a simple interactive program to design supercavitating ... · i.introduction...
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-..^i^aEY, CALIF, 93940
NAVAL POSTGRADUATE SCHOOLMonterey, California
THESISA SIMPLE INTERACTIVE PROGRAM TO DESIGN
SUPERCAVITATING PROPELLER BLADES
by
Marc B. Wilson
June 19 82
Thesis Advisor: D. M. Layton
Approved for public release; distribution unlimited,
T20A930
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE CH'hen Datm Enfted)
REPORT DOCUMENTATION PAGE1. REPORT NUMBER 2. OOVT ACCtSSION NO
READ INSTRUCTIONSBEFORE COMPLETING FORM
J. RECIPIENT'S CATALOG NUMBER
4. TITLE (mnd Subtlttm)
A Simple Interactive Computer Program
to Design Supercavitating PropellerBlades
7. AUTHORCO
Marc. B. Wilson, LT, USCG
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Naval Postgraduate SchoolMonterey, California 9 39 40
5. TYPE OF REPORT & PERIOD COVEREDMaster's thesis;June 1982
6. PERFORMING ORG. REPORT NUMBER
t. CONTRACT OR GRANT NUMSERC'J
10. PROGRAM ELEMENT. PROJECT, TASKAREA 4 WORK UNIT NUMBERS
11. CONTROLLING OFFICE NAME AND ADDRESS
Naval Postgraduate SchoolMonterey, California 93940
U. MONITORING AGENCY NAME » ADORESSf// dlllmrtit tram ControlUng OIHe»)
12. REPORT DATEJune 1982
13. NUMBER OF PAGES84
15. SECURITY CLASS, (of thim ruport)
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15«. DECLASSIFICATION/ DOWNGRADINGSCHEDULE
16. DISTRIBUTION STATEMENT r<»' iMa Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of Ui» ftrmct mntmrad In MUek 20. It rfi/f»r«i» Ir^m Map^rt)
18. SUPPLEMENTARY NOTES
19. KEY WORDS (Contlnuu on rmvf at<f II nmcmmmmrr mid Idtnttty by Mock numbtr)
Desk Top Computer Design of Propeller Blades
Ship Propeller BladeSupercavitating PropellerSemi-submerged PropellerPartial/Fullv submerged Propeller Blade
20. ABSTRACT (Continue on ,.v„.. .Id, U n.e..-^ "^""""'^i'' ""^T^*^;^ H^ Q i rrn { CAD 1
A self-contained, rapid. Computer Aided Design ^uauj
program for a desk top computer (i.e. HP 9845) was
developed for a first cut approximation for the design
l7l supercavitating propeller blade. This program eliminated
the error-orone, tedious interpolation of empirical data graphs by
providing Approximations and curve fitting techniques to augment
existing formulae. The complex Goldstein -function and the
inexact Prandtl approximation were replaced by a more simple
DD ,:FORMAN 73 1473 EDITION OF I NOV •• IS OVSOLCTC UNCLASSIFIED
UNCLASSIFIED
#20 - ABSTRACT - (CONTINUED)
function, the Wilson factor, that maintained theconfidence level of the manual calculations.
DD Form 14731 Jan .3
2UNCLASSIFIED
Approved for public release; distribution unlimited
A Simple Interactive Program to DesignSupercavitating Propeller Blades
by
Marc B. WilsonLieutenant, United States Coast Guard
B.S.,SUNY, Maritime College at Fort Schuyler, 1973
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL
June 19 82
DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CALiF. 03340
ABSTRACT
A self-contained , rapid. Computer Aided Design (CAD)
program for a desk top computer (i.e. HP 9845) was developed
for a first cut approximation for the design of a super-
cavitating propeller blade. This program eliminated the
error-prone, tedious interpolation of empirical data graphs
by providing approximations and curve fitting techniques to
augment existing formulae. The complex Goldstein function
and the inexact Prandtl approximation were replaced by a
more simple function, the Wilson factor, that maintained
the confidence level of the manual calculations.
TABLE OF CONTENTS
I. INTRODUCTION 12
II. BASIC DESIGN METHODOLOGY 19
III. COMPUTER AIDED DESIGN 30
IV. CONCLUSIONS AND RECOMMENDATIONS 42
LIST OF REFERENCES 45
APPENDIX A: HP-9845 Computer Program 46
APPENDIX B: Sample Computer Output 75
APPENDIX C: Sample Calculations 80
INITIAL DISTRIBUTION LIST 83
LIST OF TABLES
I. Radial Distribution of Chord 2 3
II. Thickness Coefficients 25
III. Speed of Advance/Diameter (Manual vs Computer) — 32
IV. Ideal Efficiency (Manual vs Computer) 33
V. Camber Correction Coefficients (Manualvs Computer) 34
VI. Wilson Factor vs Goldstein Function 37
VII. Computer Program Inputs 38
LIST OF FIGURES
1. Picture of a Propeller Blade Tip Cavitating 16
2. Practicability of Supercavitating Propellers,Showing Model Number of NSRDC-TestedModel Propellers 18
3. Blade Dimension Sketch • 23
4. Bending and Torsional Moments 27
5. Definition Sketch 29
6. Cavitation Index (Manual vs Computer) 35
7. Lifting Surface Corrections (Manual vs Computer) - 35
TABLE OF SYMBOLS
A - Area, generally
A_^ - Developed blade area
A_ - Expanded blade areaE
A-j - Disk area
C_ - Drag coefficient
C^.- Lift coefficient
Li
C_ - Torque coefficient
C_, - Thrust-load coefficient
c - Blade chord length
D - Propeller diameter, assumed
D ,- Propeller diameter, optimum
F - Blade force
F„ - Transverse force, Horizontalrl
Fn - Froude number
g - Gravitational acceleration
h - Pitch Correction Coefficient
J - Advance coefficient
J .- Advance coefficient, optimum
L - Ship length
L - Lift
M - Blade moment
N - RPM
P - Pitch of propeller
p - Pressure
Q - Propeller torque
8
q - Dynamic pressure
R - Propeller radius
Re - Reynolds number
RPM - Revolutions per minute
S - Submergence
T - Propeller thrust
t - Thickness of blade section
V - Linear velocity
V - Speed of advancea '^
X - Percent radius
z - Number of blades
a - Angle of attack
a, - Cavitation correction
a^ - Lifting surface co-rection
S
.
- Angle of hydrodynamic pitch
e - Drag/Lift Ratio
T\- Propeller efficiency
A - Advance Ratio
K - Goldstein Factor
V - Kinematic viscosity coeff.
p- mass density of fluid
a - cavitation number
r - circulation
ABBREVIATIONS
BAR - blade developed area ratio, A /A^
BTF - blade thickness factor
BWR - blade width ratio, (maximum blade width) /D
EAR - expanded blade area ratio, A^/A
MWR - [Aj./length of blades (outside hub)]/D
NSRDC - Naval Ship Research and Development Center
SUBSCRIPTS
h - load component due to hydrodynamic force
x,Y,z - load components acting in the direction of x,y,zaxes, respectively.
