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AD-A238 804(% -; REFLEX WATERJET DESIGN STUDY FOR APPLICATION TO THE AAAV HIGH WATER SPEED AMPHIBIAN FINAL TECHNICAL REPORT APRIL 2S, 1991 by Waldo E.Rodler Prepared Under Contract Number N00167-90-0058 for MARINE CORPS PROGRAM OFFICE DAVID TAYLOR RESEARCH CENTER .- i BETHESDA, ND Approved for public release; DiTstribution Unarmited High Performance Marine Products 4811 Trallvoud Waiy Springfield, HO 65804 91-05810 91 7 22 o

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AD-A238 804(%

-; REFLEX WATERJET DESIGN STUDYFOR APPLICATION TO THE AAAVHIGH WATER SPEED AMPHIBIAN

FINAL TECHNICAL REPORT

APRIL 2S, 1991

by

Waldo E.Rodler

Prepared Under Contract Number N00167-90-0058

for

MARINE CORPS PROGRAM OFFICEDAVID TAYLOR RESEARCH CENTER

.- i BETHESDA, ND

Approved for public release;DiTstribution Unarmited

High Performance Marine Products4811 Trallvoud Waiy

Springfield, HO 65804

91-05810

91 7 22 o

* 9 4

* UNCLASSIFILI=EUJ3T Y CLASSIFICATION OF THIS PAGE

REPORT DOCUMENTATION PAGEla REPORT SECURITY CLASSIFICATION lb. RESTRICTIVE MARKINGS

UNCLASSIFIED2a SECURITY CLASSIFICATION AUTHORITY 3 DISTRIBUTION/AVAILABILITY OF REPORT

Approved for Public Release:2b DECLASSIFICATION /DOWNGRADING SCHEDULE Distribution Unlimited

4 PERFORMING ORGANIZATION REPORT NUMBER(S) 5 MONITORING ORGANIZATION REPORT NUMBER(S)

6a NAM OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATIONHigh Performance If applicable) Marine Corps Program OfficeMarine Productsj David Taylor Research Center

6c ADDRESS (City. State. and ZIPCode) 7b. ADDRESS (Cary State, and ZIP Code)uarcleroc CR aboratory

4811 Trailwood Jay e t h a O O8 O

Springfield, MO 65804 Bethesda, M 20084-5000

8a NAME OF FUNDING/SPONSORNG 8b OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATIONrI arine Corps O If applicable) NOOl67-904OO58R. D. & A. Command

8c ADDRESS (City, State. and ZIP Code) 10 SOURCE OF FUNDING NUMBERS

Quantico, Va. PROGRAM PROJECT TASK WORK UNITELEMENT NO. NO NO. ACCESSION NO

___________________ 5502-N c 182-4 14q0_-O24L11 111L E (Include Security Classification)

Reflex Saterjet Design Study for Application to the AAAV Zijh .e JGCAmhiOiLn

12 PrRSONAL AUTHOR(S)

13a TYPE OF REPORT 1bTIECVRD14 DATE OF REPORT (V'ear. ot, a) o PAGE COUNTFinal FROMYIOiOTO12 1991 April 26 110

16 SUPPLEMENTARY NOTATION

17 COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP I SUB-GROUP AAAV, Jaterjet, Amphibian, Propulsion, Jet

I I19 ABSTRACT (Continue on reverse if necessary and identify by block number)A novel alternative configuration for waterjets was optimized anc evaluatedfor application to high speed amphibianslike the planned AAAV. The conceptdemonstrated good performance in two generations of prototypes and a produc-tion run of units about half the size required for this application. Optimi-zation analysis was based on methods confirmed by tests of the earlier units.Results show jet will provide satisfactory performance. Limited data indicateimproved system performance will be realized from eliminatioh of forward in-takes of conventional waterjets. The optimization study showed a 16 inchwaterjet to be optimum for the application. Adequate design engineering wasperformed to assure feasibility of the proposed design and availability ofthe needed components. The Vaterjet compares favorably to conventional de-signs in length, weightmaintainability, affordability and program risk.Installation studies show four jets can be installed on the proposed transom

20 DiSTRIBUIION/AVAILABILITY OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION-'UNCLASSIFIED/UNLIMITED C'SAME AS RPT 0 DTIC USERS

22a NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE (Include Area Code) 22c OFFICE SYMBOL

MI&N-46L 6A*I~ v~)z115.MCPO

-DO FORM 1473,84 MAR 83 APR edition may be used until exhausted SECURITY CLASSIFICATION OF THIS PAGEAll other editions are obsolete L 4 CLA 1 i&S 0ED

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE

flap and will not project above the hull when retracted. An alternatetransom flap design, optimized for these jets, provided a low level walk-way for troop entry when the flap is deployed and a troop door to 'ermitentry without lowering the transom .flap.

SC- _O

0 ,"

0}

* __I

SECURITY CLASSIFICATION OF THIS PAGE.

High Performance Marine Products4811 Trailwood Way

Springfield, MO 65804

REFLEX WATERJET DESIGN STUDYFOR APPLICATION TO THE AAAVHIGH WATER SPEED AMPHIBIAN

Final Technical ReportApril 26, 1991

f/

CPrepared Under Contract Number N00I67-90p0058

for

MARINE CORPS PROGRAM OFFICEDAVID TAYLOR RESEARCH CENTER

BETHESDA, MD

Waldo E. Rodler R. Kent Wooldridge

ABSTRACT

A novel alternative configuration for wateriets was optimizedand evaluated for application to high water speed amphibians,like the planned AAAV. The concept demonstrated good performancein two generations of prototypes and a production run of unitsabout half the size required for this application. Optimizationanalysis was based on methods confirmed by tests of the earlierunits. Results show jet will provide satisfactory performance.Limited data indicates improved system performance will berealized from elimination of forward intakes of conventionalwateriets. The optimization study showed a 16 inch wateriet tobe optimum for the application. Adequate design engineering wasperformed to assure feasibility of the proposed design andavailability of the needed components. The wateriet comparesfavorably to conventional designs in length, weight,maintainability, affordability and program risk. Installationstudies show four jets can be installed on the proposed transomflap and will not project above the hull when retracted. Analternate transom flap design, optimized for these jets,provided a low level walkway for troop entry when the flap isdeployed and a troop door to permit entry without lowering the

transom flap.

TABLE OF CONTENTS

SUBJECT PA E

1. Introduction 1

2. Discussion 2

Procedures 2Equipment 5Facilities 5Data 5Math computations 5Results 5

3. Documentation

Drawings and Illustrations 11Intermediate reports 12Laboratory reports 12Conference reports 12Other research sources 12

4. Status of Accomplishments 12

Assignments 12Performance optimization 12Hydrodynamic design 13Mechanical concept design 13Jet system concept 14Integration with vehicle 15

5. Tests 16

Conducted in this program 16Test data from previous programs 16

6. Summary 17

Goals 17Technical risk 17Maintainability 17Affordability 17

7. Conclusions 17

8. Recommendations 18

9. AP&endices

Technical Presentation, Oct. 10, 1990 Appendix ATechnical Presentation, Jan. 29, 1991 Appendix BTechnical Presentation, April 26, 1991 Appendix CSample Mathematical Computations Appendix D

0

DRAWINGS AND ILLUSTRATIONS

0Cross Section of Series #1 Prototypes

Appendix A, REFLEX JET, Page 3 of 22

Cross Section of Series #2 Prototypes

Appendix A, REFLEX JET, Page 5 of 22

Cross Section of a Conventional WaterietAppendix A, REFLEX JET, Page 11 of 22

Torque Converter Cross SectionAppendix A, REFLEX JET, Page 11 of 22

Side View, HPM Engine and Series #3 WaterietAppendix A, REFLEX JET, Page 15 of 22

Rear View, HPM Engine and Series #3 WaterietAppendix A, REFLEX JET, Page 16 of 22

HPM Outboard JetAppendix A, REFLEX JET, Page 16 of 22

AAAV Electric Wateriet ConceptAppendix A, REFLEX JET, Page 17 cf 22

AAAV Electric Wateriet Concept, RevisedAppendix B, REFLEX JET MID PROGRAM REVIEW, Page 4

AAAV Impeller and Reduction Gear Cross SectionAppendix B, REFLEX JET MID PROGRAM REVIEW, Page 5

AAAV Reflex Wateriet Elevation and Rear View, 1/2 Scale(CDRL item A001)

AAAV Reflex Wateriet Cross Section, 1/2 Scale(CDRL item A001)

AAAV Reflex Waterjet, Typical AAAV Installation

Figure 1, Page 19

Trunnion Mount Steering System

Figure 2, Page 20

Alternate "T" Flap Concept with Walkway and Crew DoorFigure 3, Page 21

INTEGRAL ELECTRIC MOTOR & REFLEX WATERJETFOR HIGH SPEED AMPHIBIANS

1. INTRODUCTION

Studies made for the LVA program indicated that higher waterspeed, on the order of 25 miles per hour, was needed for assaultamphibians. This water speed would permit launching theamphibians so far from shore that the threat of land basedmissiles would be greatly reduced. The Falkland Islandexperience confirmed the validity of the requirement forincreased speed.

The general size and configuration of an assault amphibian aredriven by the military mission and the need to maintain a trackcontact length to tread ratio under about 2.8 to 1 to assureacceptable steering characteristics. The heavy weight (over60,000 pounds) and small bottom area (about 250 square feet plusauxiliary systems) requires an unusually high lift coefficient.The size of the auxiliary systems like bow flaps, chine flapsand transom flaps is limited by practical constraints of landmode combat operation. The trim angles required to develop therequired lift coefficients produce a high drag coefficient. Theproduct of the high drag coefficient and the heavy weightproduces a very large drag value that necessitates very highthrust. The size of affordable and proven engines is limited,therefor the required thrust must be achieved by a superiorpropulsive coefficient. The critical factor for a waterjet toachieve the required propulsive coefficient at low speeds is ahigh mass flow. This required high mass flow can only beprovided by a large wateriet.

Studies of the AAAV with a conventional wateriet of the neededsize showed that when the transom flap was retracted for landmode, the wateriets would protrude more than 20 inches above therear deck. This protrusion interferes with rearward vision andgun depression. The folded flow path of the reflex waterietmerited study because it offered an opportunity to provide amuch shorter jet that would not protrude above the rear deck ofthe AAAV.

This study optimized and evaluated an integral electricmotor/waterjet design based on a unique waterjet configurationthat has demonstrated improved performance compared toconventional wateriet arrangements in pleasure boat sizes. Theaim of the effort was to develop a wateriet concept that wouldoffer improved performance and/or reduced power requirement,reduced system weight, reduced material cost, conservation ofstrategic material and easier maintenance and repair. The priorexperience with the similar concept for recreational boatsprovided confidence that these challenging goals could bereached.

FINAL REPORT, April 26, 1991, Page 1

Use of data from the design and test of previous recreationalunits of this general configuration minimized risk byconstraining the study to proven range of design factors. Use of

* existing proprietary programs for hydrodynamic optimization andimpeller configuration permitted a very detailed study to bemade within the time and cost limitations of a Phase I SBIRprogram. The accuracy of these computer programs has beenconfirmed by extensive tests of waterjets built from the results,of these programs. This detailed study assures that the

0 configurations illustrated are feasible and provides a soundbasis for the mechanical design and space requirements. Themechanical configuration is based on successful experience. Theindividual components are of simple, conventional design tominimize risk.

The scope of the study effort has been sufficient to provide thebasis for a prototype. The hydrodynamics have been pursued indepth. The mechanical concept is based on previous successfulunits and has been reviewed for producibility andmaintainability. Coordination with motor vendors providedassurance that multiple sources are available for the requiredmotor.

2. DISCUSSION

2.1 DETAILED DESCRIPTION OF TECHNICAL WORK

2.1.1 PROCEDURES

2.1.1.1 PERFORMANCE OPTIMIZATION

The performance optimization wa5 made by use of W. E. Rodler'sproprietary program JETOPT9D. This program has been developedover a period of 18 years. The accuracy of the results producedby this program has been confirmed by tests of waterjetsdesigned by its use and by comparison with the results ofwateriet analysis by organizations like Aerojet, Rocketdyne,Dowty and Byron Jackson. Tests have shc,4n pzzf~.mance variationof production wateriets built to the same design to be as muchas +/- 2%. The results of this program have been found to fallwithin that scatter band.

The program starts with the basic physics of force equals masstimes acceleration of the fluid. Corrections are then made for:

1. Inlet drag based on capture area, hullvelocity and an experimental coefficient.

2. Ram head recovery based on velocity and an

experimental coefficient.

