ANALYSIS OF A METHOD EOR OPTIMUMDESIGN OF WATERJET PROPULSION
SYSTEMS.
ftDennis Keith Kruse
LIBlttRV
NAVAL POSTGRADUATE SCHOOLXOOTHBY. CALIP. 93940
ANALYSIS OF A METHOD FOR OPTIMUM DESIGN
OF WATERJET PROPULSION SYSTEMS
by
Dennis Keith Kruse
B.S., U. S. Naval Academy
(1965)
SUBMITTED IN
PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF OCEAN ENGINEER
AND MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF
TECHNOLOGY
^ June, 1973 > y
LIBRARYNAVAL POSTGRADUATE SCHOODMONTEREY, CALIF. 93940
ANALYSIS OF A METHOD FOR OPTIMUM DESIGN
OF WATERJET PROPULSION SYSTEMS
by
Dennis Keith Kruse
Submitted to the Department of Ocean Engineering onMay 11 » 1973. in partial fulfillment of the requirementsfor degrees of Ocean Engineer and Master of Science inMechanical Engineering.
ABSTRACT
An existing computerized method for optimum design ofwaterjet propulsion systems for sub-cavitating hydrofoil craftis analyzed for sensitivity to variations in normally fixedparameters and for sensitivity to variations in. the startingpoints for the search used in the optimization procedure. Acompatible method for off design evaluation of waterjet pro-pulsion systems is developed and incorporated into the opti-mization program in a manner which permits off design evaluationto be performed separately or in conjunction with design. Theevaluation routine requires that system geometry, craft charac-teristics and pump characteristics be specified. System dragand losses are calculated to determine required flow rate andpump head and the corresponding pump speed, efficiency andrequired power are determined. Results of design optimizationfor a series of similar craft are presented and show a strongsensitivity to the input estimate of the take-off drag. Sen-sitivity to starting values of the independent variables wasnoted in some cases and appears to be due to the fact thatjet velocity ratio dominates the other independent variablesas an influence on total system weight. A FORTRAN computerlisting and sample inputs and outputs for both design andevaluation routines are included.
Thesis Supervisor! A. Douglas Carmichael
Title t Professor of Power Engineering
TABLE OF CONTENTS
Title Page 1
Abstract •••••• • •••••• 2
Table of Contents . • 3
List of Figures • ••••• ••••••••• k
List of Symbols Used in Text 5
Chapter 1* Introduction •••••••••• ••• ••• 8
Chapter 2. Methodology Used for Evaluation ••••••••• 11
2.1 Assumed General System Configuration •••• 11
2.2 General Procedure for Evaluation •••••••• 12
2 #3 Specific Evaluation Methodology ••• 13
2,k Cavitation Considerations ••••••••••••••• 2k
Chapter 3 • Design Methodology •• ...•••....... 27
Chapter k* Discussion of Results ••••••••••••••••••• 32
Chapter 5» Conclusions and Recommendations ••••••••• 36
Bibliography 38
Figures •••••••••• •••••••• ........••••. 39
Appendix A. List of Symbols Used in Program .......•• k2
Appendix B • Program Listing • 81
Appendix C. Users' Manual • ..••••. •• 162
LIST OF FIGURES
Figure No. Title Page
1 General Ducting Configuration 39
2 Propulsion Weight Fraction vs. Installed 40Power Propulsive Coefficient at Take-off
3 Cruise Speed Propulsive Coefficient vs. 41Installed Power Propulsive Coefficientat Take-off
4
SYMBOLS USED IN TEXT
Symbol Definition
A area
A nacelle surface area
C nacelle diffuser expansion loss factor
C, nacelle drag coefficient
C . strut drag coefficient
C. spray drag coefficient
C« Schoenherr friction coefficient
C Factor for strut diffuser expansion loss
c strut chord
D diameter
d mean diameterm
f Moody pipe friction factor
g acceleration of gravity
h head loss
H atmospheric headEL
H net positive suction head
K strut diffuser expansion loss coefficient
K. junction mixing loss coefficientj
K.J. form loss coefficient
L nacelle forebody length
L. nacelle diffuser length
N pump RPM
P total pressure
p static pressure
Symbol Definition
pv vapor pressure
Q volume flow rate
q dynamic pressure
RPR ram pressure recovery factor
R bend radius of elbow centerline
RO elbow internal duct radius
s suction specific speed
T thrust
t strut thickness
V velocity
a angle of attack
finozzle depression angle
e diffuser half angle
-*• divergence loss factor
/> density of salt water
<r cavitation number
4>junction angle
Subscript Definition
aux auxiliary inlet
c combined main and auxiliary flow
i main inlet
J jet
n nacelle
t nozzle throat
free stream condition
Subscript Description
1 nacelle inlet
2 nacelle diffuser exit
6 pump inlet
1. INTRODUCTION
Waterjet propulsion has attracted growing interest in
recent years due, in part, to the trend toward the development
of faster and more non-conventional vehicle types such as hydro-
foils and surface-effect ships. These vehicles have made the
potential advantages of waterjet propulsion systems more attrac-
tive, while at the same time lessening some of its disadvantages.
Among the possible advantages are*
a. Reduced vibrations and avoidance of propeller cavita-
tion noise
b. Fewer system components
c. Elimination of underwater appendages
d. Simpler transmission machinery
e. Capable of use in shallow water operations
f
.
Steering control directly from the propulsor
Additionally, the low overall system efficiency which causes
waterjet propulsion to compare unfavorably with conventional
propulsion systems at lower speeds is less of a penalty at
higher speeds.
In light of the increasing interest waterjet propulsion,
a number of studies have been made reviewing the important para-
meters involved in the selection of system components; as well
as considerations for overall system design. This led natur-
ally to efforts to computerize the design process and the most
recent, and most comprehensive, of these efforts is the com-
puterized method for design optimization of waterjet propul-
8
sion systems for hydrofoils developed by R.P. Gill, B.T. Conner,
and R.C. Percival(references 1, 2 and 3).
It is desirable to have a compatible method of evaluating
existing or proposed systems which can be used in conjunction
with such a design method. This will enable existing systems,
as well as alternative design proposals, to be evaluated on a
common basis with the computer produced optimum design. It
would also permit the performance of the computer produced
design, or any other design, to be predicted at speeds other
than the design speeds.
This report presents a revision of the computerized design
method developed by Gill, Conner and Percival which permits it
to be used for system evaluation as well as for its original
purpose of design. The inclusion of the evaluation program
within the design program permits common portions of the program
to be used for both evaluation and design and also permits the
off-design performance to be predicted in conjunction with the
design computations. Additionally, it will permit the accuracy
of the program to be analyzed since it can be used to predict
the performance of existing systems and the predicted performance
can then be compared with measured performance. This could lead
ultimately to refinements and improvements in both the design
and evaluation portions of the program.
This report describes the methodology used in the program,
presents an analysis of results obtained by using the program,
and provides a users* manual as an aid in utilizing the program
and interpreting the output obtained from the program. The
methodology used for evaluation is presented in detail, and the
design routine is summarized briefly. The design routine has
been analyzed for sensitivity of a basic design to variations
in normally fixed parameters and to variations in intial values
of the independent variables. The evaluation routine has been
tested by evaluating the performance of a system designed by the
program at design and off-design conditions. The users* manual,
contained in appendices to this report, describes the use of the
program for design as well as for evaluation; and it contains
listings of required and optional inputs, sample controlling
programs, and sample outputs.
10
2. METHODOLOGY USED FOR EVALUATION
2.1 ASSUMED GENERAL SYSTEM CONFIGURATION
The general configuration of the waterjet propulsion
system used for the evaluation routine is the same as that
which is used in the design routine, and is depicted in Figure
1. The components of the system, in order from inlet to out-
put, are i
1. The nacelle or ram inlet, which includes the auxiliary
inlet, if any, and which is assumed to be of a sub-
cavitating type for the calculations.
2. The strut elbow which derects flow from the nacelle
into the strut and which generally contains either
splitter vanes or turning vanes to reduce internal
losses.
3. The strut which supports the foils and carries the
water into the hull, and which is generally used as a
diffuser in order to avoid cavitation in the pump inlet
piping.
4. The hull elbow which directs the flow from the strut to
the pump inlet piping.
5. The pump inlet piping which consists of one or two el-
bows and either a junction, divergence or straight pipe
depending upon the total number of pumps used.
6. The pump which is driven by a gas turbine engine
through a reduction gear.
7. The nozzle or jet which discharges the water through
11
either the transom or the bottom of the hydrofoil at a
high speed thereby producing the required thrust.
The program assumes that the usual two strut configuration is
utilized.
2.2 GENERAL PROCEDURE FOR EVALUATION
The evaluation procedure assumes that the geometry of the
system is defined in its entirety and that a reliable estimate
of ship drag, ie. that portion of total drag not directly at-
tributable to propulsion system components, is available for
the speeds at which the system will be evaluated. Estimated
values of those components of drag due to the propulsion
system; ie. nacelle drag, strut drag and spray drag, are added
to the ship drag to obtain the estimated total drag and, there-
fore, the estimated required thrust. The required flow rate and
jet velocity are related to the required thrust by the equation,
T =/>Q(V. cos(/0 - VQ ) (1)
The required flow rate and required jet velocity, as well as the
required nacelle inlet velocity, can thus be determined by using
equation (1) together with the one-dimensional continuity equa-
tion for an incompressible fluid,
AiVi - Vo = Q (2)
The flow rate and inlet and jet velocities, together with
the system geometry, are sufficient to permit calculation of
all of the head losses in the system ducting. The total system
head loss and the flow rate can then be used to calculate the
required pump speed and shaft horsepower.