10
ACKNOWLEDGMENTS
I wish to express my indebtedness and gratitude to
Professor Donald M. Layton of the Aeronautics Department at
the Naval Postgraduate School for suggesting and advising me
on this topic. Additionally, I want to thank Professor
Turgut Sarpkaya of the Mechanical Engineering Department for
his many helpful suggestions and encouraging comments , and
Dr. William B. Morgan of the David W. Taylor Naval Ship
Research and Development Center for all his assistance and
support. Lastly, my wife Laura for the endless support she
has given throughout my research.
11
I. INTRODUCTION
The screw propeller was first developed by an Englishman,
Hooke, in the 17th century, but received little use until
nearly two centuries later. In the late 1800 's, while the
British steamer TURBINIA was being designed, it was first
observed that the propeller could operate in a cavitating
mode wherein at least a portion of the propeller operated in
an 'air cavity'. This air cavity was not air but a result
of critical pressure conditions in the vicinity of the
propeller blades [1]
.
Inasmuch as propeller cavitation usually results in
marked increases in required rotational speed, propeller
slip, and erosion of the blade surfaces, as well as decreases
in the power efficiency, cavitation was to be avoided, if at
all possible. One precaution was to insure that the tips
of the blades were always well submerged to as not to have
an air interface. If partially submerged then ventilation
may result yielding similar effects as cavitation.
It was not until the mid-twentieth century, while search-
ing for drive systems for racing boats, that it was discovered
that by operating in extreme cavitation regions, high water-
craft velocities could be obtained with but minimal deleteri-
ous effects. In fact, not only could the propeller be
operated in a cavitating mode fully submerged, but it could
also be operated with a portion of the blades out of the
12
water partially submerged. As a result, these systems are
referred to as either fully submerged or partially submerged
propellers. With either propeller the effect is essentially
the same although the loads may differ.
Whereas the design techniques for conventional propellers
had become well established [IJ , few techniques were available
for the supercavitating blades or foils. In general, the
subcavitating design procedures were used as an approximation,
but this left much to be desired. In the mid-19 50 's, Tulin
[1] proposed two-dimensional lift-drag characteristics for
these designs, and at the same time Morgan and Tachmindj
i
applied circulation, or lifting line, theory. The latter
techniques were based on the works of Prandtl, Hemhold, Gold-
stein and Lerb, utilizing hydrodynamic principles. Now,
nearly thirty years later, these approaches are still used in
the design of supercavitating propellers [1] .
The most rigorous of these techniques is Lerb's [2] induc-
tion factor method, while the use of the Goldstein function,
though less precise, compares quite favorably to Lerb's method,
Any of the methods used in the design of supercavitating
propellers have been labor intensive [2].
A. STATE-OF-THE-ART
The formal design methods for high speed naval ship pro-
pellers were established by Morgan and Tachmindj i of the
David W. Taylor Naval Ship Research and Development Center
(NSRDC) [6] , using the Goldstein function to correct for
13
supercavitating operations. The major problem in these tech-
niques was attributed to blade cavity effects, and a correction
in the form of an accountability factor is used to offset this
effect. This correction is based on an approximate cavity
thickness in the lifting surface calculations.
Another approach in the design method is that taken by
Hydronautics , Inc., [1] that utilizes lifting-line theory and
the Goldstein function together with a camber correction fac-
tor and two-dimensional foil analysis about a free surface.
A comparison of the two approaches by Tulin indicates
an overestimation of efficiency and thrust by the NSRDC method
[1] . Both methods rely heavily on the use of empirical data
and require frequent interpolation and extrapolation of data.
Most of the more recent research in this field has been con-
ducted between 1955 and 1975, and the confidence level in the
selection of a supercavitating propeller without full-scale
testing has been unfavorable.
B. FUNDAMENTALS OF CAVITATION
The phenomena of cavitation is the formation of bubbles
about a foil or blade. This can be explained by the Bernoulli
equation, assuming inviscid compressible behavior, where the
sum of the static pressure, p, and the dynamic pressure,
ypV , is a constant.
P+ypV = p = constant [1]
14
where
:
p = static pressure on the foil downstream side,
V = velocity of the flow,
p = density,
p = total pressure (total head) .
By relating the constant total pressure of the ambient
conditions (subscript 0) to the constant total pressure at
any point, assuming constant density,
p + ipv2 = pg + lpv2 (2)
By combining the dynamic pressure terms, it can be
observed that the pressure at any point may be expressed as
,
P = Pn + ^P (3)
If p = , so that p = -Ap, the fluid changes state and
cavitation results. In reality, the static pressure does not
completely reach zero, but will decrease to the vapor pressure
of the fluid, p^ . When the static pressure reaches this
value.
P = P^ = Pq + ^P ^^^
the fluid 'tears' or boils. This is cavitation! See Figure
1.
15
Figure 1. Picture of a Propeller Blade TipCavitating (NSRDC)
16
A measure of the amount of cavitation, called the cavi-
tation index or the cavitation number, is determined by-
dividing the pressure change, Ap, by the dynamic head of
the flow.
When the bubble formation that commences at the leading
edge extends beyond the trailing edge, so that a plume appears
to form downstream, the foil is said to be supercavitating.
C. SUPERCAVITATING PROPELLERS
A propeller designed for optimum non-cavitating or sub-
cavitating operation cannot perform efficiently in a cavitating
environment, and if it is desired to have a propeller system
that can utilize the high speed advantages of the supercavi-
tating propeller, a special design of the foils must be
accomplished that will deliver thrust efficiently in a quasi-
gaseous environment. When it is not operating in a supercavi-
tating environment, there is no real advantage to this type
of propeller system, as shown in Figure 2.
One can visualize a supercavitating propeller as somewhat
a hybrid operating between the marine and the air environment,
and it has somewhat the appearance of a stubby propeller of
an aircraft rather than looking like a conventional marine
screw.
Current design techniques, as outlined in Chapter II,
call for extracting values from empirical curves to use in
the calculations. It is the purpose of this project to semi-
automate this process, as outlined by references 1, 2, and 3.
17
A SUPEnCAVrTATlNRQ PARTIAL SUPF.RCAVITATION OR BURBLINGO PRACTICALLY NO CAVITATfON
DEST REGION FORCOm'E>mONAL—PROPELLERS
REGION OF PARTIALCAVITATION ON ANYPROPELLER
^LINE I
O.G
J33t0/, '/Z
LINE 2 -
BEST REGION FOR -
SUPERCAVITATINGPROPELLERS
0.8 1.0 1.2
SPEED COEFFICIENT1.4 t.6
Figure 2. Practicability of Supercavitating Propellers,Showing Model Numbers of NSRDC-Tested ModelPropellers [1]
18
II. BASIC DESIGN METHODOLOGY
The criteria for use of the supercavitating propeller
is essentially the relationships between the speed of
advance, V , the rotational velocity, RPM, and the cavita-a
tion number, a.