3. Inlet flow loss based on curvature and convergence of

the inlet.

4. Impeller efficieticy based on tip vc.-ocity, diameter,cavitation limits, flow, and head.

FINAL REPORT, April 26, 1991, Page 2

5. Stator and nozzle losses based on geometry andexperimental coefficients.

* 6. Unit size, flow velocities and anticipated surfacefinishes.

The program iterates through a very large number of combinationsof these interrelated factrs to achieve an optimized systemresult.

2.1.1.2 IMPELLER DESIGN

The impeller blade design program is based on an unpublisheddesign method developed by Heinich Schneider, the inventor ofthe automotive hydrodynamic torque converter. The toroid flowpath essential to the basic torque cunverter mechanical designwas not well suited to conventional blade design techniques,therefor this alternative method was established. The method wasadapted to water pumps using information published by A. J.Stepanoff with additional modifications from Fuji MotorsCorporation test data. The method has been developed into aproprietary program by W. E. Rodler and has been used tooptimize the impeller design. Some of the advantages of bladesystems designed by this method are:

A. High resistance to cavitation. Torque converters withthis type of blades will operate without cavitation ata charging pressure of 35 psi compared to the 60 psinormal required by conventional designs. In waterjets,simple impellers have provided satisfactory operationsuction specific speeds over 30,000.

B. High efficiency. In a torque converter, efficiency iscritical because it is directly related to vehicleperformance and fuel economy. This situation motivatedthe resepe-h to develop more efficient blade designs.When applied to wateriets, test. indicate animprovement of approximately 3% over conventionaldesigns.

C. Simple contours that favor economical fabrication. Themethod relates blade contours and passage crosssection. By a series of design iterations it ispossible to achieve a combination of simple bladecontours with flow passage cross sections that providehigh "through flow ability".

2.1.1.3 INLET CAPTURE AREA DESIGN

The design of the inlet is based on extensive tests made duringthe development of a 7.34" diameter recreational wateriet. Thecritical goals for this section of the waterjet system are:

FINAL REPORT, April 26, 1991, Page 3

1. Good ram head recovery2. Low drag coefficient3. Freedom from ventilation4. Protection from entrance of foreign items

During the development of the 7.34" waterjet inlet, severalsatisfactory designs evolved. There were significant variationsin the ram head recovery, but all of the satisfactory designsproduced comparable free running performance. It was concludedthat high levels of ram recovery were associated withcorresponding high levels of inlet drag. The basic laws ofconservation of energy appear to be at work. Increased ram headincreased flow and gross thrust, but the added drag resulted inno measurable gain in the speed of a free running hull.

The initial inlet design for the 7.34" wateriet experienced aventilation problem. As the hull approached planing speed, afraction of air entered the inlet, and pump performance wasseriously degraded. A minor modification of the inlet eliminatedthe ventilation problem and no problem was experienced withsubsequent designs.

Operation with several variations of inlet grill was compared tooperation without a grill. The effect of the well designedgrills was found to be negligible. The most significantdifference between the grill designs was found in their abilityto shed rather than retain foreign items. None was found to becompletely able to shed foreign items. The velocity andresulting impact forces are high. In one case a 12" length of afir 2 by 4 impaled itself on a grill. The grill bar cut into the2 by 4 as an axe might do, and significant force was required todislodge this foreign item. The test program showed that aninlet grill was very desirable and that with proper design therewas no measurable degradation of performance.

2.1.1.4 INLET ELBOW DESIGN

The inlet elbow design is based on the proven principles used inthe design of the earlier reflex waterjets. The velocities andradii are retained. The low mounting position of the waterjet onthe AAAV increases the net positive head, providing anadditional margin of safety. The passageway is convergent tominimize losses and to provide improved velocity distribution atthe impeller inlet (see appendix A, REFLEX WATERJET MID PROGRAMREVIEW, January 29, 1991, page 17).

The velocity of the water increases progressively through theentire waterjet. The wateriet is a system with a purpose ofaccelerating water to a high velocity at the nozzle. Torqueconverter design principles and experience with prior reflexwaterjets indicate that highest systems efficiency is achievedwith a "system approach" to flow velocity that provides thehighest rates of acceleration after the impeller, where the head

is the highest. Prior reflex waterjet designs have provided veryhigh efficiency by using a constant jerk (rate of change ofacceleration) from inlet to the nozzles. The velocity rates

FINAL REPORT, April 26, 1991, Page 4

0

through the inlet elbow are governed by this system principle.(see appendix B, REFLEX WATERJET MID PROGRAM REVIEW, January 29,1991, page 18)

2.1.1.5 NOZZLE DESIGN

The inlets to the nozzle passages are aligned with the absolutedirection of the impeller discharge flow. The stator of aconventional pump is eliminated as well as the stators lossesand cavitation problems. Instead of "straightening out" therotation of the impeller discharge flow, there is a smoothcontinuation of the angular acceleration started in theimpeller. The passages continue the convergence to continue theprogressive acceleration of the fluid. The nozzle size isdetermined by the area required to produce the dischargevelocity determine by the performance optimization studies.

2.1.2 EQUIPMENT

2.1.2.1 COMPUTATIONS

Most of the optimization and design calculations were made byuse of a Panasonic (IBM PC compatible) computer. The author madeuse of an extensive software library previously developed forconverter and waterjet analysis to maximize the amount ofanalysis possible within the cost constraints of the program.

2.1.2.2 DRAWINGS

Drawings were made using conventional drafting equipment.

2.1.3 FACILITIES

No special facilities were required to perform this effort.

2.1.4 DATA

Extensive use was made of an unpublished proprietary data basedeveloped from prior torque converter and wateriet studies anddevelopment programs. Public domain data has been used as notedin references throughout this report.

2.1.5 MATH COMPUTATIONS (successful and ursuccessful)

Sample calculations and copies of significant computer runs areattached as appendix D.

2.1.6 RESULTS

This study program has produced a low risk waterjet concept thatprovides the required AAAV thrust and offers the followingadvantages when compared to conventional configurations:

FINAL REPORT, April 26, 1991, Page 5

1. Reduced waterjet length2. Reduced waterjet weight3. Reduced cost4. Simplified maintenance5. Improved hull performance

2.1.6.1 REDUCED LENGTH

Three major factors contribute to the reduced length of thereflex, or folded, configuration. First, the intake capture areais located below the main body of the waterjet, rather than well

ahead of it. Second, the nczzles are located along the side ofthe pump, rather than behind it. Finally, a relative largediameter and correspondingly shorter motor can be used becauseit is not in the main water flow path where a large diametermotor would limit passage area and mass flow.

2.1.6.2 REDUCED WEIGHT

A weight estimate of 551 pounds, includes motor and intake. Themotor weight is based an estimate from Uniq Mobility. It istypical of estimates from two other motor sources. The weightof the balance of the jet is proportioned from actual scaleweights of a similar, but smaller, wateriet. See Appendix B, MidProgram Review, January 29, 1991, Page 16 for details of thecalculation.

This weight is comparable to prior AAAV waterjets, but it isbased on conventional aluminum construction. Application ofcomposites, as done in the earlier AAAV wateriet should produceadditional weight savings. A cost vs. weight study foralternative materials is planned as part of a Phase 2 program.

Extensive test experience with similar designs have shown thatan aluminum impeller of the planned configuration will providesatisfactory performance and life. For details, see Appendix B,Reflex Jet Mid Program Review, January 29, 1991, Page 15. Thealuminum material will result in savings of both weight andcost.

A further effective weight reduction will be realized from themore compact configuration and resulting reduced internal volumeof on board water.

2.1.6.3 REDUCED COST

The aluminum impeller will reduce both material and machiningcosts. Aluminum can also be used for much of the balance of thewaterjet without exceeding present target weights.

The simple interface between the motor and the wateriet issuitable for motors from most sources. This offers a potentialsavings in both development and production procurement.

The design and development problems of the land propulsion

motors are far more severe than the waterjet motors because the

FINAL REPORT, April 26, 1991, Page 6

waterjet maximum horsepower requirement occurs at maximum RPM.The maximum power of the land mode motors must be delivered atlow speeds, therefor these motors must be capable of producingmuch higher torque. The high torques result in a larger motor

* and more severe motor control problems. Any motor and controlsources that can meet the land mode requirements can easily meetthe wateriet requirements. The adaptability of the reflexwateriet to motors from various sources permits electricalsystem source selection to be made on the basis of the best landmode motor and control concepts. Reduced cost and better system

* design integration should result from having the land propulsionand wateriet motors and controls designed and produced by asingle source.

2.1.6.4 SIMPLIFIED MAINTENANCE

* The critical impeller, reduction gearing and motor componentsform a single sealed module that can be easily replaced in thefield. This component module can be serviced by higher echelonpersonnel who have the necessary equipment and facilities toperform the clean and precise maintenance that is required bysuch components.

2.1.6.5 IMPROVED HULL PERFORMANCE

The effect of the rearward location of the water inlet of thereflex waterjet appears to be a significant factor in theperformance of the watercraft system. Verification of theeffects of this rear intake location and their quantificatioare necessary factors in a proper evaluation of the applicationof this wateriet system in comparison to conventional designs.The currently available information suggests more study in thisarea would be valuable.

Experimental indications:

Outboard Marine Corporation has conducted a series of testscomparing a matched pair of Cobalt boats powered by 305 CIDChevrolet engines. One boat had an OMC inboard/outdrive mountedpropeller and the other had a conventional Jacuzzi waterjet witha forward water intake. The boat with the forward intakerequired an additional 5 mph speed to achieve plane. This curveis reproduced in Appendix A, REFLEX JET, October 10, 1990, Page20 of 22. A possible explanation is that the higher dynamicpressure provided by the additional 5 MPH speed compensates forthe loss of lift coefficient caused by the forward intake.Analysis of these data by use of Dr. Daniel Savitsky's planinghull analysis indicates the coefficient of lift was 0.045 forthe hull with an inlet opening for a conventional jet and 0.070for the propeller boat with no opening in the hull bottom. Seethe attached Appendix b, REFLEX WATERJET MID PROGRAM REVIEW,January 29, 1991, Page 24 for the details of the analysis.

Free running tests cf boats equipped with the reflex wateriethave consistently shown better performance than can be explainedjust by the performance of the waterjet itself. A Sea Ray SRV-

FINAL REPORT, April 26, 1991, Page 7

19, a Glastron V-174, and a Sportline 16 were all tested withMercruiser Inboard/Outdrive propeller installations that werereplaced and retested with reflex waterjets. Only the drive waschanged. In all cases, the top speed of the jet was 1 to 2 MPHless than the propeller drives, but the acceleration times toachieve plane were reduced about 30 percent. Conventional jetstypically require a 50 % more power to equal propellerperformance. The reflex jet achieved fuel consumption -rates,comparable to the propeller installation. Conventional jets inthe recreation boat industry are noted for their high fuelconsumption.

Analytical considerations:

Analysis indicates that placing the waterjet inlet in the bottomof a hull should be undesirable and that the significance shouldincrease with low hull speeds and high mass flow waterjets.

To achieve the desired performance, the waterjets of the AAAVwill have a mass flow of about 20,000 gallons per minute each,or a total flow of 80,000 GPM, or 178 cubic feet per second.

Studies and tests have shown the AAAV hump speed will approach18 miles per hour, or 26.4 feet per second. The cross section ofthe stream of water under the hull that will be diverted intothe waterjet will therefore be 6.74 square feet. If the hullbottom between the tracks is about 7 feet wide, nearly one footdepth of water in this area will be diverted into the waterjets.This quantity should be enough to have significant effect onhull trim, lift and drag.

Tests have shown that a transom flap has a powerful effect onhulls like the AAAV. A transom flap with a 6 foot span and a 4foot length would need to be set at a 16.3 degree deflection topresent the same 6.74 square foot frontal projected area as thestream of water entering the waterjets.

Dan Savitsky and Peter Brown have published "Procedures ForHydrodynamic Evaluation of Planing Hulls In Smooth and RoughWaters" (Marine Technology, October 1976). Page 384 of thispublication gives the following equation (5) for calculatingflap lift:

f = 0.046 * Lf * 6 * a * b * (p/2 * V2)

Where: Estimate for AAAV

f = Flap lift increment, pounds

Lf = Flap chord, ft. 4

a = Flap span-beam ratio 6/11 = 0.5455

6 = Flap deflection, degrees 16.30

b = Beam of planing surface, ft. 11

FINAL REPORT, April 26, 1991, Page 8

p = Mass density, slugs/cu. ft. 2

V = Speed, fps 26.4

Inserting values into the equation yields:

f = 0.046 * 4 * 16.3 * 0.5455 * 1* (2/2 * 26.42)

f = 12,543 pounds

Since the mass of water diverted into the wateriets approximatesthe water deflected by the above transom flap, the resultingforces may be similar.