12
The required flow rate and inlet velocity, together with
ship speed and system geometry, are also used to calculate
revised estimates of nacelle drag, strut drag and spray drag.
These values are added to ship drag to obtain a new estimate of
total drag. If the revised total drag differs by more than
one per-cent from the previous estimate of the total drag, the
new estimate is used to calculate a new flow rate and new inlet
and jet velocities. The procedure is then repeated until a
total drag estimate is obtained which differs by less than one-
percent from the previous estimate. The calculated system per-
formance is then output by the program.
The evaluation routine also calculates the structural
weight of the system components and the weight of water en-
trained in the system using the same methods as those used in
the design routine. This provides an additional check to en-
sure that the evaluated system is the same as the designed sys-
tem. Additionally, when an existing system is evaluated, the
calculated weights may be compared with actual weights in order
to provide a check of the weight prediction methods used in the
program. This could eventually result in improvements in the
weight estimation models used.
2.3 SPECIFIC EVALUATION METHODOLOGY
The evaluation routine is begun by inputting the required
parameters to the program and calculating the required flow rate
and jet and inlet velocities in the manner described in the
previous section. The parameters which must be input to the
13
program are*
a. Displacement
b. Prime mover
c. Cross sectional areas and shapes of all systemcomponents
d# Lengths of all system components
e. Bend angles of all elbows in the system
f • Nozzle depression angle
g. Pump type and number of stages
h. Pump blade tip diameter
i. Pump characteristics at design specific speed
j. Depth of submergence of nacelle
k. Height of pump centerline above waterline
1. Craft speeds for which system is to be evaluated
m. Craft drag at evaluation speeds
A more detailed list of both required and optional inputs, in-
cluding the required dimensions and the variable names used in
the program, is contained in Appendix C.
Since it is assumed that the system is of a subcavitating
design, an important consideration in the evaluation of system
performance is a check to determine whether cavitation is occur-
ing within the system at the evaluation speed. Checks for cavi-
tation are made for those points in the system where it is deem-
ed most likely to occur. Within the program, cavitation calcul-
ations are performed concurrently with other calculations; but,
for the sake of clarity and continuity in this report, they
will be described separately in section 2.^«
14
Head loss, drag and estimated weight calculations are per-
formed for each component consecutively in the order in which
the flow passes through them, thus the first component to be
evaluated is the nacelle. Losses in the nacelle are calculated
as three separate components; lip losses, pipe losses and dif-
fuser losses.
When the nacelle subroutine is entered during evaluation,
the first operations performed are the calculation of inlet
velocity ratio, V./V from the input values of V. and V i
and calculation of free stream static pressure, free stream
dynamic pressure, incipient cavitation number, and total pres-
sure for the evaluation speeds.
*o= ^V
o
^oi (po-pv)/qQ
P = p + qo *o Ho
After checking for external cavitation and for cavitation
on the inlet lip, as described in section 2.4, the subroutine
proceeds with the calculation of lip losses. Lip losses are
calculated differently depending on whether or not a positive
indication of inlet lip cavitation was obtained. If cavitation
was indicated, the auxiliary inlet area which must be used to
avoid cavitation is calculated. To accomplish this, the first
step is determining the maximum permissible inlet velocity ratio
by interpolating in the data tables.
The data tables referred to in discussion of ths nacelle eval-
15
uation are the same as those used in the design routine
and are tabulations of the information contained in Tables 1
through 12 and Figures k through 20 of reference 2.
<Wmax = f(L/Dn .<roi .«)
The required auxiliary flow rate is then calculated,
Q = Q - Q.^aux c l
Where
"i = Ai
(Wmax Vo
and Q is the required total flow per nacelle.
The ram pressure recovery of the lip is a tabulated
function of the inlet velocity ratio, now limited to (V//V )max.
The total pressure inside the lip is thus
P. = RPR, . q + pi lipHo yo
and the static pressure inside the lip is
Pi = Pt
- i/>vf.
Pressure recovery of the auxiliary inlet was assumed to be
0,8» The total pressure inside the auxiliary is then given by
P = RPR q + paux . auxHo ^o
The static pressure inside the auxiliary inlet must be the
same as that previously calculated for inside the main inlet lip.
Therefore, the velocity through the auxiliary inlet can be de-
termined by
Vaux " C2(Paux-Pi>//>]
*•
The auxiliary inlet area required is then
aux "" aux' aux*
If this area is less than the total available auxiliary
16
inlet area, the total pressure of the combined flow is calcul-
ated as the mass weighted average of the combining flows.
Pc - < QauxPaux
+ QiPi>/Qc
The average velocity of the combined flow is calculated
from the dynamic pressure
V£
= [2(PC
- Pi )^]*
and the losses are then obtained directly from the pressure
recovery coefficient to this point, which is
RPRc = (VPo'/lo-
If lip cavitation was not indicated initially, then no
auxiliary inlet area is required to be used, and the ram pres-
sure recovery coefficient of the lip is determined directly as
a tabulated function of V./V •1 o
APd
CKtii .
where C is the diffuser expansion loss factor and K. is the
form loss coefficient.
C 3.19xl0~ 3 e2 + 8.452xl0"
4e
Kt
= (1-A1/A
2)
2
is the diffuser half angle.
6 = tan" 1
[(Dg-D^/aiiJ
Pipe loss in the diffuser is
where f is the Moody pipe friction factor which is calculated
within the routine as a function of Reynold's number.
Total internal losses in the nacelle are then
APn
= (1-Pc)(i/V2) [CK
t+ f(L
d/d
m ) + fLauxli/V2.
17
The nacelle drag coefficient is given by
CD=C
f1 l. 5 (Dm/LN
)3/2 7(DB/L
N)3
where Cf
is the Schoenherr friction coefficient which is cal-
culated as a function of Reynold's number in a seperate sub-
routine.
The total external drag is then
D = CD*/VoA
where A is the external surface area of the nacelle, calcul-
ated in the same way as in the design routine, reference 2.
Calculations for the strut elbow are performed by the
same subroutine that handles all of the elbows in the system
and calculations for all of the elbows are performed in the
same manner as in the design. For purpose of the calculations
an elbow is fully defined by specifying the following parameters:
width, depth, cross sectional area, bend angle, and radius ratio.
The radius ratio, R/RO, is the ratio of the radius of the center-
line of the bend to the internal radius of the duct. The inlet
and outlet cross sectional areas are assumed to be equal.
In order to maintain compatibility with the design routine,
the shapes of the elbows are assumed to be the same as the
shapes which are assumed in the design routine. Specifically,
the strut elbow is assumed to be rectangular with the depth
equal to twice the width, the hull elbow is assumed to be
rectangular with the depth equal to one half the width, and the
pump elbow is assumed to be circular in shape. The radius ratios
and bend angles may be specified in the calling program; but.
18
if they are not, they will be assigned the same values as in the
design program. The cross sectional areas must be specified.
The strut subroutine requires that the thickness to chord
ratio, the thickness and chord at the root, the thickness and
chord at the tip, and the inlet and outlet areas be specified.
The shape of the strut internal ducting is assumed to be the
same as that of the strut elbow. The strut length and the dif-
fuser equivalent angle, 20, need not be specified as they are
calculated within the subroutine from other specified para-
meters.
The head losses within the strut diffuser are a combin-
ation of friction losses and expansion losses. The friction
loss coefficient is the Moody friction factor, calculated in
the same manner as in the nacelle subroutine. The expansion
loss coefficient is given by
Ke
= Cs(l-A./A )
2
where C is dependent upon the diffuser equivalent angle, 20,s
and is determined by interpolation in data tables contained in
the subroutine.
Two external drag components, strut drag and spray drag,
are attributable to the strut and are calculated in the strut
subroutine. The drag coefficients for both components are cal-
culated as functions of the thickness to chord ratio. The strut
drag coefficient is given by
Cds
= 2Cfs^ + 2(t/c) + SoCt/c)4]
and the spray drag coefficient is
19
Cdsp= 0.03 (t/c).
The hull elbow losses are determined in the same manner
as previously described for the strut elbow. It may be noted,
however, that the assumed shape for the hull elbow gives it a
more favorable aspect ratio than that of the strut elbow. This,
together with the lower inflow velocity due to diffusion in the
strut, will result in lower losses in the hull elbow than in
the strut elbow.
The pump inlet piping is that portion of the ducting
which connects the hull elbow to the pump inlet. It consists of
a straight pipe, the pump elbow, and a transition piece which
is either a junction, divergence, or another straight pipe de-
pending on whether there are one, four, or two pumps respective-
ly.
The geometry of the pump inlet piping is basically deter-
mined by previous assumptions and previously required inputs
with the only remaining variables being cross sectional area
of the piping and the junction angle, 0. The assumption is
made that the mean velocity is constant throughout the pump
inlet piping, thus the areas of the ducting are fixed by
specifying the area of the hull elbow. The junction angle is
assumed to be zero unless otherwise specified. The divergence
angle need not be specified since it is calculated within the
routine as a function of the distance between the specified
pump location and the specified strut location.
The athwartships pipe makes a transition from a rectangu-
lar shape to a circular shape, but losses due to change of
20
shape are neglected in the calculations. Losses in all straight
pipe sections are calculated using the Moody friction factor in
the manner previously described. Losses for the pump elbow are
calculated in the same manner as for the other elbows in the
system.
