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WATERJET PROPULSION SYSTEM OPTIMIZATIONFOR SURFACE EFFECT SHIPS
Paul Leonard Hagstrom
DUONAVAL POSTGRADUATESMONTEREY. CALIFORNIA 9:
WATERJET PROPULSION SYSTEM OPTIMIZATION
FOR SURFACE EFFECT SHIPS
by
PAUL LEONARD HAGSTROMLieutenant, United States Coast Guard
B. S. UNITED STATES COAST GUARD ACADEMY
1970
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF OCEAN ENGINEER AND THE
DEGREE OF MASTER OF SCIENCE IN
MECHANICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DUDLEY !-
Naval p?MONTEREY. CALIFO
VVATERJET PROPULSION SYSTEM OPTIMIZATION
FOR SURFACE EFFECT SHIPS
by
Paul Leonard Hagstrom
Submitted to the Department of Ocean Engineering andthe Department of Mechanical Engineering on 9 May 1975,in partial fulfillment for the degree of Ocean Engineer andthe degree of Master of Science in Mechanical Engineering.
ABSTRACT
This report presents a development of design optimizationtechniques for waterjet propulsion systems used on surfaceeffect ships. The emphasis is on developing a minimum systemweight or a maximum system efficiency. The possibility ofoptimizing a ship displacement for a given propulsion plantis also presented.
The waterjet propulsion systems presented use flushinlets, constant-area nozzles, multi-stage axial-flow pumps,planetary reduction gears and marine gas turbines. Theequations which govern the performance and design of thesesystems are developed and incorporated into a computerprogram. This program is a modified and improved versionof an earlier computer program.
The computer program is then used to conduct a studyof the U. S. Navy's contemplated 2,000 ton, 80 knot SES.The concentration of this report is on the effects of changingthe jet velocity ratio, the effects of different length-to-beam ratios, the effects of gas turbine size and theoptimization of ship displacement for a given waterjetpropulsion system.
A Fortran computer program listing and user's guideis included. This program may be used for a number ofdifferent ships and is not restricted to the 2,000 ton class.
Thesis Supervisor: A. Douglas Carmichael
Title: Professor of Power Engineering
- 2 -
ACKNOWLEDGEMENTS
The author would like to express his appreciation toProfessor A. D. Carmichael for his support and guidancein this thesis.
Gratitude is also extended to the United States CoastGuard for making this educational experience possible.
Finally, thank you to ray wife, Cathy, and daughter,Christine, for their love and support during these lasttwo years at M.I.T.
- 3 -
TABLE OP CONTENTS
Title Page 1
Abstract 2
Acknowledgements 3
Table of Contents 4
List of Figures 6
List of Symbols Used in Text 9
Chapter 1 . Introduction 13
Chapter 2. Development of Basic Equations 15
Chapter 3 . System Description 22
3.1 Inlet Systems 22
3.2 Transition Pipe 26
3.3 Pumps 26
3.4 Pump-to-Nozzle Piping 32
3«5 Nozzles 36
3 • 6 Reversing Bucket 38
3 .
7
Propulsion Engines 38
3.8 Reduction Gears 40
3.9 Fuel 42
3.10 Air Cushion System 44
Chapter 4 . Results 46
4.1 Jet Velocity Ratio Effects 46
4 .
2
Length-to-Beam Ratio Effects 48
4.3 Effects of Engine Size 50
- 4 -
TABLE OP CONTENTS(continued)
4.4 Displacement Optimization 51
Chapter 5. Conclusions 53
Bibliography 55
Figures 57
Table 1 Current Marine Gas Turbines 83
Appendix A Computer Results 84
Appendix B Computer Program Description 117
Appendix C Computer Program User's Guide 120
Appendix D Computer Program 123
List of Program Variables 124
Program Listing 133
Sample Input Data Deck 158
- 5 -
LIST OF FIGURES
NO. TITLE PAGE
1 Variation of Ship Drag-to-Weight Ratio with 57Ship Speed for a 2,000 Ton Family of SurfaceEffect Ships
2 Waterjet Propulsion System Components 58
3 Waterjet System Arrangement for Surface 59Effect Ships
4 Comparative Propulsive Efficiencies 60
5 Variation of Nozzle Efficiency with the 61Nozzle Exit Diameter-to-Inlet Diameter Ratio(d/D) for a Long Radius Nozzle
6 Variation of Waterjet System Component 62Weights with Jet Velocity Ratio for a 2,000Ton SES with a Length-to-Beam Ratio of 2
and 4 FT9D Gas Turbines
7 Variation of Waterjet System Weights with 63Jet Velocity Ratio for a 2,000 Ton SES witha Length-to-Beam Ratio of 2 and 4 FT9D GasTurbines
8 Variation of Shaft Horsepower per Engine 64with Jet Velocity Ratio for a 2,000 Ton SESusing 4 FT9D Gas Turbines
9 Variation of Hull Drag with Ship Length-to- 65Beam Ratio for a 2,000 Ton SES
10 Variation of Waterjet System Weight-to-Ship 66Displacement Ratio with. Ship Length-to-BeamRatio for a 2,000 Ton SES using FT9D GasTurbines
11 Variation of Waterjet System Component Weights 67(at Maximum Net Propulsive Efficiency) withthe Ship Length-to-Beam Ratio for a 2,000Ton SES
- 6 -
NO
12
13
14
15
16
17
18
19
20
21
22
23
LIST OP FIGURES(continued)
TITLEPAGE
Variation of Wateript qv^^ nWeights (« + +v!? ti- •
bystem Component 68
SES with FT9D Gas Turbines ' ° T °n
Variation of the Maximum Net PropulsiveEfficiency (Cruise) with the ShiHenrth ?to-Beam Ratio for a 2 000 Ton qp?
^ngtn-4 PT9D Gas Turbines
ES USlng
w?tha^°n
r°
f Shaft Ho^^Power per Engine 71
JE c5|«:Lp
.
Lenetli-t o-Beam Ratio for a 2 000?
Ton SES with 4 PT9D Gas Turbines '
wiSih^ T°
f!S?
P+SuCti0n ^ecific S»eed
Ton\?* P Len^hrt0-Beam Ratio for a" 2 ,000Ton S*,S using 4 PT9D Gas Turbines
sasr^^sra^-ys^ *— 74
Ratio ?Sfts°emCient f°r Varyin^ AsP-t 75
lSltsDrag Coefficie«t for 2.5 Aspect Ratio 79
72
73
- 7 -
LIST OF FIGURES(continued)
NO. TITLE PAGE
24 Design Speed Overall Internal Efficiency 80for 2.5 Aspect Ratio Inlets
25 Hump Speed Overall Internal Efficiency for 812.5 Aspect Ratio Inlets
26 Total Inlet System Weight Coefficient for 822.5 Aspect Ratio Inlets
- 8 -
SYMBOLS USED IN TEXT
2A^ Inlet area at cruise speed ftc
2A, Inlet area at hump speed ft
2A
.
Jet area ftj
2A Pump inlet area ftP
C Ratio of entering water momentumvelocity to ship velocity (V /V )
C. Acceleration coefficient
C, Pump blockage coefficient
C-pj Inlet drag coefficient
Ct Pump length coefficient
C Inlet system weight coefficient
C Pump weight coefficient
D Inlet system drag lb
D. Nozzle exit diameter ft
D Pump inlet diameter ft
D . Inside diameter of pump-to-nozzle ftp pipe
D Outside diameter of pump-to-nozzle ftpipe
f Moody pipe friction factor
g Acceleration due to gravity ft/sec'
h Difference in height between outside ftwaterline and diffuser exit
Ha Atmospheric pressure head ft
h Height of diffuser exit above inlet ft
- 9 -
h. Head loss between diffuser exit and ft^ pump inlet
h Height of pump above inlet ft
h Change in height between diffuser ft^e exit and the pump entrance
H Change of head across pump ft
H , Head at entrance to pump ft
H p Head at pump exit ft
Hp Head at diffuser exit ft
H „ Change of head across nozzle ftnoz °
H . Change of head across pump-to-nozzle ftpipe ° r r* r pipe
HP-, Additional horsepower required to HPovercome the pump-to-nozzle pipehead loss
HP Horsepower delivered to the water HPP
K K-factor of reduction gear
L Length of pump ft
L . Length of pump-to-nozzle pipe ft
in Reduction gear ratiog
N Pump specific speed
N RR Pump suction specific speed rpm(gal/min)
.75ss
ft
n Reduction gear input pinion RPM rpmp (engine rpm)
NPSH Net positive suction head ft
p Vapor pressure head of water ft
PC Overall propulsive efficiency
- 10 -
net
AP
Q
Q
Qc
Qh
R
Re
rh
rt
RPM
SFC
SHP
T
t
t
Ut
VAF
V
V_
V/Vo
m
Net propulsive efficiency
Pressure drop in pump-to-nozzle pipe
Flow rate
Reduction gear Q-factor
Flow rate at cruise speed
Flow rate at hump speed
Ship resistance
Reynold* s Number
Pump hub radius
Pump blade tip radius
Rotational speed
Specific fuel consumption
Required engine power output
Thrust
Time interval
Thickness of pump-to-nozzle pipe
Blade tip velocity
Variable area factor
Velocity
Inlet velocity at cruise speed
Inlet velocity at hump speed
Jet velocity
Jet velocity ratio
Momentum velocity of entering water
Ship velocity
lb/ft
ft 3/sec
ftVsec
ft 3/sec
lb
ft
ft
revolut ions/min
lb/HP-hr
HP
lb
hr
in
ft/sec
ft/sec
ft/sec
ft/sec
ft/sec
ft/sec
ft/sec
- 11 -
w
wAf
wg
ww
A/ W
t
V
If
\&
^nz
n
nOA
OA»
Velocity of water entering pump
Weight of inlet system
Pump weight
Weight of fuel consumed in a timeperiod At
ft/sec
lb
lb
lb
nT
Weight of reduction gear lb
Weight of water in pump lb
Density of titanium slug/ft'
Density of v/ater slug/ft'
Pump flow coefficient
Pump head coefficient
Viscosity of water
Pi
Maximum allowable stress
Reduction gear efficiency
Nozzle efficiency
Inlet system overall internal efficiency
Inlet system overall internal efficiency(uncorrected for height)
Pump efficiency
ft2Ar
lb/in'
- 12 -
1. INTRODUCTION
Among the new types of high-speed marine vehicles,
the surface effect ship seems to have the best potential
for developing into multi-thousand ton ships.
The surface effect ship rides on a self generated
cushion of air contained between rigid sidehulls and flexible
fore and aft seals. The very high horsepower levels that
must be transmitted through these sidehulls has made the
use of waterjet propulsion systems attractive.
Some of the advantages of water jet propulsion for
surface effect ships include:
1. Reduction of underwater noise
2. Fewer underwater appendages
3. Possible elimination of rudders
4. Fewer and simpler components
5. Increased reliability and maintainability
6. Use of multiple systems per sidehull
The two biggest disadvantages of waterjet propulsion are
its comparatively low propulsive efficiency and high system
weight. Figure 4 shows representative propulsive efficiencies
for different types of propulsors.
Propeller systems for surface effect ships have some
critical disadvantages. Subcavitating propellers are unsuited
for operation much above 40 knots due to blade cavitation.
- 13 -
Supercavitating and superventilated propellers can operate
successfully at speeds above 40 knots. The problem is the
amount of thrust that must be developed by each propeller.
The typical horsepower level for the proposed 2,000 ton SES
is approximately 135,000 SHP. If a propeller is used,
half of the horsepower would have to be transmitted through
each propeller. The system would also require either
controllable reverse-pitch (CRP) propellers or a reversing
gear.
The final support for using water jet propulsion systems
is that the Navy has given six contracts for the development
of the 2,000 ton SES design. All six of these contracts
specify that waterjet propulsion will be used.
The typical drag characteristics of a SES are shown in
Figure 1. Low length-to-beam ratios have a high drag at
hump speed and a low drag at cruise speed when compared to
high length-to-beam ratios. The selection of the length-
to-beam ratio for a SES will have an important impact
on the water jet propulsion system design because the design
is based on both the hump and cruise conditions.
- 14 -
2. DEVELOPMENT OP BASIC EQUATIONS
A waterjet propulsion system draws water from outside
the hull, imposes an acceleration on it and discharges
it astern as a jet. The thrust is developed due to a
change in momentum of the water. The momentum equation
for thrust delivered by the system is:
where: T = thrust developed (lb«)
D s= density of water (slugs/ft )/ w
o
Q = flow rate of water (ft /sec)
V. = jet velocity (ft/sec)J
V = momentum velocity of entering water (ft/sec)
The momentum velocity of the incoming water is slightly less
than the ship velocity due to the boundary layer effect.
The ratio of momentum velocity to ship velocity is
defined as C. Typical values are greater than .985 (ref. l).
The thrust equation can be rewritten in terms of C and
ship velocity as:
T =/>wQ(V./V Q- G)V
o(2.2)
The jet velocity ratio, V ./V , is the controlling system
variable. Selecting the jet velocity ratio establishes
the other important parameters.
The thrust must equal the resistance of the ship plus
- 15 -
the added drag caused by the waterjet inlet system. If
an acceleration is required, the total resistance must be
multiplied by an acceleration coefficient. Thrust required
is therefore:
T = (R + D)CA (2.3)
where: R = ship resistance (lb~)
D = inlet system drag (lbf )
C. = 1 for constant speed
C . > 1 for increasing speed (acceleration)
The added drag of the inlet system can be expressed in
terms of a drag coefficient, C^.
D = PwCDQV2 (2 ' 4)
Figures 19 and 23 present calculated design speed drag
coefficients for varying aspect ratio inlets and 2.5 aspect
ratio inlets, respectively. If no restrictions are placed
on the variable area factor, the drag coefficients are
nearly independent of hump speed and vary slightly with
design speed.
Combining equations 2.2, 2.3 and 2.4 yields:
fVKV-jA,, - C)VQ
= CA (R + ipfjflVj (2.5)
Equation 2.5 can then be solved for the required
flow rate, Q, for a given ship velocity, ship drag and
acceleration margin, plus a selected jet velocity ratio.
- 16 -
CAR
rw o v
o o " AD'
To determine the power requirements, the head across
the pump, H , must be established.
The overall internal efficiency, floA 1 ' °^ ^e inlet
system is the ratio of the total head at the diffuser
outlet to the total head of the incoming flov/, V /2g.
This efficiency includes all losses up to the diffuser
outlet. Figures 20, 21, 24 and 25 show the variation of
the overall internal efficiency with changing ship velocity.
These efficiencies are applicable for an infinite Froude
Number diffuser with an exit at the same elevation as the
undisturbed water surface. The efficiency corrected for
a change in elevation is:
vn/2e
The total head at the diffuser exit, Hp, is then:
Tl V2
iOA_m_ (2#8)
The head at the pump entrance is:
V = he " h
p+ H
2 " hlep (2 ' 9)
where: H -, = head at entrance to pump (ft)
h = height of diffuser exit above inlet (ft)e °^
h = height of pump above inlet (ft)
- 17 -
Hp = head at diffuser exit (ft)
h-, = head loss between diffuser exit andp pump inlet (ft)
The head at the exit of the pump is:
V2
Hp2 " if"
+ "pipe + HnoZ (2-10)
where: H . = head loss in the puinp-to-nozzlepipe pipe (ft)
H = head loss across nozzle (ft)
The head loss in the pump-to-nozzle pipe is a function of
the flow rate, pipe length and pipe diameter. The solution
of H . for the optimum pipe diameter is presented in
section 3.4.
