NATIONALADVISORYCOMMITTEEFORAERONAUTICS

TECHNICAL NOTE 3203

CONSIDERATIONSONA LARGE

ByUpshurT. Jo~er andWalter B. Home

LangleyAeronauticalLaboratoryLangleyField, Va.

CATAPULT

WashingtonJuly 1954

r

-I!i-=g4--

Ju!f2 () 7957

TEGIILfBRARYKAFB,NM

K NATIONALADVISORYCOMMITTEE.

●

CONSIDERATIONS

By Upshur

TECHNICALNOTE3203

ONA LARGEHYDRAULIC

T. JoynerandWalter

JETCATAFULTJB. Home

EWMMARY.

A surveyofvarioustypesof catapults,whichhasbeenmadeinconnectionwiththeprobl&-ofacceler&ing-a large(lM,000lb)csralonga trackto a speedof 1X milesperhour,isgiven.A hydraulicjetcatapultis indicatedasthebestsuitedamongthesecatapulttypesfortheproposeintended,andvsriousdesignproblemsofthistypearetreated.Equationssregivenforcalculatingtheperformanceofthejetandofthetestcar,andconsiderationisgiventothephysicalconditionsaffectingthejetflow.Designproceduresarepresentedforthejetnozzleandforthebucketonthecarwhichreceivesthejetad impartsthrustto thecar.

Theexpectedandtheeffectof.

.

.

propulsiveefficiencyofthejetcatapultisgivena sidewindontheJettrajectoryiscalculated.

INTRODUCTION

Invariousconnectionswithresearchsaddevelopmenttherehasarisenthenecessityforacceleratinga largemass.alonga trackup toa highspeed.Withregardto a particularresearchrequirement,itwasnecessaryto consideraccelerationofa 100,000-poundtestcm up to1X milesperhourwithina shortdistance.Theserequirementsindicatedcatapultmeansforprovidingtheacceleration.

A surveyofvariouscatapultmechanismsforusewiththissystemwasmade. As a resultof thissurvey,a simplehydraulicjetcatapultwasselectedasthemostsuitable.It isbelievedthattheremsybegeneralinterestinthepresentstudyofthevariouscatapultsandthatotherapplicationsexistforthehydraulicjetcatapultwhichisgivenspecialconsiderationhere. Thepurposeofthispaper,then,istopresentthesurveyandto describetheconsiderationsgiveninthedesignof a hydraulicjetcatapultonthebasisthatitistobe usedinasysteminwhichthemaximumcarvelocityandthecarweightarespecified.

l-SupersedestherecentlydeclassifiedNACARM L51627,‘*ConsiderationsAona LsrgeHydraulicJetCatapult”by UpshurT. JoynerandWsLterB. Home,

* 1951●.

2

Thevelocitystarting

NACATN 3.203

hydrauliccatapultdescribedherein’consistsofa singlehigh-jetofwaterwhichissuesfroma stationarynozzleattheendofa testingtrackandisdirectedata returnbucket

mountedonthesternofthecarriageortestcar. Thisbucket(asinaPeltonwheel)turnsthejetalmost180°andthereturnjetissuesjustbelowtheincomingstream.Theforceonthebucketcausedby thislargerateofchangeofmomentuminthejetistheforcethatacceleratesthetestcarup to a desiredvelocity.Theacceleratingdistance,orthemaximumlengthof jettravel,isconsideredtobe intheneighborhoodofkm feet.

Aftera briefsurveyofvarioustypesof catapultsinthefirstpartofthepaper,a shortanalyticalsectionwhichdealswiththeperformanceofthehydraulicjetcatapultispresented.Subsequenttotheanalysis,considerationisgiventothephysicalconditionsaffectingthejetflow.AlsoincludedaresectionsinwhichdesignproceduresareoutlinedfortheJetnozzleandforthereturnbucketonthecar. Valuesofprobablepropulsiveefficienciesasobtainedfrommodeltestsaregivenforthejet-bucketsystem.

a

e

P

A

a

ac

aL

b

cl)

d

,-

SYMBOLS

nozzleelevationabovehorizontal,degrees *

totalanglethroughwhichjetisturnedbybucket,degrees .

airdensitytakenat standardconditions,slugspercubicfoot

cross-sectionalaxeaof jet,squarefeet

acceleration,feetpersecondpersecond

accelerationof carriagedueto jetreaction,feetpersecondpersecond

lateralaccelerationof jetdueto sidewind,feetpersecondpersecond

widthofbucketat startofturningsection,feet

dragcoefficientforsidedragon jetdueto crosswind

Jetdiameter,feet

NACATN 3203 .r.

