type of analysis had been applied to the propeller when it
was designed
it vould have clearly indicated the possibility of greatly
improved performance by reducing the profile drag losses, preferably
by-using a more favorable blade section, or by reducing the number of blades
from four to three with a corresponding increase of pitch (and a resultant
increase of the angle of attack and of the lift coefficïent).
TM-102
-TM-iD 2
12
-REFERENCES
Kempf, Gunther: "A Study of Ship Performance in Smooth and Rough
Water," Transactions of The Society of Naval Architects and Marine Engineers, Vol, W4, 1936, pp. l9-227.
Van Lamrneren, Ir. W.P.A.: "Propulsion Scale Effect," Transactions
of the North-East-Coast Institution of Engineers and Shipbuilders,
1939/RO, pp. ll-12.
Prandtl, L. and Betz, A.: "Vier Abhandlengen zur rdrodynamik and
Aerodynamik," Gottingen 1927; Edwards Brothers Inc. Ann Arbor,
Michigan, 19b3.
). Goldstein, Sydney: "On the Vortex Theory of Screw Propellers," Proceedings of the Royal Society, 1929, pp.
W4o-I65,
Lock, C.N.N. and Teatman, D.: "Tables for Use in an Improved Method of Airscrew Theory Ca1culations" ARC (British) R. & M. No. 1671
October l93I. (Also included in the bound volume 1935-36.)
Kramer, K.N.: "The Induced Efficiency of Optimum Propellers Having
a Finite Number of Blades," NACA T,M, No, 88h, January 1939.
Theodorsen, Theodore: "The Theory of Propellers, I Determination
of the Circulation Function and the Mass Coefficient for Dual
Rotating Propellers," NACA Report No. 775, 19W4.
Lock, C.N.N.: "Graphical Method of Calculating Performance of
Air-screws," ARC (British) R. & M. No0 1675, 193h.
Driggs, I.H.: "Simplified Propeller Calculations" Journal of the
Aeronautical Sciences Vol. 5, No. 9, July 1938, pp. 337-3W4.
10, Hartman, Edwin P. and Feldman, Lewi.s "Aerodynamic Problems in the
Design of Efficient Propellers," NACA Wartime Report L-753,
August l9Li2. (Formerly ACR, Aug, 19L2.)
li. Lerbs, Hermann W.: "On the Effects of Scale and Roughness on Free-Running Propellers," Journal of the American Society of Naval
Engineers, Vol.
63,
No. 1, February 1951, pp. 58-9L,Lerbs, Hermann W.: "An Approximate Theory of Heavily Loaded Free-Running Propellers in the Optimum Condition," Paper presented at
the annual meeting of the Society of Naval Architects and Marine Engineers on November 9 and 10, 1950. (To be published in
Trans-actions of the Society of Naval Architects and Marine Engineers,
Vol. 58.)
Bienen, Th. and von Kimn, Th,: "Zur Theory der Luftsehrauben,"
Zeitschrift des Vereines Deutschdr Ingenieure, Vol. 68, Nos. L8
1h. Hill, J.G.: "The Design of Propellers," Transactions of the Society of Naval Architects and 1arine Engineers, Vol.
6, 19)48, pp.
1b3-192.15.
Kane, J.R.: Discussion of "The Design of Propellers," by J03, Hill,Vol.
6, 19)48,
p. 172.
TM-102
-TABLE I
MODEL PROPELLER PEFOI(ANCE AT
V/nD OF MAXIMUM EFFICICY
Designation
No.
Tested By; Prop. Designation; Diameter; j
V/riD at Maximum RPM -60n Reynolds No. at r-0.714RxlO7 K T K T T r C 3 2 t
q Pn2D5
C 22pn
Efficiency 1 Experimental Taxing 800 0.145 0.105 0.O21.9 0.1418 0.776 0.573Tank, Stevens
In-2
stitute of Tech- nology;
1000 0.56 0.116 0.0262 0.1462 0.819 0.5614 3 1200 0.67 0.120 0.0271 0.1478 0.8147 0.5614
b
Model No. 52; 1308 0.73 0.123 0.02614 0.1489 0.825 0.593 D - 0.323 ft.; 5 j 0.80 il400 0.78 0.1214 0.0256 0.14914 o.800 0.618 6 Kempf'; 201.4 0.86 0.102 0.0225 0.1407 0.702 0.580 7 Model No. 35142; 363 1.53 0.109 0.0217 0.1433 0.678 0.638 D - 0.885 ft.; 8 j = 0.80 792 3.3 0.1214 0.02146 0.1492 0.767 0.6145 9 David Taylor 175 0.80 0.106 0.0208 0.1478 0.785 0.609 Model Basi-ri; 10 500 2.27 0.126 0.02314 0.570 0.8814 o.6)*14 Model No. 22114; D - 0.885 ft.; J 0.75TABLE II
ORDINATiS 0F T ?ROPELLER 3ECION AT
0.7LR
(Scaled from Kempi' ts Áodel
Drawing,
Stationat r = 13On)