As in any design problem, the first requirement is the
establishment of the design operating point for which param-
eters are assumed, known or desired. Such a point may be a
speed condition, such as cruise, hump, maximum or patrol
velocity, or it may be a power condition. There are several
basic parameters that are unusually well known or can be
readily assumed. These include the velocity of the craft,
resistance (drag) , power available, speed of .advance (or
wake factor) , thrust (or thrust deduction factor) , number of
blades and submergence.
As a first-cut approximation for the required diameter
of the propeller, the Burtner equation is used [IJ
,
D = [50 X (HP)°-^/RPM°*^] ft (5)
The thrust is non-dimensionalized by the use of a coeffi-
cient of thrust, C_
,
^T = 1 2(^)
19
where
:
T = thrust (lbs)
3p = density (slugs/ft )
D = propeller diameter (ft)
V = speed of advance (knots)a
S = submergence
2A = disk area (ft )
The speed of advance is also non-dimensionalized to an
Advance Coefficient, J,
J = 101.34 X V /(RPMxD) (7)a
where 101.34 is the conversion factor in terms of ft. and sec.
The above factors are shown in pound-force, pound-mass,
and feet units, but the entire calculations can also be
accomplished in metric units, if desired.
Once C_ and J are determined, the expected efficiency is
obtained from empirical data, usually plotted as J versus
/C_. The radial distribution of pitch is determined from
Kramer Thrust Coefficient Curves, with inputs of their Advance
Ratio, A, and the Ideal Thrust Coefficient, C_.
, where
A = V /(N X D X it) (8;a
and.
20
C^^ = 1.07 C^ (9)
It is to be noted that only approximate values are used
inasmuch as the exact value of C^ . is,Ti
where
:
C^^ = C^/(1-2£A.) (10)
= drag to lift ratio
A. = ideal advance ratio.1
At this point, solutions can be made for the radial pitch,
(D X TT X A . ) , and the hydrodynamic pitch angle, 8 • .
Once the hydrodynamic pitch angle, 3., is established,
the ideal delivered thrust coefficient, C •, may be deter-
mined by using the more rigorous induction factors and
numerical integration (Simpson's Rule) , or by using the
Goldstein function, k, [5]
z r N > ,, ,,^ = 2TTU V ^^^^
a a
where
;
r = circulation
u = axial velocity.
The delivered ideal thrust coefficient, C •, is compared
to the required value of C„.
, and if the delivered value isTi
21
less than the required value, the hydrodynamic pitch angle,
S ., is corrected and the problem iterated until the delivered
value of C„ . is equal to the required value. If the iteration
process becomes too cumbersome or too lengthy, interpolation
may be used to validate the new value of 3
.
At this point the designer can compute the geometric
properties of the blade, first by computing the value of
Ct (£/D) , where,Li
C^ = L/(|pV^A) (12)
i = blade width
L = lift
and then by determining the blade width at seventy percent
of the blade span.
C^ il/D) ^ ^ X DQ = -± )Ll1 (13)^0.7 C^
^^-^^
where
:
Cj = coefficient of lift for a finite foil.
Reference 2 states that the optimum value for C, is 0.16
and that value is used in these computations.
22
A recoininended distribution of section chord as a function
of the chord size at the seventy percent span [2], is shown
in Table I.
TABLE I
RADIAL DISTRIBUTION OF CHORD
0.400
0.475
0.550
0.625
0.700
0.775
0.850
0.925
1.000
1.088
1.086
1.073
1.046
1.000
0.903
0.763
0.565
0.000
At each radial station, the blade shape may then be
determined, as shown in Figure 3.
Figure 3. Blade Dimension Sketch
23
From the hydrodynamics of lifting surfaces and empirical
data, the maximum dimension, (y/2,) , is [1],max
(y/£) = 0.1553 C^. - 0.00462 ctmax Li
where the angle of attack, a / is a function of the lift
coefficient.
The height-to-chord ratio is then corrected by using
camber correction factors, k, and k„, are functions of the
expanded area ratio, EAR, which is the ratio of the expanded
blade area, A^ , to the disk area, A_
,
EAR = A^/A = ^ /A dx (14)
X
The EAR is similar to the BAR blade developed area ratio with
the difference being that the EAR is with respect to radial
distribution.
The corrected thickness factor, (y/2,) , is
,
The thickness of the blade section, t, is determined from.
t/£ = F'Ct- + N'a (16:J-i
where F' and N' are as shown in Table II [1]
24
TABLE II
THICKNESS COEFFICIENTS [1]
d/£ y/y F" N'^' ^ max
0.0000 0.0000 0.00000 0.000000
0.0075 0.01888 -0.001326 0.001254
0.0125 0.03244 -0.002574 0.001870
0.05 0.14189 -0.016816 0.005704
0.10 0.29150 -0.039520 0.010074
0.20 0.56636 -0.078940 0.017349
0.30 0.78458 -0.097600 0.022222
0.40 0.93187 -0.092870 0.024647
0.50 1.00000 -0.071780 0.025710
0.60 0.98340 -0.037750 0.025853
0.70 0.87797 0.005940 0.025605
0.80 0.68055 0.056880 0.024660
0.90 0.03886 0.112090 0.023047
0.95 0.20650 0.139620 0.022048
1.00 0.00000 0.166950 0.020937
The final step in determining the geometric parameters
is the determination of the corrected pitch-to-diameter
ratio, P/D, using as inputs friction, cavitation and lifting
surface theory. The friction is considerably small and may
usually be neglected, and the pitch-diameter ratio may be
given as
,
P/D = xxTTx (1 + (A(P/D)/(P/D) ) xtan(e. + a )) (17)
25
where
:
1+ (A(P/D))/(P/D) = (tan(B^ + a^ + a2)Q^^)/tan{3^ + a^)Q^^
(18)
a, = 57.3 K (0.0849 xc^ + 0.0152 x a) (in degrees)1 a L ^
a. = a, + (3. - 3) X (2/(1 + cos^S- (|- D) - D2 D 1 in
h is the pitch correction factor, and a, is the vortex
correction factor (may be neglected due to its magnitude)
.
K is a function of the cavitation index at the seventya -^
percent station, a_ -. , which is in turn.
Q^ . = 2 X gx H X J^/V^ (J^ + 4.84) (19)u « / a
where
:
H is the absolute pressure at the shaft centerline
minus the cavity pressure, measured in feet of water.
With the above information in hand, the designer can
verify the shape of the blade by determination of the pro-
peller efficiency and the delivered power.