The mixing loss coefficient is dependent on the junction
angle, 0, and the divergence loss factor, 7. , and is determined
by
K. 1 +%- 2cos(f(0))J
where
f(0) - 1.40-O.OO58302 .
The divergence loss factor is computed by interpolation
in a data table which is taken from Figure 15 of reference 1.
When a divergence is used, another elbow is required at the
pump entrance. This elbow is treated in the same manner as the
other elbows except that the angle of the bend is equal to the
divergence angle.
The input parameters required for the nozzle calculations
are throat area, jet area, and nozzle depression angle. Nozzle
length is calculated from the pump exit position and the nozzle
depression angle. Nozzle head loss is calculated in the same
manner as in the design routine, where head loss is given by
hn
= [f(Lj/2)/(D
t-D
j) 1-16/(1 + D
t )
lf]Y2/D
j2g
when D. is greater than 1. For D. less than 1, head loss isJ J
assumed to be 1.5% of dynamic head.
With all head losses in the system having thus been deter-
21
mined i they are then summed, the required pump head is calcul-
ated and the pump subroutine is entered for calculation of pump
performance. The required pump head is given by
Hp
= (V2.v2)/2g + heiey+ Ahtotal .
The calculations of pump performance are performed in es-
sentially the same manner as that used by the design routine
for calculating performance at cruise speed. These methods are
described in detail in reference 3 and will only be summarized
here, with emphasis placed on the points where the evaluation
routine differs.
The input parameters to the pump subroutines for evaluation
are pump length, pump type, number of impellers, impeller tip
diameter, and a set of performance characteristics which are
representative of the design condition; ie. a pump speed, pump
head and flow rate which are representative of the design speci-
fic speed of the pump. Additionally, the subroutine utilizes
the required flow rate, required pump head, and various craft
characteristics which are either input or calculated elsewhere
in the evaluation routine.
As in the design routine, the pump characteristic head
and efficiency curves are assumed to be parabolic and off-design
pump speed and efficiency are calculated on that basis. The
off-design pump speed is obtained from the equation
H/HD
- A(Q/QD )
2 + B(Q/QD )(N/ND ) + C(N/ND )
2
where subscript D indicates the design condition. The equation
is solved for N, which is the off-design pump speed. The coef-
22
ficients, A f B and C f are determined for the particular pump
type in the same manner as in the design routine. The off-
design efficiency is calculated in an identical manner after
the design point efficiency has first been determined as a
function of impeller tip diameter in the same way as in the
design routine.
In the design routine , the flow coefficient, head coef-
ficient and suction specific speed are determined and output
for the design condition only. In the evaluation routine these
parameters are determined and output for the evaluated conditions
in order to more fully describe the pump performance at these
conditions.
During design, the pump subroutine calls the gear and fuel
subroutines which are used to calculate reduction gear weight
and weight of fuel required for specified endurance at cruise
speed. These subroutines are also called during evaluation,
but their use is somewhat different than in design. For eval-
uation the gear ratio must be specified whereas in design it is
calculated as the ratio of prime mover design speed to pump
design speed. The type of reduction gear may be either speci-
fied, or selected on the basis of gear ratio and number of in-
puts and outputs in both design and evaluation routines. The
fuel subroutine does not calculate a fuel weight during eval-
uation, but instead, it calculates the fuel consumption rate at
the evaluated speed, assuming the craft is at specified dis-
placement. If the fuel weight is desired to be included in the
23
total system weight output at the end of evaluation, it must
be specified in the inputs.
2.4 CAVITATION CONSIDERATIONS
There are six points, two external and four internal, where
cavitation is most likely to occur, and an important part of the
evaluation of a system is a determination of whether cavitation
is expected to occur at any of these points at the evaluated
speeds. The six points which must be checked for cavitation aret
It The exterior surface of the nacelle.
2. The exterior surface of the strut.
3. Inside the nacelle inlet lip.
4. Inside the strut elbow.
5. At the pump inlet.
6. On the pump impeller.
The check for cavitation on the exterior of the nacelle is
accomplished by interpolating in a data table to obtain the
forebody length to maximum diameter ratio, L/D » for a nacelle
having an external pressure coefficient equal to the negative
of the free stream incipient cavitation number. The inlet to
maximum diameter ratio, D./D , corresponding to this L/D_ isl m ° m
determined by interpolating in another data table. This value
is compared with the actual D./D and if the actual value isi m
greater cavitation can be expected to occur and an indication
to that effect is printed in the output data.
The cavitation number for flow around a strut can be ap-
proximated by
^= [1.15(t/c) + 1]2-1.
24
The incipient cavitation number for flow around the strut is
crjL
= (Ha-p
v)g/|(1.137V
o )
2,
If <ri< <r at the evaluated speed, then cavitation is likely and
is so indicated in the output data.
The check for cavitation on the inside of the nacelle in-
let lip is accomplished by interpolating in a data table to de-
termine the limiting inlet velocity ratio beyond which cavitation
will occur inside the lip#
(V./V ) . f(L/D ,cr . ,<*)i' o max ' m 01'
If V./V at the evaluated condition is greater than (V./V )V o 1 o max
cavitation will occur unless sufficient auxiliary flow is pro-
vided to reduce the effective inlet velocity to that correspond-
ing to (VV,^.The auxiliary inlet area required to provide sufficient
auxiliary flow to avoid cavitation is calculated in the manner
described in Section 2.3« If the required auxiliary inlet area
is greater than the available auxiliary inlet area, then cavita-
tion can not be avoided and the output of the program will indi-
cate that inlet lip cavitation will occur at the evaluated speed.
If cavitation can be avoided only by using some portion of the
auxiliary inlet area, then the output will indicate the aux-
iliary inlet area which is required.
The incipient cavitation number on the turning vanes in
the strut elbow is given by
where subscript 2 indicates conditions at the exit of the nacelle
25
diffuser. The incipient cavitation number, <r, . , is a character-xvi
istic number which has been determined experimentally, thus the
critical velocity at the diffuser exit can be determined.
Vcrit "&ii + 1 -p
1o8S/<^o >3*CV /(1 +9jTl )*l
These two values are compared. If V2max is greater than
V rit cavitation is likely to occur and will be indicated in the
program output.
Cavitation is assumed to occur in the pump inlet if the
local static pressure, p^, is less than vapor pressure, pi or
more precisely, if local dynamic head is less than local total
head minus vapor head, ie. (P^-P*) < ^ p6"^v^'
where P6-p
6= (Q/A
6 )
2/2g
and P/;-P,r= V^/2g + H -P, -P,,.x-v o a loss v
If this condition exists at the evaluated speed, an indication
to that effect is printed in the program output.
Cavitation on the pump impeller is not intrinsically deter-
mined by the program, but the suction specific speed, S, at
which the pump is operating at the evaluated speed is determined
and printed out. The suction specific speed at which cavitation
occurs may vary depending upon the pump design; but, by knowing
the suction specific speed at which the pump is required to
operate, the user can readily determine if the limiting value is
exceeded. The suction specific speed at the evaluated condition
is determined by
s = nqVh°;75
where H - the net positive suction head, is given by
Hsv = V
o/2§+ H
a * Pv " Ploss-
26
3. DESIGN METHODOLOGY
The design methodology used in the design portion of the
program is described in detail in references 1, 2, and 3i and
is summarized here to lend continuity and completeness to this
report.
The design routine uses a directed pattern search to select
a system which is optimized from the standpoint of having the
lowest overall system weight of any satisfactory system. The
system weight includes all structural and machinery weight at-
tributable to the propulsion system, as well as the weight of
all water entrained in the system above the waterline and the
weight of fuel required to provide the specified endurance at
cruise speed. The craft displacement is held constant during
the optimization routine, thus the selection of a minimum
weight propulsion system maximizes the payload for that part-
icular craft.
The variable parameters used in the design optimization
are jet velocity ratio, V ./V , inlet velocity ratio, V./V ,
and nacelle inlet to maximum diameter ratio, D./D • The pat-
tern search subroutine selects different values of these para-
meters for each design iteration and retains the values which
produced the minimum weight system. When the search pattern
has been completed! V ./V . V./V . and D./D are reset to thej o I o l m
values corresponding to the minimum weight system and the
design routine is entered for a final time in order to re-
produce that system.
2?
In addition to V./VQ
, Vi/V ()t and D
i/D
m ; the design
routine requires that at least the following information be
specified to define the craft for which the propulsion system
is being designed!
a* Displacement
b. Range
c. Prime mover
d. Craft speed at take-off and cruise
e. Craft drag at take-off and cruise
f • Depth of submergence of foil
g. Distance of strut from transom
h. Distance of pump exit from transom
i. Height of pump centerline above waterline
The design routine begins by using the inlet and jet
velocity ratios chosen by the pattern search subroutine, to- .
gether with the specified craft speed, to calculate the required
inlet and jet velocities at the cruise condition. The optimum
nozzle depression angle is then determined by
fi -tW-1(Dtatal/A).
These values are then used to calculate the required flow rate
and the required inlet and jet areas.
The design routine then proceeds to size the components
of the system in the same sequence as previously described for
the evaluation routine; and , after each component has been
sized, losses and drags are determined in the same manner as in
the evaluation routine.
28
The nacelle inlet to maximum diameter ratio, as selected
by the pattern search subroutine, determines the amount of dif-
fusion possible prior to the strut elbow. Since the inlet dia-
meter has already been determined, the maximum diameter is
therefore fixed by the diameter ratio. The length of the
nacelle forebody is determined by selecting the length to max-
imum diameter ratio which is just at incipient cavitation on
the external surface at cruise speed. The ratio of inlet to
maximum diameter which corresponds to the forebody shape thus
chosen is compared with that ratio previously specified. If
the previously specified ratio exceeds the maximum ratio allow-
ed by cavitation, the forebody is resized using the maximum
allowable ratio. An iteration is then performed to determine
the overall nacelle length which will result in the least total
power loss due to external drag and diffusion in the ducting.