The head loss due to the nozzle can be expressed in
terras of a nozzle efficiency, Y| . Figure 5 shows the
nozzle efficiency for a typical long radius nozzle. The
nozzle efficiency is the ratio of the head of the jet to
the head at the nozzle entrance.
V2/2g^ = H -H .- t 2 - 11 )
p2 pipe
Solving equation 2.11 for the head at the exit of the pump
gives:
H„, = ^JZ + H„, „. (2.12)nz'
p2 ''n^e pi Pe
- 18
Combining equations 2.10 and 2.12 gives:
V.'
H «, Jnoz
2 r
g Tl
-
1
(2.13)nz
Equations 2.9 and 2.12 can then be combined to get the head
rise required across the pump, H .
VHp 2g*l
+ H.
nzpipe 2g
+ hp " h
e+ hlep <
2 - 14 >
Assuming that the loss between the diffuser outlet and
pump entrance is small compared to the other terms, hne e' lep
can be neglec
2.14 becomes:
can be neglected. By setting h equal to h - h , equation
hp
= (W' 2
-tT— '
CT)oa
nz
X 1
2g+"pipe
+ V < 2 ' 15 >
The power delivered to the water, HP , can now be determinedP
since:
HP» = VAvS/550p p /W q
Substituting equations 2.6 and 2.15 into 2.16 gives:
(2.16)
HPcA*[((yv
2/nnz> -c 2w (H
pipe + ygg^o2
)] , 217)P (2)(550)((V./V
o)-C-^ACD )
The shaft horsepower required is then:
HP_SHP =
Vg(2.18)
where: t\ = pump efficiency
y\ = gear efficiency6
- 19 -
The overall propulsive coefficient, PC, is defined as
the thrust times velocity divided by the shaft horsepower.
2yU(v.A> ' c)
,PC =5
P ^ '] ° r- (2.19)
((v./v r/n ) - c^n nA + (h . + h )(2g/v2
)vv3X o' ' mz' l0A x pipe pe v ^ o '
By taking the derivatives of 2.17 and 2.19 with respect
to the jet velocity ratio and setting the results equal to
zero, expressions can be found for the jet velocity ratios
for which the required horsepower is a minimum and the
propulsive coefficient is a maximum. These are:
V./V =0+^.0^+ (C +^C A C 1.)2 -C^rk-.T) +2(H . +h )T) g/V
2
y o ^ A D Jv ^ A D' XjA lnz v pipe pe lnzB' o
(2.20)
for minimum power and
V./V =C + CT(1 +^ AA"n ) + 2(H . + h )g?1 /V^ (2.21)j o n v "-OA^nz' v pipe pe /&lnz/ o
For maximum PC. These two optimum jet velocity ratios do not
occur at the same jet velocity ratio. However, they are close
enough so that either could be used in determining a
representative power required by the surface effect ship.
The net propulsive coefficient, PC . , is defined as
the hull drag times velocity divided by the shaft horsepower.
PC . = RV/SHP (2.22)nex o
Once a jet velocity ratio at cruise has been selected,
the flow rate through the system at cruise is determined
from equation 2.6. The area of the jet is then:
- 20
Aj
=V (v./V )
< 2 - 2 3)
Assuming a constant area jet, the jet velocity ratio at
any velocity, V, is:
V./V = Q/A.V (2.24)o J
Equation 2.23 can then be combined with equation 2.6 to
solve for the jet velocity ratio at hump.
(YVhump - ' 5C + ¥^ +CACD
.50 + -4-^C A R
+ V- (2.25)
AvVo A2
3
All the terms in equation 2.24 are at hump speed. Once
the jet velocity ratio is determined, the other system
variables such as flow rate and power requirements can be
found using the appropriate equations developed in this
chapter. The procedure used to find the hump speed variables
could be used to predict the performance at any speed.
It is apparent from equations 2.20 and 2.21 that
different speeds will lead to different optimum jet velocity
ratios for minimum power or maximum propulsive efficiency.
Therefore, selecting the optimum jet velocity ratio at cruise
will lead to a less than optimum jet velocity ratio at hump.
- 21 -
3. SYSTEM DESCRIPTION
The general configuration of a waterjet propulsion
system for a surface effect ship is shown in Figure 2.
The components of the system include the inlet system,
the transition pipe, the pump, the pump-to-nozzle piping,
the nozzle, the reversing gear, the propulsion engines,
the fuel and the air cushion system. The arrangement and
numbering of the individual waterjet systems used in this
report are shown in Figure 3.
3.1 INLET SYSTEMS
The inlet system will be defined in this report to
include the inlet, diffuser, fairing required by the inlet
and a movable ramp or movable lip.
The inlet aspect ratio is the ratio of inlet width to
inlet height. Two basic series of inlet aspect ratios are
considered, one has a constant 2.5 aspect ratio and the other
has an aspect ratio which varies with design speed.
The flush inlet appears to be superior to pod-strut
inlets for surface effect ship application. A flush inlet
lies in the same plane as the bottom of the sidehull.
The important advantages of the flush inlet include less
added drag, simpler methods of changing the inlet area and
less chance for inlet damage caused by floating debris.
For these reasons, only flush inlet systems are considered
- 22 -
in this report.
The most important factors effecting the inlet drag
are: lip leading-edge radius, variable area factor (ratio
of maximum to minimum inlet opening area), inlet aspect ratio,
flow rate and sidehull fairing.
Surface effect ships usually have significant sidehull
deadrise angles. Fairing of the sidehull is required to
prevent inlet ventilation and cavitation. The fairing
must also be designed to minimize any additional drags.
Sidehull deadrise angles of more than 50 degrees are not
well suited for flush inlet systems.
The surface effect ship has a need for a variable inlet
area capability. The flow rate requirements at maximum
speed and at hump speed (high drag) are nearly equal.
This dictates that the inlet must either have a variable
area capability or be able to operate over a wide range of
inlet velocity ratios. Operation over a wide range of inlet
velocity ratios requires large variations in the inlet lip
angle-of-attack. Changing the angle-of-attack will require
a larger lip leading-edge radius to prevent cavitation at
the leading-edge. The larger lip radius v/ill lead to
increased inlet drag.
With a variable inlet capability, the inlet velocity
ratio variations can be reduced. The lip angle-of-attack
will then be small. A small lip leading-edge can then be
- 23 -
used which results in lower inlet drags. The minimum lip
radius will usually be specified by such practical
considerations as the need to place sensors near the lip or
to limit vulnerability to debris damage. The variable
area factor, VAF, required is:
A V QVAF=Jl =^ (3.1.1)
c he2
where: A = inlet area (ft )
V = inlet velocity (ft/sec)
Q = flow rate (ft-ysec)
c a at cruise conditions
h = at hump conditions
For varying aspect ratio inlets, the aspect ratio is equal
to the diffusion ratio. The varying aspect ratios inlets
are normally more efficient and lighter. Varying aspect
ratio inlets may be limited by sidehull geometry.
A movable ramp or movable lip is needed to have a
variable area capability. If a movable lip is used, the lip
leading-edge must not be allowed to vary more than a small
amount. Figure 3 illustrates the movable ramp and the
movable lip.
A diffuser is required to slow the flow down to prevent
cavitation at the pump. The diffuser design has a significant
effect on inlet system weight and efficiency. Minimum
acceptable values of overall diffusion ratios are determined
- 24 -
by pump cavitation characteristics. The diffuser
characteristics used are based on a study by R. A. Barr,
reference 1. The study was based on a pump with a maximum
suction specific speed of 16,000 and a flow coefficient of
0.15. Diffusion ratios of 3.0, 4.0 and 5.0 were required
for 60, 80 and 100 knots respectively. The diffuser
schedule used is as follows:
to 20 percent of length Diffusion = 6
20 to 90 percent of length Diffusion = 6°+ 12°(p - 20)/75
90 to 100 percent of length Diffusion = l8°(100-p)/5
where p is the percent of total diffuser length measured
from the inlet. The use of smaller diffusion angles will
result in higher efficiencies but heavier system weights.
A diffuser outlet angle of 45 degrees is assumed in this
report.
Other considerations in selecting diffuser geometry
include the transition from rectangular inlets to circular
pump inlets.
The weight of the inlet system, W, in terms of an
inlet weight coefficient, C , is given in reference 1 as:
W = C Q1,5
(3.1.2)w
Values of C are shown in Figure 21 for varying aspect ratios
and in Figure 25 for 2.5 aspect ratios. In both cases,
the lip leading-edge radius is .25 inches. The weight
- 25 -
includes structural weight and water weight. Equation 3.1.2
suggests that many smaller and separate inlets may be
superior due to lighter weight than fewer and larger inlets.
However, smaller systems are generally less efficient and
the weight gains are offset by higher fuel weights.
3.2 TRANSITION PIPE
The transition pipe is a constant diameter pipe
extending from the diffuser outlet to the pump inlet. The
angle of the pipe, 45 degrees, is the same as the diffuser
outlet angle. The transition pipe is used to account for any
small differences in pump height and diffuser exit height.
The diffuser schedule given in section 3.1 will lead to a
diffuser exit height of 6.5 feet. If the pump height and
the diffuser exit height vary substantially, consideration
should be given to developing a new diffuser schedule.
Data for flush inlet diffusers is limited to a few specific
configurations. New diffuser geometries should be model
tested to adequately establish final performance predictions.
The transition pipe represents a means to adapt a known
diffuser configuration to a specific waterjet system
requirement
.
3 .
3
PUMPS
Waterjet pumps should have high efficiency, high
rotative speeds and light weight. To achieve light weight
it will be necessary to use pumps with high suction specific
- 26 -
speeds. The acceptable values of suction specific speed
are limited by the onset of cavitation. The high rotative
speed leads to smaller differences in RPM between engine
and pump, and thus lighter reduction gear weights.
Pumps are generally characterized by their specific
speed, N .r • s
„ immi (3.3.DHp 75
Pumps can be of the axial-flow, mixed-flow or centrifugal-
flow types, depending on the design requirements.
Centrifugal pumps operate best for specific speeds between
500 and 4,000. Mixed-flow pumps should operate at specific
speeds between 4,000 and 10,000. Axial-flow pumps are
best for specific speeds greater than 10,000. Previous
comparisons of pump types in references 2 and 6 determined
that axial-flow pumps are the best suited for surface effect
ship application. The advantages include ease of arrangement,
maximum compactness and ease of adding stages. Centrifugal
and mixed-flow pumps are not considered in this report.
The procedure used is to determine the rated pump RPM,
pump diameter, annulus area and other related pump
characteristics based on a designated flow coefficient (0),
head coefficient (V), flow rate and pump head. The purpose
is not to design the pump, but to determine the general
requirements and characteristics of the pump.
- 27 -
The diffusion ratios used in section 3.1 were based
on a pump with an inlet flow coefficient of 0.15 and a
maximum suction specific speed of 16,000. These values
were therefore fixed in the pump design procedure.
Pump cavitation performance is based on the suction
specific speed, N4ss
ss NPSH*°
The net positive suction head, KPSH, is:
NPSH = Ha + Hpl
- py (3.3.3)
where: Ha = atmospheric pressure head (ft)
H , = head at pump entrance (ft)
p = vapor pressure head of water (ft)
The large discharge and low net positive suction head
at hump speed indicate that the greatest danger of cavitation
will be at hump speed. The maximum suction specific speed
at which water jet pumps can operate at without excessive
cavitation damage is unclear. Waterjet pumps v/ith inducers
have been built that can operate free of cavitation damage
at suction specific speeds of 25,000.
Cavitation normally occurs on the first inducer stage.
The inducer should produce enough headrise to keep the
remaining stages from cavitating. The performance of
multi-stage pumps is not badly effected by cavitation on
- 28 -
the inducer stage. Cavitation will normally begin at a
much lower suction specific speed than the limiting suction
specific speed.
The- pump used in this report is assumed to operate
at acceptable cavitation levels up to a specific suction
speed of 16,000. The pump design procedure is based on the
method described in reference 14 and will only be summarized
in this report.
The head coefficients for the pump were set at 0.41
for the inducer and 0.3 for the remaining stages. The
maximum allowable blade tip velocity was set at 200 feet per
second. These values are consistent with existing pumps.
Changing these values will only have a small effect on the
overall system design since the pump represents such a small
percentage of the total system weight.
The flow rate and the headrise can be calculated by
equations 2.6 and 2.15 respectively. The flow coefficient,
0, is the ratio of the axial velocity of the entering water
to the blade tip velocity.
0= Vz/U
t(3.3.4)
where: V = velocity of water entering pump (ft/sec)S3
U. = blade tip velocity (ft/sec)
The headrise coefficient,^, relates the headrise across the
pump to the blade tip velocity.
- 29 -
Y = gH /U2
(3.3.5)
With the values of the flow coefficient and the headrise
coefficient set, the velocity of the water entering the
pump is:
Vz
= 0Vt
(3.3.6)
The blade tip radius, r. , is then found by:
rt
= Q7T i - <V*t>2 Az (3.3.8)
Finally, the pump RPM is:
RPM = 30Ut/lfr
t(3.3.8)
The suction specific speed is then calculated by
equation 3.3.2. If the suction specific speed exceeds the
set limit of 16,000, the blade tip velocity is reduced
resulting in a lower suction specific speed.
When an acceptable suction specific speed is found,
the efficiency of the pump is determined. A pump with a
diameter of 3.66 feet and an efficiency of 91.5 percent at
design speed is assumed. A Reynold's Number correction is
applied for the actual pump diameter to determine the pump
efficiency. The propulsive efficiency and required shaft
horsepower at hump speed is then calculated and compared
to the available shaft horsepower. If the required shaft
horsepower (including acceleration margin) is greater than
the available power, the blade tip velocity is reduced.
Decreasing the blade tip velocity increases pump diameter,
pump weight, pump efficiency and the headrise coefficient
- 30 -
of the pump. The number of stages is then determined based
on head coefficients of 0.41 for the inducer and 0.30 for
subsequent stages. The pump head, efficiency and RPM
characteristics are assumed to be parabolic. Using this
assumption, the off-design pump RPM and efficiencies can
be determined. With the pump RPM and efficiency at cruise
speed determined, the overall propulsive coefficient,
required shaft horsepower and blade tip velocity can be
found. The required shaft horsepower is then compared to
the available shaft horsepower and the blade tip velocity
is compared to the maximum allowable blade tip velocity.
If either value is unacceptable, the blade tip velocity at
hump is reduced and the entire procedure is repeated.
Finally, the suction specific speed at cruise is calculated.
If it is too high, the blade tip velocity at hump is reduced
and the entire process repeated.
The pump dry weight is approximated by:
wd = CwDp
2 ' 3< 3 ' 3 '9)
where: C = pump weight coefficient
D = pump diameter (ft)
and the weight of water in the pump by:
w™ = C, A L p g (3.3.10)w b p p/w& * '
where: C, = blockage coefficient
A = pump inlet area (ft )
- 31 -
L = pump length (ft)
The pump length is calculated in terms of a length
coefficient, Cj, and the pump diameter.