A. DESIGN ITERATIONS
In the previously discussed steps, it was assumed that
the ideal thrust coefficient, C_.
, was approximately seven
percent higher than the thrust coefficient. Equation (9)
.
26
Once the initial design phase has been concluded, the drag
to lift ratio, z, can be determined and a more precise value
of ideal thrust coefficient may be calculated. This may
be used for additional iterations until a final value of
thrust coefficient and power coefficient have been obtained.
The ratio of thrust coefficient to the power coefficient
determines the efficiency of the propeller.
A check of the adsorbed horsepower is made to see if the
design meets the requirements of power available.
SH^absorbed) = C^ x p x d^ x v^ x s/ (550 x 8) (20)
B. STRENGTH OF THE BLADES
The final design step is the determination of the bending
and torsional moments of the blades.
d^-x.
Figure 4. Bending and Torsional Moments
From the geometry of Figures 4 and 5 and from structural
considerations
,
27
«xo - "rb ^"^ 8. + M^^ sin B. (21)
"yO = '\b ^^" 8. - Mgj^ cos6i (22)
^b ^ 2"^^^^^^^"^a^^ ^ ^^"^0^ (1 -£ tan 6^)_ dx
^0
(23)
^Ob^ jx P X TT X R^ X v^/z / (tan ^) {x-Xq)
^0
x(l+e/tan 6 . ) —r^^x (24)1 dx
where x is the dimensionless station being analyzed.
It is to be noted from Figures 4 and 5, that M - and
M ^ are approximate inasmuch as the precise expression is
a function of (|) rather than 3 • . The difference between <p
and 3. is a_/ where a„ = a, + a^, with a value of about 21 F F 1 2
degrees. Except for heavily loaded blades, the use of 3.
instead of cp is valid, since with heavy loads the angle of
attack criticality increases.
The described design techniques have used thrust as a
base. It is possible to use, instead, power as the base,
i.e., C vice C„
.
p T
28
FoilBl^de
- ADVANCE ANGLE
01 • HYDBOOYNAMIC PITCH ANGLE
^ FINAL PITCH ANGLE
0<_ • FINAL ANGLE OF ATTACK (<*,-*•'*-l')
CtI
" COMeiNEO ANGLE OF ATTACK THAT CONSIDERS THE ItJEAL ANGLE OF
ATTACK AND THE FRICTION CORRECTION -Jt
0^2 • ^NGl-E OF ATTACK THAT CONSIDERS LIFTING SURFACE EFFECT
T • THRUST • DRAG L« LIFT
F • TOROtX FORCE I • SUBSCRIPT FOR NON-VISCOUS
Shaft
* rjote. a^ In -this ^sKt-tdk /i <x ^ oi^
3i dt.fin€.d &dr//'en.
Figure 5. Definition Sketch
29
III. COMPUTER AIDED DESIGN
A. INTRODUCTION
The basis of a Computer Aided Design (CAD) program is
to make available to the designer the information that he
needs for at least a first iteration. To be efficient, the
CAD should have the following characteristics:
1. Be self-contained.
The entire program with all subroutines should be
stored in a single data source, e.g., a computer disc, so
that additional programs need not be loaded once the design
process has commenced.
2. Be self-querying.
The variable inputs should be inserted in response to
a computer question statement.
3. Be labor non-intensive.
Fixed parameters should be included in the program
and not be required to be entered each time the program is
exercised.
4. Be logical.
The computer program should follow a logical pro-
gression that is similar to the steps in a manual calcula-
tion, unless mathematical considerations dictate otherwise.
5. Be Segmented.
The program should contain logical breakpoints to
facilitate future editing, including changes, deletions and/
or insertions.
30
B. APPROXIMATIONS
The use of empirical data requires extensive curve
fitting, interpolation and extrapolation. Frequently approxi-
mations may be made to the data that significantly reduces
the calculation time. Such approximations are useful and
valid only if they provide a high confidence level in the
results. The following section details several of these
approximations, together with numerical examples as a proof
of confidence.
An expression of the optimum speed of advance, J ,
was developed as.
J, - (C^ /J X J - 0.56396 + 0.71765 X Ln(J) )
"^or.^ = —rrh ^— (25 )
°P^ (C^ /J + 0.71765/J )
where
:
J^ = 1.206/(C°*^/J + 0.63225)
This approximation provides a confidence level of 9 8%.
The expected efficiency is extracted from the predicted
performance charts extrapolated from 40 knots to 80 knots,
for blades between ten and fourteen feet in diameter. This
extraction was performed by Lagrangian curve fitting. To
demonstrate the accuracy of these approximations, five runs
were made at different values of RPM with the following
conditions;
31
V = 80 kts R = 120,000 lbs z = 6
SHP = 45,000 Hp w = t = p = 2 slug/ft^
Submergence = 0.5
The results of these runs are shown in Table III where
the subscript 'h' refers to manual calculations and the
subscript 'c' refers to computer calculations. All calcula-
tions have been generated by this author.
TABLE III
SPEED OF ADVANCE/DIAMETER (MANUAL VS COMPUTER)
RUN RPM J, J J ^ J ^ Hu n D ^ D ^h c °P^ °P^c °P^ °P
1 400 1.69 1.69 1.45 1.46 0.70 0.70 13.98 13.91
2 500 1.35 1.35 1.35 1.36 0.67 0.70 12.01 11.92
3 600 1.12 1.13 1.26 1.28 0.65 0.65 10.72 10.56
4 700 0.96 0.97 1.20 1.21 0.63 0.62 9.65 9.57
5 800 0.84 0.84 1.04 1.15 0.60 0.59 9.74 8.82
The determination of the uncorrected radial distribution
of the blade's characteristics as well as the determination
of the ideal thrust coefficient requires a knowledge of the
ideal efficiency. In the manual mode, values were extracted
from the curves of Kramer's Thrust coefficient. Once again,
curve fitting techniques were employed. Because of the
32
shape of the empirical curves , the numerical approximation
required five partitions.
The manual and computer values for the ideal efficiency
are shown in Table IV for five runs at different values of
n . and C_ . for z = 6
.
1 Ti
TABLE IV
IDEAL EFFICIENCY (MANUAL VS COMPUTER)
:un X Si ^ih ^ic
1 0.500 0.0930 0.941 0.948
2 0.400 0.1260 0.930 0.949
3 0.400 0.1605 0.927 0.925
4 0.400 0.1954 0.905 0.901
5 0.400 0.2304 0.875 0.878
The camber correction coefficients, k, and k„, must also
be approximated, and are based on the ratio of expanded blade
area to disk area, Ap,/A^ . Table V shows a comparison of
the values obtained from an empirical graph, subscript 'g'
to the computer solution values, sucscript 'c'.