Independent comments:

Art Carlson, Designer of Glastron's "Carlson" line of highperformance boats:

When shown the concept, he was the first person to pointout the probable advantage of avoiding the wateriet inletin the bottom of the hull.

Quoting a letter based on engineering analysis from W. H. Knuth,Program Manager, Midrange Wateriets, Marine Systems, AerojetLiquid Rocket Company:

"The aft-mounted intake would appear to benefit from theup-welling flow as it escapes from astern the transom tobecome the wake.

All things considered, we should expect to see a boat thatmaintains a more level attitude traversing hump, achievesand holds plane at lower speeds, has less inlet relatedlosses and therefore, improved thrust efficiency, reducedtendency to cavitate at startout, giving betteracceleration and possibly reduced tendency to broach theinlet in a turn.

A variety of mechanical design advantages come to mind aswell which need not be listed here. I do believe the aftlocation of the intake offers potential for being shown tobe superior to a through-hull intake in many if not allcases."

Quoting from a test report by David Moseley, Chief Engineer,Propulsion Systems, Glastron Boats:

"The pulling power of the package was demonstrated bytowing a 180 pound slalom skier with three people in theboat. The boat pulled the skier up with no trouble at all,much easier than a CV-16 with a Merc 140.

FINAL REPORT, April 26, 1991, Page 9

In general, the Sternjet unit was a very impressive

prototype."

Notes by W. E. R.:

1. The CV-16 is a very similar Glastron boat.2. The Merc 140 is an inboard/outdrive propeller

with the same engine as used with the wateriet.

Quoting a letter from Gunnar Frandsen, Sales Development Managerof Volvo Penta of America, Inc.:

"The demonstration of the Sternjet extended to themanagement of VOLVO PENTA of AMERICA by Mr. Mallon lastsummer gave an indication that the concept has satisfactoryperformance and offers acceptable maneuverabtiity whencompared to an inboard outboard drive, and it was mostimpressive compared to existing jet drives.

Recommendation:

More study and test is necessary to confirm the magnitude of theeffect of forward intake of a conventional wateriet vs. rearwardintake of a reflex waterjet. The above material indicates thatsome effect exists and that the effect may be significant.Further study appears justified as a system approach to reducingthe AAAV power requirement.

2.1.6.6 MINIMIZING PROGRAM RISK

The program risk has been minimized by basing the design on aproven concept and by a careful desiqn effort that has retainedall major design factors in a range of prior experience.

The basic concept has demonstrated its performance capability byextensive tests and operation of:

A. A first series of three prototypes as shown inAppendix A, REFLEX JET, October 10, 1990, pages 2, 3 &4.

B. A second series of three prototypes and 50 productionunits as shown in Appendix A, Reflex Jet, October 10,1990, pages 5 through 14

Throughout the Phase 1 design effort, the basic engineeringfactors from the above designs have been retained to minimizerisk. Water velocities, curvature of passages, impeller bladeangles, tip velocities, cavitation factors, and convergence aretypical of the values retained within ranges established byprevious successful experience.

The level of risk is therefor considered to be very low.

FINAL REPORT, April 26, 1991, Page 10

3. DOCUMENTATION

3.1 The following documentation is provided in support of thiscontract:

3.1.1 DRAWINGS AND ILLUSTRATIONS

A. Cross Section of Series #1 Prototypes(See Appendix A, REFLEX JET, October 10, 1990, Page 3of 22)

B. Cross Section of Series #2 Prototypes(See Appendix A, REFLEX JET, October 10, 1990, Page 5of 22)

C. Cross Section of a Conventional Wateriet(See Appendix A, REFLEX JET, October 10, 1990, Page 11of 22)

D. Torque Converter Cross Section(See Appendix A, REFLEX JET, October 10, 1990, Page 11of 22)

E. Side View, HPM Engine and Series #3 Wateriet(See Appendix A, REFLEX JET, October 10, 1990, Page 15of 22)

F. Rear View, HPM Engine and Series #3 Wateriet(See Appendix A, REFLEX JET, October 10, 1990, Page 16of 22)

G. HPM Outboard Jet(See Appendix A, REFLEX JET, October 10, 1990, Page 16of 22)

H. AAAV Electric Waterjet Concept(See Appendix A, REFLEX JET, October 10, 1990, Page 17of 22)

I. AAAV Electric Waterjet Concept, Revised(See Appendix B, REFLEX JET MID PROGRAM REVIEW,January 29, 1991, Page 4)

J. AAAV Impeller and Reduction Gear Cross Section(See Appendix B, REFLEX JET MID PROGRAM REVIEW,January 29, 1991, Page 5)

K AAAV Reflex Waterjet Elevation and Rear View, 1/2Scale(CDRL item A001)

L. AAAV Reflex Waterjet Cross Section, 1/2 Scale(CDRL item A001)

M. AAAV Reflex Wateriet, Typical AAAV Installation(figure 1) Page 19

FINAL REPORT, April 26, 1991, Page 11

N. Trunnion Mount Steering System(figure 2) Page 20

0 0. Alternate "T" flap concept with walkway and crew door

(figure 3) Page 21

3.1.2 INTERMEDIATE REPORTS

The following intermediate reports have been supplied:

A. Monthly progress reports for October, November andDecember of 1.990 and for January, February And Marchof 1991.

B. October 10, 1990 Kickoff Meeting presentation data• attached herewith as appendix A.

C. January 29, 1991 Reflex Jet Mid Program Reviewpresentation data, attached herewith as Appendix B.

3.1.3 LABORATORY REPORTS

No laboratory reports were prepared or submitted as part of thiscontract.

3.1.4 CONFERENCE REPORTS

* No conference reports were prepared or submitted as part of thiscontract.

3.1.5 OTHER RESEARCH SOURCES

None.

4. STATUS OF ACCOMPLISHMENTS

4.1 ASSIGNMENTS

4.1.1 PERFORMANCE OPTIMIZATION

The optimization study started with a matrix of computer runs tousing W. E. Rodler's proprietary "JETOPT9" program. This programhas been developed over a period of eighteen years. Computerresults have been compared to test results to confirm theeffectiveness of the program. Comparisons of computed and test

* values are show in Appendix A, REFLEX JET, October 10, 1990,Page 14 of 20. Additional comparison have been made withanalytical results from Aerojet, Rocketdyne, Byron Jackson andothers to provide additional confidence in the accuracy ofprogram results. The results fall within the +/- 2% scatter bandthat is typical for production wateriets.

The results of these are shown in Appendix B, REFLEX WATERJETMID PROGRAM REVIEW, January 29, 1991, Pages 7 through 13. The

FINAL REPORT, April 26, 1991, Page 12

results of an optimum combination of these factors is shown onpage 6 of the same Appendix B.

4.1.2 HYDRODYNAMIC DESIGN

The first step was to establish the normal velocity of the waterflowing through the waterjet system. The velocity at thecapture area of the inlet was established based on previousexperience at 31 feet per second at the 18 MPH hull speed. Thisresults in an inlet velocity ratio of 1.17, which has provensatisfactory in prior designs.

The nozzle size and discharge velocity was determined by thcoptimized computer run using the "JETOPT9" program. The nozzlearea of 104.9 square inches resulted in a discharge velocity of64.11 feet per second.

Between these two points, the flow velocity was determined bymaintaining constant jerk (rate of change of acceleration). Thisvelocity distribution produces convergent flow throughout thesystem.

The inlet duct design was derived from previous successfuldesigns. Test of the previous units have shown a favorablevelocity distribution at the impeller inlet using this design(see Appendix A, REFLEX JET, October 18, 1990, page 13 of 22).

The impeller is of a forced vortex design. This type of bladedesign has been extensively used in automotive torqueconverters. It produces a blade that has less difference betweenblade angles at the blade tips and roots than free vortexdesigns. The resulting blade shapes are stronger and easier toproduce. The blade angle is also a function of the radius toeach specific point on the blade. A series of impeller crosssection modifications were made that retain the desired normalvelocity distribution, but refine the blade angles to achievesimple, easily produced contours. The results of thisoptimization is shown in Appendix B, REFLEX WATERJET MIDPROGRAM REVIEW, January 29, 1991, Page 20.

The design of the stator and nozzle assembly, like the intake,follows the principles of previous successful designs. The ratesof acceleration are higher, but the head is also much higher,which avoids the risk of cavitation.

4.1.3 MECHANICAL CONCEPT DESIGN

The general mechanical design follows previous successfuldesigns. For this application the entire waterjet is supportedby the intake elbow. This arrangement has been selected toassure that the transom flap deflections induced by the pressurevariations from wave action are isolated from the pump and motorsections of the waterjet. This isolation minimizes the requiredimpeller tip clearance, which improves pump efficiency and

FINAL REPORT, April 26, 1991, Page 13

S

extends the service life before excessive tip wear necessitatesmaintenance.

The motor is mounted to the waterjet by means of a mountingface, pilot ring and bolt circle. This arrangement has beenextensively used in aircraft applications for mounting highspeed (12,000 RPM) alternators and hydraulic pumps. The motor iseasily removed for repair or replacement and the electrica.1terminals are readily accessible which simplifies installationand sealing of the electrical wiring. A key advantage to thisarrangement is that it is adaptable to motors of varioussources. While no "Off the shelf" motors have been found to meetthe requirements of this application, four sources have beenfound who are able to produce motors for this requirement. (SeeAppendix B, REFLEX WATERJET MID PROGRAM REVIEW, January 29,1991, Page 22)

The impeller is driven from the motor by means of star gearreduction gearing. A star gear set is similar to a planetarygear set, but the carrier is stationary and the sun and ringgears rotate in opposite directions. A single stage of gearingprovides the needed ratio to match the speed of the availablemotors to the impeller speed. The impeller is mounted to andextension of the stationary carrier by means of a pair oftapered roller bearings. The generous spacing between thesebearings provides the rigidity necessary to minimize anypossibility of rubbing between the impeller tips and thewaterjet housing. An external spline on the ring gear drives theimpeller and axial location of the ring gear is maintained by aninternal snap ring. Gear loads, bearing sizes and seal rubbingvelocity have been checked and suitable sources located forthese components. Enough analytical work has been done to assurefeasibility of the design, but an optimization effort isanticipated as part of phase 2 of the development. A cross

4 section of these items is shown in Appendix B, REFLEX WATERJETMID PROGRAM REVIEW, January 29, 1991, Page 5.

4.1.4 JET SYSTEM CONCEPT

The reflex wateriet configuration offers significant advantagesover conventional arrangements.

There is considerable flexibility in the installed dimensions ofa given diameter reflex waterjet. Various combinations of nozzlelocations, nozzle shapes and inlet horn widths permitsignificant variations to suit specific applications. Thecurrent configuration proposed for the AAAV is 52 inches long,21 inches high and 21 inches wide. A typical alternative couldhave a wider, but shorter inlet elbow. This could offer awaterjet that was only 40 inches long, 21 inches high and 27inches wide. A coordinated effort with the vehicle manufactureras part of the Phase 2 effort would permit optimizing thewateriet configuration for the specific vehicle application.

The motor envelope is relatively flexible. The face mounting tothe drive is a widely used in aircraft, machine tools and pumps.

FINAL REPORT, April 26, 1991, Page 14

The motor diameter can be as high as 18 inches without effectingthe overall package dimensions of the motor-wateriet system. Themotor length adds directly to the system length, but the shortlength of the reflex jet allows use of any motors of normalproportions without exceeding the 60 inch overall target lengthfor the motor-wateriet system. This dimensional flexibilityenables many sources to supply a suitable motor and provides thesignificant advantage of competitive procurement.

The manufacturing cost of the reflex jet compares favorably withmore conventional designs. The compact configuration requiresless material. The favorable velocity distribution at theimpeller inlet avoids the need for the complex inducer type ofimpeller. The simple mixed flow impeller is much easier toproduce. The motor is not exposed to pump output pressure,minimizing seal cost and potential failures of a high speed,high pressure seal. The difficult problem of providing andsealing passages to an internal motor for the electrical powersupply is completely avoided. The modular construction of themotor/reduction gear/impeller assembly significantly facilitatesboth manufacturing and maintenance.

4.1.5 INTEGRATION WITH THE VEHICLE

The reflex wateriet can be mounted directly to the transom flapas shown in figure 1. As noted in section 4.1.4, there is areasonable degree of flexibility in the proportions of thereflex wateriet. A Phase 2 study should include a coordinatedeffort with the vehicle manufacturers to achieve the bestintegration of the transom flap system with the wateriet.