The inlet area of the strut elbow is set equal to the exit
area of the nacelle diffuser. The elbow shape, radius ratio
and bend angle are determined according to assumptions pre-
viously described for the evaluation routine. The number of
splitters or guide vanes is then determined to minimize losses
in the elbow.
The strut diffuser inlet area and shape is set equal to
the exit of the strut elbow, and the diffuser area ratio is
chosen to avoid cavitation in the pump inlet piping. The ex-
ternal surface of the strut is sized as necessary to enclose
the ducting, and the shape is chosen to avoid external cavi-
29
tation.
The nacelle, strut and spray drags which have been calcul-
ated during this iteration are compared with previous estimates
of these drags. If a significant difference exists, the drag
estimates are revised and calculations begin anewi otherwise the
rest of the system is then designed.
The hull elbow is designed in the same manner as the strut
elbow, and the configuration of the pump inlet piping is select-
ed according to the number of pumps. The pump inlet piping be-
gins with a transition from the shape of the hull elbow to a
circular shape, and the rest of the piping is circular is shape.
The size of the pump inlet piping is chosen to maintain a con-
stant velocity throughout its length.
The nozzle is assumed to have an inlet area equal to the
pump outlet area. This and the jet area which has been previous-
ly determined are used to calculate losses in the nozzle.
The ducting losses prior to the pump are used to deter-
mine net positive suction head, and nozzle losses are added to
determine the required pump head. Two basic pump designs are
considered i axial with an inducer impeller, and centrifugal
with double suction impellers. The alternative pumps are sized
by using assumed specific speeds, flow coefficients and impeller
diameter ratios for each alternative. The number of axial stages
is determined by cavitation criteria, while the number of stages
in the centrifugal pump is chosen to minimize combined pump,
gear and fuel weight. The required gear ratio is determined
30
as the ratio of prime mover normal operating speed to required
pump speed at take-off and this ratio, together with the re-
quired shaft horsepower at take-off, determines the type and
size of gear to be used. The fuel weight required to provide
the specified endurance at cruise speed is calculated for each
alternative design, and that pump design which requires the
lowest combined weight of pump, gear and fuel is then chosen
as the pump to be used by the design.
31
k. DISCUSSION OP RESULTS
Sample outputs for both the evaluation and the design
routine are contained in Appendix C. The format used for output
from the evaluation routine is essentially the same as that used
for design. This permits maximum compatibility within the out-
put subroutine; and, additionally, facilitates comparison of
data produced by. the design routine with that produced by the
evaluation routine for the same or any other system.
The design routine was analyzed for sensitivity of a basic
design to variations in initial values of the independent vari-
ables and to variations in normally fixed parameters. The basic
design used in the analysis was for a 750 ton hydrofoil with a
take-off speed of 30 knots, a cruise speed of 45 knots, and an
endurance of 2000 miles at cruise speed. Two LM2500 gas tur-
bines were the specified prime movers, and the specified number
of pumps was two.
In most cases there was little or no variation in the result-
ing system design when the starting values of the independent
system parameters were varied. In some cases, however, signifi-
cant variations occured with total system weight varying by as
much as 3.5$. In those cases where results did vary, the jet
velocity ratio of the resulting design deviated very little from
that of the basic design. The inlet velocity ratio and nacelle
diameter ratio both varied over a considerable range, however,
consequently the changes in system weight resulted primarily
from changes in the nacelle and strut designs. This suggests
32
that the optimum design is primarily defined by the jet velocity
ratio and that the inlet velocity ratio and nacelle diameter
ratio become important only after the optimum jet velocity ratio
has been determined. This may also explain the apparent lack of
correlation between inlet velocity ratio and other parameters
in designs produced by the program. Further study of this
problem is needed and it may be necessary to revise the design
routine so that once an initial solution is obtained, the jet
velocity ratio is fixed at the resulting value while further
variations in the other two system parameters are explored.
The results showed a considerable sensitivity to varia-
tions in craft drag; particularly that component of drag which
is not directly attributable to the propulsion system, referred
to here as ship drag. Ship drag is a craft characteristic which
is independent of the propulsion system design and it is held
constant at the input value throughout the design calculations.
Relatively small variations in ship drag produced comparatively
large changes in total system weight. This sensitivity is ap-
parently due to the fact that the cases studied for this report
fall in a region where the selection of a system design is con-
strained by a power limitation imposed by the specified prime
movers. If there were no power limitation * the optimum system
would have a very high jet velocity ratio and consequently a
low volume flow rate thereby reducing both ducting weight and
the weight of entrained water. If take-off drag, and therefore
the required take-off thrust, is so high that a power limita-
33
tion is imposed; then the jet velocity must be reduced in order
to reduce the required pump head sufficiently to bring required
power back within limits. The reduction in thrust due to the
lowered jet velocity must then be compensated for by increasing
the flow rate. This requires larger and heavier ducting and
results in a larger volume of entrained water. This suggests
that the optimum combination of craft and propulsion system
would be one in which the propulsion system design selected by
the design routine just bordered on being power limited.
In view of the above discussion, it appears that the pro-
pulsion coefficient based upon installed horsepower is an impor-
tant system parameter since it is basically a measure of the
fraction of installed horsepower required to overcome drag.
PCi = (Dtotal
V)/(55 ° SHPi»
The propulsion weight fraction and the propulsive coefficient
based on used horsepower at cruise speed are plotted against the
installed power propulsive coefficient at take-off in Figures 2
and 3 respectively. The curves are plotted for designs in which
ship drag was the only parameter varied. The other points plot-
ted represent designs in which other parameters were varied.
The results also showed some sensitivity to variations in
the strut length. This was to be expected since reducing the
strut length would reduce the required pump head as well as
reducing the amount of ducting and entrained water in the
system. The sensitivity was not nearly as pronounced as the
sensitivity to ship drag.
3^
The evaluation routine was tested by evaluating systems
designed by the design routine at both design and off design
speeds. The results were satisfactory and, when the evaluation
conditions were the same as design conditions, the operational
characteristics of the system as determined by the evaluation
routine were nearly identical to those calculated by the design
routine.
35
5. CONCLUSIONS AND RECOMMENDATIONS
A computer program to evaluate the performance of a
waterjet propulsion system has been developed and incorporated
into the program for design optimization of waterjet propulsion
systems. The evaluation routine can be used successfully to
evaluate a wide array of possible system configurations. A
lack of available data on the configuration and performance of
existing systems precluded the use of the evaluation routine to
analyze the performance of an actual system for this report*
When such information is available, it is recommended that this
be done. The results obtained from the evaluation routine could
then be compared with actual performance data to further eval-
uate the accuracy of the methods used in the program.
The sensitivity of the design routine to initial values of
the independent variables requires further study. The use of
either a random search or an additional pattern search is sug-
gested to explore further variations in inlet velocity ratio
and nacelle diameter ratio once the best jet velocity ratio has
been determined in the manner currently used in the program.
The results of the design routine are highly sensitive to
variations in ship drag when the available power is barely
adequate for the design conditions. This indicates that the
total hydrofoil design should be carefully tailored to the prime
mover so that the total power required at design conditions is
somewhat less than the total available power in order to allow
for growth. If the hydrofoil is designed so that maximum
36
available horsepower is required at either take-off or cruise
condition, the specified craft conditions must include an ade-
quate margin for growth. If not, a serious degradation of per-
formance would occur when the inevitable growth took place
because, if maximum power is already being used, there would be
no way of increasing available thrust to compensate for increased
drag without exceeding the power limitations of the prime mover.
37
BIBLIOGRAPHY
1. Gill, R.P., Design Optimization of Waterjet PropulsionSystems for Hydrofoils, Ocean Engineer Thesis, M.I.T.,May 1972.
2. Conner, B.T., A Study of Ram Type Intake Parameters,Ocean Engineer Thesis, M.I.T., June 1972.
3. Percival, R.C., Optimization of Waterjet Propulsion Pumpsfor Hydrofoil Applications, Ocean Engineer Thesis, M.I.T.,May 1972.
4. Brandau, J.H., Performance of Waterjet Propulsion Systems -
A Review of the State of the Art, Journal of Hydronautics,vol, 2, no. 2, pp. 6l-73t April 1968.
5. Arcand, L. and Comolli, C, Optimization of Waterjet Pro-pulsion for High Speed Ships, Journal of Hydronautics, vol.2, no. 1, pp. 2-8, 1968.