The graph used for this approximation, [1], has a maximum
value of 1.2 for the ratio of the expanded blade area to disk
area, Ap/A^ . Even with an extension of this value to nearly
1.6, the computed values of k, and k^ appear to be well
within reason.
33
TABLE V
CAMBER CORRECTION COEFFICIENTS (MANUAL VS COMPUTER)
^/^o igK-,Ic ^2g ^2c
1.54 * 1.06 * 2.31
0.75 1.03 1.00 2.10 2.13
0.72 1.06 1.06 2.10 2.09
0.33 1.01 1.00 1.70 1.67
0.25 1.02 1.00 1.65 1.67
Point off empirical graph
Two additional curve fit solutions deal with the cavitation
index and the lifting surface correction angles (a, and a^)
.
As indicated in Equation (16) , the correction angles are a
9
function of sigma and h. To indicate the degree of fit of the
computer generated data for these approximations. Figures 6
and 7 show the computer plots with manually extracted data
points from reference 6 superimposed.
The- boldest modification in the development of this
Computed Aided Design program was the complete removal of the
Goldstein function and the induction factors from the calcu-
lations. This modification is required in order to simplify
the design process. The Prandtl solution for irrotational
motion of a screw surface in an inviscid, incompressible,
continuous fluid lends itself to a simplified means of
34
K
1.0
0.9
0.Q
0.7
0.5
0.S
0.00 0.02 0.0H 0.0E 0.0Q 0.10
Figure 5. Cavitation Index (Manual vs Computer) [1]
I .B
h I .H -
0.0 0.2 0.H 0.B 0.B I. a 1.2
Sin^i7-;=^
Figure 7. Lifting Surface Corrections (Manualvs Computer) [Ij
35
determining the circulation and the lift coefficient. This
approximate solution is.
2zFN z , \x . -1-f , ^c\(
—
^) cos e (26)IT u V 2tt ,
,2
a a 1 + U
where
f = (1 + ^o^^'^^d - p/Pq^
y = Nx/V
However, according to Goldstein [5J
,
The accuracy of the (Prandtl) approximation increaseswith the number of blades and the ratio of the tip speedto the velocity of advance, but for given values of thesenumbers, we have found no means of estimating the error,since the exact solution has not been found.
Since Goldstein' s* work in 1929, NSRDC [2] has developed
a more precise solution utilizing induction factors.
In the development of this program it was found that the
direct use of the Prandtl approximation [5] as a substitute
for the more complex Goldstein function produced excessive
errors when compared to empirical results. It was therefore
decided to use a modified solution which did not contain the
2 2term (y /I + u ) . This modified term, which is called the
Wilson factor, Wf, provided a conservative solution with much
less mathematical manipulation than was required if the
Goldstein function of Lerb ' s induction factor method were
used. The Wilson factor is defined as.
36
Wf = (Z/27T) X cos"-'- e"^^ (27)
Table VI shows a comparison of the Wilson factor, Wf
,
and the Goldstein function, k, at several radial stations.
Table VI
WILSON FACTOR VS GOLDSTEIN FUNCTION
Wf KC/Wf
0.400 1.000 1.209 0.83
0.475 0.982 1.160 0.85
0.550 0.962 1.101 0.87
0.625 0.940 1.031 0.91
0.700 0.908 0.946 0.96
0.775 0.805 0.841 0.96
0.850' 0.760 0.704 1.08
0.925 0.570 0.511 1.12
C. PROGRAM DESCRIPTION
1. Segment A
The first segment of the program, lines 10 through
630, is the input segment where the desired parameters are
inserted in response to queries by the computer. These
inputs, by line number, are shown in Table VII.
37
TABLE VII
COMPUTER PROGRAM INPUTS
Line Input (units)
190 Ship maximum velocity (kts)
220 Ship maximum resistance (lbs)
2 50 Maximum available horsepower
280 Wake fraction (use zero if V = 60 kts)
310 Thrust deduction factor
340 Number of blades
370 Fraction of submergence of propeller
400 Assumed RPM
430 Fresh or salt water operation
450 Water temperature (Rankine)
540 Preliminary propeller diameter decision
610 Preliminary propeller diameter (ft)
630 Fluid density (slugs/ft )
2 . Segment B
The second segment of the program, lines 6 40 through
930, computes and prints the basic parameters for the ensuing
calculations. The printout, in the computer symbology,
includes the thrust load coefficient, Ct , from existing
formulae; the advance coefficient, J; the optimum advance
coefficient, Jl ; from numerical approximations; the optimum
propeller diameter, Dl; the expected efficiency, E, also from
numerical approximations; and the Shaft Horsepower, P.
38
3
.
Segment C
Because of the complexity and non-linearity of the
empirical Kramer Thrust Coefficient curves, an extensive
curve fitting process is required to cover the entire range.
This is accomplished in a multi-step process from lines 940
through 3170. Lines 940 through 1370 are used to approxi-
mate the advance ratio, L, in order to enter the Kramer curves,
and lines 1380 through 3170 determine the adjusted value,
Ln, from the curves.
4
.
Segment D
Once the adjusted value Ln has been obtained, the
ideal values of the parameters L., C^ . and E. are determined^ 1 ti 1
in lines 3180 through 3300. All values, except E. are from
existing equations.
These values are then used in the first iteration for
the ideal thrust coefficient, C^.
, in lines 3310 through 4460.ti ^
This segment is concluded with a printout of the
delivered ideal thrust coefficient, C, . , , and the required
ideal thrust coefficient, C, . , for comparison purposes. Also
printed at this point are the values of the tangent of the
advance angle, tan B, the values of the Wilson factor, Wf,
the circulation, G, and the distribution of the coefficient
of lift times the chord-diameter ratio. All calculations,
with the exception of the Wilson factor, are from existing
equations.
39
5
.
Segment E
Lines 4050 through 4460, by the use of Simpson's
Rule, calculate a first iteration of the ideal thrust coeffi-
cient, C+- dl ' ^^^ ^ final iteration of the blade hydrodynamic
delivered ideal thrust coefficient, C. . , as well as the
required C . .
6
.
Segment F
A second iteration of the ideal thrust coefficient is
accomplished in lines 4470 through 50 20 in order to verify
the blade's hydrodynamic pitch angle. This is necessary
inasmuch as the previous calculations were based on the
original values of the ideal thrust coefficient vice the
iterated values. The iteration continues until the delivered
value is within 98% of the required value. All calculations
are based on existing equations.
7. Segment G
Although the solution may be in hand by this point,
it is of interest to recompute lambda based on the new param-
eter values and then to use this value as an alternate method
in the design process. This is available in lines 5040
through 5390, but is currently by-passed in the program.
8
.
Segment H
The value of C {l/D) is recalculated and i^ is
printed out in lines 5400 through 54 30 with the aid of a
subroutine, and the shape of the blade is determined in lines
5440 through 5550, in addition to a first cut approximation
of the EAR via existing formulae.