L = C T D (3.3.11)p L p
Decreasing the blade tip velocity increases the pump
efficiency, pump diameter and the pump weight.
For two or three water jet systems in a sidehull, the
pump is designed to the requirements of System 2 (Figure 3).
For four or five waterjet systems in a sidehull, the pump is
designed to the requirements of System 3. The same pump
would be used in all the systems and the small changes in
thrust requirements would be achieved by using slightly
different nozzle exit areas.
3.4 PUMP-TO-NOZZLE PIPING
Figure 3 shows the arrangement of each individual
waterjet system. The only major difference in the individual
systems is the distances from the pump exit to the nozzle
located at the stern of the ship. In large surface effect
ships such as the proposed Navy 2,000 ton class, the
pump-to-nozzle length could be 40 feet or more. This
represents a considerable weight addition and a potentially
high head loss.
A large diameter pipe will have very small head losses,
but very high water and pipe weights. Conversely, small
diameter pipes will have small pipe and water weights,
- 32 -
but larger head losses.
The approach taken was to design the pipe based on a
total minimum weight for cruise conditions. The v/eights
considered were pipe weight, water weight, the proportion
of the engine weight required to overcome the head loss
and weight of the additional fuel required.
Wt = Wt . + Wt .. + Wt -,,,, + Wt ,,,., (3.4.1)pipe water add f l add'l w'
fuel eng
The weight of the pipe depends upon the pressure head
in the pipe, pipe diameter, pipe thickness and pipe material.
Due to the high flow rates, titanium was chosen as the
pipe material. The allowable stress was set at 20,000
p.s.i. The thickness of the pipe is then calculated by:
H . pi)t-J&BSPsL (3.4.2)
24<rn
where: t = thickness of pipe (in)
H . = head at pipe entrance (ft)
D . = inside diameter of pipe (ft)
0-r = maximum allowable stress (p.s.i.)
If the thickness is found to be less than 0.1 inches, it
is set equal to 0.1 inches.
The weight of the pipe is:
2 2pipe rt"~pipe N "po ~ pi«—
- - P^Lv±veKo - \\)(^A) (3.4.3)
,3where: p, = density of titanium (slug/ft )
- 33 -
L . = length from pump to nozzle (ft)
D = outside diameter of pine (ft)po * '
Substituting:
Dpo
= Dpi
+ 2t (3.4.4)
into equation 3.4.3 gives the weight of the pipe as:
Wt . = £A.L (D .t + t2
) (3.4.5)pipe 6rt pipe v pi ' v->-**«^
The weight of water in the pipe is:
Wt , = gpL . D2
ir/4 (3.4.6)water B/w pipe pi ' v'
The additional fuel and engine weights are based on
the additional horsepower required to overcome the head
loss in the pipe.
HPlQss=APQ/550 (3.4.7)
The pressure drop,AP, in the pipe is:
4fL p V2
AP = ^ (3.4.8)Pi
where: f = Moody pipe friction factor
V = velocity of water in pipe (ft/sec)
The Moody pipe friction factor is:
, .2
Re*" V fc
Df.^ B '°f^ (3.4.9)
Pi
Since the flow rate throughout the system is constant:
Q = VDp
2/4 = V^D^/4 (3.4.10)
The velocity in the pipe is then:
- 34 -
V = V.D^/Dp2, (3.4.11)
Combining equations 3.4.8, 3.4.9 and 3.4.11 gives:
AP = .092L . p z/#2V.1,8D.3,6/D 4-' 8 (3.4.12)
pipe/ w 3 2 Pi
Combining equations 3.4.7, 3.4.10 and 3.4.12 gives:
HPloss = • 0002 5 8Vpe^w^'2Q2 ' 8
/D p\'8
(3.4.13)
The weight of the additional fuel and power requirements
can now be determined by:
(3.4.14)Wtadd'l - (HPloss)(SPC)(RANGE/V
o )
fuel
and
Wt ,,.., = (HP, )(Wt )/SHPadd'l v loss /v eng '
eng
(3.4.15)
Substituting equations 3.4.5, 3.4.6, 3.4.14 and 3.4.15
into equation 3.4.1 gives the total weight equation.
Wt = AfTgL (D .t + t2
) + p gL D2TT/4 +rX e pipe v pi ' n/v6 pipe pi '
(3.4.16)
.000258L . p V §piue/ w ^.2^2.8
DPi
(SFC) (RANGE) Wt
V. SHP
To find the pipe diameter resulting in minimum weight,
the derivative of total weight is taken with respect to the
pipe diameter. and the results set equal to zero. The
equation to be solved is:
- 35 -
= gP.TftL + 2p gD .L . TT/A -& /t pipe "w& pi pipe '
(4.8)(.000258)L /)w^- 2
Q2 * 8
D378-
Pi
-EiH!(SFC) (RANGE) Wt
(3.4.17)
eng
SHP
or in simplified form:
=A t/y°w
+ °- 5Dpi
-p:
.0003949^#2
Q2,8
(3.4.18)
D"575-
Pi
(SFC) (RANGE) Wteng
SHP
The head loss in the pipe for any flow rate is:
H = Ap//v (3.4.19)pipe ' r w l
The head loss in the pipe will cause an increase in
the total headrise across the pump which will lead to a
slight change in the flow rate. This change in flow rate
is handled by repeating the pipe design process with the
new flow rate.
3.5 NOZZLES
The purpose of the nozzle is to convert a pressure
head into a velocity head by throttling. A nozzle will
increase the velocity of the water substantially. In
doing this, a certain amount of pressure head is lost.
This loss is mainly a frictional loss.
Normally, for water;} et propulsion systems, a fixed
area nozzle designed for cruise conditions is used.
Some improvement in off-design performance could be achieved
- 36 -
by using variable area nozzles. By varying the jet area,
a better jet velocity ratio could possibly be found at off-
design speeds. Increasing the nozzle area for lower speeds
would increase the pump discharge and reduce the pump head.
This will normally result in increased pump RPM, increased
pump efficiency and lower fuel consumption. Variable area
nozzles are normally not used due to increased mechanical
complexity, decreased nozzle efficiency and only small
overall performance gains.
In the flow, the point where the streamlines are
perfectly parallel to the centerline of the nozzle is
slightly beyond the exit of the nozzle. This point is
commonly referred to as the "vena contracta." The cross-
sectional area is slightly smaller at this point than at
the nozzle exit. For application in the thrust equation
2.1, the jet velocity should be the velocity at the vena
contracta. This presents a problem in that the vena contracta
area is unknown and therefore the velocity is difficult
to determine.
According to experimental results presented in reference
11, the velocity at the vena contracta is roughly 0.5 to
1.0 percent higher than the jet velocity calculated by
dividing the flow rate by the nozzle exit area. These
experiments were based on a long radius nozzle. The vena
contracta effect will recover much of the nozzle efficiency
- 37 -
loss if the nozzle exit velocity is defined as the jet
velocity. Nozzle efficiencies greater than 99 percent are
obtainable when the Reynold* s Number is greater than 200,000.
Figure 5 presents the nozzle efficiency as a function of
the ratio of nozzle exit diameter to nozzle inlet diameter
for a long radius nozzle. The vena contracta effect has
been incorporated into the nozzle efficiency. Therefore,
the jet velocity is actually the velocity at the nozzle
exit.
The length of a long radius nozzle is approximately
twice the inlet diameter. Changes in flow rate have only
a small effect on nozzle efficiency if the Reynold's Number
is greater than 200,000.
3.6 REVERSING BUCKET
Reverse thrust and ship control can be obtained by
controlling the direction of the jet. These devices are
added behind the nozzle and do not effect the normal forward
performance. Such devices are much lighter and therefore
more desirable on a weight basis than auxiliary propulsion
systems (for reverse thrust) or rudders (for directional
control)
.
3.7 PROPULSION ENGINES
Engines for surface effect ships are normally limited
to marine gas turbines. However, in the case of small
ships requiring less than 10,000 total shaft horsepower
- 38 -
and desiring maximum ranges, the use of lightweight, high-
speed diesels should be considered. Although the high-speed
diesels weigh much more, the weight difference may be
recovered due to the poor specific fuel consumption of
small gas turbines.
Table 1 lists the characteristics of some of the marine
gas turbines available now or presently under development.
The inputs required for the design sequence are normal SHP,
maximum SHP, specific fuel consumption at normal SHP, shaft
RPM, engine dry weight and engine length. As in reference
12, the specific fuel consumption is approximated by:
n
SFC *SHP
requiredSHPnormal
(3.7.1)
where: n = 0.25 if SHT /SHPnnr, > 0.7
n = 0.75 if SHPreq
/SHPnor <0.7
Off-design engine RPM is based on the corresponding
pump RPM and the reduction gear ratio. It is assumed that
the engine can develop the required power at the indicated
shaft RPM. Good pump and gas turbine matching is achievable
in waterjet systems. Maximum pump efficiency usually occurs
along the same power-RPM path as engine minimum specific
fuel consumption. If the pump and engine are matched at the
design point, they tend to be closely matched at most
operating conditions.
- 39 -
The selection of engine type depends on many
considerations. Operating engines close to maximum power
is desirable because the best specific fuel consumption
normally occurs at maximum power. Larger engines are normally
better because of the general decrease in specific fuel
consumption as engine size increases. The use of the fewest
possible engines is desirable for simplicity and reliability
reasons. The operational profile of a ship is also important.
For ships that operate at many different speeds, it may
be attractive to have slightly more, but smaller systems
so that at certain speeds some systems could be shut down
to achieve better fuel consumption.
Because of limited engine availability, it is often
necessary to use larger than optimum engines. At the
present time, there is a significant lack of marine gas
turbines in the 5,000 to 12,000 horsepower range.
3.8 REDUCTION GEARS
Planetary reduction gears are assumed because they
are normally about half the weight and more compact than
conventional spur or helical reduction gears. Due to their
compactness, planetary gears can be placed low in the
sidehull, while other types of reduction gears must be
placed on the lowest complete deck.
Planetary reduction gears have been built to handle
up to 40,000 SHP at a maximum reduction gear ratio of 4 : 1.
- 40 -
The largest marine gas turbine, the FTA-C , has a SHP of
36,800 so that planetary reduction gears do not constrain
the waterjet system design. Large reduction gears are
normally custom designed, so availability is not a
controlling factor.
The reduction gear ratio is determined by either the
hump condition or cruise condition, depending on which
horsepower level is closest to the normal horsepower rating
of the selected engine. The reduction gear ratio is then the
ratio of the pump RPM to the engine RPM at normal horsepower.
The weight of the reduction gear is estimated using the
Dudley method. The Dudley method involves the use of two
factors, K ajid Q. The gear tooth stress is approximately
proportional to the square root of the gear's K-factor. A
K-factor of 500 is representative of planetary gears proposed
for surface effect ships. Q relates the gear's required
geometry to the reduction gear weight and is defined as:
Q = SHP(mg
+ l) 3/(npmg
) (3.8.1)
where: SHP = maximum horsepower required
in = reduction gear ratiog
n = engine RPM at normal SHP
The weight equation for planetary reduction gears is then:
W = 9,500Q/K (3.8.2)
This weight includes the gear, casing oil reservoir, oil
- 41 -
pump and stub shaft.
The use of planetary reduction gears does restrict
the waterjet system design to one engine per pump.
3.9 FUEL
The fuel consumption is found by dividing the endurance
time into many small time increments. The fuel required
for each time increment is based on the average SHP required
during that particular time period.
WAf = (SFC)(SHP)(At) (3.9.1)
where: W.f
= fuel weight consumed during aparticular time period (lb)
SFC = fuel consumption rate correspondingto the average SHP (lb/HP-hr)
SHP = average SHP required duringparticular time period
The fuel weight used is then subtracted from the total
ship weight and a new drag for the ship is calculated using
a constant weight-to-drag ratio. The weight-to-drag ratio of
an actual surface effect ship will not remain constant, but
will decrease slightly as ship displacement decreases. The
percent decrease is greater on a small SES than on a large
SES. For the 2,000 ton example, the fuel weight represents
only about 15 percent of the total displacement. Therefore,
the assumption of a constant weight-to-drag ratio does not
introduce any significant errors. For small surface effect
ships and those that have a high ratio of fuel weight to
- 42 -
ship displacement, the variation of the weight-to-drag
ratio as fuel is consumed should be accounted for.
Since the jet area is constant and Q = V.A., equation
2.5 can be rewritten as:
A.p (V2
- V V.) = R + -K^p A.V.V (3.9.2)
where: R = ship drag after fuel weight is removed (lb)
V. = required jet velocity for new R (ft/sec)j
The required jet velocity is the only unknown in equation
3.9.2 and can therefore be solved for.
The new shaft horsepower required is then:
ArgA.V. V
2/(T) 2g) - V
2y) r,j2g + H . a + h/w to
-1 -] L 2 lnz &/ m (-0A/ & pipe 1
SHp = /wa ,1
55onp ng
(3.9.3)
The fuel for the next time increment is calculated
using the new SHP calculated in equation 3.9.3.
If there is an odd number of waterjet systems per
sidehull, the fuel consumption is based on the middle system.
The assumption made is that the larger amount of fuel required
for the forward system will be offset by the smaller amount
of fuel required by the after system.
If there is an even number of waterjet systems per
sidehull, the decrease in fuel required by the after system
is subtracted from the total fuel weight.
- 43 -
3.10 AIR CUSHION SYSTEM
A surface effect ship is supported partially by the
sidehull buoyancy, but mostly by a cushion of air. Normally,
10 to 20 percent of the total propulsive horsepower is
required to operate the air cushion system. The air cushion
system is normally designed before the rest of the propulsion
system because of its large impact on ship drag. It is
possible that the lift fans and propulsors could be operated
off the same engines, but this leads to complicated and
less reliable systems.
The optimization of the air cushion pressure is a
function of such variables as length-to-beam ratio, payload
weight ratio, range, operating environment, seal design
and stability requirements. The controlling variables are
the payload weight ratio and the seal design. Increasing
the payload weight ratio will require higher cushion pressures
and an increased drag if the total displacement is not
allowed to change.
The momentum drag of the air cushion represents an
important part of the total ship drag. The total ship drag
is assumed to be known in this report which therefore
requires that the air cushion system design must have been
completed.
There are two areas in which the air cushion system
has a direct effect on the propulsor design. First, up to
- 44 -
10 percent of the air cushion horsepower can be recovered
as a jet thrust through the rear seals. The percent recovered
is a function of seal design, cushion pressure and forward
speed. The jet thrust recovered through the seals represents
less than 2 percent of the total thrust. The second effect,
is that as fuel for the air cushion system is consumed the
drag of the ship will decrease. In the 2,000 ton example,
the total fuel weight represented about 13 percent of the
ship weight. This indicates that the fuel for the air
cushion system would represent between 1 and 3 percent of
the ship's total weight.
The total effects of the air cushion system on the
waterjet design are small and are not considered in this
report.
Including the air cushion system would not make the
waterjet propulsion system more competitive with a propeller
system. The resultant effects of the air cushion system
are independent of the propulsor type used.