The wateriets are required to provide tie moments to steer andcontrol the vehicles motion at the higher speeds when themaneuvering jets are ineffective. There are three potential waysto do this. It can be done by differential motor (and impeller)speeds, by individual nozzle jet deflectors or by swiveling ajet that is mounted on vertical trunnions.

The differential motor speeds is probably the best and lightestsolution for the AAAV. It adds no mechanical components. Theelectronic controls for land mode operation have the variablespeed capability that is necessary to provide this control forthe waterjet motors. This is increased possibility of waterietcavitation at low speeds when much of the total power might bedelivered to only two of the jets, but at those speeds theyprimary steering control is from the maneuvering jets. Thesteering moment with this type of control is greatest withwidely spaced jets.

The use of individual nozzle deflectors produces a complexmechanical design. It offers the advantage of redundant controlsystems in case of damage or failure. This system does notimpose added requirements on the electric controls and does notincrease the possibility of cavitation.

FINAL REPORT, April 26, 1991, Page 15

Jets mounted on a vertical trunnion as shown in figure 2 providea relatively simple steering arrangement. Such steering has beenused on prior reflex waterjets. It was found to provide verypositive steering and the energy to control the system was verylow. There would be a minor loss of effective transom flap area.

A further optimization of the AAAV transom flap might beachieved by use of a reflex style wateriet for the maneuveringjets. The general configuration of a reflex maneuvering jetwould be similar to the HPM waterjet shown in Appendix A, REFLEXJET, October 10, 1990, Pages 15 & 16 of 22. For the maneuveringjet application, the nozzle assembly would be rotated 90 degreesto place the two discharge nozzles almost tangent to the hullsides. Steering and reverse would be achieved by means of thedeflection plate and reverse port as illustrated. Improvement inthe maneuvering jet performance would result from a lessrestricted inlet condition behind, rather than above the uppertrack chord and from the greater moment arm between the waterjetnozzles. The greatest advantage would result from the widertransom flap made possible by the greater distance between thedischarge from the left and right maneuvering jets. This addedwidth would permit a troop walkway between the jets as shown infigure 3.

5. TESTS

5.1 No tests were conducted as a part of this program.

5.2 Extensive use was made of the data base developed from

prior tests.

The first series of tests was made with the Series #1 prototypesillustrated in Appendix A, REFLEX JET, October 10, 1990, Pages 3& 4 of 22. This series of jets were of a 195 mm (7.68 inch)diameter. Three prototypes were built. One was bench tested forstatic thrust and durability. The second was installed andtested in the illustrated Sidewinder hull. Tests included freerunning performance, pressures, flows, inlet losses andcavitation characteristics.

The second series of tests was made with the Series #2prototypes illustrated in Appendix A, REFLEX JET, October 10,1990, pages 5, 6, & 7 of 22. The three prototypes were installedin a Sea Ray 190, a Sportline 16 and a Glastron SRV174. The SeaRay was tested for thrust, flow, losses, free runningperformance and durability. The Sportline was tested for thrust,flow, losses and free running performance. The Glastron wastested for free running performance and durability.

Approximately fifty production units of the Series #2 designwere manufactured, sold and installed in various boats. Data wasgathered from a few of these installations. Performance wasgenerally comparable to propeller installations. Very few spareparts have been required to support these units.

FINAL REPORT, April 26, 1991, Page 16

The tested units were approximately one-half the size of theproposed waterjet for the AAAV. As such, the test data replacesmuch of the data that would be obtained from the half sizeprototype frequently incorporated in larger wateriet programs.

*Program risk is greatly reduced by this relevant experience anddata. The would be a minimal gain from additional half sizeprototypes in the AAAV program, therefor proceeding directly toa full size prototype is recommended.

6. SUMMARY

6.1 MEETS GOALS

The Reflex Waterjet is an attractive alternative to conventionalwateriets for the AAAV. The thrust performance can equal thebest conventional waterjets. The rear water inlet locationappears to have a beneficial effect on hull performance. Theunit is very short. The noise signature should be low because ofthe simple impeller, high cavitation margin and no direct soundradiation paths from the impeller blade tips to the outsidewater. There are trade offs in length, width and height that canbe used to optimize the reflex wateriet for specificapplications. Weight goals are met with conventional materialsand further weight reductions could be realized by use ofalternative materials like composites for the intake elbow andsilicon carbide aluminum for the impeller.

6.2 LOW TECHNICAL RISK

The data gathered from the extensive tests and experience withreflex jets about one half the size that would be needed for theAAAV greatly reduces program risk. Engineering tests, hundredsof hours of durability tests and practical experience withcommercial users minimizes the technical risk associated withthe development of the reflex jet for the AAAV application.

6.3 MAINTAINABLE

The modular construction of the motor, reduction gear andimpeller assembly greatly facilitates maintenance. These mainmaintenance items are readily accessible for repair orreplacement. Simple, conventional construction avoids the needfor many special tools.

6.4 AFFORDABLE

Since the design goals can be met with conventional constructionand materials, costs will be minimized. A further significantcost reduction can be anticipated from the potential to havemultiple competitive sources for the motor. Tests have shownthat an expensive inducer impeller is not required for thereflex jet, therefor a much less expensive mixed flow impellerwill be used. Extensive experience with smaller similar unitswill minimize development cost. The costly fabrication and testof a half scale model appears unnecessary. The funding thatmight otherwise be used for the half scale model, could be

FINAL REPORT, April 26, 1991, Page 17

invested in a complete set of the non standard parts to supportthe test program. This ample supply of spares would minimize therisk of expensive delays during the test program.

7. CONCLUSION

7.1 The reflex jet is an attractive alternative for theAAAV water propulsion system.

The Reflex Jet meets the requirements for water propulsion ofthe AAAV in a compact, light weight package that combines lowtechnical risk, easy maintainability and affordability. Theunique configuration offers a potential system performanceadvantage by avoiding the losses associated with conventionalwateriet inlet located in the primary hydrodynamic lifting areaof the hull.

The use of reflex maneuvering jets in combination with thereflex propulsion jet offers an opportunity to use a widertransom flap that could incorporate a troop walkway between thewaterjets. This arrangement would provide improved combateffectiveness by partially protecting troops from enemy fire andby speeding their entry and egress.

8. RECOMMENDATIONS

8.1 Proceed with a phase 2 program to build and test aprototype reflex waterjet.

Key factors of this program should include:

A. Close coordination of the reflex water design with thetransom flap assembly design and development toimprove over water performance and combateffectiveness.

B. Use of existing data base to avoid the need for halfscale prototypes and tests.

C. Obtaining a complete set of non standard spare partsto assure that the test program remains on scheduleand budget.

FINAL REPORT, April 26, 1991, Page 18

AAAV REFLEX WATERJET. TYPICAL INSTALLATION

00

zN

0FIGURE_1FINA REPRTApri 26,199, Pae 41

TRUNNION MOUNT STEERING SYSTEM

TRANSOM FLAP 24 OVER ALL MOUNTING TRUNNION

54 /

IJET

00-

FTCULRE 2

FINAL REPORT, April 26, 1991, Page 20

ALTERNATE- "T"-FLAP CONCEPT WITH WALKWAY AND CREW DOOR

IRE FLEX MANEUVER JET

ST/ 32 X46 DOOR

004

I K 6ALKWAY--132

DEPLOY ED FLAP, PLAN VIEW

FIGURE 3

FINAL. REPORT, April 26, 1991, Page 21

0

APPENDIX A

• REFLEX JET TECHNICAL PRESENTATION

by

Waldo E. Rodler1488 Cherry Garden Lane

San Jose, CA 95125

Presented at Kick Off MeetingSpringfield, MO

October 10, 1990

APPENDIX A

Springfield, MO

REFLEX JET TECHNICAL PRESENTATION

By: Waldo E. Rodler

October 10, 1990

This presentation is providedunder NSRDC contract number N00167-90-0058

SKEY CONTRAC~T PERSONNfEL=

BUSINESS MANAGER

R. Kent Wooldridge• 4811 Trailwood Drive

Springfield, MO 65804(417) 822-9218

PRINCIPAL INVESTIGATOR

* Waldo E. Rodler1488 Cherry Garden LaneSan Jose, CA 95125(408) 264-5592, 416-5663

OR IG31 3 N. CONCEPT COMB IRNED

High Speed Steam Locomotive Water Pick Up

Torque Converter Stator

Torque Converter Pump Impeller

Annular Nozzle, Like Converter Flow Into Turbine

SERIES #30n XROTOTYES

CONSTRUCTION

Rear IntakeAnnular Jet DischargeDeflected ReverseSwivel Steering

PERFORMANCE

Speed Equals Other JetsAcceleration Equals Other JetsVery Good SteeringFair Reverse

REFLEX JET, October 10, 1990, Page 2 of 22

1 3S

75 7 z

00

>o 820,

0 0

006

do . 10

46 "

"(0

CROSS SECIW, SERIES #1 PROTOTYPES

REFLEX JET, October 18, 1990, Page 3 of 22

04

STATIC FLOATING POSITION, SERIES #1 PROTOTYPE

... ... ... .... ..

OPFRATION OF SERIES #1 PROTOTYPE

REFLEX JET, October 10, 1990, Paqe 4 of 22

SERIES *2.

E'ROT'OTYPES & PRODUCTI ON

CONSTRUCTION.

Rear IntakeIndividual NozzlesSeparate Reverse NozzlesSwivel Steering'

PERFORMANCE

Speed and Acceleration Equals PropellersSteering Very GoodReverse Very GoodGood Fuel EconomyGood Hump Speed Performance

01

0l so 20 21 ZS

N1 55 54111 1 1^ ,

Wo a 30 37 40

0 1

00

S-oc

10 4

CROSS SECTION, SERIES 12

REFLEX JET, Oct0ober 1, 1990, Page 5 of 22

0 0

PARTIAL ASSEMBLY, SERIES #2

IMSTALLATION OF SERIES ff2

REFLEX JET, October 10, 1990, Page 6 of 22

SERIES #2 OPERATION (IN 180 HP SEA RAY SRV1S)

SERIES #2 OPERATION (IN 140 HP SPCRT'.TNE 16)

REFLEX JET, October 10, 1990, Page 7 of 22

4 . ....

*5 C

PE E D I r---WI P R H I1

4.,1 H F He e *417-1 HF ''tc~d#1. 4 C)7 HF PI #2 1 15 HF Clutbo.Lr d #4

SERIES #2 FUEL CONSUMPTION COMPARED TO PROPELLER DRIVES

tt-iFIHE J-ET YTI1- FUEL TES-TS-.

IT4--

4 . U

LI..I .. . . .

J.FLED Hl t !ILL - HIJ-Fa .di IH H~ #e 1., 0-4 S HI- EBertI: eey #~

I~9iH :.t[~e j 1-- . L Ihr-- sJr #

SERIES #2 FUEL CON'SUMPTION COMPARED TO OTHER WATERJETS

0 REFLEX JET, October 10, 1990, Paqe 8 of 22

...E . ....i~~I ~ ....... _

........ .......1.' .........

... .. . . . ...... . . . . .

-7 #e±F- -d -71~.-

FUEL ECONOMY COMPARISON, CORRECTED FOR DISPLACEMENT

#1. Boat: Chrysler Conqueror S 111, 18' (Low Profile)Engine: Chrysler 348 CID

*Drive: Chrysler Wateriet

#2 Boat: Marlin Venus 16', Tni-hullEngine: Mercury 140 HP (Converted Chevrolet 181 CID)

Drive: Mercruiser I/O Propeller

*#3 Boat: Mirro-Craft 14' (aluminum)Engine: Evinrude 40 HP OutboardDrive: Propeller

#4 Boat: Thunderbird 17' Tri-hullEngine: Mercury 115 HP Outboard

*Drive: Propeller

#5 Boat: Kona Maki 18' (Low profile)Engine: Oldsmobile 390 HPDrive: Berkeley Jet

*#6 Boat: Glastron/Carison CVC-18Engine: Oldsmobile 330 HPDrive: Berkeley Jet

REFLEX JET, October 10, 1990, Page 9 of 22

#7 Boat: Sportline 16' (Low profile)*Engine: Chevrolet 140 HP, 181 CID

Drive: Reflex Jet, 7.37"1

Note:

Tests #1 -#6 were conducted by Bob DeVault, Technical* Editor of Trailer Boats Magazine.

Test #7 was conducted by Ralph Lambrecht of Outboard MarineCorporation

ki'5f.....

14 i . ........ ........ ... .

.. ...............

100 -~ . ........-..

.. . .... . . ...