40
9 . Segment I
The geometry of the foil, i.e., cross-sectional shape
and all of the dimensions at each predetermined radial sta-
tion, are calculated in lines 5560 through 6300. For each
station there is a printout that specifies blade element
thickness, height of curvature from the x-axis and blade
width.
10
.
Segment j
The blade pitch is corrected for cavitation, friction
and the lifting surface effects in lines 6310 through 6570.
The printouts for this segment are similar to, but are of
corrected values of, the data in the preceding segment,
with the final pitch diameter ratio being determined.
11. Segment K
The segment from lines 6600 through 6850 determines
the predicted propeller efficiency and manifests that the
power demanded by the propeller does satisfy the available
or required power.
12. Segment L
The bending and torsional moments along an arbitrary
radial station are determined in the segment from lines 686
through 72 30 for various predetermined stations.
13
.
Segment m
The remainder of the program, through line 8450, is
devoted to subroutines that perform the repetitive calcula-
tions required by the various segments and data.
41
IV. CONCLUSIONS AND RECOMMENDATIONS
A. CONCLUSIONS
This program is an approximate method for aiding in the
design of supercavitating propeller blades. The numerical
approximations complemented by the conversion factors and
other constants result in a design that is about 90% accurate
in the final sense as compared with information from reference
1. Inasmuch as this method uses essentially the same formulae
and empirical curves as the 'manual' method, one could not
hope for much better accuracy.
The principal advantage to this CAD program is that it
reduces the conceptual design phase to minutes. It also pro-
vides a straightforward approach to the problem that can be:
(a) easily followed, and (b) modified to fit the specific
needs of the designer. The use of proven, computerized
equations is much faster than table- look-ups and picking
points off a graph. In addition, the repeatability of output
is greatly enhanced.
The program will definitively demonstrate what combination
of fundamental parameters will not yield a satisfactory design,
e.g., negative coefficient of lift for a desired forward
motion. This information provides the designer with great
flexibility.
If the program does produce unsatisfactory solutions, the
designer may vary the basic parameters. From the fluid
42
dynamics viewpoint the best parameter to change is RPM,
inasmuch as RPM plays a major role in the design of propellers,
and by adjusting the assumed RPM the resulting output is
changed.
This program is equipped with an alternative design tech-
nique so that when the final tangent, 3•
/ at x = . 7 is veri-
fied, a new ideal advance ratio may be calculated. This
alternative is not a portion of the basic program but has
been included for use if desired at a later time.
A comparr.son with a manually calculated theoretical design,
as shown in Tables III, IV and V, demonstrates that this
program is feasible and equally as accurate. However, the
only definitive means of determining the validity of this
program is to make a comparison with an experimental design.
This program can be used for all supercavitating propeller
blades in an extremely wide range of speeds, submergences,
thrusts and efficiencies.
B. RECOMMENDATIONS
A graphics routine would enhance the program and might
even upgrade this program to a Computer Aided Engineering
(CAE) and/or Computer Aided Manufacturing (CAM) status.
At present five- and seven-bladed propellers are excluded
in this program, since it was too difficult to read the ad-
vance ratio off the Kramer Thrust Curve. This could be
changed in the future.
The effect of the change of advance ratio on the final
output has not been examined. The effect of this alternative
43
should be challenged in the future. In addition, the intro-
duction of induction factors would be well worth the effort
44
LIST OF REFERENCES
1. Lockheed Missile & Space Company Contract ReportN00024-73-A-0919 , Surface Effect Ship Propulsion Tech-nology Design Manual, Volume III, SupercavitatingPropellers, 16 May 19 74.
2. Eckhardt, M.K. and MOrgan, W.B., "A Propeller DesignMethod", SNAME Transactions, Vol. 63, pp. 325-374, 1955.
3. Habermann, W.L. and Venning, E., "SupercavitatingPropeller Performance", SNAME Transactions, Vol. 70,pp. 355-417, 1962.
4. Altmann, R.J. and Hecker, R. , "High Performance MarinePropellers—An Overview", Marine Propulsion ASHE O.E.D.,Vol. 2, pp. 23-95, 1976.
5. Goldstein, S. "On the Vortex Theory of Screw Propellers",Proceedings of the Royal Society of London, Series A,Vol. 63, 1929.
6. Morgan, W.B. and Tachmindji, A.J. "The Design andEstimated Performance of a Series of SupercavitatingPropellers, Second Symposium on Naval Hydrodynamics ,
Hydrodynamic Noise and Cavity Flow , ONR, 1958.
45
APPENDIX A
HP-9 845 COMPUTER PROGRAM
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74
APPENDIX B
SAMPLE COMPUTER OUTPUT
The purpoif of this program is to determine the roMowing specifications of a
superc a>>i t at i ng propeller:Dlaf.ieter < as a function of an assumed RPM)Blade shape Cchord dimensions at various radia) stations)Blade pitch and pitch distributionFoil camber and thickness distributionBlade bending nioment at radial stations
In order to give you the desired propeller please enter the knowncharacteristics of the ship folloued by pressing COHT.
Alpha is the angle of attackfllphal is the correction to alpha for cavitationBi IS the hydrodvnanii c pitch angleC) is the coefficient of liftCpc is the final power coefficientCt is the thrust load coefficientetc is the final thrust load coefficientCt i is the ideal thrust load coefficientD is the diameter <ft.)d is the percent of blade widthERR is the e-<pand6d area ratio <fle/flo)
Ei is the id^al propeller efficiencyEpsilon is the drag^lift ratioEta is the propeller's efficiencyC is the circulationKl i, K2 are the cairibcr correction coefficientsL is the advance ratio (lambdasLn is the adjusted ad'^ance ratioLi is the id'Sal advance ratioLo is the blade width at x=0.71 is the blade widthNxo is the moment about the x axis(lyo IS the moment about the y axist is the thickness of the blade elementX is the percent radius of the bladeWf i* the Ulilion factory IS the height of curvature of the blade element
75
SHIP'S MftX SPEED IS 80SHIP'S TOTAL SESISTRKCE IS 120090SHIP'S Mfi;; flVftlLMBUE SHP 13 45008THE UflKE FRflCTIOM IS
THE THRUST DEDUCTION FriCTOR IS
NUMBER OF ILfillEi ON PROPELLER IS S
THE PERCENT OR FRACTION OF SUBMERGENCE EXPECTED OF THE CRAFT IS .5
RSSUtlED RFM IS -500
CALCULATIONS ARE FOR SlJ
THE ASSUMED :jhTER TEMPERATURE IS 520.000000VISCOSITY (NU)' .000013 fi''2/sec
The thrust-load coefficient = .1674The square root of the thrust-load coefficient is .4091The ad'-'ance coefficient, J = 1.3512The opt i tiuim advance coefficient is 1.2731The optiiiiufii propeller diarneter is 10.5634 ft.