6. Chironis, E.P. ed., Gear Design and Application* McGraw-HillBook Co., New York, 1967.
7. Hatte, R. and Davis, H. , Selection of Hydrofoil WaterjetPropulsion Systems, AIAA Paper 66-732, August I966.
8. Hoerner, S.F., Fluid Dynamic Drag, published by author,1965.
9. Johnson, V.E., Waterjet Propulsion for High Speed Hydro-foil Craft, AIAA Paper 64-306, June 1964.
10. Levy, J., The Design of Waterjet Propulsion Systems forHydrofoil Craft, Journal of Marine Technology, vol. 2,no. 1, pp. 15-26, January 1965*
11. Traskel, J. and Beck, W.E., Waterjet Propulsion for MarineVehicles, AIAA Paper 65-2^5, March I965.
38
}
TOP VIEW
-*- V
FIGURE 1 : GENERAL DUCTING CONFIGURATION
39
o
&4
0.7
0.6
5 0-5
0.4
ow
a °- 3
w
0.2
0.1
0.0
TWO LM 2500 f s
TWO PUMPS
750 TON DISP.
2000 MILE RANGE
30 KNOT TAKE-OFF
45 KNOT CRUISE
_i_ j_
WITH FUEL
A WITHOUT FUEL
0.0 0.1 0.2 0.3
INSTALLED POWER PROPULSIVE COEFFICIENT AT TAKE-OFF
FIGURE 2: PROPULSION SYSTEM WEIGHT FRACTION VS. INSTALLED
POWER PROPULSIVE COEFFICIENT AT TAKE-OFF
40
0.7
0,6
0.5
0.4
0.3-
wMOH&,
&Oow>MWE3OhOos
QWwOh
wa 0.2
OSo
0.1 -
0.0
TWO LM 2500'
s
TWO PUMPS
750 TON DISP.
2000 MILE RANGE
30 KNOT TAKE-OFF
45 KNOT CRUISE
© ONLY DRAG VARIED
A OTHER PARAMETERS VARIED
0.0 0.1 0.2 0.3
INSTALLED POWER PROPULSIVE COEFFICIENT AT TAKE-OFF
FIGURE It CRUISE SPEED PROPULSIVE COEFFICIENT VS. INSTALLED
POWER PROPULSIVE COEFFICIENT AT TAKE-OFF
41
APPENDIX A
LIST OF SYMBOLS USED IN PROGRAM
SYMBOLS USED IN COMMON Jj-3
SYMBOLS USED IN H20JT NOT IN COMMON 56
SYMBOLS USED IN FCT NOT IN COMMON 58
SYMBOLS USED IN NACEL NOT IN COMMON 60
SYMBOLS USED IN ELBOW NOT IN COMMON 65
SYMBOLS USED IN STRUT NOT IN COMMON 6?
SYMBOLS USED IN JUNCT NOT IN COMMON 69
SYMBOLS USED IN PIPE NOT IN COMMON 70
SYMBOLS USED IN DIVRG NOT IN COMMON 71
SYMBOLS USED IN NOZZL NOT IN COMMON 73
SYMBOLS USED IN PUMP NOT IN COMMON 7^
SYMBOLS USED IN FUEL NOT IN COMMON 77
SYMBOLS USED IN PTTRN NOT IN COMMON 78
SYMBOLS USED IN OUTPUT NOT IN COMMON 79
kZ
Label
PARMS
DRAG
FLOW
LIST OF SYMBOLS
USED IN COMMON
VariableName Subscript
VJVO
VIVO
DIDM
TDRAG(I) I
1
2
3-5
STRTD(I)
POD(I)
SPRAY ( I
)
REST(I)*
VO(I)
TRIM(I)
Q(I)
De script ion/U sage
System parameters
Jet velocity ratio
Inlet velocity ratio
Inlet diameter tomaximum nacelle diameterratio
Drag estimates
Total craft drag atcondition I, pound force
Cruise condition
Take-off condition
Evaluation conditions
Strut drag at conditionI, pound force
Nacelle drag at conditionI v pound force
Spray drag at conditionI, pound force
TDRAG ( I ) -SPRAY ( I ) -STRTD ( I
)
-POD(I),pound force
Craft velocity at conditionIt foot per second
Craft trim angle at con-dition I, degree
Flow characteristics
Volume flow rate at con-dition I, cubic foot persecond
*3
Label
ELBW
CHARS
VariableName
AIN
AJET
AREA(ICOMP)
VJ(I)
VI(I)
Subscript Description/Usage
Inlet area, square foot
Jet area, square foot
Ducting cross-sectionalarea at station ICOMP,square foot
Jet velocity at conditionI, foot per second
Inlet velocity at con-dition I, foot per second
Elbow data
XK(IELB) IELB Radius ratio of elbowIELB
1 Strut elbow
2 Hull elbow
3 Pump elbow
4 Divergence elbow
RO(IELB) Duct radius at elbowIELB, degree
THATA ( IELB
)
Angle of bend of elbo
WIDTH
DEPTH
TYPE(3»ITYPE)
WGTS(LS,LC)
IELB, foot
Width of duct at elbowinlet
Depth of duct at elbowinlet
Contains name of elbowshape ITYPE
System characteristics
Weight of component LC
,
pound
M
LabelVariable
Name Subs
LS
cript Description/Usage
1 Structure
2 Water (or fuel)
LC
1 Nacelle
2 Strut elbow
3 Strut diffuser
k Hull elbow
5 Athwartships length
6 Pump elbow
7 Transition piece
8 Pump
9 Nozzle
10 Reduction gear
11 Fuel
12 Prime mover
13 Lift from nozzledepression
14 Total weight
15 Spare location
CGS(LG.LC) Centers of gravity <
LG
component LC, excludingfuel, gearbox, or primemover, foot
1 Structure vertical centerof gravity (from keel)
^5
LabelVariable
Name Subscript
2
3
DELH(I.ICOMP)
ICOMP
8
9
10-15
CGSX
CGSZ
H20
TEMP
PV
RHOW
Description/Usage
Structure longitudinalcenter of gravity(from transom)
Water vertical center ofgravity, (from keel)
Water longitudinal centerof gravity, (from transom)
Total head loss up to andincluding component ICOMPat condition I, foot
Same as defined except
Nozzle head loss only
Total system head loss(including elevation),DELH(I,9)=DELH(I,8)+DELH(I,7)
Spare locations
Total longitudinal centerof gravity systemexcluding gearbox, primemover and fuel, fromtransom, foot
Total vertical center ofgravity of system exclud-ing gearbox, prime moverand fuel, from keel, foot
Sea water (3*5% salinity)properties
Temperature, degreeFahrenheit
Vapor head, foot
Density, pound forcesecond squared per footto the fourth
46
Label
TOLER
PSUB
VariableName
GNU
HA
DELTA
GERAT(NSTG)
SHP(I.NSTG)
RPM(I,NSTG)
PERF(L,IENGN)
Subscript Description/Usage
Viscosity, footsquared per second
Atmospheric head, foot
Check for optimum system
Pump system
Gear ratio required forpump NSTG
Shaft horsepower perprime mover requiredat condition I for pumpNSTG, horsepower
Axial speed of pump NSTGat condition I, revo-lution per minute
Prime mover IENGNCharacteristics (L)
L
1
5
ETAP(I.NSTG)
Maximum normal horsepowerat design speed, horse-power
Maximum intermittenthorsepower at designspeed, horsepower
Specific fuel consump-tion (SFC) at design speedand maximum normal horse-power, pound fuel perhorsepower hour
Design speed, RPM
Prime mover weight, with-out auxiliaries, pound
Efficiency of pump NSTGat condition I
^7
Label
SHIP
NACLL
VariableName Subscript
I
7
6,8
DISP
RANGE
BEAM
HS
HE
HCL
XLS
XLPE
XLP
DRAT
DM
A TA J.