- 45 -
4. RESULTS
Five different surface effect ships were analyzed to
provide examples of waterjet propulsion system performance
and characteristics. All the ships had a 2,000 ton
displacement and an 80 knot cruise speed. The only
characteristics that did vary were the length-to-beam ratio,
hump speed, hump drag, cruise drag and the engine type.
These characteristics are:
Shi p Length/Beam Ratic
HumpSpeed
HumpDrag
CruiseDrag
EngineType
1 1.5 27 440,000 223,000 FT9D
2 2.0 30 325,000 230,000 FT9D
3 3.0 38 265,000 235,000 FT9D
4 4.0 45 210,000 241,000 FT9D
5 2.0 30 325,000 230,000 LM2500
4.1 JET VELOCITY RATIO EFFECTS
The jet velocity ratio was the only independent variable
in the design process. All the other terms were either
inputs or dependent on the jet velocity ratio and inputs.
The jet velocity ratio was increased in steps until a
limiting constraint was encountered. Figures 6 and 7
present changes in the system component weights for an
increasing jet velocity for Ship 2. The numbers were
different, but the basic trends were the same in all ships
analyzed.
From the weight summaries, it can be seen that the
- 46 -
inlet system represents only about 7 percent of the total
system weight, while the fuel weight (1,000 mile range)
represents about 76 percent of the total system weight. The
inlet system, however, is the controlling component in
establishing the jet velocity ratio for a minimum weight ratio.
For Ship 2, the inlet system weight decreased by 24 tons over
the range of feasible jet velocity ratios while the maximum
change in fuel weight was only 4 tons.
The maximum net propulsive efficiency occurs at a much
lower jet velocity ratio. For the five ships considered,
the jet velocity ratio for maximum net propulsive efficiency
had a system weight 4 to 6 percent greater than the minimum
weight system. Conversely, the minimum weight system had
a net propulsive efficiency which was 3 to 5 percent less
than the maximum possible net propulsive efficiency.
However, due to poorer engine performance at lower power
levels, not all the gains in net propulsive efficiency were
reflected in fuel useage. The minimum weight system used
less than 2 percent more fuel than the system with maximum
propulsive efficiency. As the length-to-beam ratio decreased,
the percent savings in fuel useage between the minimum weight
system and the system with the maximum net propulsive
efficiency also decreased.
Using the net propulsive efficiency leads to a better
design than using the overall propulsive efficiency. The
- 47 -
overall propulsive efficiency does not penalize the system
which has a high inlet system drag, since the thrust required
is a function of the hull drag and the inlet system drag.
The results show that the lowest cruise horsepower requirement
occurs at the same jet velocity ratio as the maximum net
propulsive efficiency. The jet velocity ratio for maximum
net propulsive efficiency is always higher than the jet
velocity ratio for maximum overall propulsive efficiency.
Beside the system weight and the propulsive efficiency,
the other controlling parameter is the pump cavitation level.
The suction specific speed is a good indicator of the amount
of cavitation. In all cases, the cruise suction specific
speed decreased with an increasing jet velocity ratio, while
the hump suction specific speed increased with an increasing
jet velocity ratio.
4.2 LENGTH-TO-BEAM RATIO EFFECTS
Changing the length-to-beam ratio for a surface effect
ship will cause significant changes in the cruise drag,
hump drag and hump speed. Figure 9 shows the effect of the
length-to-beam ratio on cruise drag and hump drag. The
changes in drag and ship speed will have an effect on all
the components of the waterjet system. The results for
Ships 1, 2, 3 and 4 demonstrate these effects.
Figure 10 shows the effect of a changing length-to-beam
ratio on the minimum weight ratio attainable. The results
- 48 -
indicate that for the 2,000 ton class, a length-to-beam
ratio of about 3 is best for obtaining the minimum weight
ratio. Ship 3 (L/B = 3) is superior to Ship 2 (L/B = 2)
because of the constraining effect of Ship 2»s hump drag.
Both ships were constrained by the hump horsepower, but
Ship 3 reached a much higher jet velocity before this
limiting constraint was reached. When these two ships are
compared at the same jet velocity ratio, Ship 2 has a lower
weight ratio. Figures 11, 12 and 13 show the system component
weights as a function of the length-to-beam ratio.
Comparing propulsive efficiencies, Figure 14, with
length-to-beam ratios is somewhat misleading, in that the
differences in drag will result in different power levels
at hump and cruise speeds. A better comparison can be made
on a basis of fuel and horsepower requirements at the jet
velocity ratio corresponding to the maximum net propulsive
efficiency. Figure 15 shows the shaft horsepower requirements
at different length-to-beam ratios for the minimum weight
ratio system and the maximum propulsive efficiency system.
Generally, low length-to-beam ratios have lower power
requirements near cruise speed while high length-to-beam
ratios have lower power requirements near hump speed. At
cruise speed, a length-to-beam ratio of 2 results in the
best fuel consumption.
Figure 16 presents the pump suction specific speed for
- 49 -
for changing length-to-beam ratios. The cruise suction
specific speed favors a low length-to-beam ratio while the
hump suction specific speed favors a high length-to-beam
ratio. The hump suction specific speed is much higher than
that at cruise speed and therefore for pump design purposes
a high length-to-beam ratio is desirable.
Ship 1 (L/B = 1.5) required two more engines than Ships
2, 3 and 4 due to the hump power requirements. This system
was competitive with the other systems on a weight basis
only if cruising is performed on 4 engines.
For the 2,000 ton class SES, a length-to-beam ratio
between 2 and 3 appears to be the best. The final selection
of the length-to-beam ratio depends upon the relative
importance of system weight, system efficiency and pump
performance
.
4.3 EFFECTS OF ENGINE SIZE
The impact of the number of individual water jet systems
was analyzed by comparing Ship 2 and Ship 5. Ship 2 used
4 FT9D gas turbines while Ship 5 used 6 LM2500 gas turbines.
These two types of gas turbines were selected because the
total combined horsepower and the specific fuel consumption
rates were approximately equal.
A waterjet system weight comparison shows Ship 2 to be
6.4 tons lighter than Ship 5. Ship 2 has larger reduction
gear, pump and inlet system weights, while Ship 5 has larger
- 50 -
engine, fuel, pump-to-nozzle pipe and nozzle weights.
Generally, poorer performance characteristics in smaller
engines will cause much larger increases in fuel weights.
A comparison of the pump data shows that the design
with fewer engines has larger, but slower pumps. For Ship 2,
the pump RPM, suction specific speed and "blade tip velocity
are all lower than those on Ship 5. Due to these better
pump characteristics, Ship 2 is able to operate at a higher
jet velocity ratio, which leads to the lower system weight.
The reliability and maintainability of Ship 2 will be
better because of fewer components and better pump
characteristics.
4.4 DISPLACEMENT OPTIMIZATION
The optimization of ship displacement for a given
waterjet propulsion system v/ith 4 FT9D gas turbines was
computed for ships with length-to-beam ratios of 1.5, 2,
3 and 4. The results, shown in Figure 17, indicate that a
length-to-beam ratio of 3 has the largest optimum ship
displacement. The optimum ship displacement for maximum
propulsive efficiency was the same as the optimum
displacement for the minimum system weight ratio.
Figure 18 shows a typical system weight ratio versus
jet velocity ratio curve. The slope of this curve at the
point where the limiting constraint (available power or
pump suction specific speed) is reached, indicates the
- 51 -
direction in which the displacement should change. A
negative slope indicates the displacement should be decreased
while a positive slope indicates the displacement should
increase. The optimum displacement will occur as the
absolute value of the slope decreases. In most cases it
occurs before the slope actually reaches zero. The optimum
displacement in the ships studied, with the exception of
the ship with a length-to-beam ratio of 1.5, had less than a
one-half percent improvement in either the minimum weight
ratio or the maximum propulsive efficiency. This is due to
the fact that the engines and the ships are very well matched
in these particular cases. For the ship with a length-to-beam
ratio of 1.5, the displacement had to be reduced significantly
just to have enough power to accelerate through the hump
region.
- 52 -
5. CONCLUSIONS
The relatively high system weight and low propulsive
efficiency of waterjet propulsion are the major disadvantages
when compared to other types of propulsion systems.
Any attempts at reducing the system weight should be
directed toward the fuel weight, which represents over
70 percent of the system weight. Gas turbines such as the
LM2500 and the FT9D have excellent specific fuel consumption
rates making it doubtful that a reduction in system weight
could be obtained by using different engines. The high fuel
weight is caused by the low efficiency of the system.
Although small improvements in the flush inlet system or the
internal efficiency may be possible, only a small improvement
in the overall system efficiency would result. A 10 percent
increase in internal efficiency will result in less than a
1 percent increase in overall system propulsive efficiency.
The possibility of improving the propulsive efficiency
or minimum weight ratio by optimizing the ship displacement
does not appear to offer any significant improvements for
the 2,000 ton class. The non-propulsion system considerations
will probably have a much more important effect on the ship
displacement selected. If the engines and the contemplated
ship displacement are not well matched, optimizing the ship
displacement will result in significant improvements.
- 53 -
Length-to-beam ratios betv/een 2 and 3 plus the fewest
possible number of engines appear to give the best results
for either maximum efficiency or minimum system weight.
Pump suction specific speed favors high length-to-beam
ratios at hump speed and low length-to-beam ratios at cruise
speed. At length-to-beam ratios of 2 or less, the fuel
weight for the system with maximum net propulsive efficiency
and the minimum weight ratio system is about the same.
Therefore, for low length-to-beam ratios, the minimum system
weight optimization appears to be the best. At high length-
to-beam ratios the best optimization technique will depend
on the relative importance of system weight, system efficiency
and pump cavitation levels.
In conclusion, it appears that significant improvements
cannot be made in either water jet system weight or net
propulsive efficiency. Minor improvements will occur as
more experimental data on flush inlets, diffusers, axial-
flow pumps and ship drag becomes available. Waterjet
propulsion for surface effect ships will remain a good
alternative due to system simplicity, reliability and
maintainability.
- 54 -
BIBLIOGRAPHY
1. Barr, R. A., Systematic Calculations of the Performanceof Flush Inlets for Surface Effect Ships, Hydronautics,Incorporated, Technical Report 7224-4, October 1973.
2. Barr, R. A. and Etter, R. J., Selection of PropulsionSystems for High-Speed Advanced Marine Vehicles,Marine Technology, vol. 12, no. 1, pp. 33-50,January 1975.
3. Brandau, J. H., Performance of Water jet PropulsionSystem - A Review of the State-of-the-Art , Journal ofHydronautics, vol. 2, no. 2, April 1968.
4. Bruce, R. H., Modeling, Simulation and Control of WaterJet Propulsion for Surface Effect Ships (SES), OceanEngineer Thesis, M.I.T., May 1974.
5. Butler, E. A., An Advanced Concept for Propeller-drivenSurface Effect Ships (SES), Naval Engineers Journal,vol. 85, no. 5, pp. 55-64, October 1973.
6. Carmichael, A. D. and Johanek, W. R., Optimization ofWaterjet Propulsion Systems for Surface Effect Ships,Department of Ocean Engineering Report No. 74-10, M.I.T.,May 1974.
7. Garcia, A. P., Waterjet Pump Performance Determinations,Naval Engineers Journal, vol. 82, no. 5, pp. 35-44,October 1970.
8. Gill, R. P., Design Optimization of Waterjet PropulsionSystems for Hydrofoils, Ocean Engineer Thesis, M.I.T.,May 1972.
9. Johanek, W. R., Optimization of Water-Jet PropulsionSystem for Surface Effect Ships, Naval Architectureand Marine Engineering Masters Thesis, M.I.T., May 1974.
10. Johnson, V. E., 'Water jet Propulsion for High-SpeedHydrofoil, AIAA Paper No. 64-306, Washington D. C,June 1964.
11. Kim, H. C, Hydrodynamic Aspects of Internal Pump JetPropulsion, Marine Technology, vol. 78, no. 4, pp. 32-46,January 1966.
- 55 -
12. Kruse, K. K., Analysis of a Method for Optimum Designof Waterjet Propulsion Systems, Ocean Engineer Thesis,M.I.T., June 1973.
13. Mantle, P. J., Development of the USN Surface EffectShip, SES-100B, Naval Engineers Journal, vol. 85,no.- 5, pp. 65-78, October 1973.
14. Percival, R. C., Optimization of Waterjet PropulsionPumps for Hydrofoil Application, Ocean Engineer Thesis,M.I.T., May 1972.
15. Sladky, J., Principles of Surface Effect Vehicles,George Washington University, Course 60, June 1974.
16. Traksel, J. and Beck, W. E., Waterjet Propulsion forMarine Vehicles, AIAA Paper No. 65-245, Washington D. C,March 1965.
17. Conceptual Design Handbook for Surface Effect Ships,Surface Effect Ship Program Office, Washington D. C,
• February 1973.