Fc

g

n

P

P

P.

Q

forceon carriagedueto jetreaction,pounds

accelerationdueto gratity,32.2feetpersecondpersecond

exponentforpolytropicchsmgeinvolumetakenequalto 1.2(p+ = Constant)

arithmeticaverageairpressureusedtoaccelerateWaterlpoundspersquareinch

instantaneousairpressureusedto acceleratewater,poundspersquare-inch

initialpressureof compressedair,poundspersquareinch

volumeofwaterdischargedduringcatapultstroke,cubicfeet

WcR= wA(1- COSe)

.Sc

SL. t

tc.

‘iiv~

v~

vi

VJ

U.vp/

v

‘o

distsnceof carriage

lateraldisplacement

time,seconds

timeof carriagerun

travel,feet

of jetdueto sidewind,feet

duringcatapultstroke,seconds

durationof jetdischarge,seconds

averagejetveloci~,feetpersecond

carriagevelocity,feetpersecond

instantaneousjetvelocityat anypoint,feetpersecond

instantaneousjetvelocityof efflux,feetpersecond

instantaneousjetvelocityof effluxat tJ = 0, feetsecond

velocityof crosswind,feetpersecond

volumeof compressedair,cubicfeet

initialvolumeof compressedair,cubicfeet

per

4 NACATN 3!203

w densityofwater,62.4poundspercubicfoot

w= weightof carriage,pounds

x,z coordinatesofnozzlesurfacecontourintableI

Y instantaneoustrajectoryheight,feet

Subscript:

Max maximumvslue

SURVEYOFCATAPULTTYPES

Presentedinthissectionisa surveyofvarious~es ofcatapultswhichmightbe suitableforacceleratinga 100,000-~oundtestcaruptoa translationalspeedof150milesperhour.Becauseoftheadverseeffectoflargeaccelerationonthemeasuringinstrumentswhichwouldbeused,thepeakaccelerationisconsideredtobe Mmitedto aboutjg.Inorderto illustratethemsgnitudeoftheforceinvolvedduringaccel-eration,anaverageaccelerationof 2g,whichwouldindicatea cataultingforceof200,000pounds,maybe taken.Onm-energybasis,75x 1$ foot-poundsofener~mustbe deliveredtothecarby thecatapult.This Rcatapultcapacitywasfoundto exceedbymanytimesthecapacityofthelargestcatapultsdevelopeduptothistimeanditfollowsthatanadequatecatapulthadtobe designedor developedforthecaseunder *

consideration.A considerableamountofefforthas,therefore,beenspentinpreliminaryengineeringstudiesandcostestimatesofthevariouscatapultsystems.An adjectivecomparisonbetweeninitialcostsandoperatingcostsof thevarioustypesof catapultsconsideredisgiveninthefollowingtableanda morecompIetediscussionofthecatapulttypesfollowsthetable:

.

.

NACATN3203 5

.

.

—

lo.

—1

2

3

4

5

6

7

0

9

LO

L1

L2

—

T~e ofcatapult

lroppingweight

Fl~heel

Blowgun

Slottedtube

Piston

Rocket

Rocket

Hydraulic(jet)

Rocket

Rocket

Kydraulic(jet)

Electropuli

Motivation

~roppingweight(cablesndsheavesystem)

‘Qwheel(clutch,cable,andsheavesysta)

row-pressure,large-area.piston(expansionofpowderor compressedair)

.----------do------------

high-pressure,small-sreapiston(hydraulicandcompressedair,compressedairorpowderactuated)

?eactiontype,solidfuelpropellant(addsextraweightto carriage)

leactiontype,liquidfuelpropellant(addsextraweightto carriag(

?eactiontype,watersndcompressedair(addedcarriageweightprohibitive)