F'..EL-'-H~ Fi% I -. ri 1 IT F'j i -! I 9Z9C

NOTE: The above curve illustrates losses as related to the* amount of curvature in an elbow. It shows losses to be high at

the beginning of the turn, but less for each increment ofcurvature. Reference data is for 0 to 90 degrees, but it appearsreasonable that the slope of the curve will continue to decreasewith added curvature. A reversed turn, like some waterjetinlets,should have higher losses in the second turn.

REFLEX JET, October 10, 1990, Paqe 10 of 22

CROSS SECTION OF A CONVENTIONAL WATERJET

ZIAc7Y

TORQUE CONVERTER CROSS SECTION

REFLEX JET, October 10, 1990, Page 11 of 22

L0-F'T ' P :-F

V i. t rPr UF _ [

.. ...I. ... ...

4~~~ ~ ~ ~ 1-** ... ... ...............

.. .. .. . .. .. .

.. . . . . . . . . . . . .. . . . . . .

0 U lc

E LI I .:IEHT R)I H I- 1-

CONVERTERS ARE EFFICIENT IN SPITE OF CURVED FLOW PATHS

05

ix -I- -- N

. . . . . . . .. ........................ ....

Lij - --j

CROSS SECTION CONTROLS BLADE ANGLE BECAUSE AT ANY POINT ON ASTATION LINE (COTANGENT OF THE ANGLE)/RADIUS) IS CONSTANT

REFLEX JET, October 10, 1990, Paige 12 of 22

LIIIEEP'..lLf li T .'E i:T I-' F~ 1 E7'1 I'

L

U -1 .. .. .. . . .. ..

.. .. ... .. -

*- 5 .... ... ... .. .. .. .. .. .... .. ....

CL-.I _ _ _ _ _ _ _ _ _

uL I' 10 2.- 0 401 50-- INLET 1..ELriI-ITY fr-T IrPELL.ER FT --*=El-

a ST'i;DHRD, 9. 79 [MPlH * Tt-E;TNrF:C', It.. 12, t[PHClSTiVNDfiROl, 2---. 125 tr-F'H :::REFLE:.-- at 39. 0 MPF:H

SERIES #2 INLET VELOCITY DISTRIBUTION VS. CONVENT1ONAL JET

* r~~NISLE -ii FjF~ll..IEF:, $E HY 'zPU .-1 '4F0 r~hi

1.5

.. .- ..'.. ....... .......... ............... ....... .. .

SERIES #2 JET NOISE LEVEL COMPARISON WITH PROPELLER

REFLEX JET, October 10, 1990, Page 13 of 22

F:I...MF'ET. .H~ . .. .F ......... I-

4_0 414 4-2 4 1 4

C ujlP ..- r4 CI _.T PT. T ,.

L : 4: -=-i0 .... .

1 2 4 44 45

IMFELLEF -F* ....H..... DS

SERIES #2 TES ETS VS. PROGRAM FOR RPMW VS. BLADLE ANGLE

RELE ET'ctbr 1F,FI' 1990 PaeTF 14 of 22 TT

SERIES #3.

HI GH PEMRFORM MIC MInWR INE

CONSTRUCTION

Rear IntakeDual Low NozzlesSeparate Reverse NozzleSteering DeflectorGeneral SimplificationReduced Size

PERFORMANCE

No Change In Performance Factors

SIDE VIEW, HPM ENGINE AND SERIES #3 WATERJET

REFLEX JET, October 10, 1990, Page 15 of 22

REAR VIEW, HPM ENGINE AN4D SERIES #3 WATERJET

* r

HPM WATERJET OUTBOARD

REFLEX JET, October 10, 1990, Page 16 of 22

AAAVJ ELE CTR IC WAE JET CON CEPT

. /AAA*L T k A I ISOM MOTO PUMP VINTAK ELBOw NOZZLE" (41

* Aj

Z TRANSOM FLAP WATER INLET

AAAV REFLEX JET

ST-F.'.TIriI Pir-.T '-." ELECTFIC. JET FORF: '...'

-. - - ..

5 0 0 0 ...... ..................................... ......r . ... . .. . . ..............................4 0 0 01 ........... ............... -. : _ _ ............ ................ -,....... ...

0.cl _1'1,; ............. -. "................ ... ........... , ,:- ................... ........................................

1 C- ¢1 .... r , ....... .... .. ... . . ......... ......... .......................................................... . . . . .

Cl I I0 23 40HULL ;PEED ([MPH,

" FLl ,II *I3Fr... 101::, + THF'.LST PIOUrIDS,-',EFFIlrI:'..- 1. 10000 THRU'-T THF'I3ET

AAAV ELECTRIC WATERJET INITIAL PERFORMANCE ANALYSIS

REFLEX JET, October 10, 1990, Page 17 of 22

AAAV WATE:R JET CON CEPT

CONSTRUCTION

Front Motor For:Simple Installation and RepairSiMplified Gear ReductionSimple Electrical Connections

Rear Intake For:Low Losses and Good Velocity DistributionImproved Hull Hydrodynamics

Quad Nozzles For:

Fit Available SpaceGood Clearance of Foreign Material

* AAA YV WATE:RJET

LERFORMANCE O PT IM I Z AT ION

CAPTURE AREA

Optimized For Hump Speed

Use Proven Recovery Factor

Use Proven Drag Factor

Use Proven Recovery & Drag Relation

Provide For Trash Rake Losses

AAV~ WATER JET

* PERF'ORMANCE OP TIM14I ZAT IO0N

INTAKE ELBOW

Head Loss Factors

CurvatureNumber of TurnsDiffusion

Discharge Velocity Distribution

Conventional IntakeElbow Intake

REFLEX JET, October 10, 1990, Page 18 of 22

IAA.A V WALTERJ7ET

PERFORMAN=E~ OPT IMk4I Z AT ION

IMPELLER

IntakeVelocity DistributionPreferred AnglesTip Velocity Limits

DischargeVelocity DistributionPreferred Angles

Cross SectionOptimized for Best Blade ContourMinimize Wet Area

AAA' V WrATER 7E T

PERFOR~i4A]N4[ OT IMI4Z AT ION

NOZZLE SYSTEM

Controls Flow and Jet Velocity

High Flow Increases Internal LossesLow Flow Reduces Ideal Efficiency

Flow Optimization

Proprietary Program Will Be UsedProgram Has Been Validated By:

Prototype TestsComparison With Results From Major WaterJet

Manufacturers

DROD YNM IIC I NTEGRAT I ON

THEORY

Rear Inlet Avoids Intake Sink In Lifting AreaOf The Hull

Trim Angle Is Reduced

Hull Drag Is Reduced

Intake of Air Is Minimized

Boundary Layer Dump Can ImproveCondition of Water Entering Jet

REFLEX JET, October 10, 1990, Page 19 of 22

HYDRODXN/IkI4 I C I NTEGRAT I ON

TEST RESULTS

Outboard Marine Corporation Tests By R. E. LambrechtShow a Five Mile Per Hour Reduction in the SpeedNeeded to Plane a Hull When Jet Inlet Was Removed Fromthe Hull

W. E. Rodler Test Results With the Rear Intake HaveShown Better Performance Than Can Be Explained by theEfficiency of the Reflex Jet

5.00018ft. BOAT - 2 PASSENGERS307 CI V8

4. 00 1 .. ---o400TER -JET DRIVE

MINIMUM PLANING SPEED, NIG

3,000 10 154a:

0Wz

2,000- MMINIMUM PLANING SPEEDz

INBOARD- OUTBOARD DRIVE

1.000-

*0 5 10 15 20 25 30 35 4 10 4:5 50

BOAT SPEED MI/HR

OMC CURVES SHOW EFFECT OF STANDARD WATERJET INLETON MINIMUM PLANING SPEED

REFLEX JET, October 10, 1990, Page 20 of 22

aAv WATERJRT

PE~RF ORMI][ICR O T IMHI ZAT ION

ELECTRIC DRIVE

Will Be Based On:

U. S. Army TACOM Report No. 13236Ry Rodler, Shafer, etc.

Anticipated Majo.r Components:

High Speed PM AlternatorHigh Speed Induction MotorSimple Controls

ELE.CTR I C DR I VM COP4EONRN T S

HIGH SPEED PERMANENT MACNET ALTERNATOR

Simple ConstructionSmall SizeLight WeightDependableAffordableVery Efficient

ELMCTRI C DRIP:v COMPONENTS

HIGH SPEED INDUCTION MOTOR

Simple ConstructionSmall SizeLight WeightLow CostDependableGood EfficiencyEasy To Control

EL.CTR I C DRI7 COMPONENT S

SIMPLE CONTROL SYSTEM

The Use of an Induction Motor Operating NearSynchronous Speed Results In:

High DependabilityMinimum Space RequirementEasy MaintenanceHighest Possible Efficiency

REFLEX JET, October 10, 1990, Page 21 of 22

AAkV7 REFLE E X WATRJET PRG C) R AM

PLANNED ACTIONS

1. Update AAAV Data

2. Prepare Comparison Data

3. Optimize Reflex Design

4. Prepare Reflex Drawing

5. Design Review, Washington, D. C.

6. Develop Data Comparison

7. Make Comparison Matrix

8. Present Final Report

REFLEX JET, October 10, 1990, Page 22 of 22

APPENDIX B

REFLEX JET MID PROGRAM REVIEW

by

Waldo E. Rodler1488 Cherry Garden LaneSan Jose, CA 95125

Presented at Mid Program ReviewDTRC, Bethesda, MD

January 29, 1991

APPENDIX B

iIH PERFRMANCE IMA INE PRFMDDUCTS

* Springfield, MO

0

REFLEX JET MID PROGRAM REVIEW

Technical Presentation

By: Waldo E. Rodler

January 29, 1991

77-1

This presentation is provided under1DTRC Contract number N00167-90-0058

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REFLEX WATERJET MID PROGRAM REVIEW, January 29, 1991, Page 5

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.. ......... .. . .. . . . .. .. . .

i ~ ~ .. ...... .. ..... .. .. .... .

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Ii10~ 30 4 0HULL S;PEED IN t'IPH

THRUS$T IN PLIO; * FL0L'I, :3PrM.- 11*P. C. 1XI 10.1 000 18 M-PH DESIGN SPD.

...............

SPCFCAIN

.... ... ...

1.TrsUt1 P 75Ls

2.Sa oreoe 0

REFLEX f WT R PM PRGA17VEJnar590 99,Pg

4.Iple0imee 61Ice

0l

0i

size.

EF FEC.i CF '--HIt I THF'UI_.[ rdiHL i'IE' ,H]T4 0

4t- +SI~

IL 1 4 F1i

F 1 '1 'llI

REFLE T J M- I-, 2 1L ,: .. . . . . . . . .A- . . . . .. . . . . . .

LI [ 1 II

* ~ r F I I It H i * l n.• I i ti ' ,

* , ','F' l 4, IItI t I ryI

REFLEX WATFPJFT MID PRUG(RAM RFVIFK, ,Iir~i.ry 2q, 1q91, f'aqe

0 ,:i 1 . i . .I

Dia Thus 'D- q ae- -qt To al -*bs I U U

In Lb.Ls

16 :-4 -56 1 325

ThutinraeinJ 2"jt 4LChng in thus magi ... 0

1. Reuc moo torque

2.Rdcesz

3. Reuc wegh

Moo mnfacuer r qatUun

thes -e its.

IMELERSPE

0F

w -u0-h m "n-

4. Inrae RP pemt hihe moto

spe wit a sigl stg of reudct

rn--u -. - - - U

- - - rn. *

r--J ]uO -' - - - -

geaing wichrdce iewih

- and -cs of m otoa' c-ntrols

E I 1' I FFfF:, F :'.H THF U1. 1': F t T- I :

Lif

C- i - -I

tt F I I11t1

J 1 11f' 1 ! I -.,F t I 1 i 1:i T 1( I f ' : 1. F j

REFLEX WATERJET MID PROGRAM REVIEW4, January 29, igql, Pq

L75 3,45

Los7

EFFECT. ONCVTTO

RP uto peii pe

102013r8

Ui75 18,r733- - .

Coprsn*._ prtda 7,0

0AIATO

0aiaini rtia osdrto

1. It ca cas-aatopioso

0efomne

2.I0a eiui imtlf qeo nimpeller- -

Cavitatio WonTderaion l RGA EIW hiit the, watder

f0o houhajt

CAIATO

A APE

LIIIGRS0B NLSS

Posiilt of cavtio ismaurdb

covntoa suto specific-speed

anlyi an by UF (Vlct Conversion

Fato) V is th par of t tota

2. Use by Mel Hupe-t - U -

!I of i i t 1

REFIX WAEFIF 1 1 PG A RE IW Jali

0

0::HI..hITA-TION r-1RGIN U~S. IS NI PH THRUSET

. .............................