Thi-102 -
15
-Distance (,in % of
chord
Ordinates y,in % of
chordLower 'Jpper
Oedian
Line Half ThicknessO O D O D 1.25
-o.6h
1.38 0.37 1.01 2.5 i.o6 2.320.63
1.67
5-iJ8
3.W10.98
2J6
7.5
-1.72
.l8 1.23 2.95 10 -1.901..67
1.L9
3.39
15 -1,905.87
1.993.89
20-.1.80
6.1i5
2.33 I,l3 30 -1.007,2!
3.12
b.12
-0.13
7iO
3.6k
3.70
So 0.27 7.253.76
3,50
6o
0.53
6.60
3.57
3.02 70o,)8
5.55
3.01 2.5I 60 o.i6 t,,.02 2.09 1.93 90-0.05
2.22 1.09 100 o o oRadius Trailing Edge =
CHARACTERISTIC CURVES
"SAN FRANCISCO" 4- BLADED VARYING PITCH PROPELLER
( STEVENS PROPELLER NO. 52)
(CONSTRUCTION & REPAIR DWG. NO. C- 989)
FIG. i.
RIGHT- HAND ROTATION
MODEL DIAM.,FT.
0.323
MODEL PITCH, FT.
0.332
AT 0.7 RADIUS
IDEV.AREA RATIOzO.309
PROPELLER IMMERSED 0.323 FT., 00% d.
i-1400 R.P.M.
o 1200 R.P.M.
D1000 RPM.
800 R.PM.
.7
.9
LO
8
2
3
.4
.5
.6
AXIAL INDUCED VELOCITY W W COS ß
AXIAL COMPONENT OF INDUCED VELOCITY U W COS2
TANGENTIAL COMPONENT OF INDUCED VELOCITY u8: W COS Sin
VELOCITY DIAGRAM
AT INFINITY
DISPLACEMENT VELOCIT'! W OF HELICOIDAL SURFACES dT---- -
dT D. dT-AdT AdQ IL_i
dQ dQ+ AdaFIG. 2: DIAGRAM SHOWING HELICOIDAL VORTEX SHEETS
IN THE WAKE OF A PROPELLER
rr
2
VELOCITY DIAGRAM AT PROPELLER BLADE
FIG. 3
T M-102
-17-TM-IO2
-Is-FIG. 4: MAXIMUM EFFICIENCY VS. Tc Pc, AND C FOR J
.80
.80
.95
.90 .85 uo
Z70
wo
u-w.65
.55
.50
O .1 .2 . .4 .5 .6T/i/2r17R2V2
.70 .65.60
.55.50
.3 .4 .5 .6 .7.8
.9 1.0 1.1P/I/2f1TR2V3
.95
.90
85.80
.75.95
.90
.85
i,.75
g-
>-o
z
LU.70
o
u-w
.65
.60
.55
FIG. 5
MAXIMUM EFFICIENCY
vs. Pc AND E
FOR J=75
.50
0
.12
.3
.4
.5
.6
.7
.8
.9
1.0
LI
¡.2
IC: T/I/2r1TR2V2
T M-102-'9-.50
.80
-o
g-.10
.09 .08
D
.07
o03
025
007
LZ»Q09
.008
.007
.006
IO
1.5
2.0
3.0
4.0 5.0 6.0
8.0 IO
1.5
2.0
3.0
4.0 5.0 6.0
ao iø'
REYNOLDS NUMBER, Re
Ub/t)
-f
o-H
___
____
FtG6
DRAG COEFFIC$ENT
.TIR VS. REYNOLDS
----F--fl__.4
PROflLE
SECTiONS
NUMBEP
-HH----1
&_4__ _J
OF BLADE
RAF
ft..6
F OL1
i
-1:
J rPRANDTL- (ARA FPCTQN
:
j
MEAN JNE: T
= log,0
eCf
Ti
L_BLAS;1S LAAR LE.
2 L32'
t
-j
SCHOEMEPR
O.242//(Jf/2
o
LUDO
o
LU>2
I-
o
UJu-
u
-u-J--4
-5
-6
FIG. 7
ANGLE OF ZERO LIFT a0 PLOTTED VS. REYNOLDS NUMBER
2 3