@ulse type,solidfuelpropellant

inpulsetype,liquidfuelpropellant

lupulsetype,waterandcompressedair

3quirrel-cageelectricmotorlaidoutflat

Initialcostsdevelopmentsndconstruction)

Veryhigh

High

High

High

High

IIOW

Medium

Medium

High

Low

Veryhigh

Operatingcosts

Low

ligh(withpowder)Jwriwith

Ii@ (withpowder)~~r\with

ligh(withpowder)hw (withcompressedair)

Veryhigh

Medium

Low

Veryhigh

Medium

Low

Low

6 NACATN 3203.

Themoreconventionalcatapultingsystem(forexample,numbers1,5,and6) arediscardedbecauseofeitherhighinitialcostsorhighoperatingcosts,orboth. Navyexperiencewithsheaveandcablesystems .indicatesthattherequirementsstatedpreviouslyarebeyondtheprobable -limitsforsatisfactoryoperationof suchsystems;thus,becauseofthisconsiderationandofhighinitialcosts,thedro~ingweight,thefly-wheel,andthepistontypeof catapultsarediscarded.

Theblowgunandslotted-tubetypesof catapults(numbers3 and4,respectively)utilizingcompressedairshowedsomepromise.Theblowgundeviceemploysa largetribewiththecaritselfactingasthepiston.Itthereforehastheseriousdisadvantageoflimitingto anextremedegreetheform,size,andheightof dropofthetestspecimen,sincenothingmayprojectbeyondthesmoothcaroutline.Intheslotted-tubecatapultthetestspecimenis externalandisconnectedto a pistonina slottedcylinderandthereforehastheadvemtagethatthecarandtestspecimenarenotlimitedasto dimensions.Boththeblowgunandslotted-tubecatapults,however,requireexpensivedevelopmentandhavea highinitialcost.

A studyof reactiontypeof catapultingsystemsdisclosesthatnocatapultor stored-energysystemcanbe carriedeconomicallyonthecarriageitself.Ifthesourceof ener~ i.scarriedonthecarriage,themassthatmustbe propelledisincreasedby theweightofthepropulsionsystem.Sincethe100,000-poundvalueforcarriageweightincludesbarestructuralweightandmodelweight,useofa systemsuchasdescribedmeansthattheenergyofthecatapultsystemmustbeincreasedto compensatefortheaddedweight.Becauseoftheaddedweightandthehighoperatingcosts,allthereactiontypesofcatapults(numbers6, 7, and8) arenotconsideredfeasible.

..

.

hptisejetsystemsemployinganyofthegasesasthefluidmedium(nmibers9 and10)areof suchlowefficiencythattheycannotbe usedeconomically.

Ofthesystemsconsidered,theonesystemfoundthatgivestherequiredcapacityatlowinitialcostandlowoperatingcostisthehydraulicimpulsesystem,nuder 11. Onearrangementofthissystemisshowninfigure1.

Thehydraulicimpulsecatapultshownoperatesonthesme principleastheimpulseturbine,exceptthata singlebucketisusedwithstraightrunincontrasttotheusualmultibucketarrangementwitha circularrun.Inthesystemshown,airiscompressedintoanairtankwhichisconnectedthroughanaircontrolvalvetothetankcontainingtheworkingchargeofwater.Thewatertankhasa nozzledirectedatthejet-returnbucketwhichIsmountedatthesternofthecarriage.Pressureismaintained ●

.

NACATN 3203 7

onlyintheairtankuntilimmediatelybeforethecatapultingrun,atwhichtimetheaircontrolvalveis opened.Thewatercontrolvalveoutsidethenozzleisthenopenedandtheresultantjetdrivesthecarriagedownthetrack.Thelowerrelativecostofthissystemis duelargelytothelackofa complexmechanicalconnectionto thetestvehicleduringthecatapultingstroke.Withthissystem,thecostofelectricalpumpingpowerandwatermake-uppermaximumcapacityrunbecomesa veryminorpartofthetotaloperatingcosts.Thesystemisdescribedhereinandtheimportantengineeringaspectsarediscussed.