3500................. ... .... . .....

3 4 5 .............

330 .45 .55 .65.7VELOCITY CONVERSION FACTOR (VCF)

*IDEA)L INLET + BEST INLETo IM PROVJED INLET x STANDARD INLET

CAIATO

.. ...... ....

LIMITING ISK BY PACTCLDSG

Si~ni icn catio f acosfprr0uc s ul ein r eand

1. Ine cofgrto an veU U - U

2. Imele ti velocity

3.Iple iltage

4. Imele contours-

REFLEX WATERJET MID PROGRAM REVIEW, January 29, 1991, Page 12

E0i

EFETO IT

"LFT is th vetia offstf h

sttcwtriet h enhih

of t nozls

Th enrg reuie to lif th wt r

is a~~ signi -n losi h o ed

hig mas f lo - U - A. 1 required

low peedappicatons

* EFFFT -IF LIFT 1111 II

I*~qw

S4 TL .Iv4l

REFEX ATEJFTMI PRGRA REI F , Jntjir

INE0EBW

3. Inid raiu

4.Te0l ai

5.Hdalcrdu

INLET- DRGFATR

INESATR SDI H NLSS

Ine r g.....:0O

Ine veoct hedrcvr .5

EXESV REUNN ULTSSO

RESNBEILT0EIN HW-1 -i i ia -vaitin in th s au s

2.N0esrbecag efomne

3. -Te~ no f m uc."Dsg

RE~L f WAeaJtue that improvM REIW aure9,1o1,Pver

aloices0rg

LIEETMT

Reut of lietsso .4 e t

35-6auiu melr

1.Cer0ae et

300 ours 0.01" ti wea

Werrt0.004 e-hu

2.SnUbec et

6 or .30 0A)a

-Wa rat 0.05 pr hour

RE ~ ~ LIF WAEITMDPORMRVETIMAT ~ 19, aE

ESIAE IEI AVAPIAIN

Les ra nsm - - U - -8 me U

Les swve mounin -

0 - 0m 3- p0

PFFLEXW =E 75, D I=PA 7.V34, P~Inr 65.32~I

D2 61 2 84

CONERGNT UCT0HP

"Th auho -a f un tha a reduin

is fL WATRJE netize ROyA h~e steadying ef , 191

ofacnegn hne.

LUU

....... ..

T. 10

1- , 4I '.

....... .. ... ..

.. ..................

S7

---- ----

RELXU TRE I PORMRVEJnar 9 91 ae1

38.540 FPS

0 IMPELLER IN

IMPELLER OUT

*/

___ 6 6a1I FPS

NOZZLE OUT-"

*r

INTERNAL FLOW\ Z'

ELBOw IN

REFLEX WATERJET KID PROGRAM REVIEW, January 29, 1991, Page 19

0 /

Tag nta veoit- - U U iuf U

* ~Fl "[DE WA~cLES FORP 16~. 1 h"-TEFJET

I Ii t t i d 1[ 1 1

REFLF WAE4-I- RGA RV ,Jaur 9 19,Pg

REUTO GErARING.1.A rlmnrgersthsbeseetdo

th bai of a covntoa U--~si f oru

bea stegh sur ac copesv - - -

an0niiatdrto

2.Srs0ee ssihl eo h ee h

apaetuwsue nteWsigos

S ~ ~ mo o and__is_____________conservative ___for

0mltr vehicles.

3. Peiiau 12 Pd gea set:

Dieso0u PaesIRn

1 TUo -i nube 15 1 39 93-

Pi haamfr5

0u ie&mfr 1 .2 7 711

REFe WiaJ FU PRGA EIW hUar 1901 PMqO

MANANBLT

- OO SOURCES

STTSO0OORSPLES

:StoinI. I -i I Active hevy Iose0tv ih lent

t weg-t .1. *

Wetngos Actve good undrstnd

use ad inegraio

RELX AERE CDPONRT EINUW, EFFORT,, 99, ~q

1.MTRSUC0ESG ORIAIN

EFFECT OF ANGLED I.AITEF._IET NOZZLES

90 0.......::- : C i 0 .... ... .................................................................................. ....................... ...... ..

7 0 0- - -.. .. I........... .................................................... ........... ...... ................... - A.... .7 -..........~ ~ .. ........... ................. ........ .. ..... .,": .................... ..........

5 71 0 . .............................. ........................................ . . . .. . ... .. . ..............

4 0 0: ............................... .. .. ....................... ...... ...... ........ ..... ... ......... ....................

4,0 0 -..... .............................. ... . . . . . . . ....... ..... :....................................... ................ . .

2 0 0o .. . . . . . . . . . .. . . ..- : ""- ..... : 7 . . . ., . . . . . ............................ W 7..........

1 0 ..... ........ i : " ................ .............................................0 r 2 5 6 T ? 9 10 11 2Z

ANIGLE IN DEGREESTHRUST LOSS.. LBS. * LIFT GHIN LBS.LIFT,'DRAG.X 10

*CLERAR Ic:E GAIN FROM fANlGLED NOZZLES5

. ............................................................................................................. .. ... .'. :...... .4

* i 3 -- ; .. .. r-

-:1: _.-'""-- -'-:= ~ ~ ~~~ .................... ...................................... ;..: .. .............. ' ................ . . . . , ... l........

..J ... .,-.. ,_ .- _ '- -- - "... ... ... .. ... ... ..

'- 1 ~ ........................... '":' " '-" - '-..................... _..;K . = w ' - - ' .......... _ * ...

...... .......... ., - .. ....-. ... ...,,- m .. .-- ------ 4!U. I-. -4

1 2 .3 4 5 6, 8 10 11 1NtOZZLE ANGLE., DEGREES

5" AFT OF NOZZ'LE 1 I0" rFT OF NOZ7LE, 15" f*T IIF NOZZLE X. 'C! "hFT OF NL'CLE

REFLEX WATERJET MID PROGRAM REVIEW, January 29, 1991, Page 23

Data Wae Je Prplso -Copeito

CL3 Lm/(E/ * i.nV2E

CLU =Ui o ffiin

=L a nwt r - ,V=V lct PjP Wtermassdenity = eamf t

El NE LCTO

REFLE O W TE IFT PR CROEVI, N Janar A9 H991 RPap

HYRDNMCPAI6SRAE

INE0OCTO

EFETO OVNINLFRADWTRE

2 . apwtm fotsa- 4 f -

chr n 63dge e eto iet

th aeaon fwtr

I* . - -U. L +- 6 * cY b*- ( p- -

4.~~~~ U Thseuto ie iftvlefo yia

-AA trno f la of 1250 pounds.

THR US PEFOMACE

1.Terflxjtthutpr rac

RE sE comparabl toD PRORA REVIEW Jauay 9,191,e

2.Te0R aeittrs efomn

. nle loato eff c

2. Speia igh sain i. -. --

4. Moo./ern lurcto an oln

1.REXUCTRJTIN OWIDT REIEW Anr CRITI9A1,GOAL.

2.TECNETOFESAVNAE N

APPENDIX C

REFLEX JET FINAL PRESENTATION

by

Waldo E. Rodler1488 Cherry Garden Lane

San Jose, CA 95125

Presented at

Quantico, VA

April 26, 1990

APPENDIX C

00

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APPENDIX D

SAMPLE CALCULATIONS

By: Waldo E. Rodler1488 Cherry Garden Lane

San Jose, CA 19125

APPENDIX D

_F6 r, -T SA SIT D I v VT t'yVA.E

~ ~J~,* PP~-~ f Rm,.% VQFTHPE

J IJvro0P-1cj pi.r&a ,J co *W & A6i > IL ~flMv4y

11 .6 Rkt~ cfX1 .,s--

* 9 CAVTr~ OFn.C-TAIC br T> p,.A

is5JJ O PsGv'

I _ _ _ _ __ _ _ _ __ _ _ _ _ ___At_ _____ _____ ___%-r__V#____M

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*__ 7 v R &.s W rv.& C-:. L c ' 0

___4 - -- 3 PF_ Iiiii..i f

R~~v~i~~i!~ c...1r p)JA nvP 7 .i 1>

Itr.%~ Pag (k a-iscP ICr"I.

?Llb ~~ 41 L At1 l E.P .G NT i> I ks, 6T v

_f.sp I-'r. b .M .664-Ci lvCbfo4tJ 0.1!I I4

I~~~~~** VNIL PLO 48 .7L p rrsu

**.- --- *-*-* .-I(*-*'.*-.* .JWf flEP' J. I: f OPT IM I ZAT ION PRO3RAM JE-OF'r *****************-OP**

FILE CODE: JEiFOPT9D REVISION 101/7/1986NOTE: THIS PROGRAM IS PFf-:UfRIETARY DATA OF W. E. RODLER AND IS NOT TO BE USED OR

COPIED WITHOUT HIS EXPRESS WRITTEN PERMISSION

DATA INPUT:RUN DATE:900910 IMPELLER D., IN: 16 NET SHAFT HF --- : 397

* DIFFUSION Kdf-: .85 uk-LGREES INLET--: 165 TURNS IN---- 1':AV. LIMIT MPH: 8 INLET LIFT, FT-: -2 VEL. CONV. Kv--: .6500001

TIP SPEED, FPS: 125 INLET DRAG Cd--: .05 RAM RECOVERY Kr: .75RUN NUMBER: --- : 25 AC:URACY LEVEL-: 100

DESIGN POINT RESULTS:* INLET VELOCITY, FEET PER SECOND .................... 34.25707

INPUT SHAFT R ..'M .................................... 1790.495SUCTION SF'ECIFIC SPEED .............................. 20413.38PUMP EFFICIENCY IN PER CENT ........................ 84.51998PUMP PRESSURE, PSI ................................. 29.77992PUMP SPEIFIi-: SPEED ................................ 10426.17NOZZLE AREA IN SQUARE INCHES ....................... 97.42499JET SPEED IN MPH RELATIVE TO HULL .................. 43.37734

-'EED VS. THRUST:SPEED, MPH . 1HRIUST,LBS FLOW, GPM . IDEAL EFF% . PROP. EFF% EFFEC. HP

0.00 .3.:,.- .70 19316.77 0.00 0.00 0.002.50 5038.06 19370.02 10.87 8.46 33.59

4/48.34 19370.02 20.62 15.95 63.315.0 4748.. -155 89.5

7.50 4475.74 19477.42 29.28 22.55 89.5110.00 4211 .3'.5 19586.01 37.05 28. 29 112..3012.50 3955.13 19695.82 44.07 33.21 131.8415.00 37 08. 07 19862.87 50.34 37.36 149.3217.50 3467.73 20032.77 56.02 40.76 161.8320.00 3233.88 20263.88 61.07 43.44 172.47222.50 3005.30 20500.39 65.66 45.42 180.3_:,,_25.00 780.56 20803.90 69.72 46.69 185.3727.50 2561.30 21053.26 73.56 47.31 187.8330.00 2 341.94 21438. 7a 76.79 47. 19 187.3632.50 2127.46 21770.86 79.87 46.44 184.383.00 1912.28 .27183.2 82.54 44.96 178.4337.50 1702.39 22539. 10 85.12 42.88 170.244o. 00 140191. 13 22981.45 87. 34 40. 03 158. "c42.50 1277.61 23441.51 89.35 36.47 144. 8045.00 10139. 22 24(3(2.07 91.01 32. 0'2 127.11

47., I)VI 845. 43 245 04 .3,5 92.66 26.97 107. 0':)50.00 ' 30.34 ,52. 0 94. 20/ 21. 17 04. 01

Fi()W [I *i 1tI ( - 66j FPJMI' EFF. [TFRAI" IONS= 557*/

E KE"T I-'F '- c' -r THI-.I :. MH..I, IFI-, H I

I~,. ....... ............ . . .............

.=L ; 2 E , ... ..... ....... ......... ..................... ... .... ........ .... ... ... ........... .. ... .. ...

l' , ...... .... ... ..... . .... .. .. .. , ,,.......................... .. .

11IELE Clii 4:

I -P THRUS ,- E '-=.. +c;t1* H L' LE,IIT

,-,49 . _EIG T I.,. . . . ..r..E

X Data 16 MPH THRUST LBS. 18 MPH THRUST LBS WEIGHT WITH INLET

10 2767 2690 16211 2954 2862 20612 3124 3017 25613 3277 3154 31314 3412 3271 37715 3530 3370 44816 3629 3449 52617 3709 3509 61218 3769 3548 70619 3811 3567 809

20 3830 3563 919

)

1 ,_ F'! K~F OF- FF'i 1 ;it T --. 'I .T ' :F I . [".