The expected efficiency is .6516The SHP for this optimuan propeller is 45240.6329
Ln = .260
G C 1/D.0065 .0294.0074 .0305.0080 .0299.0082 .0281.0030 .0254.0075 .0220.0066 .0173.0049 .0125
THE DELIVERED Ct i = .122 THE REQUIRED Ct i = .160THE VERIFYING DELIVERED Ct i = .2772 THE REQUIRED Cti = .1605THE VERIFYING DELIVERED Or. i = .5545 THE REQUIRED Cti = .1605THE FINAL TANGENT Or BETA SUB i IS .6206THAT ANGLE IN DEGREES AT 0.7R IS 31.3238THE FINAL EETAi HAS BEEN VERIFIED. YOU MAY PROCEED WITH A CONFIDENCE FACTOR OF98:;.
L = .400 Ctj= .160The ideal ef f i c ienc y ( E i ) IS .925Li= .433
X TAN Bi COS Bi UP;4OO0 1.0815 .6789 1.2088.4750 .9107 .7393 1. 1596.5500 .7865 . 7360 I. 1012.6250 .6921 .8223 1.0312.7000 .6130 .8507 .9463.7750 .5582 .3732 .8407.8500 .5089 .8912 .7042.9250 .4677 .9058 .5107
THE SUM OF THE PRODUCTS 13 4. 387
76
Lo- 1.6784
THE flPPROXIMflTE (WITHIH 3^3^:) EXPflHDED fiREfl RATIO <EflR) IS .4540
1^19.7 1x CI flLPHfl V^'lmax yirtax
.408 1 .osso 1.3262 1698 2.0000 .0171 .0313
.475 I .6360 1.8223 1766 2.0000 .0182 .0331
.550 1 .0730 1.3010 1753 2.0000 .0180 .0324
.'625 1 .0460 1.7557 1691 2.0000 .0170 .0299
.706 1 .0000 1.6784 IbOO 2.0000 .0156 .0262
.775 .9030 1.5156 1534 2.0000 .0146 .0221
.850 .7630 1.2807 1472 2.0000 .0136 .0174
.925 .5650 .9483 1389 2.0000 .0123 .0117
d/1 y txl t<ft).0075 .0005 .8023 0039.0125 .0003 .0033 0056.0500 .0037 .0087 0146.1000 .8076 .0138 0232.2000 .0148 .0221 0370.3000 .0206 .0233 0434.4000 .0244 .0344 0578.5000 .0262 .0399 0670.6060 .0258 .0457 0766.7000 .0230 .0522 0875.8000 .0178 .05S4 0931.9000 .0102 .0640 1075.9500 .0054 .0664 1115
1.0000 .0800 . 0636 1151ERR" .32 11
IC1» 1.000 K2 = 1.666d^l y y/1 Cy/'l > : yc
.0075 .0005 .0002 0003 .0003
.0125 .0008 .0004 0006 .0014
.0500 .0037 .0016 6026 .0062
.1000 .0076 .0032 0053 .0128
.2000 .0143 .0062 0103 .0249
.3000 .0206 .0036 0143 .0345
.4000 .0244 .0102 0170 .0410
.5000 .0262 .0109 0132 .0440
.6000 .0258 .0107 0179 .0432
.7000 .0230 .0096 0160 .0386' .8000 .0178 .0074 0124 .0299.9000 .0102 .0042 0071 .0171.9500 .00?4 .0023 0033 .0091
1.0000 .oee-o . 0000 0000 .0000X TRK Bi TftN B B B 1 1? . 7 Bi?.7 C flLPHrt rtLPHM 1 P'D
.400 1 .0815 1.0179 7943 .5535 .5268 1693 2 0000 .0403 1. 4644
.475 .910? .£572 7086 .5535 .5268 1 766 2 0000 .0403 1. 4653
.550 .7665 .7403 6373 .5535 .5268 1753 2 0000 .0407 1.4672
.625 .6921 .6515 5774 .5535 .5268 1691 2 0000 .0402 1.4697
.700 .6180 .5817 5268 .5535 .5263 1600 2. 0000 .0395 1 .4727
.775 .5532 .5254 4837 .5535 .5263 1534 2 0000 .0390 1.4769
.850 .5089 .4790 44(57 .5535 .5268 1472 c 0000 . 0385 1. 4817
.925 .4677 .4402 4147 .5535 .5268 1389 2 0000 .0379 1.4861X EPSILON
.400 . 073
.475 . 080
.550 . 080
.625 . 079
.780 . 078,775 . 077.850 . 077.925 . 078
77
L1» .433THE FOLLOWIHC IS RECALCULATED USIHG EPSILON'
X TftN Bi COS Bi Uf G C 1/D.4088 1.0815 .6789 1.2088 .0065 .0294.4758 .9107 ,7393 1.1596 .0074 .0305.5588 .7865 .7860 1.1012 .0080 .0299.6258 .6921 .8223 1.0312 .0082 .0281.7888 .6180 .8507 .9463 .0080 .0254.7758 .5532 .8732 .8487 .0075 .0228.8588 .5039 .8912 .7042 .0066 .0178.9258 .4677 .9058 .5107 .0049 .0125
THE SUM OF THE PRODUCT'5 IS 4.887THE DELIVERED Ct i = . 122 THE REOUIPED Ci 1 = . 161THE VERIFYING DELIVERED Cii = .2788 THE REuUIPED Ct I
=. 1603
THE VERIFYING DELIVERED Ct i = .55^1 THE REQUIRED Cl 1 = . 1608THE FIHhL TrtMGEMT OF BETR SUB i IS . o206THfiT fiMGLE IM DECREES AT 0.7R IS 31.8250THE FIHf=iL BETAi HAS BEEH VERIFIED. YOU MAY PROCEED WITH A CONFIDENCE FACTOR OF.98^..