MATEEMATICl!LDEVIZU)PMENT

Inthissection,equationsaredevelopedforthejetflow,whichisassumedtobe ideal,andforthemotionofthecarriagewhichiscata-pultedby thejet. Becausetheavailabletreatmentof jet-bucketrelationsisco~cernedwiththehpulseofa Jetona successionofbucketson a wheelmovingatconstantspeedandthistreatmentisnotapplicableto thepresentproblem,an analysisismadewhichusesasmuchofthewell-knowntreatmentas isusefulandmakesmodificationsasrequired.Figure2 illustratestheconfigurationbeinganalyzed.

Theequationforthevelocityof effluxofthewaterjetfromthenozzleas a functionoftimecanbe developedby recognizingthatthevolumeofwaterdischargedinanygiventimeisequaltotheincreaseinair-chsrge~d~ej also,useismadeoftheequationforpolytropicexpansionofairto determinethevariationofairpressurewithtimeandtheequationforvelocityof effluxto convertthevsriationof airpressurewithtimeintothevariationof jetvelocitywiththe. Thesetworelationsintheirfsmiliarformsaregivenbythefollowingtwoequations:

p+ = Constsllt= nPovo (1)

(2)

where povo inequation(1)representsinitialconditionsmd equation(2)appliesfor p inpoundspersquareinchand w inpoundspercubicfoot. .

8 NACATN 3203

By useofequations(1)and(2),anexpressioncanbe obtainedwhichgivestheinstantaneousjetvelocityof effluxintermsoftheinitialconditionsandtheinstantaneousvolume

Sincethevolumemusthold:

oftheaircharge:

(3)VJ .v2g,144povon~n

theair-chargevolwneisequaltotherateof increaseofrateofwaterdischarge

whereA isthejetarea.

By combiningequationschargevolumeisobtainedinandtheinitialconditions:

dvE

bythejet,thefollowingequation

= VJA (4)

[3)and(4),therateofchangeofair-terms

dv==

oftheinstantaneousair-chargevolume

c~v-n/2 (5)

i

14.4povonwherec1=A 2g—.w

Integrationof-equation(5)yieldsanexpressionfortheinstsmtan-eousati-=hargevola- v asa fimctionoftime. Stisti,tutionofthis,expressioninequation(3) givesthefollowingequationforinstantaneousJetvelocityintermsoftimeof jetflow tj andtheinitialconditions:

= Vjo(1 +c’#j) -n/(n+2)‘J

(6)

where C2 =(~+ l)V~oA,

ThisequationforinstantaneousJetvelocityV.

isusedinthefollowingdevelopmentoftheequationsofmotionforthecatapultedmass.

TheequationofmotionforthecatapultedmassisdevelopedinaccordwithNewton’ssecondlaw;thatis,theforceexertedonthecatapultedmassby thewaterjetis.equaltotheproductofthecatapultedmassanditsacceleration.

*

*

NACATN 3203

Thevelocitybucketis denoted

thetime t~ = t=

timeoftravelof

9...

ofthewaterstresmattheinstantof tipactupontheby Vi andisthessmeasthejetvelocityVJ,ats=, wherethisexpressiontakesintoaccountthe

-~thestresmfromthenozzleto thebucket.Thewater

streamthusentersthebucketwitha relativevelocityVI - Vc and,ifit isturnedthroughanangle 8 andisassumedto leavethebucketwiththessmerelativevelocity(noenergyloss),thecatapultingforceexertedonthecatapultedmassisgivenby theequation

Fc =;A(Vi - VC)2(1- COSe) (7)

Equati~theforcefromequation(7)totheaccelerationgivestheequationofmotion,whichfollowingform:

dVc— = *(VI - VC)2dt

productofmassandmaybe writteninthe

(8)

w=where R ‘WA(l - cos6) “ Theequationofmotiongivenbyequation(8)

hasbeenintegratednumericallyfortwosetsof conditio~jthesecon-ditions=d theresultsareshownaspsrtof figure3.