AIAUX
ELEXT
ELENT
Description/Usage
Same as defined except
Reduction gear
Spare locations
Craft characteristics
Craft displacement, pound
Endurance, nautical mile
Beam, foot
Depth of submergence offoil, foot
Height of pump centerlineabove mean water, foot
Height of pump centerlineabove keel, foot
Distance of centerlineof strut root from transom,foot
Distance of pump exitfrom transom, foot
Length of pump, foot
Nacelle characteristics
Diameter ratio, Dl/DM
Maximum external diameter,foot
Inlet area per nacelle,square foot
Auxiliary inlet area pernacelle, square foot
Length of forebody, foot
Length of lip, foot
kQ
Label
CONST
STRTC
INDEX
VariableName
ELAUX
ELDIF
ELN
AAX(I)
PI
G
RHOD
TC
T
C
Tl
CI
CFM
IEVAL
Subscript Description/Usage
Length due to auxiliaryinlet, foot
Length of diffuser, foot
Length of nacelle, foot
Portion of auxiliaryinlet area in use atcondition I, square foot
Constants
3.14159265
Acceleration of gravity,32.174, foot per secondsquared
Density of steel, 480,pound per cubic foot
Strut characteristics
Thickness to chord ratio
Thickness at root, foot
Chord at root, foot
Thickness at tip, foot
Chord at tip, foot
Chord at flying water-line, foot
Indices for programcontrol
<0
=0
Design/evaluation index
Evaluate at IEVAL points,no design
Design at cruise and take-off conditions only
49
LabelVariable
Name
IEQPT
ISTRT
NUMB
IENGN
Subscript
>0
1
3
1
3
2+|lEVAL
1
2
3
5
6
7
8
9
10
Description/Usage
Design at cruise and takeoff conditions and eval-uate at IEVAL points
No equipments or config-uration entered; totalsystem design/evaluation
Number of gas turbines isspecified
Number of gas turbines andnumber of pumps are speci-fied
Initial program condition
Design and/or evaluate
Evaluate only
Final program condition
Design only
Design and/or evaluate
Prime mover type
TF 35
TF 40
Proteus, 1500 rpm
Proteus, 1000 rpm
Tyne 1A
Tyne 1C
FT12A
LM 1500
LM 2500
FT4A-2C
50
LabelVariable
Name Subscript
11
Description/Usage
FT4A-12
12 FT^C-2
ITYPE Elbow shape
1 EllipseV
2 Circle
3 Rectangle
k Square
ICOMP Component index
1 Nacelle outlet
2 Strut elbow
3 Strut diffuser exit
4 Hull elbow
5 Athwartships length
6 Pump elbow
7 Transition piece
8 Pump inlet
9 Nozzle throat
NPUMP Number of pumps
NGT Number of gas turbines
IGEAR Type of reduction gear
1 Single reduction with idler
2 Planetary
3 Double reduction, doublebranch
ITABL Interpolation parameters
51
Label
CDRAG
WEGT
PUMM
VariableNames
CSTRT(I)
CPOD(I)
CSPRY(I)
XWD(NSTG)
XWW(NSTG)
XWG(NSTG)
XWF(NSTG)
QQ(I)
DlS(NSTG)
D2S(NSTG>
XNS(NSTG)
SM(I.NSTG)
PLP(NSTG)
NSTG
Subscript Description/Usage
Computed drags
Computed strut drag atcondition I, pound force
Computed nacelle drag atcondition I, pound force
Computed spray drag atcondition I, pound force
Pump, gear and fuel weights
Pump NSTG dry weight,pound
Pump NSTG wet weight,pound
Gearbox weight associatedwith pump NSTG, pound
Fuel weight associatedwith pump NSTG, pound
Pump characteristics
Flow rate per pump atcondition I, cubic footper second
Inlet tip diameter ofpump NSTG, foot
Exit tip diameter of pumpNSTG, foot
Specific speed of pumpNSTG, cfs units
Suction specific speed ofpump NSTG at condition I,cfs units
Length of pump NSTG, foot
Indicator of pump type
1 Axial pump with singleinducer impeller
52
LabelVariable
Name
HEAD
SHI (I, NSTG)
XIM
HPP(I)
HSV(I)
THOM(I)
PHI (I, NSTG)
WF
WG
FRATE(I)
PINLP
Subscript Description/Usage
2 Axial pump with inducerand one impeller stage
3 Axial pump with inducerand two impeller stages
k Centrifugal pump withmaximum of ten paralleldouble suction impellers
5 Spare location
Head coefficient of pumpNSTG at condition I
Number of parallel doublesuction impellers forcentrifugal pump
Number of impellers, notincluding inducer, forcentrifugal pump
Pump flow characteristics
Pump head at condition I,foot
Net positive suction headat condition I, foot
Thoma's cavitation indexat condition I
Flow coefficient of pumpNSTG at condition I
Working variable for fuelweight, pound
Working variable for gearweight, pound
Fuel consumption rate atcondition I, pounds perhour
Pump inlet piping para-meters
53
Label
WARN
NOZL
VariableName
ALPHA
IFUEL
IPUMP
TYGER
Subscript Description/Usage
Junction angle
Warning generated duringevaluation
CAV(I,,J) J Cavitation indicator atcondition I at location J
1 Nacelle exterior
2 Strut exterior
3 Nacelle inlet lip
4 Strut elbow
5 Pump inlet
6 Pump impeller
Nozzle characteristics
JANGL Nozzle depression angle
***** Unlabeled common variables
.TRUE.
.FALSE.
.TRUE.
.FALSE.
.TRUE.
Logical variable for fuelcalculation
Make fuel calculation
Do not make fuel calcula-tion
Logical variable for pumpcalculation
Pump design parametershave been calculated/speci-fied
Pump design parametershave not been calculated/specified
Logical variable for gearcalculation
Gear type is specified
5^
VariableLabel Name Subscript Description/Usage
•FALSE. Gear type is to beselected by program
55
Variable
PARM(3)
ENGN(3,IEGN)
EHP(I)
DEL(3)
DELMIN(3)
VK(I)
IPRNT
DISPL
IN
MAX
XJ
IK
IL
KM
Kl
WEIGT
IM
DISPL
I
IJ
J
VARIABLES USED IN H20JTNOT IN COMMON
Description
Working system parameters
Contains name of engine IENGN for output
Effective horsepower at condition I, horsepower
Initial step sizes of system parameters
Minimum step sizes of system parameters
Craft speed at condition I, knot
Print data set reference number
Craft displacement, long ton
Estimate of minimum number of gas turbinesrequired to power craft
Estimate of maximum number of gas turbinesneeded to power craft
Working variable for number of gas turbines
Working variable for craft condition I
Working variable for IN
Minimum number of pumps to be used for XJgas turbines
Maximum numberof pumps to be used for XJ gasturbines
Propulsion system weight, long ton
Working variable for prime mover character-istic L
Craft displacement, long ton
Index for do loops
Working variable for check on power adequacy
Index for do loop
56
Variable
ISAVE
N
XMIN
MK
JNUM
Description
Working variable for MAX
Working variable for output of prime movertype
Factor for minimum acceptable prime moverSHP operation
Working variable for prime mover character'istic L
Working variable for NUMB
57
Variable
APOD(I)
ASTRT(I)
ASPRY(I)
C(I)
TSUM
DSIG
TOTAL
SIGMA
SUMZ
SUMX
SUM
ZSUM
XSUM
SPD
J
JDRAG
1
2
LIST OF VARIABLES USED IN FCTNOT IN COMMON
Description
Difference between present and previousnacelle drag calculations at conditions I,pound force
Difference between present and previous strutdrag calculations at condition I, pound force
Difference between present and previous spraydrag calculations at condition I, pound force
Margin factor for thrust at condition I
Working variable for propulsion system weight,pound
Working variable for SIGMA
Total head less vapor head, foot
Head above vapor head, foot
Working variable for moment in vertical plane,due to weights, foot pound force
Working variable for moment on longitudinalplane due to weights, foot pound force
Working variable for system weights, pound
Total moment in vertical plane due to weights,foot pound force
Total moment on longitudinal plane due toweights, foot pound force
Working variable for jet velocity calcula-tion, foot per second
Working variable for NUMB
Indicator of acceptable drag accuracy
New drag calculation is within $% of previouscalculation
New drag calculation is greater than 5% ofprevious calculation, redesign strut andnacelle
58
Variable
ANGLE
COEF
1
KOUNT
I
PARM(K)
K
1
2
DDRAG ( I
)
DSPRY(I)
DSTRT ( I
)
DPOD(I)
Description
Optimum nozzle depression angle , radian
Factor for nacelle drag calculation
Strut must be resized due to cavitation
Use nacelle design
Working variable for craft condition I
Craft condition
Working variable for system parameters
VJVO
VIVO
Previous acceptable total drag calculation atcondition I, pound force
Previous acceptable spray drag calculation atcondition I, pound force
Previous acceptable strut drag calculation atcondition I, pound force
Previous acceptable nacelle drag calculationat condition I, pound force
59
Variable
ZK
SPO
PVP
SIGTV
JNUMB
I
CPEX
K
J
XD
DIDMX
QI
DI
CPIN
QIN
QC
QAUX
KDEX
VR
KNUMB
LIST OF VARIABLES USED IN NACELNOT IN COMMON
Description
Percentage of auxiliary inlet area permittingflow
Static pressure at inlet, pound per squarefoot
Vapor pressure, pound per square foot
Incipient turning vane cavitation number,referenced to diffuser exit velocity
Working variable for NUMB
Craft condition, also index for do loops
Peak external pressure coefficient
Working index for do loop for ELEXT/DM values
Working index for do loop for VIVO values
Length of forebody to maximum diameter ratio,ELEXT/DM
Maximum permissible diameter ratio
Flow rate per strut, cubic foot per second
Nacelle inlet diameter, foot
Peak internal pressure coefficient
Take-off flow rate per nacelle through inlet,cubic foot per second
Take-off flow rate per nacelle, total, cubicfoot per second
Auxiliary flow rate required to avoid cavita-tion, cubic foot per second
Counter for iterations on diffuser length
Velocity ratio at take-off condition, basedon flow through inlet
Working variable for NUMB
60