LUILI-

4.dl 0 l. ....u _ 4 E 0 . .. .. .. .. . . ....... ........ ... ... ... ... . . . . .. .... . . . .. . ..

L .-3 , ! r , 0 ... .... .... ... .... ... .... ... ........... .. . ..... ......... . . . . . . ..

.. .. .. ... ... .... ..

1 CCIt . -iLCL A.

1-'. t-lFH THRUS~T LE~.. 1: K: t-11FH 'T HFI?1" LPi.i :IF i- , , - :,F'E.1 ...

X Data 16 MPH THRUST LBS. 18 MPH THRUST LBS. SPECIFIC SPEED SUCTI ON SPEC. SPD.

716 3796 3616 360.60 771.90

1074 3741 3561 549 1157.80

1432 3686 3506 743.30 1543.80

1790 3629 3449 943.90 1929.80

2148 3570 3393 1151.30 2315.70

2507 3511 3332 1366.10 2701.70

2865 3449 3271 1588.80 3087.70

)I'FKLREF

,, 1S-FH T F:I=T L 'S ' 1, :11-1 H: '.I L ".

C' -r I P:5

... .... .. .. .. ... .... ... ... ... ... ... ... ... ... ... ... ...

.. . . . ... . . .. .. . .. .. . . .. . .. .. . . ... . . . .. .. . . .. .

.... .... ._ . .. . .. . .. .. . . .. . .. . .. .

41 1 i I i. . . . . . . .. .. ... -... .. .. .. ... .. . . . . . . - 1 . . . . . . . . .. . . . . .7. . . . . . . . . . .ci1

LIFT. !H- FEET16I '- MPH T H F' U :1' LH E:_ * 1 MPIFH THFU.:IT L. E:,..

)X Data 16 MPH THRUST LBS. 18 MPH THRUST LBS.

-4 3709 3525-3 3668 3486-2 3629 3449-1 3589 34120 3551 33761 3512 33402 3475 33043 3438 32714 3402 3237

CHIJITNTliri r--lhFRGlr4 VS. 1E. M--F'H THRUS1,-T4050

39 0 ................................ ...............................

4 9 0 .IkI - ........................... ....... . .......................................... - . .......................... ..........

c l. 3 8 5 0 .................... ........................................... "-- ............................................... ..........

- 3650 ......$-

o 3550 ............ .............................................................................................._ 3 86 0 0 ................ ........................................................

';'--: 3 75-

.45 .55 .65 .75VELOCIT'" CONVERSION F-CTOR (UCF)

IDEiL INLET * BEST INLETo IMPRF.O'ED INLET x STANDARD INLET

)X Data IDEAL INLET BEST INLET IMPROVED INLET STANDARD INLET

.45 3823 3659 3612 3596

.55 3916 3700 3644 3625• 65 3987 3718 3651 3629.75 4042 3718 3640 3612

)

3:-:5C._-

3 7T 5 0 ............................................... ' "": - - .................................................................3 T ... .... ... .... ... .... ... .. :- - : -......................................................................................

o 3 7 0 0 . ............... . -....... ....... .......... ........................................

3 E .51 7 . ................. .. . ................................... ......................................................................(C.

' . 6 0 .= ............................................................. .....................................................................

3550 ................... ......... ............ .... ...... ... .......... ...............' 3 ........ ....................... I . ......-. ........ ..............

34500 .............. . .......__

3 4 0 0 I ................. '.... ......................................................... .. ".............. ...... ..... . " .7: .... ...........

.45 .55 .65 .75VELOCITY CONUERSION FACTOR (UCF::

IDEAL INLET * BEST INLET'0 IMPROUEE' IHLET x STPNDARD INLET

X Data IDEAL INLET BEST INLET IMPROVED INLET STANDARD INLET

.45 3649 3489 3446 3431

.55 3726 3519 3464 3446

.65 3785 3525 3460 3438

.75 3826 3513 3439 3412

)

AA-.) W0TERJET PERFORMANCE RUN 901031.5

6001

• ~ ~ ~~~4088 ........... ..-- -.. ........... . .. ....... ................. ........................*4800 ......... ......... .61

4 2 0 0 ............................ . ... .. ...... ..... ............. ......................................... ........ ...... .

3 E .0 0 . ........................... __. ... .. .- a , . ...... ........................ .........................................3 0 0 0 . ..................... ' ............................... ..- . .... ....................................................

I e e -- .. t -- ... .-... . ..... .-... '... .................................. ........................

1 2 8 .. .. " " ... .. ...................................... .......................................................................

4200 .

6 0 0 -. .................................. ....... .................................................................................. .*10 18, 3z4

HULL SPEED IN 'IPHU THRUST IN POUNDS FLOVI, '_PtIr. 10Co P. C. x 10,OOLI1

X Data THRUST IN POUNDS FLOW, GPM/10 P. C. x 10,000

0 5830.04 2095.80 02 5568.57 2095.80 7424 5317.76 2098.70 14186 5076.61 2104.50 20318 4844.16 2113.20 258410 4617.56 2122.10 307812 4398.48 2133.90 351914 4184.62 2145.90 390616 3977.13 2161.20 424218 3775.20 2179.70 453020 3577.30 2198.60 477022 3383.85 2222.10 496324 3194.07 2247.20 511126 3007.02 2270.60 521228 2822.94 2298 526930 2641.02 2329.60 528232 2461.02 2362 5250.34 2282.74 2395.40 517436 2105.99 2429.80 505438 1929.33 2469.10 488840 1753.30 2509.80 4675

"********* THREE ELEMENT TORQUE CONVERTER PROGRAM, TC-4G ****************

FILE CODE: TC-4G REVISION 5/31/1990NOTE: THIS PROGRAM IS PROPRIETARY DATA OF W. E. RODLER AND IS NOT TO BE USED OR

COPIED WITHOUT AIS EXPRESS WRITTEN PERMISSION

DATA INPUT:

RUN DATE:900912 IMPELLER RIP---: 3.383 IMPELLER R2P -- : 5IMPELLER AlP -: 60 TURBINE AlT --- : 45 REACTOR AIR --- : 60

IMPELLER A2P -: 50 TURBINE A2T --- : 25 REACTOR A2R --- : 25SECTION H ---- : .6875 SIGMA --------- : .15 MIN. S. R. ---- :DESIGN RPM ---- : 1750 INCREMENTS ---- : .05 RUN NUMBER ---- : 900912

RESULTS:

SPEED RATIO= TORQUE RATIO= EFFICIENCY= CAPACITY K= FLOW Vn=

0.0000 3.8298 0.0000 238.3513 0.3016

0.0500 3.5643 17.8213 235.2564 0.29490.1000 3.3143 33.1430 232.3920 0.28"-0.1500 3.0792 46.1880 229.7743 0.2803

0.2000 2.8582 57.1643 227.4208 0.27240.2500 2.6506 66.2640 225.3514 0.26410.3000 2.4555 73.6636 223.5898 0.25550.3500 2.2721 79.5240 222.1654 0.24630.4000 2.0998 83.9909 221.1154 0.23670.4500 1.9377 87.1955 220.4884 0.22650.5000 1.7851 89.2550 220.3494 0.21570.5500 1.6413 90.2728 220.7877 0.20430.6000 1.5056 90.3386 221.9295 0.19220.6500 1.3774 89.5280 223.9595 0.77920.7000 1.2557 87.9007 227.1612 0.16520.7500 1.1400 85.4972 231.9967 0.15000.8000 1.0291 82.3306 239.2840 0.1332

0.8250 0.9752 80.4536 244.2999 0.12400.8500 0.9220 78.3677 250.65P7 0.11420.8750 0.8692 76.0532 258.9280 0.1037

0.9000 0.8164 73.4753 270.1062 0.09200.9250 0.7629 70.5700 286.1802 0.0790

0.9500 0.7074 67.2053 311.9668 0.0638

1II

T ,FICiL TflF'L.IF cIrI.EFTEF: FE'E F:RHr:H'IE

: , . . ...... . . . . . .... .. .M._ ............-. .........., - .... ....... . ... .. . .-0 .- .. ... .. r . ......... ..... . .... ......... I -.. .............. I ."... ....... ...... .

6 - ...... ....... .... . ............. .....

5 0 ...... .. .... ... .. ..-.. ... .. .. .... .. .. ... .... ..... ... ... ... ... .. .. .. ... ........ .. ... .. .. ........ ... .... ... .. .... .

4 C: .1 ................ ....... i '..... ... ... .. ........................................................... .................. ..91i ....... .... ................................

4 VI . ..... .... .. ' ... .... ..... ... ....................................... .......... . . . . . . . . . . . . . . . . . . .......... ................................................... ...........

I -1 . .. . . . . . . . . . . . . . . . . . . . . . . ... . . .. . . ." ...........: : ,h -.. . . . . . . .... . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .Al /

, p p .. iI .

0 0. 2 0 0.40 0. 6E,0 0. 80IF'1 OITFUT ,/ RPM-' INPUT

EFFICIEC:", . TORQ--.U_'E PTIO ," 10

X Data EFFIC:IENCY, % TORQUE RATIO X 10

0 0 38.300.05 17.82 35.64

0.10 33.14 33.140.15 46. 19 30.79

0.20 57. 16 28.530.25 66.27 26.51

0.30 73.66 24.56

0.35 79.52 22.72

0.40 83.99 21

0.45 87.20 19.38

0.50 89.26 17.65

0.55 90.27 16.,41

0.60 *90.34 15.06

0.65 89.52 13.77

0.70 87.90 12.550.75 85.50 11.40

0.80 82. -0.90.85 80.45 9.75

0t

to ASS ~ C .A. C_.j LA1~ N jC.

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* t.4LC. I 54N&"I,. i L he. -u & p y 0 LT1 0

on- t'w w-.r * a).& A~S~~l.. ~T~~.V~'g*~~~' 0 Cl WI.')A R s~-Tt- \L- fILt.LCL

vn P4 GG f iA r6GL"T; L,

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ix Ji i r4 ven A.( IL 'r e1.if . m PAOc- I ).

5 jrj -,ba . 1 6 G r -& - I -hL T- cV

F Ei -2-T T 1 AW f it ib (- >'O: LW OfPAV

W0r>r 4--oR rN

NJc. r --r a; -T LA wbj r bA 671 c4cgi. Lor A yI *

3 -9 J;- U(1,6M%5 -TE.fI. oJ~ j-PL~ A 4 1LI .r Cl aC-W %

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* -OCdn-A" .Ca4:- :03 -J - u a m

A n. L o -- p j 57 r.r f r J I4I CrxX J7L

IMPELLER CROSS SECTION FOR RUN #PX19315B, 1756 RPM

RUN I: IMI93158.SS DATE: 98/11/28 BY:W.E. RODLEP FOR:

111II1* **I****I ff#I***II*#I*##*If#***#****##***#**I*I*****f**II**#*#*#**I****I#***I**I*4*I****4*II***

FROM RUNSI: 981031.5 IF 99/19/31 AND 99131.58 OF 91/11/29

DATA INPUT:RPM ....................... 1,750 MERIDIAN RADIUS OPTIMIZATION:FLOW, 6PM ................ 21,132.89INLET AREA, IN-SO ........ : 183.16 EST RAD .....: 211.5380INLET FACE ANGLE, DEG ..... 3.98 H C/L I ..... 217.2191

MERIDIONAL DIAMETER, IN..: 11.94 H C/IL 2 ..... 217.2191

DISCHARGE Vt = S2 ........ 31.5180 ERROR, IN...: 9.9899DISCHARGE AREA, IN-SO ..... 165.11

DISC. FACE ANGLE, DEG ..... 5.8 AREA CHG/STA ....... 1.8860MERIDIONAL DIAMETER, OUT.: 12.97 FACE ANGLE/STA ..... 1.2888

STATION #1 12 #3 14 #5 #6 67 #8 19 #19 111

AREA 183.16 181.35 179.55 177.74 175.94 174.13 172.32 178.52 168.71 166.91 165.18ANGLE 3.89 3.29 3.49 3.61 3.89 4.8 4.28 4.49 4.69 4.89 5.0OFFSETS

