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-

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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 -

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SYSTEM 2 STARBOARD

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SYSTEM 1 STARBOARD

SYSTEM 1 PORT

STERN

i

f

IFigure 3 - WATERJET SYSTEM ARRANGEMENT FOR SURFACE

EFFECT SHIPS

- 59 -

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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-

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ENGINE

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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 -

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FUEL WEIGHT

SYSTEM WEIGHTEXCLUDING FUEL)

1.70 ' 1.78~~"

1.86 1.'9^f

JET VELOCITY RATIO

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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 -

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JET VELOCITY RATIO

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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

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S 300

250-

200-

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1.5 2.0 3.0

SHIP LENGTH-TO-BEAM RATIO

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Figure 9 - VARIATION OF HULL DRAG WITH SHIP LENGTH-TO-BEAMRATIO FOR A 2,000 TON SES

- 65 -

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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 -

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PUMP-TO-NCJZZLE PIPE

I PUMP-TO-NOZZLE PIPE

-NOZZLES-

1.5 2.0 3.0

SHIP LENGTH-TO-BEAM RATIO

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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

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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

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SYSTEM WEIGHT^ ^UNCLUDINGJTUELL _ —

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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«

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CO

oK

.48-

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SHIP LENGTH-TO-BEAM RATIO

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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

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PROPULSIVE \EFFICIENCY

MINIMUM SYSTEMWEIGHT RATIO

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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

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MAXIMUM NETPROPULSIVEEFFICIENCY

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SHIP LENGTH-TO-BEAM RATIO

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Figure 16 - VARIATION OF PUMP SUCTION SPECIFIC SPEED WITHSHIP LENGTH-TO-BEAM RATIO FOR A 2,000 TON SESUSING k FT9D GAS TURBINES

- 72 -

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Figure 17 - VARIATION OF OPTIMUM SHIP DISPLACEMENT WITHSHIP LENGTH-TO-BEAM RATIO FOR k FT9D GASTURBINES

- 73 -

oHEh

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Figure 18 - REPRESENTATIVE VARIATION OF WATERJET SYSTEMWEIGHT RATIO WITH JET VELOCITY RATIO

- 74 -

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SHIP HUMP SPEED - KNOTS

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Figure 19 - INLET DRAG COEFFICIENT FOR VARYING ASPECT RATIOINLETS (reference 1)

- 75 -

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SHIP HUMP SPEED - KNOTS

Figure 20 - DESIGN SPEED OVERALL INTERNAL EFFICIENCYFOR VARYING ASPECT RATIO INLETS (reference 1)

- 76 -

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- 78 -

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igure 23 - INLET DRAG COEFFICIENT FOR 2.5 ASPECT RATIOINLETS (reference 1)

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Figure 24 - DESIGN SPEED OVERALL INTERNAL EFFICIENCYFOR 2.5 ASPECT RATIO INLETS (reference 1)

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- 81 -

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- 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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