- 56 -
.10
.08-
<K .06Eh
OMH
I
OE-i
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.02
20 M3 60
SHIP SPEED - KNOTS
86 100
Figure 1 - VARIATION OF SHIP DRAG-TO-WEIGHT RATIO WITHSHIP SPEED FOR A 2,000 TON FAMILY OF SURFACEEFFECT SHIPS
- 57 -
WOh/
1 MOPhEh o
1 H 525
w a, J M Eh(-3 SN CO WN t>lSI K Xeq feO H Oo S > !=>
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- 58 -
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I
SYSTEM 3 STARBOARD
SYSTEM 3 PORT
SYSTEM 2 STARBOARD
SYSTEM 2 PORT
SIDEHULL
SYSTEM 1 STARBOARD
SYSTEM 1 PORT
STERN
i
f
IFigure 3 - WATERJET SYSTEM ARRANGEMENT FOR SURFACE
EFFECT SHIPS
- 59 -
oo
LT\ CO
C^ Ht—
i
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l
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- 60 -
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OM
w .97wNCs]O
.96
.95.2 .Zf 6 .8 1.0
NOZZLE EXIT DIAMETER-TO-INLET DIAMETER RATIO
Figure 5 - VARIATION OF NOZZLE EFFICIENCY WITH THENOZZLE EXIT DIAMETER-TO-INLET DIAMETERRATIO (d/D) FOR A LONG RADIUS NOZZLE
= -.0375(d/Dr + ,0275(d/D) + .988)
- 61 -
100-
90
ooo
X
copq
coEhWCJ3M
OCm
§oosEnCO
CO
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80
70
60-
50;
IfO-
30 -
20 ;
10 -
INLETSYSTEM
ENGINE
2 STAGE
PUMP (INCLUDING WATER)
3 STAGESTAGE
REDUCTION GEAR
PUMP-TO-NOZZLE PIPE(INCLUDING WATER)
NOZZLE (INCLUDING WATER
)
1.70 1.78 1.86 ' l.tyf
JET VELOCITY RATIO
2. '02 '
Figure 6 - VARIATION OF WATERJET SYSTEM COMPONENT WEIGHTSWITH JET VELOCITY RATIO FOR A 2,000 TON SESWITH A LENGTH-TO-BEAM RATIO OF 2 and k FT9DGAS TURBINES
- 62 -
ooo
X
COPQh3
Eh
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EhCO
CO
EhW«
900i
800
700
600-
500-
ifOO
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200 -
100 -
SYSTEM WEIGHTINCLUDING FUEL)
FUEL WEIGHT
SYSTEM WEIGHTEXCLUDING FUEL)
1.70 ' 1.78~~"
1.86 1.'9^f
JET VELOCITY RATIO
2.02
Figure 7 - VARIATION OF WATERJET SYSTEM WEIGHTS WITH JETVELOCITY RATIO FOR A 2,000 TON SES WITH ALENGTH-TO-BEAM RATIO OF 2 AND k FT9D GAS TURBINES
- 63 -
ooo
Osm
CD
H
Oh
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30-
25
20
/
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/
HUMP
— L/B = 2
— L/B = Zf
1.67 1.87 2.07 2.27 Z.hl
JET VELOCITY RATIO
2.67
Figure 8 - VARIATION OF SHAFT HORSEPOWER PER ENGINE WITHJET VELOCITY RATIO FOR A 2,000 TON SES USINGk FT9D GAS TURBINES
- 64 -
450 n
400-
8 350o
COPQ
I
CD
S 300
250-
200-
CRUISE
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
4.0
Figure 9 - VARIATION OF HULL DRAG WITH SHIP LENGTH-TO-BEAMRATIO FOR A 2,000 TON SES
- 65 -
En<KEHWCD
wEhto
to
EhW>KWEn<3
S
Hl-H
s
.25-
.20
.15-
ENGINES<
ENGINES
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
k.O
Figure 10 - VARIATION OF V/ATERJET SYSTEM WEIGHT-TO-SHIPDISPLACEMENT RATIO WITH SHIP LENGTH-TO-BEAMRATIO FOR A 2,000 TON SES USING FT9D GASTURBINES
- 66 -
ooo
CO >HPQOW
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ENGINES
80-
60 -
INLET SYSTEM
k FT9D GAS TURBINES
TURBINES
ifO -
20 -
PUMP-TO-NCJZZLE PIPE
I PUMP-TO-NOZZLE PIPE
-NOZZLES-
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
^.0
Figure 11 - VARIATION OF WATERJET SYSTEM COMPONENT WEIGHTS(AT MAXIMUM NET PROPULSIVE EFFICIENCY) WITH THESHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SES
- 67 -
80-1
60-ooo
COPQK-3
^ENGINE
4 FT9D GAS TURBINES
TURBINES
oI H
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H KW CD^ HEhS
O EhPh CO
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Figure 12 -
20 -
PUMP-TO-NOZZLE PIPE
PUMP-TO-NOZZLE PIPE
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
¥70
VARIATION OF WATERJET SYSTEM COMPONENT WEIGHTS
(AT THE MINIMUM SYSTEM WEIGHT RATIO) WITH THE
SHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SES
- 68 -
900
800 -
§ 700
x
co 600PQhH"
i
co 500EnWCDMB ifoo -
a 300
EnWS 200WEh<
100 -
SYSTEM WEIGHT^ ^UNCLUDINGJTUELL _ —
FUEL WEIGHT -
MAXIMUM NETPROPULSIVEEFFICIENCY
MINIMUM SYSTEMWEIGHT RATIO
SYSTEM WEIGHT** - i. -A_ (EXCLUDING FUELJ
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
k.O
Figure 13 - VARIATION OF WATERJET SYSTEM WEIGHTS WITHSHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TONSES WITH FT9D GAS TURBINES
- 69 -
wCOM«
owMOM
CO
oK
.48-
.if?
.46-
sHXs
.451.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
4.0
Figure 14 - VARIATION OF THE MAXIMUM NET PROPULSIVEEFFICIENCY (CRUISE) WITH THE SHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SES USING4 FT9D GAS TURBINES
- 70 -
35
ooo
X
w 30
CD
«wPh
OPhWCOKo
Eh
to
23 -
20
\ ^HUMP'\\\\\\\\
MAXIMUM NET \
PROPULSIVE \EFFICIENCY
MINIMUM SYSTEMWEIGHT RATIO
\
1.3 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
k.O
Figure 15 - VARIATION OF SHAFT HORSEPOWER PER ENGINE WITHSHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SESWITH if FT9D GAS TURBINES
- 71 -
16000,
1/f000
12000-
wCO
oG 1 oooooWPnCO
&Ol-H
EHOCO
Pm
8000
Ph
6000
HUMP
MAXIMUM NETPROPULSIVEEFFICIENCY
MINIMUM SYSTEMWEIGHT RATIO
\
1.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
k.O
Figure 16 - VARIATION OF PUMP SUCTION SPECIFIC SPEED WITHSHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SESUSING k FT9D GAS TURBINES
- 72 -
2500r
BOEh
So
2300-
EH 2100-
o
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1900
EH
&
1700-
15001.5 2.0 3.0
SHIP LENGTH-TO-BEAM RATIO
4.0
Figure 17 - VARIATION OF OPTIMUM SHIP DISPLACEMENT WITHSHIP LENGTH-TO-BEAM RATIO FOR k FT9D GASTURBINES
- 73 -
oHEh
EH
CD
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to
EhH•-3
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JET VELOCITY RATIO
Figure 18 - REPRESENTATIVE VARIATION OF WATERJET SYSTEMWEIGHT RATIO WITH JET VELOCITY RATIO
- 74 -
oo
V = 100 KNOTS
/po 0.2
EhKWMo
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OCD
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15 25
SHIP HUMP SPEED - KNOTS
35
Figure 19 - INLET DRAG COEFFICIENT FOR VARYING ASPECT RATIOINLETS (reference 1)
- 75 -
0.65
O
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V = 80 KNOTS
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15 25 35
SHIP HUMP SPEED - KNOTS
Figure 20 - DESIGN SPEED OVERALL INTERNAL EFFICIENCYFOR VARYING ASPECT RATIO INLETS (reference 1)
- 76 -
0.80
o
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SHIP HUMP SPEED - KNOTS
35
Figure 21 - HUMP SPEED OVERALL INTERNAL EFFICIENCY FORVARYING ASPECT RATIO INLETS (reference 1)
- 77 -
15
o
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Figure 22 - TOTAL INLET SYSTEM WEIGHT COEFFICIENT FORVARYING ASPECT RATIO INLETS (reference 1)
- 78 -
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15 25 35
SHIP HUMP SPEED - KNOTS
igure 23 - INLET DRAG COEFFICIENT FOR 2.5 ASPECT RATIOINLETS (reference 1)
- 79 -
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15 25
SHIP HUMP SPEED - KNOTS
35
Figure 24 - DESIGN SPEED OVERALL INTERNAL EFFICIENCYFOR 2.5 ASPECT RATIO INLETS (reference 1)
- 80 -
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15 25
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35
Figure 25 - HUMP SPEED OVERALL INTERNAL EFFICIENCYFOR 2.5 ASPECT RATIO INLETS (reference 1)
- 81 -
15
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Figure 26 - TOTAL INLET SYSTEM WEIGHT COEFFICIENT FOR2.5 ASPECT RATIO INLETS (reference 1)
- 82 -
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- 83 -
APPENDIX A
COMPUTER RESULTS
The computer results of the surface effect ships studied
are presented in 4 page groups. The first page lists the
general ship characteristics. The second page presents a
table of summary data for all the acceptable jet velocity
ratios. The third page presents the complete system data
for the minimum weight ratio system. The fourth page
presents the complete system data for the maximum net
propulsive efficiency system.
The results for the 2,000 ton SES presented are:
Length/Beam Ratio
CruiseSpeed
HumpSpeed
EngineType
Pages
4.0 80 45 FT9D 85 - 88
3.0 80 38 PT9D 93 - 96
2.0 80 30 PT9D 101 - 104
2.0 80 30 LM2500 105 - 108
1.5 80 27 FT9D 109 - 112
The results for the optimum displacement of an SES
using 4 FT9L gas turbines presented are:
Length/Beam Ratio
CruiseSpeed
HumpSpeed
Displacement Pages
4.0 80 45 2050 89 - 92
3.0 80 38 2100 97 - 100
2.0 80 30 2000 101 - 104
1.5 80 27 1600 113 - 116
- 84 -
*** SES WATERJET PROPULSION SYSTEM WITH FLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
241000.1.00
HUMP45.0
210000.1.20
LENGTH-TO-BEAM RATIO 4.00DISPLACEMENT, LONG TONS 2000.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 85 -
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- 86 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.471
ENGINE *********=REDUCTION GEAR *=FUEL ***********= 650575.38PUMP DRY *******= 19014.52PUMP WATER *****=INLET SYSTEM ***=
53600.0012534.08
4138.8938816.45
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 2895.58PUMP-TO-NOZZLE WATER= 7361.93NOZZLE *************= 275.47NOZZLE WATER *******= 533.85
TOTAL WEIGHT = 789746.00 LBS OR 352.57 LONG TONS
PUMP DATA
NUMBER OP STAGES *=PUMP RPM-CRUISE **=PUMP EPF. -CRUISE *=S. SPEC. SP.-CRUISE=N.P. S.H. -CRUISE **=PUMP HEAD-CRUISE *=PUMP INLET DIA. **=FLOW COEF. -CRUISE =TIP VELO. -CRUISE *=PUMP FLOW-CRUISE *=
41421.28 PUMP RPM-HUMP ******= 1315. 0089.6455 PUMP EFF.-HUMP *****= 91. 05297240.23 S. SPEC. SP.-HUMP **= 12399.32195.39 N.P. S.H. -HUMP ******= 80.61
1632.00 PUMP HEAD-HUMP *****= 1424.702.6869 PUMP LENGTH ********= 5.99170.1529 FLOW COEF. -HUMP ****= 0.1500199.95 TIP VELO.-HUKP *****= 185.00157.70 PUMP FLOW-HUMP *****= 143.18
INLET DRAG-CRUISE = 11237.1 TOTAL RESIST .-CRUISE= 252237.1
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 2.9178INLET HEIGHT -CRUISE= 0.9085INLET WIDTH *******= 3.2116VARIABLE AREA FACT.= 1.6141
INLET AREA-HUMP *****= 4.7097INLET HEIGHT-HUMP ***= 1.4665INLET DIFFUSION RATIO= 3.5349REDUCTION GEAR RATIO = 2.5329
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.3182
NOZZLE LENGTH *******= 2.6364NOZZLE EXIT DIA. ****= 0.7755
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.3182PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ************= 0.3385PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.4300
- 87 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF., VJVO = 1.911
ENGINE *********=REDUCTION GEAR *=FUEL ***********=PUMP DRY *******=PUMP WATER *****=INLET SYSTEM ***=
53600.00 TRANSITION PIPE ****= 0.0016215.30 TRANSITION WATER ***= 0.00
636251.69 PUMP-TO-NOZZLE PIPE = 3834.6827005.64 PUMP-TO-NOZZLE WATER= 11539.696979.70 NOZZLE *************= 497.8282309.56 NOZZLE WATER *******= 1241.52
TOTAL WEIGHT = 839475.56 LBS OR 374.77 LONG TONS
PUMP DATA
NUMBER OP STAGES *= 2PUMP RPM-CRUISE **= 1108.30PUMP EFF. -CRUISE *= 87.8049S. SPEC. SP.-CRUISE= 7253.43N.P.S.H. -CRUISE **= 195.39PUMP HEAD-CRUISE *= 924.11PUMP INLET DIA. **= 3.4413FLOW COEF. -CRUISE = 0.1540TIP VELO. -CRUISE *= 199.70PUMP FLOW-CRUISE *= 260.29
PUMP RPM-HUMP ******= 982.33PUMP EFF. -HUMP *****= 91.4108S. SPEC. SP.-HUMP **= 11603.80N.P.S.H. -HUMP ******= 80.61PUMP HEAD-HUMP *****= 746.42PUMP LENGTH ********= 6.1599FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 177.00PUMP FLOW-HUMP *****= 224.71
INLET DRAG-CRUISE = 18547.2 TOTAL RESIST .-CRUISE= 259547.1
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.8160INLET HEIGHT-CRUISE= 1.1708INLET WIDTH *******= 4.1133VARIABLE AREA FACT.= 1.5348
INLET AREA-HUMP *****= 7.3914INLET HEIGHT-HUMP ***= 1.7970INLET DIFFUSION RATIO= 3.5131REDUCTION GEAR RATIO = 3.2482
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.6504
NOZZLE LENGTH *******= 3.3007NOZZLE EXIT DIA. ****= 1.1329
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.6504PUMP-TO-NOZZLE PIPE THICKNESS - FEET ***************= 0.3593PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.6400
- 88 -
*** SES WATERJET PROPULSION SYSTEM WITH PLUSH INLET ***
SHIP CHARACTERISTICS
CRUISE HUMPVELOCITY, KNOTS 80.0 45.0SHIP DRAG, LBS 247025 215250,ACCELERATION COEFFICIENT 1.00 1.20
LENGTH-TO-BEAM RATIO 4.00DISPLACEMENT, LONG TONS 2050.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 89 -
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- 90 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.471
ENGINE *********= 53600.00REDUCTION GEAR *= 13021.26FUEL ***********-_= 661821.31PUMP DRY *******= 19565.58PUMP WATER *****= 4296.02INLET SYSTEM ***= 40291.27
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 2658.12PUMP-TO-NOZZLE WATER= 7747.96NOZZLE *************= 257.37NOZZLE WATER *******= 568.54
TOTAL WEIGHT = 803827.25 LBS OR 358.85 LONG TONS
NUMBER OF STAGES **PUMP BPM-CRUISE **=PUMP EFF. -CRUISE *=S. SPEC. SP.-CRUISE=N.P.S.H. -CRUISE **=PUMP HEAD-CRUISE *=PUMP INLET DIA. **=FLOW COEF. -CRUISE =TIP VELO. -CRUISE *=PUMP FLOW-CRUISE *=
PUMP DATA
41401.79 PUMP RPM-HUMP ******= 1298.7689.6633 PUMP EFF. -HUMP *****= 91.07127230.28 S. SPEC. SP.-HUMP **= 12399.32195.39 N.P.S.H. -HUMP ******= 80.61
1627.96 PUMP HEAD-HUMP *****= 1427.272.7205 PUMP LENGTH ********= 6.06660.1531 FLOW COEF.-HUMP ****= 0.1500199.68 TIP VELO. -HUMP *****= 185.00161.67 PUMP FLOW-HUMP *****= 146.79
INLET DRAG-CRUISE = 11520.0 TOTAL RESIST .-CRUISE= 258544.9
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 2.9913INLET HEIGHT-CRUISE= 0.9199INLET WIDTH *******= 3.2517VARIABLE AREA FACT.= 1.6141
INLET AREA-HUMP *****= 4.8281INLET HEIGHT-HUMP ***= 1.4848INLET DIFFUSION RATIO= 3.5349REDUCTION GEAR RATIO = 2.5681
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.3523
NOZZLE LENGTH *******= 2.7046NOZZLE EXIT DIA. ****= 0.7852
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.3523PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ************= 0.3037PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.5200
- 91 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF., VJVO = 1.911
ENGINE *********= 536OO.OOREDUCTION GEAR *= 16885.86FUEL ***********= 648190.69PUMP DRY *******= 27791.28PUMP WATER *****= 7245.72INLET SYSTEM ***= 85450.69
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 3906.29PUMP-TO-NOZZLE WATER= 11784.31NOZZLE *************= 513.05NOZZLE WATER *******= 1284.24
TOTAL WEIGHT = 856651.94 LBS OR 382.43 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 2PUMP RPM-CRUISE **= 1094.55PUMP EFF. -CRUISE *= 87.8201S. SPEC. SP.-CRUISE= 7253.44N.P. S.H. -CRUISE **= 195.39PUMP HEAD-CRUISE *= 923.68PUMP INLET DIA. **= 3.4844FLOW COEF. -CRUISE = 0.1540TIP VELO. -CRUISE *= 199.70PUMP FLOW-CRUISE *= 266.87
PUMP RPM-HUMP ******= 970.16PUMP EFF. -HUMP *****= 91.4285S. SPEC. SP.-HUMP **= 11603.80N.P. S.H. -HUMP ******= 80.61PUMP HEAD-HUMP *****= 746.13PUMP LENGTH ********= 6.2371FLOW COEF. -HUMP ****= 0.1500TIP VELO.-HUI.iP *****= 177.00PUMP FLOW-HUMP *****= 230.39