Variable Description
VIJ
PRLJ
YI2
PRL2
PTI
SPI
VIAUX
PRAUX
PTAUX
DYP
PC
QDIF
PHI
PHS
X
D2
Dl
ELMAX
ELMIM
II
Inlet velocity at evaluation condition,based on flow through inlet
Pressure recovery coefficient of lip atevaluation condition
Inlet velocity at take-off condition, basedon flow through inlet
Pressure recovery coefficient of lip at take-off
Inlet stagnation pressure immediately aft oflip at take-off, pound per square foot
Inlet static pressure immediately aft of lipat take-off, pound per square foot
Inlet velocity in auxiliary inlet, foot persecond
Pressure recovery of auxiliary inlet
Stagnation pressure inside auxiliary inlet,pound per square foot
Net dynamic pressure immediately aft of lip,pound per square foot
Average inlet stagnation pressure of combinedflow, pound per square foot
Working variable for diffuser flow rate,cubic foot per second
Equivalent angle of forebody, radian
Sine of equivalent angle of forebody
Length of auxiliary inlet, foot
Diffuser exit diameter, foot
Inlet diameter, foot
Maximum permissible length of diffuser, foot
Minimum permissible length of diffuser, foot
Working variable for craft condition I
61
Variable
EL
DEL
ELD
ELL
ELFAC
DDM
XKT
REL
RED
DL
CDRG
ANGL
CDIF
POW
POWI
EM
AEXN
REND
DDIF
PLOSS
VAOUT
SQUAR
Description
Working variable for diffuser length, foot
Working variable for change in diffuser length,foot
Working variable for nacelle length, foot
Working variable for nacelle length, foot
Working variable for excess in nacelle lengthdue to diffuser, foot
Average diffuser diameter, foot
Form loss coefficient of diffuser
Reynolds number, based on nacelle length
Reynolds number, based on inlet diameter
Ratio of maximum external diameter to nacellelength
Computed drag coefficient
Equivalent half angle of diffuser, degree
Diffuser expansion factor
Power loss due to drag and duct loss ofdiffuser, horsepower
Previous power loss calculation for diffuserlength, horsepower
Factor in wetted surface calculation
Wetted surface area, square foot
Reynolds number, based on inlet diameter
Total pressure loss in diffuser, pound persquare foot
Total pressure loss in nacelle, pound persquare foot
Average exit velocity, foot per second
Factor in critical velocity calculation
62
Variable Description
VCRIT
VMAX
RENL
NL(2)
ML(2)
KL(2)
JL(2)
IL(2)
VRT(6)
XDT(IO)
PRLT ( 6
)
SIGI(I)
PTO(I)
XDTT(J)
CDUMX(K)
CDUMY(L)
CD(I)
DIDMT(J)
VRTT(J)
DLIP(I)
QO(I)
VELR(I)
Critical velocity in strut elbow, foot persecond
Maximum velocity at nacelle exit, foot persecond
Reynolds number, based on nacelle length
Interpolation parameters
Interpolation parameters
Interpolation parameters
Interpolation parameters
Interpolation parameters
Data array of velocity ratios
Tabulated forebody length to inlet diameterratios
Tabulated lip pressure recovery coefficients
Free stream cavitation index at condition I
Stagnation pressure at craft condition I,pound per square foot
Tabulated ELEXT/DM ratios for trim angle J
Dummy array of peak pressure coefficients forVIVO K
Dummy array of velocity ratios for ELEXT/DM L
Drag coefficients at craft condition I
Tabulated Dl/DM values for ELEXT/DM J
Dummy array of velocity ratios for angle ofattack (J), internal
Lip loss coefficient at craft condition I
Free stream dynamic pressure at craft conditionI, pound per square foot
Inlet velocity ratio at craft condition I
63
Variable
TLIP(I)
VRTEX(I)
VRMAX(I)
FRICT
Description
Working variable for DLIP(I)
Same as VRTT(I) but external
Maximum permissible velocity ratio at craftcondition I
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
6J+
Variable
SHAPE(3tITYPE)
THETA(J)
XLOSS(J)
ROA(IO)
RE
FRICT
CORR
REMAX
KOUNT
IELB
FACTR
RIN
ROUT
RATIO
XN
N
1
2
3
4
VARIABLES USED IN ELBOWNOT IN COMMON
Description
Contains name of shape ITYPE
Data array of elbow angles
Data array of elbow loss coefficients withthin, circular arc turning vanes
Outside radius of splitters, foot
Reynolds number of duct
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
Function statement, calculates head losscorrection factor for different Reynoldsnumbers
Maximum Reynolds number permitted for splitterloss equation
Working variable for craft condition I
Index indicating which elbow is beingdesigned/evaluated
Strut
Hull
Pump
Divergence
Factor used in splitter loss calculation
Inside radius of bend, foot
Outside radius of bend, foot
Desired radius ratio, 4.3
Number of subdivided elbov/s required toachieve RATI0=4.3
Number of subdivided elbov/s used
65
Variable
Nl
SUM
RIA
V
HGT
AA
RAD
XCORR
XKT
DIAM
VOLV
VOL
AREA1
IJ
IK
I
RATEO
HEAD
Description
Number of splitters corresponding to N
Working variable of sum of head times sub-divided elbow area, foot cubed
Inside radius of subdivided elbow, foot
Average velocity, foot per second
Height of subdivided elbow, foot
Equivalent cross-sectional area of subdividedelbow based on HGT , square foot
Equivalent radius of subdivided elbow, foot
Ratio of head loss correction factors fordiffering Reynolds numbers
Head loss coefficient of subdivided elbow
Equivalent diameter, foot
Volume of splitters, cubic foot
Volume of splitters and elbow structure,cubic foot
Duct area per elbow, square foot
Working variable for shape determination
Working variable for shape determination
Working variable for number of subdividedelbows N
Ratio of inside radius to outside radius ofsubdivided elbows
Average head loss in elbow, foot
66
Variable
THET2
EXPAN
ARATO
VL
SIGMA
SIGMI
CM
DEIN
WIDE
DEOUT
DEAVE
STRT
XLONG
STAN
THETA
ECOEF
FORML
VELIN
VLOUT
RES
CDS
CDSP
RE
LIST OF VARIABLES USED IN STRUTNOT IN COMMON
Description
Array of data of equivalent angle of dif-fuser, degree
Array of data of expansion coefficient
Area ratio of strut diffuser
Local maximum velocity, external, foot persecond
Local cavitation number, external
Incipient cavitation number, external
Mean chord, foot
Strut inlet equivalent diameter, foot
Width of duct at strut exit, foot
Strut exit equivalent diameter, foot
Average equivalent diameter, foot
Vertical strut length, foot
Actual strut length, foot
Arctangent of equivalent diffuser angle
Equivalent angle of diffuser, 29, degree
Diffuser expansion factor
Diffuser expansion loss coefficient
Average inlet velocity, foot per second
Average exit velocity, foot per second
Strut Reynolds number, based on mean chord
Strut drag coefficient
Spray drag coefficient
Duct Reynolds number, based on inlet velocity
67
Variable
PIPEL
TOTAL
HEAD
KOUNT
HGT
CGWS
Description
Duct friction loss coefficient
Total loss coefficient
Head loss of diffuser, foot
Working variable for craft condition I
Elevation of strut, foot
Vertical center of gravity of duct, foot
68
Variable
DIAM
FRCTL
KOUNT
AJCT
FRCTJ
XLAMD
FLONG
AJCTL
AMIXL
V
XPUMP
RE
BETA(J)
ALAMD(J)
FRICT
LIST OF VARIABLES USED IN JUNCTNOT IN COMMON
Description
Duct diameter, foot
Friction loss coefficient for athwartshipslength
Working variable for craft condition I
Length of fore and aft ducting to pump inlet,foot
Friction loss coefficient for junction
Working variable for AMIXL calculation
Length of athwartships ducting, foot
Total loss coefficient of junction
Mixing loss coefficient of junction
Average velocity, foot per second
Number of gas turbines + 1
Reynolds number of duct
Data array of junction angles, degree
Data array of mixing loss coefficientcorresponding to BETA(J)
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
69
Variable
KOUNT
V
DIAM
RE
APIPE
FRCTL
XPUMP
XKT
XLONG
FRICT
LIST OF VARIABLES USED IN PIPENOT IN COMMON
Description
Working variable for craft condition I
Average velocity, foot per second
Duct diameter, foot
Reynolds number of duct
Length of fore and aft pipe to pump inlet,foot
Friction loss coefficient for athwartshipslength
Number of gas turbines
Friction loss coefficient of fore and aftlength
Length of athwartships pipe, foot
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
70
Variable
FRICT
KOUNT
RE
DIVL
DWGT1
DWGT2
DWGT3
WWGT1
WWGT2
WWGT3
CGWX1
CGWX2
CGWX3
DIAM
FRCTL
DIVLC
XPUMP
ANGLE
HEADL
FLONG
LIST OF VARIABLES USED IN DIVRGNOT IN COMMON
Description
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
Working variable for craft condition I
Reynolds number of duct
Divergence loss coefficient, not includingfriction
Duct weight of divergence angle, pound
Duct weight of divergence length, pound
Duct weight of pump inlet angle, pound
Water weight of divergence angle, pound
Water weight of divergence length, pound
Water weight of pump inlet angle, pound
Longitudinal center of gravity of divergenceangle, from transom, foot
Longitudinal center of gravity of divergencelength, from transom, foot
Longitudinal center of gravity of pump inletangle, from transom, foot
Duct diameter, foot
Friction loss coefficient for athwartshipslength
Total divergence loss coefficient
Number of gas turbines + 1
Divergence angle, also pump inlet angle, radian
Total divergence head loss, foot
Athwartships length, foot
71
Variable
XLONG
V
ADIV
THETA(J)
COEF(J)
Description
Fore and aft length, foot
Average velocity, foot per second
Divergence length, ADIV = XLONG/COS (ANGLE)