Xi 11.9796 11.8179 12.5451 13.2821 14.8189 14.7556 15.4921 16.2284 16.9645 17.7984 18.4361YM 5.978 6.9959 6.9524 6.8975 6.1452 6.1954 6.2482 6.3035 6.3615 6.4220 6.4859Yi 2.5554 2.7928 2.8472 2.9911 3.1342 3.2767 3.4186 3.5683 3.7918 3.8433 3.9849Yo 8.9468 8.1584 8.9720 8.9878 8.1957 8.1258 8.1481 8.1727 8.1996 8.2288 8.2693Xi 11.2496 11.9929 12.7355 13.4775 14.2189 14.9597 15.6999 16.4395 17.1785 17.9169 18.6548Xo 11.9618 11.6934 12.4251 13.1569 13.8887 14.6266 15.3526 16.9845 16.8166 17.5487 18.2897

Vo(fps) 37.12 37.38 37.76 38.14 38.54 38.94 39.34 39.76 49.19 49.62 41.97

NE@ 6.880 6.1490 9.1559 0.2799 0.3858 1.59999 8.6150 8.73H 1.8459 1.9699 1.981UN 91.1716 91.7814 92.4395 93.1189 93.8466 94.6135 95.4197 96.2652 97.1499 98.739 99.9371DiSi 0.008 8.1737 31.6733 55.1728 78.6723 102.1718 125.6713 149.1709 172.6704 196.1699 204.3436Si 9.909 1.3619 5.2331 9.9484 12.823 16.4916 29.1133 23.6646 27.1432 38.5467 31.5199

8 22.1973 22.4626 23.4151 24.4147 25.4387 26.4914 27.5847 28.7977 29.8571 31.1289 31.3859Bi 43.4867 42.6929 42.6317 42.7662 42.9927 43.2997 43.6774 44.1167 44.6993 45.1474 44.7927

Do 16.7632 17.1371 17.9887 18.8841 19.8234 21.8964 21.8322 22.8994 24.9957 25.1484 25.5214

)

Page I

1 I

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/7-

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0 .pf, - -6 P r

S Pa . 1 5

AAAV WATEFJET GEAR SET LOADING CHART, GEARLD21

* GEAR LOAD ANALYSIS PROGRAM FILENAME: GEARL021 11121/90

DATA INPUT:

PINION 'Np' 12 13 14 15 16 17 18 19 28 21

GEAR "Nq' 7Q 3_ 39 3q 39 39 39 39 39 39fACE WIDTH, INCHES 1.100 i.100 1.180 1.180 1.188 1.188 1.10 1.180 1.100 1.188DIAMETRAL PITCH is 1 18 18 18 Is 18 18 18 I

RPM 10,588 10,58 18,500 18,588 18,588 11,588 18,588 18,580 10,580 18,510HORSEPOWER 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3ACCURACY 'e' 8.83 6.6803 8.183 8.883 8.1883 1.1883 8.1813 8.1083 1.803 1.8883'k' FOR 28 DEG FD 8.8888333 0.8888333 8.88333 8.808333 8.808333 1.8888333 0.888333 0.808333 1.8888333 8.8881333'C" FOR STEEL 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5

RESULTS:

RATIO = Ng/nP 3.2588 3.888 2.7857 2.680 2.4375 2.2941 2.1667 2.8526 1.9508 1.8571* PINION Dp, INCHES 1.2808 1.3808 1.4808 1.508 1.680 1.710 1.8888 1.980 2.8808 2.1008

GEAR Dp, INCHES 3.9888 3.9108 3.988 3.9888 3.9888 3.980 3.9888 3.9808 3.9888 3.9808CENTER DIST. IN. 2.558 2.6888 2.6508 2.788 2.7588 2.8888 2.8588 2.9800 2.9588 3.808PINION OD, IN. 1.488 1.518 1.6808 1.708 1.888 1.98 2.818 2.1888 2.288 2.388GEAR OD, IN. 4.1880 4.180 4,180 4,118 4,1088 4.188 4.1888 4.1888 4.108 4.188

* ' PITCHLINE FT/MIN 3,298.7 3,573.6 3,848.4 4,123.3 4,398.2 4,673.1 4,948.8 5,222.9 5,497.8 5,772.7PIN. TORQUE LB-FT 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7STATIC TOOTH LBS. 1,333.5 1,230.9 1,143.8 1,866.8 1,8.1 941.3 889.8 842.2 888.1 762.8DYNAMIC TOOTH LBS. 5,602.8 5,549.7 5,585.8 5,466.9 5,434.1 5,485.5 5,388.4 5,358.2 5,338.4 5,328.6

LEWIS FACTOR 'Y" 8.245 1.264 1.276 8.289 8.295 8.382 8.388 8.314 8.328 8.326BENDING PSI 287,897 191,105 181,324 171,970 167,461 162,719 158,808 155,131 151,659 148,373FACTOR 'K' 5,551 5,175 4,858 4,588 4,354 4,151 3,972 3,813 3,671 3,544SURFACE PSI 425,788 411,184 398,328 387,889 377,114 368,194 368,161 352,886 346,262 348,281MIN BACKING,IN. 8.155 0.161 8.167 1.173 8.179 8.184 8.198 8.195 0.280 0.205

AAAV WATERJET GEARLOAD, 12 PITCH, 1,5 FACE

SLOA[ ANALYSIS PROGRAM FILENAME: 6EAPLOI5 11/21/99

DATA INPUT:

PINION *Np :2 13 14 15 16 17 18 19 29 21GEAR 'N' 3c 39 39 39 3. 39 39 39 39 39FACE WIDTH, INCHES :,589 1.50 1.58 1.502 1.500 1.598 1.588 1.599 1.598 1.580DIAMETRAL PITCH 12 12 12 12 12 12 12 12 12 12

RPM 10,51 il,5i@ ;8,501 19,510 10,510 19,509 19,590 19,50 19,598 11,599HORSEPOWER 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3 133.3ACCURACY Be' 9.9993 9.1893 9.9993 8,193 9,993 9.9093 1.8993 9.1993 8.9993 1.9893k' FOR 29 DEG FO 9.9900332 8.809333 9.809333 8.890333 9.88333 8.980333 8.98333 9.98333 9.980333 9.89333"C' FOR STEEL 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5 499.5

RESULTS:

RATIO = Ng/nP 3.2518 3.9999 2.7857 2.688 2.4375 2.2941 2.1667 2.9526 1.958 1.8571PINION Dp, INCHES 1.898 1.8833 1.1667 1.259 1.3333 1.4167 1.5001 1.5833 1.6667 1.7581GEAR Dp, INCHES 3.2599 3.2599 3.2599 3.2599 3.2599 3.2599 3.258 3.2599 3.2599 3.2598CENTER DIST. IN. 2.1259 2.1667 2.2883 2.258 2.2917 2.3333 2.3750 2.4167 2.4583 2.5000PINION 00, IN. 1.1667 1.2589 1.3333 1.4167 1.5999 1.5833 1.6667 1.7599 1.8333 1.9167GEAR OD, IN. 3.4167 3.4167 3.4167 3.4167 3.4167 3.4167 3.4167 3.4167 3.4167 3.4167

PITCHLINE FT/MIN 2,748.9 2,978.9 3,297.9 3,436.1 3,665.2 3,894.3 4,123.3 4,352.4 4,581.5 4,818.6PIN. TORQUE LB-FT 66.7 66.7 66.7 66,7 66.7 66.7 66.7 66.7 66.7 66.7STATIC TOOTH LBS. 1,699.2 1,477.1 1,371.6 1,288.2 1,299.2 1,129.6 1,966.8 1,19.7 969.1 914.4

) DYNAMIC TOOTH LBS. 6,247.7 6,294.2 6,169.4 6,141.2 6,118.! 6,899.0 6,883.1 6,969.7 6,958.3 6,948.6

LEWIS FACTOR 'Y' 9.245 9.264 8.276 9.289 9.295 9.392 6.388 9.314 9.328 .326BENDING PSI 294,87 188,985 178,822 169,999 165,915 161,564 158,892 154,642 151,458 148,433FACTOR 'K' 5,447 5,991 4,791 4,535 4,314 4,121 3,951 3,891 3,666 3,545SURFACE PSI 421,778 497,756 395,578 384,863 375,379 366,884 j59,246 352,339 346,832 349,279MIN BACKING,IN. 9.129 8.134 9.139 9.144 1.149 9.154 9.158 1.162 9.167 9.171

Page

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0 C A'4,a 1 0 PT-i)I

ELBOW DIMENSIONS, 14" WIDE INLET

ELBOW SECTION DEVELOPMENT PROGRAM FILENAME:ELBOSE8E.SS(Revision E)RUN 901214.1

SECT. SECT. TAPER WIDTH CORNER HALF Ri R/D R c/l Ro SECT.NUMBER AREA IN/SEC IN. RAD. SECT. IN. IN. IN. ANGLE

IN-2 IN. THICK DEG.

1 . 216.410 0.000 14.000 0.000 7.729 2.800 0.862 10.529 18.258 165.000

2 213.280 0.000 14.000 0.805 7.637 2.845 0.873 10.482 18.119 148.500

3 210.150 0.000 14.000 1.610 7.585 2.890 0.881 10.475 18.060 132.000

* 4 207.019 0.000 14.000 2.415 7.572 2.935 0.888 10.507 18.080 115.500

5 203.889 0.000 14.000 3.220 7.600 2.980 0.892 10.580 18.179 99.000

6 200.759 0.000 14.000 4.025 7.667 3.025 0.895 10.692 18.358 82.500

7 197.629 0.201 14.201 4.830 7.663 3.070 0.901 10.733 18.397 66.000

8 194.498 0.525 14.726 5.635 7.529 3.115 0.914 10.644 18.174 49.500

9 191.368 0.648 15.374 6.440 7.382 3.160 0.928 10.542 17.923 33.000

10 195.440 0.525 15.899 7.245 7.563 3.205 0.924 10.768 18.332 16.500

11 203.583 0.201 16.100 8.050 8.050 3.250 0.904 11.300 19.350 0.000

0

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rv vyLLPIE S7ZE 17- &

COLLECTOR/NOZZLE DEVELOPEMENT FILENAME:NOZZLEOI

* C:OLLECTOR/NOZZLE DEVELOPMENT

FILENAME: NOZZLEOI

STA. AREA CORNER i::ORNER VERT. WIDTH# IN'2 RADIUS LOST HEIGHT IN

IN. AREA IN.IN 2

1 32.553 0.000 0.000 4.250 7.6602 31.920 0.289 0.072 4.403 7.2663 31.288 0.578 0.287 4.556 6.9314 30.655 0.867 0.645 4.709 6.647

5 30.022 1.156 1.147 4.862 6.4116 29.390 1.445 1.792 5.014 6.218

7 28.757 1.734 2.581 5.167 6.065

8 28.124 2.023 3.513 5.320 5.9479 27.491 2.312 4.588 5.473 5.861

10 26.859 2.601 5.807 5.626 5.80611 26.226 2.890 7.170 5.779 5.779

EFFECT OF ANGLED NOZZLES ON THRUST AND CLEARANCE

EFFECT OF ANGLED NOZZLES filename:NOZSPLAY:SSDEC. 13, 1990

ANGLE THRUST THRUST SIDE SIDE ----- ADDED CLEARANCE AT:--------DEG. THRUST LOSS LOSS THRUST THRUST I" 5" 1.0" 1.5" 20"

LBS. (M) LBS. (M) LBS.

0 3,775 0.000 0 0.000 0 0.000 0.000 0.000 0.000 0.0001 3,775 0.015 1 1.745 66 0.017 0.087 0.175 0.262 0.3492 3,775 0.061 2 3.490 132 0.035 0.175 0.349 0.524 0.6983 3,775 0.137 5 5.234 198 0.052 0.262 0.524 0.786 1.0484 3,775 0.244 9 6.976 263 0.070 0.350 0.699 1.049 1.399

5 3,775 0.381 14 8.716 329 0.087 0.437 0.875 1.312 1.7506 3,775 0.548 21 10.453 395 0.105 0.526 1.051 1.577 2.1027 3,775 0.745 28 12.187 460 0.123 0.614 1.228 1.842 2.4568 3,775 0.973 37 13.917 525 0.141 0.703 1.405 2.108 2.811

9 3,775 1.231 46 15.643 591 0.158 0.792 1.584 2.376 3.16810 3,775 1.519 57 17.365 656 0.176 0.882 1.763 2.645 3.52711 3,775 1.837 69 19.081 720 0.194 0.972 1.944 2.916 3.88812 3,775 2.185 82 20.791 785 0.213 1.063 2.126 3.188 4.251

13 3,775 2.563 97 22.495 849 0.231 1.154 2.309 3.463 4.61714 3,775 2.970 112 24.192 913 0.249 1.247 2.493 3.740 4.98715 3,775 3.407 129 25.882 977 0.268 1.340 2.679 4.019 5.35916 3,775 3.874 146 27.564 1,041 0.287 1.434 2.867 4.301 5.735

Page I