INLET DRAG-CRUISE = 19016.1 TOTAL RESIST .-CRUISE= 266041.1
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.9377INLET HEIGHT -CRUISE= 1.1856INLET WIDTH *******= 4.1649VARIABLE AREA FACT.= 1.5347
INLET AREA-HUMP *****= 7.578IINLET HEIGHT-HUMP ***= 1.8195INLET DIFFUSION RAT 10= 3.5130REDUCTION GEAR RATIO = 3.2890
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= I.6678
NOZZLE LENGTH *******= 3.3355NOZZLE EXIT DIA. ****= 1.1472
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= I.6678PUMP-TO-NOZZLE PIPE THICKNESS - FEET ***************= 0.3622PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.7300
- 92 -
*** SES WATERJET PROPULSION SYSTEM WITH FLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
235000.1.00
HUMP38.0
265000.1.20
LENGTH-TO-BEAM RATIO 3.00DISPLACEMENT, LONG TONS 2000.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHIEGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEOGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 93 -
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- 94 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.406
ENGINE *********= 53600.00REDUCTION GEAR *= 12469.02FUEL ***********= 629295.87PUMP DRY *******= 19613.06PUMP WATER *****= 4309.62INLET SYSTEM ***= 38991.81
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 2765.07PUMP-TO-NOZZLE WATER= 7656.14NOZZLE *************= 268.34NOZZLE WATER *******= 569. 11
TOTAL WEIGHT = 769538.31 LBS OR 343.54 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 4PUMP RPM-CRUISE **= 1389.95PUMP EFF. -CRUISE *= 91.0676S. SPEC. SP.-CRUISE= 7314.29N.P. S.H. -CRUISE **= 189.92PUMP HEAD-CRUISE *= 1544.24PUMP INLET DIA. **= 2.7233FLOW COEF. -CRUISE = 0.1535TIP VELO. -CRUISE *= 198.20PUMP FLOW-CRUISE *= 161.26
PUMP RPM-HUMP ******= 1402.59PUMP EFF. -HUMP *****= 91.0728S. SPEC. SP.-HUMP **= 15589.43N.P. S.H. -HUMP ******= 69.43PUMP HEAD-HUMP *****= 1610.89PUMP LENGTH ********= 6.0730FLOW COEF. -HUMP ****= 0.1500TIP VELO.^-HUMP *****= 200.00PUMP FLOW-HUMP *****= 159.02
INLET DRAG-CRUISE = 11642.6 TOTAL RESIST. -CRUISE= 246642.6
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 2.9837INLET HEIGHT-CRUISE= 0.9166INLET WIDTH *******- 3.2552VARIABLE AREA FACT.= 2.0760
INLET AREA-HUMP *****= 6.1942INLET HEIGHT-HUMP ***= 1.9029INLET DIFFUSION RATIO= 3.5513REDUCTION GEAR RATIO = 2.5667
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.3443
NOZZLE LENGTH *******= 2.6885NOZZLE EXIT DIA. ****= 0.7947
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ***************= 1.3443PUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.3175PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.5300
- 95 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF . , VJVO = 1.886
ENGINE *********= 536OO.OOREDUCTION GEAR *= 15451.75FUEL ***********= 614743.81PUMP DRY *******= 27012.12PUMP WATER *****= 6981.88INLET SYSTEM ***= 80610.56
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 3690.73PUMP-TO-NOZZLE WATER= 11748.39NOZZLE *************- 483.43NOZZLE WATER *******= 1275.88
TOTAL WEIGHT = 815598.37 LBS OR 364.11 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 2PUMP RPM-CRUISE **= 1107.12PUMP EFF. -CRUISE *= 90.4507S. SPEC. SP.-CRUISE= 7421.73N.P.S.H. -CRUISE **= 189.92PUMP HEAD-CRUISE *= 900.99PUMP INLET DIA. **= 3.4416FLOW COEF. -CRUISE = 0.1550TIP VELO. -CRUISE *= 199.51PUMP FLOW-CRUISE *= 261.71
PUMP RPM-HUMP ******= 1054.37PUMP EFF.-HUMP *****= 91. 4110S. SPEC. SP.-HUMP **= 14434.96N.P.S.H. -HUMP ******= 69.43PUMP HEAD-HUMP *****= 846.04PUMP LENGTH ********= 6.1605FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 190.00PUMP FLOW-HUMP *****= 241.27
INLET DRAG-CRUISE = 18894.3 TOTAL RESIST .-CRUISE= 253894.2
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.8421INLET HEIGHT-CRUISE= 1.1771INLET WIDTH *******= 4.1137VARIABLE AREA FACT.= 1.9408
INLET AREA-HUMP *****= 9-3979INLET HEIGHT-HUMP ***= 2.2845INLET DIFFUSION RATIO= 3.4949REDUCTION GEAR RATIO = 3.2517
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.6652
NOZZLE LENGTH *******= 3.3304NOZZLE EXIT DIA. ***= 1.1435
PUMP-TO-NOZZLE PIPE DIAMETER - FEET **»************«= 1.6652PUMP-TO-NOZZLE PIPE THICKNESS - FEET ***************= 0.3430PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.6400
- 96 -
*** SES WATERJET PROPULSION SYSTEM WITH FLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
246750.1.00
HUMP38.0
278250.1.20
LENGTH-TO-BEAM RATIO 3.00DISPLACEMENT , LONG TONS 2100.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE Y/ATERLINE ABOVE BASELINE 2.0 FEET
- 97 -
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- 98 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.406
ENGINE ********#-REDUCTION GEAR *=FUEL ***********=PUMP DRY *******=PUMP WATER *****=INLET SYSTEM ***=
53600.00 TRANSITION PIPE ****= 0.0013484.79 TRANSITION WATER ***= 0.00
652150.63 PUMP-TO-NOZZLE PIPE = 2649.3020752.09 PUIXP-TO-NOZZLE WATER= 8159.504638.94 NOZZLE *************- 264.71
41974.09 NOZZLE WATER *******= 621.43
TOTAL WEIGHT = 798295.25 LBS OR 356.38 LONG TONS
PUMP DATA
NUMBER OP STAGES *= 4PUMP RPM-CRUISE **= 1354.85PUMP EFP. -CRUISE *= 91.1036S. SPEC. SP.-CRUISE= 7306.86N.P. S.H. -CRUISE **= 189.92PUMP HEAD-CRUISE *= 1540.73PUMP INLET DIA. **= 2.7910PLOW COEP. -CRUISE = 0.1537TIP VELO. -CRUISE *= 197.99PUMP PLOW-CRUISE *= 169.39
PUMP RPM-HUMP ******= 1368.58PUMP EFF.-HUMP *****= 91.1088S. SPEC. SP.-HUMP **= 15589.41N. P. S.H. -HUMP ******= 69.43PUMP HEAD-HUMP *****= 1612.49PUMP LENGTH ********= 6.2239FLOW COEF.-HUMP ****= 0.1500TIP VELO. -HUMP *****= 200.00PUMP FLOW-HUMP *****= 167.02
INLET DRAG-CRUISE = 12228.9 TOTAL RESIST .-CRUISE= 258978.9
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 3.1340INLET HEIGHT -CRUISE= 0.9394INLET WIDTH *******= 3.3360VARIABLE AREA FACT .=. 2.0759
INLET AREA-HUMP *****= 6.5058INLET HEIGHT -HUMP ***= 1.9502INLET DIFFUSION RATIO= 3.5511REDUCTION GEAR RATIO = 2.6305
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.3878
NOZZLE LENGTH *******= 2.7755NOZZLE EXIT DIA. ****= 0.8146
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ***************= 1.3878PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ************= 0.2953PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.7200
- 99 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF., VJVO = 1.886
ENGINE *********= 536OO.OOREDUCTION GEAR *= 16741.55FUEL ***********= 637755.38PUMP DRY *******= 28586.53PUMP WATER *****= 7517.33INLET SYSTEM ***= 86803.69
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 3835.58PUMP-TO-NOZZLE WATER= 12237.74NOZZLE *************= 514.07NOZZLE WATER *******= 1363.28
TOTAL WEIGHT = 848954.94 LBS OR 379.00 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 2PUMP RPM-CRUISE **= 1080.19PUMP EFF. -CRUISE *= 90.4830S. SPEC. SP.-CRUISE= 7422.11N.P. S.H. -CRUISE **= 189.92PUMP HEAD-CRUISE *= 900.22PUMP INLET DIA. **= 3.5274FLOW COEF. -CRUISE = 0.1550TIP VELO. -CRUISE *= 199.51PUMP FLOW-CRUISE *= 274.95
PUMP RPM-HUMP ******= 1028.72PUMP EFF. -HUMP *****= 91.4458S. SPEC. SP.-HUMP **= 14434.97N.P. S.H. -HUMP ******= 69.43PUMP HEAD-HUMP *****= 845.38PUMP LENGTH ********= 6.3141FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 190.00PUMP FLOW-HUMP *****= 253.45
INLET DRAG-CRUISE = 19850.0 TOTAL RESIST .-CRUISE= 266600.0
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 5.0871INLET HEIGHT -CRUISE= 1.2065INLET WIDTH *******= 4.2163VARIABLE AREA FACT.= 1.9407
INLET AREA-HUMP *****= 9.8724INLET HEIGHT-HUMP ***= 2.3415INLET DIFFUSION RAT10= 3.4946REDUCTION GEAR RATIO = 3.3327
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.6995
NOZZLE LENGTH *******= 3.3991NOZZLE EXIT DIA. ****= 1.1722
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.6995PUMP-TO-NOZZLE PIPE THICKNESS - FEET ***************= 0.3493PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 38.8300
- 100 -
*** SES WATERJET PROPULSION SYSTEM WITH FLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
230000.1.00
HUMP30.0
325000.1.20
LENGTH-TO-BEAM RATIO 2.00DISPLACEMENT, LONG TONS 2000.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 101 -
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- 102 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.057
ENGINE *********= 53600.00REDUCTION GEAR *= 18941.25FUEL ***********= 601769.94PUMP DRY *******= 31054.92PUMP WATER *****= 7848.17INLET SYSTEM ***= 57120.17
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 2463.90PUMP-TO-NOZZLE WATER= 10688.15NOZZLE *************= 290.43NOZZLE WATER *******= 990.58
TOTAL WEIGHT = 784767.50 LBS OR 350.43 LONG TONS
PUMP DATA
NUMBER OF STAGES *=PUMP RPM-CRUISE **=PUMP EFF. -CRUISE *=S. SPEC. SP.-CRUISE=N.P.S.H. -CRUISE **=PUMP HEAD-CRUISE *=PUMP INLET DIA. **=FLOW COEF. -CRUISE =TIP VELO. -CRUISE *=PUMP FLOW-CRUISE *=
4994.10 PUMP RPM-HUMP ******= 1045.19
91.3071 PUMP EFF. -HUMP *****= 91.36236108.71 S. SPEC. SP.-HUMP **= 15875.05185.81 N.P.S.H.-HUMP ******= 56.12
1091.69 PUMP HEAD-HUMP *****= 1254.673.3257 PUMP LENGTH ********= 7.41620.1555 FLOW COEF. -HUMP ****= 0.1500173.10 TIP VELO. -HUMP *****= 182.00212.80 PUMP FLOW-HUMP *****= 215.80
INLET DRAG-CRUISE = 15592.6 TOTAL RESIST .-CRUISE= 245592.6
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 3.9373INLET HEIGHT-CRUISE= 0.9905INLET WIDTH *******= 3.9751VARIABLE AREA FACT.= 2.7042
INLET AREA-HUMP *****= 10.6473INLET HEIGHT-HUMP ***= 2.6785INLET DIFFUSION RATIO= 4.0132REDUCTION GEAR RATIO = 3.4444
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.5883
NOZZLE LENGTH *******= 3.1766NOZZLE EXIT DIA. ****= 0.9873
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.5883PUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.2411PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 40.2100
- 103 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF., VJVO = 1.857
ENGINE *********= 536OO.OOREDUCTION GEAR *= 19083.50FUEL ***********= 600454.69PUMP DRY *******= 34336.61PUMP WATER *****= 9373.45INLET SYSTEM ***= 79682.81
TRANSITION PIPE ****= 0.00TRANSITION V/ATER ***= 0.00PUMP-TO-NOZZLE PIPE = 2854.71PUMP-TO-NOZZLE WATER= 12918.05NOZZLE *************= 384.40NOZZLE WATER *******= 1418.19
TOTAL WEIGHT = 814106.19 LBS OR 363.44 LONG TONS
PUMP DATA
NUMBER OF STAGES *=PUMP RPH-CRUISE **=PUMP EFF. -CRUISE *=S. SPEC. SP.-CRUISE=N.P.S.H. -CRUISE **=PUMP HEAD-CRUISE *=PUMP INLET DIA. **=FLOW COEF. -CRUISE =TIP VELO. -CRUISE *=PUMP FLOW-CRUISE *=
3940.48 PUMP RPM-HUMP ******= 954.73
91.4244 PUMP EFF. -HUMP *****= 91.49046457.43 S. SPEC. SP.-HUMP **= 15875.09185.81 N.P.S.H. -HUMP ******= 56.12866.62 PUMP HEAD-HUMP *****= 934.883.6408 PUMP LENGTH ********= 7.39070.1564 FLOW COEF. -HUMP ****= 0.1500179.28 TIP VELO. -HUMP *****:= 182.00265.68 PUMP FLOW-HUMP *****= 258.63
INLET DRAG-CRUISE = 19467.1 TOTAL RESIST .-CRUISE= 249467.1
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.9157INLET HEIGHT-CRUISE= 1.1296INLET WIDTH *******= 4.3517VARIABLE AREA FACT.= 2.5958
INLET AREA-HUMP *****= 12.7604INLET HEIGHT-HUMP ***= 2.9323INLET DIFFUSION RATIO= 3.8524REDUCTION GEAR RATIO = 3.7707
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.7461
NOZZLE LENGTH *******= 3.4923NOZZLE EXIT DIA. ****= 1.1611
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.746IPUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.2543PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 40.1800
- 104 -
*** SES WATERJET PROPULSION SYSTEM WITH PLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
230000.1.00
HUMP30.0
325000.1.20
LENGTH-TO-BEAM RATIO 2.00DISPLACEMENT, LONG TONS 2000.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED LM 2500REQUIRED NUMBER OF GAS TURBINES 6
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 105 -
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- 106 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 1.970
ENGINE *********= 63000.00REDUCTION GEAR *= 14437.49FUEL ***********= 606390.25PUMP DRY *******= 28566.59PUMP WATER *****= 6517.64INLET SYSTEM ***= 53386.62
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 4398.90PUMP-TO-NOZZLE V/ATER= 21101.11NOZZLE *******-******= 274.53NOZZLE WATER *******= 1025.30
TOTAL WEIGHT = 799098.12 LBS OR 356.74 LONG TONS
PUMP DATA
NUMBER OP STAGES *«=
PUMP RPM-CRUISE **=PUMP EFF. -CRUISE *=S. SPEC. SP.-CRUISE=N.P. S.H. -CRUISE **=PUMP HEAD-CRUISE *=PUMP INLET DIA. **=FLOW COEF. -CRUISE =TIP VELO. -CRUISE *=PUMP FLOW-CRUISE *=
1188.33 PUMP RPM-HUMP ******= 1233.6291.1260 PUMP EFF. -HUMP *****= 91.12286236.98 S. SPEC. SP.-HUMP **= 15875.07185.81 N.P. S.H. -HUMP ******= 56.12985.85 PUMP HEAD-HUMP *****= 1109.002.8177 PUMP LENGTH ********= 5.71990.1561 FLOW COEF. -HUMP ****= 0.1500175.32 TIP VELO. -HUMP *****= 182.00155.24 PUMP PLOW-HUMP *****= 154.91
INLET DRAG-CRUISE = 17062.6 TOTAL RESIST .-CRUISE= 247062.6
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.3085INLET HEIGHT-CRUISE= 1.0445INLET WIDTH *******= 4.1248VARIABLE AREA FACT .= 2.6609
INLET AREA-HUMP *****= 11.4645INLET HEIGHT-HUMP ***= 2.7794INLET DIFFUSION RATIO= 3.9490REDUCTION GEAR RATIO = 2.7561
TRANS. PIPE LENGTH 0.0000NOZZLE INLET DIA. *= 1.4135
NOZZLE LENGTH *******= 2.8269NOZZLE EXIT DIA. ****= 0.8618
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.4135PUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.1943PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 34.9600PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 3 - FEET *****= 69.9200
- 107 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFP., VJVO = 1.850
ENGINE *********= 63000.00REDUCTION GEAR *= 14422.69FUEL ***********- 606904.63PUMP DRY *******= 32557.20PUMP WATER *****= 7729.71INLET SYSTEM ***= 65865.75
TRANSITION PIPE «***= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 4751.68PUMP-TO-NOZZLE WATER= 23838.26NOZZLE *************=: 322.43NOZZLE WATER *******= 1286.49
TOTAL WEIGHT = 820678.62 LBS OR 366.37 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 3PUMP RPM-CRUISE **= 1147.84PUMP EFF. -CRUISE *= 91.1287S. SPEC. SP.-CRUISE= 6461.38N.P.S.H. -CRUISE **= 185.81PUMP HEAD-CRUISE *= 853.96PUMP INLET DIA. **= 2.9825FLOW COEF. -CRUISE = 0.1567TIP VELO. -CRUISE *= 179.25PUMP FLOY/-CRUISE *= 178.58
PUMP RPM-HUMP ******= 1165.44PUMP EFF. -HUMP *****= 91.2057S. SPEC. SP.-HUMP **= 15875.06N.P.S.H. -HUMP ******= 56.12PUMP HEAD-HUMP *****= 923.48PUMP LENGTH ********= 6.0545FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 182.00PUMP FLOW-HUMP *****= 173.56
INLET DRAG-CRUISE = 19627.4 TOTAL RESIST .-CRUISE * 249627.