In ordertomakea rapidsurveyoftheeffectofvariousparametersoncatapultperformance,an approdmatesolutionto equation(8)canconvenientlybe madeonthebasisthattheimpactvelocityVi isconsideredconstantat a valuecorrespondingtotheaveragewatertankpressure.Thisaveragejetvelocityis denotedbyVl,andequation(8)canthenbe writtenasfollows:

ac = * (V1 - VC)2 (9)

Equation(9) can’beexactlyintegratedto givethefollowingapprox-teequationsofmotion:

V12VC=R (lo)

—+V1t~

10 NAC!ATN 3203

= v~tc Vltc+ R*c - R loge ~ (11)

Calculations,usingequations(10)and(11),forthesameconditionswhichwereusedinthenumericalintegrationof equation(8)areshownalsoinfigure3 forcomparisonwiththecorrectintegratedvalues.Forconditionswheretheinitial.airvolumeis14-9ttiesaslargeasthewatervolumedischarged,theapproximateequationsgiveresultswhicharealmostIndistinguishablefromthecorrectlyintegratedresults.Forthelowerratioof initialairvolumetowaterdischsrgevolume,‘o— = 2.7,however,a slightdifferenceresultsfromtheexactsadtheQapproximateequations.

Theresultsshowninfigure3 indicatethattheapproxhnateequationswillgiveanaccuracywhichshouldbe sufficientformostapplicationswhentheratioof initialairvolumetowatervolumedischargedis intheneighborhoodof3 ormore.

Ontheassumptionthattheapproximateequationsofmotionaresufficientlyaccurateforpracticaluse,approximateequationsaredevelopedhereinfortheotherparametersofinterest,suchasthemaxi-mumheightoftheJettrajectoryandthequantityofwaterdischarged.

.

If itisassumedthatthejetemergesfromthenozzlewithavelocitygivenby equation(2)forconstantaveragepressureandthatthejetleavesthenozzleatan angularelevationa abovethehorizontalandfollowsa parabolicpath,thentheequationsfora bodyfallingfreelycanbeusedto obtainthefollowingequationrelatingairtankpressure,maximumriseofthejettrajectory,andrange,whichisassumedequaltothecatapultingdistance:

(12)

Thejetisassumedtohavereturnedto itsinitialelevationattheendofthecatapultingdistance.

Fora veryflattrajectoryandhigh-pressure,whichwouldprobablybe usedinjet-catapultapplications,the -1 undertheradicalinequation(12)msybe neglectedforeaseinsubsequentcalculations,andtheequationcanbe rewrittento givethefollowingequationformeximumtrajectoryheight:

Sc%Y- ‘ (~6)(~4@) (23)

.

.

.

NACATN3203

Thevolumelatedsimplyassectionalarea,

n

ofwaterdischargedduringa catayultstrokeiscalcu-theproductofthemeanjetvelocity,thenozzlecross-andthetimeof durationofthedischarge.Thecatapulted

massis initiailyverycloseto thejetnozzleandisconsideredto startmovingatthesameinstantthat”thejetemergesfromthenozzle.Thejetcontrolvalveisclosedat suchtimethatthetailofthejetwillreachtheendofthecatapultstrokeatthesametimeasthecsrriage(seefig.2]. Thetimeof durationofthejetdischargeis,therefore,lessthanthetimeofcarrisgerunby anamountequalto thetimerequiredforthetailof theJetto travelfromthenozzleto theendofthecatapultstroke.Basedontheforegoingdiscussion,theequationforvolumeofwaterdischargedcanbe statedas follows:

Q‘ “’Akc-3 (14)

In“l and

orderto obtainthevalueof Q in.termsof averagejetvelocitytherequiredterminalcarriagevelocityVc~.thefo~~~~ equa-

tionsfor tc ad Sc areobtainedfromequations(10)and(11):

Rvc-kc= “1(”1-Vc)

( “cSc =R “1

- 10ge“1 - v=v~ -“c )

(15)

(16)

Thesetwoequations,whensubstitutedinequation(14), give

(17)

Inorderto displsytheinterdependenceoftheseveral.variablesaffectingtheperformanceofthehydraulicjetcatapult,figure4 hasbeenpreparedfora catapultwhichwillaccelerate“a100,000-poundtestcarriageto 150milesperhour. A similarfigurewouldbe requiredforeachdifferentsetof catapultrequirementsconsidered,buttheprepara-tionisnotarduous.Theequationsusedinthepreparationofthisfigureareequation(2)forjetvelocity,usingaverageairtankpressureP, equation(9)forinitialcarriageaccelerationbysetting“c = O, equation(16)forcatapultstrokeandjetarea,equation(17)forthevolumeofwaterdischargedduringthecatapultstroke,andequation(13)forthemaximumheightofthejettrajectory.