,
foot
Data array of divergence angles, degree
Data array of divergence loss coefficientswithout friction, corresponding to THETA(J)
72
Variable
KOUNT
XLPS
XFAC
XPUMP
ANOZ
XLNOZ
DT
DJ
XCORR
RE
AREA1
AJET1
FRICT
LIST OF VARIABLES USED IN NOZZLNOT IN COMMON
Description
Working variable fro craft condition I
Dummy nozzle length, foot
Check on whether nozzle exits through bottomor stern
Number of pumps
Optimum nozzle depression angle, radian
Nozzle length, foot
Nozzle throat diameter, foot
Nozzle jet diameter, foot
Nozzle head loss factor
Reynolds number, based on average diameter andvelocity
Throat pipe area, square foot
Jet pipe area, square foot
Flow rate per nozzle, cubic foot per second
Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber
73
Variable
K
J
I
XPUMP
THOMI
DRAT
XXLP
CW
QX
CA
CB
HX
RX
PHRAT
XNGT
ETAPP
HP
THOMS
HHP
BETA2
JNUMB
ETAX
LIST OF VARIABLES USED IN PUMPNOT IN COMMON
Description
Cruise condition indicator
Take-off condition indicator
Index for do loops
Number of pumps
Lower limit of Thoma's criterion for singleinducer axial pump
Hub to tip diameter ratio
Factor for pump length
Weight coefficient
Ratio of cruise flow rate to take-off flow rate
Factor for RPM calculation
Factor for RPM calculation
Ratio of design pump head to off design head
Ratio of design to off design pump RPM
Ratio of off design to design flow coefficients
Number of gas turbines
Product of pump and gearbox efficiencies
Inducer head for one and two stage axialpump designs, foot
Thoma's cavitation criterion for inlet toaxial stage
Axial stage pump head, foot
Exit blade angle, radian
Working variable for numb
Ratio of off design to design purot) efficiencv
7^
Variable
XNNS
BD
CC
AA
IMPL
M
N
PC(K,J)
PCA(K.J)
PCC(K.J)
XRPM(M)
XD1(M)
RPK(M)
XPUP(M)
YLP(M)
XERAT(M)
APUP(NSTG)
WRAT(NSTG)
WD(M)
WW(M)
Description
Non-dimensional specific speed
Impeller exit width ratio
Factor in flow coefficiect calculation
Factor in flow coefficient calculation
Maximum number of impellers permitted forcentrifugal pump, =10
Working variable for number of centrifugalpump impellers
Working variable for NSTG
Inducer head curve coefficients
Inducer plus axial stage head curve coefficients
Centrifugal pump head curve coefficients
Working variable for off design RPM ofcentrifugal pump with M impellers , RPM
Working variable for inlet tip diameter, D1S,foot
Working variable for design RPM of centrifugalpump with M impellers, square foot
Working variable for centrifugal pump area withM impellers, foot squared
Working variable for centrifugal pump lengthwith M impellers, foot
Working variable for gear ratio required forcentrifugal pump with M impellers
Inlet area of pump NSTG, square foot
Weight ratio of pump NSTG, including pumpdry and wet weight, gearbox and fuel
Working variable for XWD(NSTG) for centri-fugal pump with M impellers
Working variable for XWW(NSTG) for centri-fugal pump with M impellers
75
Variable Description
WWG(M) Working variable for XWG(NSTG) for centri-fugal pump with M impellers
QQ(I) Flow rate per pump at condition I, cubicfeet per second
76
Variables
CFS
CA
CD
N
XN
TI
UK
XJ
I
H
SHPP
SHNG
M
WT(ITIME)
DIS(ITIME)
VJJ(ITIME)
ENN
LIST OF VARIABLES USED IN FUELNOT IN COMMON
Description
Constant for SFC calculation
Cruise condition drag to lift ratio
1 + total system head loss coefficient,based on jet velocity
Number of intervals endurance is divided into+ 1
Number of intervals endurance is divided into
Time to cover one range interval at constantV0(1), hour
Index for shifting SFC curves
Factor to convert SFC if SHP is less than 70#of design SHP
Working index for N
Head required, foot
Total thrust required, horsepower
Total thrust required per engine, horsepower
Working index for N
Weight of fuel used in time increment ITIME,pound
Displacement at time increment ITIME, pound
Jet velocity at time increment ITIME, footper second
Working variable for XJ
77
Variable
PSI(N)
THETA(N)
PHI(N)
DEL(N)
DELMIN(N)
DIR(N)
SAVE(N)
S
SPHI
SPSI
NUMB
RHO
ICALL
K
I
N
SIGN(N)
LIST OF VARIABLES USED IN PTTRNNOT IN COMMON
Description
Current basepoint coordinate of parameter N
Previous basepoint coordinate of parameter N
Present exploratory point coordinate ofparameter N
Current step size of parameter N
Minimum step size of parameter N
Last successful direction of parameter N
Working variable for PHI(N)
Working variable for function value
Working variable for function value at PHIcoordinates
Current best function value at PSI coor-dinates
Counter for minimum step size check
Step size change factor
Indicator of current point move
Index for do loop
Index for do loop
Number of parameters of search
Directed step size of parameter N
78
Variable
IPRNT
J
SUM
I
DRATO
IK
XNGT
K
L
LL
KLL
H
NIMP
TFM
WTRAT
WRATF
ENGN(IENGN)
YJRAT(I)
VIRAT(I)
HEADL(I.ICOMP)
CONDS(2,I)
ELBWS(2,IK)
LIST OF VARIABLES USED IN OUTPUTNOT IN COMMON
Description
Print data set reference number
Working variable for condition I
Total duct head loss, excluding elevation,foot
Index for do loop
Strut diffuser area ratio
Index for number of elbows in system
Number of gas turbines
Index for do loop
Index for implied do loop in output statement
Working variable to point to correct headloss for output
Working variable to point to correct formatstatement for head loss output
Index for implied do loop in output statement
Number of impellers in pump
Strut thickness at flying waterline, foot
Total propulsion system weight ratio
Propulsion system weight ratio, excluding fuel
Contains name of engine IENGN
Jet velocity ratio at craft condition I
Inlet velocity ratio at craft condition I
Head loss of component ICOMP at craft con-dition I
Label for craft condition I
Label for elbow IK
79
Variable Description
PC (I) Propulsive coefficient at craft condition I
LABEL(5,M) Labels for output
VK(I) Craft speed at condition I, knots
L0CAT(6,J) Labels for cavitation locations
80
APPENDIX B
PROGRAM LISTING
SAMPLE INPUT 82
SUBROUTINE H20JT 84
SUBROUTINE FCT 92
SUBROUTINE ELBOW 97
FUNCTION CFS 102
FUNCTION TABLE 103
SUBROUTINE STRUT 106
SUBROUTINE JUNCT 111
SUBROUTINE PIPE 114
SUBROUTINE DIVRG 116
SUBROUTINE NOZZL 120
SUBROUTINE PUMP 122
SUBROUTINE GEAR 133
SUBROUTINE FUEL 136
SUBROUTINE NACEL 138
SUBROUTINE PTTRN 149
SUBROUTINE OUTPUT 153
BLOCK DATA 160
Note t Statement numbers in right hand margin indicatestatements retained from design program listed inreference 1
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APPENDIX C
USERS* MANUAL
REQUIRED INPUTS FOR OPTIMIZATION I63
OPTIONAL INPUTS FOR OPTIMIZATION 164
SAMPLE INPUT FOR OPTIMIZATION I65
SAMPLE OPTIMIZATION OUTPUT 16?
REQUIRED INPUTS FOR EVALUATION 170
OPTIONAL INPUTS FOR EVALUATION 172
SAMPLE INPUT FOR EVALUATION 173
SAMPLE EVALUATION OUTPUT 176
162
REQUIRED INPUTS FOR OPTIMIZATION
Symbol Required Units
VO(l) feet per second
V0(2) feet per second
REST(l) pounds
REST ( 2
)
pounds
STRTD(l) pounds
STRTD(2) pounds
SPRAY(l) Pounds
SPRAY(2) pounds
POD(l) pounds
POD(2) pounds
TRIM(l) degrees
TRIM(2) degrees
RANGE nautical miles
DISP pounds
BEAM feet
TYGER (none)
163
OPTIONAL INPUTS FOR OPTIMIZATION
Symbol
XK(1)
XK(2)
XK(3)
XK(<0
THATA(l)
THATA(2)
THATA(3)
THATA(^)
TEMP
HS
HE
HCL
XLS
XLPE
IEQPT
IENGN
IEVAL
NGT
NPUMP
IGEAR
ALPHA
Required Units
(none)
(none)
(none)
(none)
degrees
degrees
degrees
degrees
degrees Farenheit
feet
feet
feet
feet
feet
(none)
(none)
(none)
(none)
(none)
(none)
degrees
Default Value
1.5
1.5
1.5
2.0
90.
90.
90.
30.
59.
5.
10.
2.
20.
2.
8
calculated
calculated
calculated
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169
REQUIRED INPUTS FOR EVALUATION
Symbol Required Units
STRTD(I) pounds
POD(I) pounds
SPRAY(I) pounds
REST ( I
)
pounds
VO(I) feet per second
TRIM(I) degrees
AIN feet squared
AJET feet squared
AREA(l) feet squared
AREA(3) feet squared
AREA(8) feet squared
RANGE nautical miles
DISP pounds
BEAM feet
TYGER (none)
DRAT (none)
DM feet
AIAUX feet squared
ELEXT feet
ELENT feet
AI feet squared
ELAUX feet
ELDIF feet
ELN feet
170
Symbol Required Units
TC (none)
T feet
C feet
Tl feet
CI feet
IEVAL (none)
IEQPT (none)
NPUMP (none)
NGT (none)
NSTG (none)
RPM(2,NSTG) revolutions per minute
QQ(2) cubic feet per second
DIS(NSTG) feet
D2S(NSTG) feet
PLP(NSTG) feet
HPP(2) feet
JANGL radians
171
OPTIONAL INPUTS FOR EVALUATION
Symbol Required Units Default Value
XK(1) (none) 1.5
XK(2) (none) 1.5
XK(3) (none) 1.5
XK(4) (none) 2.0
THATA(l) degrees 90.
THATA(2) degrees 90.
THATA(3) degrees 90.
THATA(4) degrees 30.
TEMP degrees Farenheit 59.
HS feet 5.
HE feet 10.
HCL feet 2.
XLS feet 20.
XLPE feet 2.
IENGN (none) 8
IGEAR (none) calculated
ALPHA degrees 0.
WGTS(2,11) pounds 0.
172
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Thesis
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Analysis of a method
for optimum design ot
waterjet propulsion sys-
tems. DlSPtAV-1 ft OCT 73 2232 1
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TnesisK876 Kruse 145654
Analysis of a methodfor optimum design ofwaterjet propulsion sys-tems .
thesK876
Analysis of a method for optimum design
3 2768 002 11552 9DUDLEY KNOX LIBRARY