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.9562INLET HEIGHT-CRUISE= 1.1351INLET WIDTH *******= 4.3661VARIABLE AREA FACT.= 2.5917
INLET AREA-HUMP *****= 12.8451INLET HEIGHT-HUMP ***= 2.9420INLET DIFFUSION RATI0= 3.8464REDUCTION GEAR RATIO = 2.9173
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.5023
NOZZLE LENGTH *******= 3.0047NOZZLE EXIT DIA. ****= 0.9536
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.5023PUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.1976PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 35.3800PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 3 - FEET *****= 70.7600
- 108 -
*** SES WATERJET PROPULSION SYSTEM WITH PLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
223000.1.00
HUMP27.0
440000.1.20
LENGTH-TO-BEAM RATIO 1.50DISPLACEMENT, LONG TONS 2000.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 6
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTER!INE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 109 -
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- 110 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 2.024
ENGINE *********= 80400.00REDUCTION GEAR *= 25180.83FUEL ***********= 895881.56PUMP DRY *******= 39466.41PUMP WATER *****= 9102.52INLET SYSTEM ***= 46238.93
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 5242.38PUMP-TO-NOZZLE WATER= 23546.81NOZZLE *************== 259.08NOZZLE WATER *******= 896.96
TOTAL WEIGHT = 1126215.00 LBS OR 502.77 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 5PUMP RPM-CRUISE **= 933.95PUMP EFF. -CRUISE *= 87.9944S. SPEC. SP.-CRUISE= 4711.12N.P. S.H. -CRUISE **= 184.86PUMP HEAD-CRUISE *= 1053.93PUMP INLET DIA. **= 2.96630FLOW COEF. -CRUISE = 0.1560TIP VELO. -CRUISE *= 145.05PUMP FLOW-CRUISE *= 142.30
PUMP RPM-HUMP ******= 1126.75PUMP EFF. -HUMP *****= 91.1978S. SPEC. SP.-HUMP ***= 15990.97N.P. S.H. -HUMP ******= 51.39PUMP HEAD-HUMP *****= 1600.55PUMP LENGTH ********= 7. 2080FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 175.00PUMP FLOW-HUMP *****= 165.08
INLET DRAG-CRUISE = 15725.8 TOTAL RESIST .-CRUISE = 238725.
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 3.9492INLET HEIGHT-CRUISE= 0.9095INLET WIDTH *******= 4.3424VARIABLE AREA FACT.= 3.4372
INLET AREA-HUMP *****= 13.5744INLET HEIGHT-HUMP ***= 3.1260INLET DIFFUSION RATIO= 4.7747REDUCTION GEAR RATIO n 3.1950
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.3611
NOZZLE LENGTH *******= 2.7222NOZZLE EXIT DIA. ****= 0.8140
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= 1.3611PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ********»**= 0.1997PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 39*9500PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 3 - FEET *****= 79.9OOO
- Ill -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EPF., VJVO = 1.744
ENGINE *********= 80400.00REDUCTION GEAR *= 24947.88FUEL ***********= 893486.69PUMP DRY *******= 43746.89PUMP WATER *****= 11363.47INLET SYSTEM ***= 77005.31
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 6687.61PUMP-TO-NOZZLE WATER= 31359.61NOZZLE *************= 403.85NOZZLE WATER *******= 1539.98
TOTAL WEIGHT = 1170941.00 LBS OR 522.74 LONG TONS
PUMP DATA
NUMBER OF STAGES *=
PUMP RPM-CRUISE **=
PUMP EFF. -CRUISE *=
S. SPEC. SP. -CRUISE:N.P. S.H. -CRUISE **=
PUMP HEAD-CRUISE *=
PUMP INLET DIA. **=
FLOW COEF. -CRUISE :
TIP VELO. -CRUISE *=
PUMP FLOW-CRUISE *=
3869.32 PUMP RPM-HUMP ******= 985.54
90.4186 PUMP EFF.-HUMP *****= 91.39015197.81 S. SPEC. SP. -HUMP ***= 15990.96184.86 N. P. S.H. -HUMP ******= 51.39750.60 PUMP HEAD-HUMP *****= 1018.723.3913 PUMP LENGTH ********= 6.88430.1576 FLOW COEF. -HUMP ****= 0.1500154.36 TIP VELO.-HULIP *****= 175.00199.93 PUMP FLOW-HUMP *****= 215.77
INLET DRAG-CRUISE = 22094.8 TOTAL RESIST .-CRUISE= 245094.8
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 5.5487INLET HEIGHT-CRUISE= 1.1177INLET WIDTH *******= 4.9646VARIABLE AREA FACT.= 3.1977
INLET AREA-HUMP *****= 17.7430INLET HEIGHT-HUMP ***= 3.5739INLET DIFFUSION RATIO= 4.4419REDUCTION GEAR RATIO = 3.6528
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.5707
NOZZLE LENGTH *******= 3.1415NOZZLE EXIT DIA. ****= 1.0394
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ***************= I.5707PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ************= 0.2208PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 39.5400PUMP TO NOZZLE PIPE LENGTH FOR SYSTEM 3 - FEET *****= 79.0900
- 112 -
*** SES WATERJET PROPULSION SYSTEM WITH PLUSH INLET ***
SHIP CHARACTERISTICS
VELOCITY, KNOTSSHIP DRAG, LBSACCELERATION COEFFICIENT
CRUISE80.0
178400.1.00
HUMP27.0
352000.1.20
LENGTH-TO-BEAM RATIO 1.50DISPLACEMENT, LONG TONS 1600.ENDURANCE, NAUTICAL MILES 1000.GAS TURBINE PLANT SELECTED FT 9DREQUIRED NUMBER OF GAS TURBINES 4
INLET ASPECT RATIO VARYINGHEIGHT OF DIFFUSER OUTLET ABOVE BASELINE 6.5 FEETHEIGHT OF PUMP CENTERLINE ABOVE BASELINE 6.5 FEETHEIGHT OF OUTSIDE WATERLINE ABOVE BASELINE 2.0 FEET
- 113 -
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- 114 -
SYSTEM WEIGHTS AT MIN. TOTAL WEIGHT RATIO, VJVO = 1.742
ENGINE *********= 536OO.OOREDUCTION GEAR *= 22721.66FUEL ***********= 623358.63PUMP DRY *******= 36053.78PUMP WATER *****= 9989.48INLET SYSTEM ***= 67756.37
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP TO NOZZLE PIPE = 2040.02PUMP TO NOZZLE WATER= 12913.31NOZZLE *************= 271.66NOZZLE WATER *******= 1389.79
TOTAL WEIGHT = 830094.50 LBS OR 370.58 LONG TONS
PUMP DATA
NUMBER OP STAGES *= 3PUMP RPM-CRUISE **= 790.19PUMP EFF. -CRUISE *= 90.5610S. SPEC. SP.-CRUISE= 5182.56N.P.S.H. -CRUISE **= 184.86PUMP HEAD-CRUISE *= 743.67PUMP INLET DIA. **= 3.7188PLOW COEP. -CRUISE = 0.1582TIP VELO. -CRUISE *= 153.86PUMP PLOW-CRUISE *= 240.56
PUMP RPM-HUMP ******= 898.74PUMP EFF.-HUMP *****= 91.5201S. SPEC. SP.-HUMP **= 15990.97N.P.S.H, -HUMP ******= 51.39PUMP HEAD-HUMP *****= 1020.71PUMP LENGTH ********= 7.5492PLOW COEF.-HUMP ****= 0.1500TIP VELO. -HUMP *****= 175.00PUMP PLOW-HUMP *****= 259.46
INLET DRAG-CRUISE = 17723.3 TOTAL RESIST .-CRUISE= 196123.3
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.4509INLET HEIGHT-CRUISE= 1.0013INLET WIDTH *******= 4.4450
INLET AREA-HUMP *****= 14.2239INLET HEIGHT-HUMP ***= 3.1999INLET DIFFUSION RATIO= 4.4392
VARIABLE AREA FACT.= 3.1958 REDUCTION GEAR RATIO = 4.0056
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.7468
NOZZLE LENGTH ****** = 3.4917NOZZLE EXIT DIA. *** = 1.1407
PUMP-TO-NOZZLE PIPE DIAMETER - FEET *************** m 1.7458PUMP-TO-NOZZLE PIPE THICKNESS - INCHES ************ - 0.1824PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET **** = 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET **** = 40.3700
- 115 -
SYSTEM WEIGHTS AT MAX. NET PROPULSIVE EFF., VJVO = 1.742
ENGINE *********= 536OO.OOREDUCTION GEAR *= 22759.80FUEL ***********= 623272.38PUMP DRY *******= 36053.78PUMP V/ATER *****= 9989.48INLET SYSTEM ***= 67756.37
TRANSITION PIPE ****= 0.00TRANSITION WATER ***= 0.00PUMP-TO-NOZZLE PIPE = 1949.68PUMP-TO-NOZZLE WATER= 13001.01NOZZLE *************= 259.97NOZZLE WATER *******= 1398.68
TOTAL WEIGHT = 830040.87 LBS OR 370.55 LONG TONS
PUMP DATA
NUMBER OF STAGES *= 3PUMP RPM-CRUISE **= 789.63PUMP EFF. -CRUISE *= 90.5610S. SPEC. SP.-CRUISE= 5178.90N.P.S.H. -CRUISE **= 184.86PUMP HEAD-SRUISE *= 743.22PUMP INLET DIA. **= 3.7188FLOW COEF. -CRUISE = 0.1583TIP VELO. -CRUISE *= 153.75PUMP FLOW-CRUISE *= 240.56
PUMP RPM-HUMP ******= 898.74FUMP EFF. -HUMP *****= 91.5201S. SPEC. SP.-HUMP **= 15990.97N.P.S.H. -HUMP ******= 51.39PUMP HEAD-HUMP *****= 1022.43PUMP LENGTH ********= 7.5492FLOW COEF. -HUMP ****= 0.1500TIP VELO. -HUMP *****= 175.00PUMP FLOW-HUMP *****= 259.46
INLET DRAG-CRUISE = 17723.3 TOTAL RESIST .-CRUISE= 196123.3
MISCELLANEOUS SYSTEM DATA
INLET AREA-CRUISE *= 4.4509INLET HEIGHT CRUISE= 1.0013INLET WIDTH *******= 4.4450VARIABLE AREA FACT.= 3.1958
INLET AREA-HUMP *****= 14.2239INLET HEIGHT HUMP ***= 3.1999INLET DIFFUSION RATIO= 4.4392REDUCTION GEAR RATIO = 4.0056
TRANS. PIPE LENGTH = 0.0000NOZZLE INLET DIA. *= 1.7517
NOZZLE LENGTH *******= 3.5035NOZZLE EXIT DIA. ****= 1.1407
PUMP-TO-NOZZLE PIPE DIAMETER - FEET ****************= I.7517PUMP-TO-NOZZLE PIPE THICKNESS - INCHES *************= 0.1738PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 1 - FEET *****= 0.0000PUMP-TO-NOZZLE PIPE LENGTH FOR SYSTEM 2 - FEET *****= 40.3700
- 116 -
APPENDIX B
COMPUTER PROGRAM DESCRIPTION
This waterjet optimization computer program for surface
effect ships is a modified and expanded version of the
computer program presented in reference 6. This program
optimizes the waterjet system on a basis of maximum net
propulsive efficiency or minimum system weight ratio. It
also is capable of optimizing the displacement of the ship
for a given number of specified engines. The computer program
consists of the main program and four subroutines. The
characteristics of up to fifteen different engines can be
stored in the main program.