Ctc« .1160 Cpc- .1464 ETA- .7923SHP<absorb«d)= 212.9514 AVAILABLE SHP IS 45000.0000 (the propeller can notdemand more than the ivailabl* SHP)THE FQLLOUING GROUP IS FOR Xo=.-tOO fNOTE ALL MOMENTS ARE IH FT LBS;AT Xo" .4000 THE BENDING MOMENT IS 50535.5667RT Xo= .4000 THE TORSIONAL MOMENT IS 34183.3510
X Mxo Myo.488 59407.6102 13896. :.829
.475 60380.0900 8753. 5033
.558 60354.3779 4373. 0844
.625 61007.3103 652.8375
.700 60959.5444 -2512.5919
.775 60737.7514 -5213.0832
.858 605-43.8925 -7544.3736
.925 60258. 1747 -9556.7543THE FOLLOWING GROUP IS FOP ;<o= .4750AT Xo» .4750 THE BENDING MOMENT IS 33811.5335AT Xo- .4750 THE TOR 3I0NAL MOMENT IS 59049. I 160
X Mko Myo.475 105421.6572 16141.3945.558 106311.7099 . 3491.5793.625 106631. 7135 1990. 7759.788 106591.4329 -3543.0232.775 106323.3192 -3274.5853.858 105933.5517 -12343.7920.925 105463.5488 -15865.3893
THE FOLLOWING GROUP I-. FOR :-:o= .5500AT Xo- .5500 THE BENDING MOMENT IS :114S27.9004AT Xo« .5500 THE TOR SIONAL MOMENT IS 74595.7943
X Mxo Myo.558 136371.9960 12355.4846.625 136871.7231 4013.3152.788 136895.6654 -3091.2933.775 136623.2034 -9169.4928.858 136171.3775 -14399. 1404.925 135616. 1224 -13927.4050
THE FOLLOWING GROUP IS FOR ;<o- .6250AT Xo- .62?0 THE BENDlr<G MOMENT IS 1128584.6674AT Xo- .6250 THE TOR SIONAL MOMENT IS 80823.3875
X Mxo Myo.625 151727.8247 6721.9553.788 151372.2420 -1 157. 4038.775 151670.9039 -7902.3091.858 151256.5700 -13710. 1237.925 150715.8953 -18741.3015
78
THE FOLLOWING GROUP IS FOR Xo= .7006AT Xo= .rOOO THE EEMDIMG MOMENT IS 138081.8345AT Xo= .7000 THE TORSIONAL MOMENT IS 77733.3941
X Mxo Myo.760 151521. lo27 2253.6468.775 151471.9207 -4474.5349.850 151189.1292 -1827*5.7420.925 150762.8676 -15307.5737
THE FOLLOWING GROUP IS FOR Xo= .7750AT Xo= .7750 THE rE'lPIMG MOMEMT li 119319.4017AT Xo= .7750 THE TORSIONAL MOMENT IS 65324. 314«i
X Mxo Myo.775 136026.2539 1115.3300.850 135969.0551 -4093.9951.925 135757.0394 -aSii.Zdoi
THE FOLLOWING GROUP IS FOR Xo= .3500AT Xo= .8500 THE BENDING MOMENT IS 96297.3690AT Xo= .3500 THE TORSIONmL MOMENT IS 43596.6491
X Mxo Mvo.850 105596.3476 4323.1168.925 105698.4106 1302.7247
THE FOLLOWING GROUP IS FOR Xo= .9250AT Xo= .9250 THE fENDlNG MOMENT IS 61015.7364AT Xo= .9250 THE TOPSIONFiL MOMENT IS 12550.3974
X Mxo Myo.925 60586.9812 14479.3054
THE FOLLOWING GROUP IS FOR Xo= I . 0000,
THERE IS NO GROUP FOR ;<o=l.O! THIS RUN IS COMPLETE.
79
APPENDIX C
SAMPLE CALCULATIONS
Calculations have been made at the seventy percent radial
station (x = 0.7) in both manual and computer modes with the
following input data:
Maximum Velocity 80 kts (Desi.gn Point)
Power Available 45,000 SHP
Ship Resistance 120,000 lbs
Propeller Speed 600 RPM
Submergence 0.5
Wake Fraction 0.0
Number of Blades 6
Density 2.0 (Salt Water)
CALCULATIONS
LINE PARAMETER COMPUTER MANUAL
570 D 9.17 9.2 ft
640 V 80 kts 80 kts
650 T 120,000 lbs 120,000 lbs
660 Ct
0.1162 0.1162
720 J 1.126 1.126
740 J ^ = Jlopt
1.279 1.28
790 Dj_ 10.563 ft 10.56 ft
880 L 0.400 0.407
890 C^to 0.150 0.153
900 C^. 0.160 0.164ti
80
LINE PARAMETER COMPUTER MANUAL
3250^i 0.975 0.922
3290 L.1
0.433 0.4414
3420^bi 0.618 0.6306
3430^b
0.5817 0.582
3440 B 0.527 0,527
3720 Mou 0.0518 0.0518
3730 Mouo 0.00740 0.00740
3770 Wf 0.9463 0.9463
4350 C .-.-, 0.122 0.1675'tidl
Note: The manual value is based on but one point, while thecomputer program is based on ten points.
5360 C. 0.0080 0.0084irc
5370 C,^^, 0.0254 0.0266lldl
5420 Lq 1.678 ft 1.756 ft
5480 C^ 0.16 0.16
5710 Y, 0.0156 0.0156Imax
5720 Y 0.0230 0.0274max
5820 Y 0.0230 0.0274
5830 T, 0.0522 0.0399Ir
5960 Ear 0.3211 0.3200
6150 K2 1.6666 . 1.70
6160 K, 1.000 1.04
6240 Y, 0.0096 0.0109
6250 Y, 0.0160 0.0193Ic
6260 Y 0.0386 0.0339c
81
LINE PARAMETER COMPUTER
6500 Alpha, 0.0395
6560 Pdf 1.4727
6690 Eps7 0.078
6720=tc 0.116
6820 Eta 0.79
MANUAL
0.0394
1.56
0.078
0.155
0.78
82
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Technical Information Center 2
Cameron StationAlexandria, VA 22 314
2. Library, Code 014 2 2
Naval Postgraduate SchoolMonterey, CA 9 39 40
3. Department Chairman, Code 69 1Department of iMechanical EngineeringNaval Postgraduate SchoolMonterey, CA 93940
4. Professor D. M. Layton, Code 6 7Ln 5
Department of AeronauticsNaval Postgraduate SchoolMonterey, CA 9 3940
5. Prof. T. Sarpkaya, Code 69Si 1Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, CA 9 39 40
6. Professor J. F. Sladky, Code 69Zy 1Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, CA 9 3940
7. LT Marc B. Wilson USCG 2
USCGC INGHAM (WHEC-35)4000 Coast Guard BoulevardPortsmouth, VA 2 3 702
8. Dr. Terry Brockett 2David W. Taylor NSRDCCode 1544Propulsor Technology BranchBethesda, Md 200 84
9. Commandant G-MMT 12100 2nd St. SWWashington, D.C. 20593
10. Commandant G-ENE 12100 2nd St. SWWashington, D.C. 20593
83
11. Commandant G-DMT-22100 2nd St. SWWashington, D.C. 20593
12. Commandant G-PTE2100 2nd St. SWWashington, D.C. 20593
84
Thesis X O 1 vj 4 3W64045 Wilsonc.l A simple inter-
active program to de-sign supercavitatingpropeller blades.
f
1 O "' '^
,3Thesis 1. •-1 ._
W64045 Wilsonc.l A simple inter-
active program to de-sign supercavitatingpropeller blades.
thesW64045
^ Simple interactiive program to design s
3 2768 001 90144_DUDLEY KNOX LIBRARY
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