After reading in the ship data and selecting the engines
and inlet system, the main program call subroutine SESIN.
This subroutine computes the inlet system internal efficiency,
inlet drag coefficient and the ratio of entering water
momentum velocity to ship speed at hump and cruise speeds.
This subroutine is essentially a computerization of Figures
19 through 26.
The main program then computes the approximate jet
velocity for maximum overall propulsive efficiency. Using
this jet velocity ratio, an assumed efficiency (pump and
reduction gear) of .865 and neglecting the pump-to-nozzle
pipe, the program computes the number of engines required.
- 117 -
With the number of engines known, the flow rate per system
is determined and subroutine PIPE is called. Subroutine
PIPE returns the head loss due to the pump-to-nozzle piping.
The main program then recomputes the number of engines
required.
The jet velocity ratio is the only system variable.
The velocity ratio is increased in steps and subroutines
PIPE and PUMP are called respectively. Subroutine PIPE
returns the optimum characteristics of the pump-to-nozzle
pipe and the head losses due to the pipe at hump and cruise
speeds. Subroutine PUMP returns all the system data.
A summary of this data, including the system weight ratio
and net propulsive efficiency, is stored in an array in the
main program. The jet velocity ratio is increased until
either the number of required pump stages exceeds six or the
required power at hump or cruise speed exceeds the available
power. The program then prints out a table of summary data
for every jet velocity ratio. Finally, the program
recalculates and prints out all the system data for the
minimum weight ratio system and the system with the maximum
net propulsive efficiency.
At this point, the program will either go to the next
set of input data or it will optimize the displacement.
This option is controlled by the variable KK.
If displacement optimization is desired, the program
- 118 -
will check the slope of the weight-to-drag ratio versus
the jet velocity ratio curve at the point when a limiting
constraint is reached. If the slope is positive the
displacement v/ill be increased and if the slope is negative
the displacement will be decreased. New drags are then
determined using a constant lift-to-drag ratio. The entire
program is then repeated for the new displacement and drags.
This process will continue until the minimum weight ratio
is found.
Subroutine PUMP uses the equations developed in Chapters
2 and 3 to define the basic pump characteristics and
performance. The subroutine designs the pump at hump speed
to meet the constraints of blade tip velocity and suction
specific speed. The pump efficiency is then determined by
the pump diameter and a test is made to determine if
sufficient power is available to accelerate through the
hump region. Next, the cruise performance is calculated and
the constraints of blade tip velocity, suction specific
speed and available power are checked. If these constraints
are not satisfied, the blade tip velocity at hump speed is
decreased and entire pump design process is repeated.
Once the pump is determined, subroutine WEIGHT is
called. Subroutine WEIGHT returns the system weights
according to equations developed in Chapter 3.
- 119 -
APPENDIX C
COMPUTER PROGRAM USER»S GUIDE
This program has two arrays available for storing the
characteristics of fifteen different engines. The
characteristics are entered in two card groups, thus thirty-
cards are required. The characteristics of fourteen gas
turbines are listed in Table 1. If fifteen engines are not
required, blank cards can be used to fill the remainder of
the thirty cards. The engine characteristics cards consist
of fifteen groups of two cards containing:
Card 1 - Name of the engine
The format for this card is 3A4.
Card 2 - PERF(IENG, l) - Normal SHP
PERF(IENG, 2) - Maximum SHP
PERP(IENG, 3) - SFC at normal SHP
PERF(IENG, 4) - RPM of engine
PERF(IENG, 5) - Weight of engine
PERF(IENG, 6) - Length of engine
The format for this card is 6F10.3.
Following the thirty engine characteristics cards,
the user must input two cards to describe the inlet systems
that can be used. In this program the inlet systems available
are a 2.5 aspect ratio inlet and a varying aspect ratio
inlet
•
Card 31 - 2.5
Card 32 - VARYING
The format for cards 31 and 32 is 2A4.
- 120 -
Next the user must input three cards for each waterjet
system. There is no limit to the number of different
systems that can be designed in a single computer run as
long as the engine characteristics are entered somewhere in
cards 1 through 30.
Card 33 - IENG
IAR
NGT
- The type of engine selectedcorresponding to its positionamong the fifteen enginesdescribed in cards 1 through30.
- The type of inlet system selected.1 for a 2.5 aspect ratio inlet2 for a varying aspect ratio inlet
- The number of engines to be used.If this space is left blank, theprogram will determine the numberof engines required.
KK - If KK = 2, the program will optimizethe ship displacement. If KK ^ 2,the program will optimize thewater jet design for the givendisplacement only.
KINCRE - The size of the displacementincrement as a fraction of thetotal original displacement.This space may be left blank ifKK ^ 2.
The format for this card is 515.
Card 34 - HEP
HEW
- The height of the pump abovethe inlet in feet.
- The height of the outsidewaterline above the inlet infeet.
CAC - The acceleration coefficientrequired at hump speed.
XLENG(l) - The length of the pump-to-nozzle pipe for system 1.
The format for this card is 4F10.2.
- 121 -
Card 35 - VO(l) - Cruise speed in knots
V0(2) - Hump speed in knots
DRAG(l) - Hull drag at cruise speed
DRAG(2) - Hull drag at hump speed
DISP - Ship displacement in long tons
RANGE - Range in nautical miles
XLTOB - Length-to-beam ratio
The format of this card is 7F10.2.
Final Card - This card is left blank
A sample input data deck to optimize three different
waterjet systems is shown on pages 158 and 159- This data
deck will produce results for three 2,000 ton surface effect
ships. A brief summary of the characteristics of the three
ships are:
hip Length/Beam Ratio
TypeEngine
OptimizeDisplacement
1 4.0 PT9D Yes
2 2.0 LM2500 Yes
3 1.5 FT9D No
- 122 -
APPENDIX D
COMPUTER PROGRAM
- 123 -
LIST OF PROGRAM VARIABLES
A
AAJET
AD
AINLET
AJET
APUP
AR
ASPRT(I,J)
CA
CAC
CAC1
CAL
CB
CDIN1
CDIN(I)
COR1
C0R2
The individual water jet system forwhich the pump is designed
Jet area per pump
Diffuser outlet area
Inlet area at cruise speed
Total jet area
Pump inlet area
Inlet aspect ratio
Variable used to print out type ofinlet aspect ratio1 for 2.5 aspect ratio inlets2 for varying aspect ratio inlets
The square of the ratio of themomentum velocity of entering waterto the ship velocity (GU)
Coefficient used in determining RX
Acceleration coefficient at humpspeed
Acceleration coefficient at cruisespeed
Ratio of ship drag to displacement
Coefficient used in determining RX
Inlet drag coefficient at cruisespeed
Inlet drag coefficient
Correction factor for ETAOA(l)
Correction factor for ETA0A(2)
ft /pump
ft2
ft2
ft2
ff
- 124 -
CORRD
CORRN
CU
CW
CWIN
Dl
D2
DC OF
DEL
DEL
DIS(l)
DISP
DISPIN
DISP1
DJET
DPIPE
DR
DRAG(I)
DRAT
EFFNOZ
Correction factor for CDIN(I)
Correction factor for ETAOA(l)
Ratio of momentum velocity of inletwater to ship velocity-
Pump weight coefficient
Inlet system weight coefficient
Variable used to determine nozzleweights
Variable used to determine nozzleweights
Inlet drag coefficient (subroutineWEIGHT)
Increment of change in jet velocityratio (MAIN program)
Increment of change in pump-to-nozzlepipe diameter (subroutine PIPE)
Displacement after removing fuel lb
Displacement - entered in long tonsconverted to pounds
Amount of change in ship displacement tonsused in ship displacement optimization
New ship displacement used in ship tonsdisplacement optimization
Diameter of nozzle exit ft
Diameter of pump-to-nozzle pipe ft
Diffusion ratio
Ship drag lb
Ratio of pump inlet hub radius toblade tip radius
Efficiency of nozzle
- 125 -
ENGN(IJ,IENG)
ETA1
ETA2
ETAOA(I)
ETAP(I)
ETAX
ETERM
PACT
G
GERAT
H(I)
HA
HE
HEP
HEPHE
HEW
HIN
HIN2
HPIPE(I)
HPP(I)
HSV(I)
Variable used to print out typeof engine selected
^OA» a"k cru ^- se speed
T\q»i a"t hump speed
Pump efficiency-
Ratio of off-design point pumpefficiency to design point efficiency
Variable used in determining fuelweight
Variable used in determining thejet velocity ratio at hump speed
Acceleration due to gravity
Reduction gear ratio
Atmospheric pressure head
Height of diffuser outlet abovebaseline
Height of pump above baseline
Length of transition pipe
Height of outside waterline abovebaseline
Inlet height at cruise speed
Inlet height at hump speed
Head loss in pump-to-nozzle pipe
Head across pump
Net positive suction head
ft/sec'
Head loss due to difference in height ftbetween pump inlet and diffuser exit
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
- 126 -
HX
(I)
IAR
Ratio of pump head at cruise topump head at hump
Indicates ship velocity1 for cruise speed2 for hump speed
Input to program1 for 2.5 aspect ratio inlets2 for varying aspect ratio inlets
ICONT Program control
IENGN Type of gas turbine1 - TF 352 - TP 403 - Proteus, 1,500 RPM4 - Proteus, 1,000 RPM5 - Tyne 1A6 - Tyne 1C7 - FT12A8 - LM 15009 - LM 2500
10 - FT4A-2C11 - FT4A-1212 - FT4C-213 - FT9B14 - GTPF 99015 - Unused space
IMAX Program control
INIT Program control
IPRINT Output device number
IREAD Input device number
ISTEER Program control
IWVJ Program control
KK Program control
KKK Program control
KINCRE The size of the displacas a fraction of the total originalship displacement
- 127 -
KOUT
LAST
M
MN
NGT
NSTG
PC(L,M)
PCA(L,M)
PC1MAX
PC2MAX
PC1VJ
PC2VJ
PCOEF(J,K)
PERF(N,IENGN)
PHI
PHI1
PI
PIDIA
PLP
PRC(I)
PRG1
Program control
Program control
Program control
Program control
Number of gas turbines
Number of pump stages
Inducer stage characteristics
Axial stages characteristics
Maximum overall propulsive coefficient
Maximum net propulsive coefficient
Jet velocity ratio for PC1MAX
Jet velocity ratio for PC2MAX
Pump length and weight coefficients
Engine data where N is:1 - Normal SHP2 - Maximum SHP3 - SFC at normal SHP4 - RPM5 - Weight of engine (dry)6 - Engine length
HPHP
lb/HP-hrrpmlbft
Pump flow coefficient at hump speed
Pump flow coefficient at cruise speed
Constant = 3.1415927
Pump inlet diameter
Pump length
Propulsive coefficient (overall)
Propulsive coefficient (overall) atcruise speed (MAIN program)
ft
ft
- 128 -
PRNC1
PRNC2
Q(D
QQ(D
QQ1PC2
QQ1WVJ
OX
RANGE
RESIST
RHOT
RHOW
RNSTG
HPM(I)
RPM2
RQ
RTIP
RX
SCONT
SPG
Net propulsive coefficient atcruise speed
Net propulsive coefficient athump speed
Flow rate through system ft /sec
Flow rate through each pump ft /sec
Flow rate through each pump at the ft /secjet velocity ratio for the maximumnet propulsive efficiency system
Flow rate through each pump at the ft /secjet velocity ratio for theminimum weight ratio system
Ratio of flow rate at cruise speedto the flow rate at hump speed
Ship range
Total resistance of ship includinginlet drag
Density of titanium
Density of water
Variable used in determining thenumber of pump stages
Pump RPM
Pump RPM at hump speed
Reduction gear Q-factor
Pump inlet tip radius
Ratio of pump RPM at cruise speedto RPM at hump speed
Variable used in determining fuelweight
Specific fuel consumption lb/HP-hr
nauticalmiles
lb
slug/ft 3
slug/ft 3
rpm
rpm
ft
- 129 -
SHI
SHNG
SHP(I)
SSS1
SSS2
STRESS
THICK
TI
VAF .
vise
VJ
VJVO(I)
VO(I)
VOTERM
VTIP(I)
WIDTH
WT(K)
WTMIN
WTOT
Pump head coefficient
Shaft horsepower required after HPfuel is removed
Shaft horsepov/er HP
Suction specific speed at cruisespeed
Suction specific speed at humpspeed
Maximum allowable normal stress in lb/in'pump-to-nozzle pipe
Thickness of pump-to-nozzle pipe in
Time interval for fuel consumptioncalculation
Variable area factor (ratio of inletarea at hump speed to inlet area atcruise speed)
Viscosity of water
Jet velocity
Jet velocity ratio
Ship velocityInput and subroutine SESIN knotsRemainder of program ft/sec
Variable used in determining fuelweight
Pump blade tip velocity ft/sec
Width of inlet opening ft
Weight of fuel required for one lbtime period
Minimum weight ratio
Total system weight lb
ft2/nr
ft/sec
- 130 -
WTOTLT
WTRAT
WVJ
XDRAG
XK
XLBSHP
XLENG(II)
XLENGP
XLN
XLTOB
XN
XNGT
XWD
XWENG
XWF
XWGR
XWIN
XWPIP
XWPIW
XWPN(II)
XWPNO
XWW
Total system weight
Weight ratio
Jet velocity ratio for minimumweight ratio
Inlet system drag
Reduction gear K-factor
Ratio of v/aterjet system weightto shaft horsepower required
Pump-to-nozzle pipe length forsystem II
Estimated pump-to-nozzle lengthused in determining number of gasturbines required
Nozzle length
Ship length-to-beam ratio
Factor for SFC versus power curve
Number of gas turbines
Pump dry weight
Weight of engines
Total fuel weight
Weight of reduction gears
Weight of inlet systems
Weight of transition pipes
Weight of water in transition pipes
Weight of pump-to-nozzle pipe forsystem II
Total weight of pump-to-nozzle pipe
Weight of water in pumps
long tons
lb
ft
ft
ft
lb
lb
lb
lb
lb
lb
lb
lb
lb
lb
- 131 -
Weight of water in pump-to-nozzlepiping for system II
Total weight of water in pump-to-nozzle piping
Total weight of nozzles
Total weight of water in nozzles
Main program outputs1 - Jet velocity ratio2 - Weight ratio3 - Overall propulsive efficiency4 - Net propulsive efficiency at
cruise speed5 - Net propulsive efficiency at
hump speed6 - Shaft horsepower at hump speed7 - Shaft horsepower at cruise speed8 - Suction specific speed at hump
speed9 - Pump RPM at hump speed
10 - Number of pump stages
Pump length coefficient
Variable used to iterant the finalpump-to-nozzle pipe diameter
lb
lb
lb
lb
HPHP
rpm
- 132 -
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ThesisH1125 Hagstrom
Waterjet propulsiosystem optimizationfor surface effectships.
f FEB 7«5 FEB 76<• 3 JD i. S3
DISPLD 1,6 PL27218
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[Thesis
H1125 HagstromWaterjet propulsion
system optimizationfor surface effectships.
' *»h"» ,.,„„.vslei»op»maa»o"watenei P<»P"'!?" S.II.MIM1I1I
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