12 NACATN 3203.

Theusefulnessofa chartsuchas showninfigure4 ismainlyinthepreliminaryplanningstage.Everypointonthechartrepresentsatheoreticalhydrauliccatapultsystemwhichwillmeetthedesignrequire-

9-—

mentofacceleratingthegivenmasstotherequiredspeed.Thevariationof suchquantitiesasrequiredairtankpressure,catapultstroke,initialacceleration,maximumheightoftrajectory,volumeofwaterdischarged,andjetareacanbe determinedfromthefigure,andundesirablevaluesofanyofthesequantitiescanbe avoided.Aftera satisfactorysetofconditionsisreachedforthespecificdesignunderconsideration,detailedcorrectionforlossesandoperatingconditionscanbe consideredinorderto esthnatetheperformancetohe expectedfroma workinginstallation.

As shownsubsequently,sometestsindicatethattheaverageenergylossesintheoperationofthejetandbucketmaybe heldto about15percent.Theselossesareconsideredtobe compensatedinthedesigndescribedhereinbydividingthenozzleareadeterminedfromfigure4by thejet-bucketefficiency.If itisassumedthattheselosseshavebeencompensated,allothervaluesreadfromthechartmaybe useddirectlyfordesignpurposes.Otherlosses,suchascarriagerollingfrictionandcarriagewindresistance,alsoaffectthedesignofthepropulsionsystem.Forthedesignconsidered,theselosseswerefoundtobe oftheorderof 2 percentofthejetenergyandareconsideredsmallenoughtobe neglectedinthemathematicaltreatment.

As anaidtovisualizationofthetremendouspowerwhichcouldbedevelopedby a hydraulicjetcatapultsuchashasbeendescribed,performancecurvesarepresentedinfigure5 fortheparticularcatapultrepresentedby thedesignpointindicatedinfigure4. Thenozzleareashownisfor100-percentefficiency.,Correctionofthisareaforpracticalefficiencieshasbeendescribed.Itcanbe seenfromperformancecurvesthatthiscatapultisexpectedto acceleratecarweighing100,000poundsfromrestupto 150milesperhour(220ft/see)intheshorttimeof 3.2secondsandin a distanceonly400feet.

thesea test

of

Thereareseveralotherquantitieswhichwillbe requiredinacompletedesignaftera suitablecatapultdesignisselectedfromthechart,suchastherequiredangularelevationofthenozzle,theheightof impactofthejetonthebucketthroughoutthecatapultstroke,andthelateraldri,ftofthejetdueto a sidewind.

Theangularelevationofthenozzlerequiredto.makethejetreturnto itsinitialelevationabovetheleveltrackattheendofthecatapultstrokeisdeterminedfromthecotiinationofthemaximumrequiredcatapultstrokeandthejetvelocityofthetailofthejetas follows:Fromthevelocity-therelationof a bodyfallingfreely,thetimerequiredfor

.

.

NACATN 3203

thejetto reachitsmaximumheightmaybe deducedandisgivenby

tVj Sins=

~

Thetotalhorizontaldistancetraveledbytheitsinitialelevationis,then,

scm= = 2tvj CosCIJ

jetbeforereturningto

Eliminationof t betweenthesetwoequationsgives

Bcgsin2a=— (18)

vj*

Theactualheightofthepointof jetimpactonthebucketisof aidwhencomputationsaremadeoftheover-turningmomentsimposedonthecsrriageby thejet. Thecalculationofthisquantityforthecasewitha variablejetvelocityisgivenherebecausetheheightofthepointof impactforthiscasemayat certainplacesbe slightlygreaterthanthevaluegivenbytheparabolicapproximation.Sincetheapproximateequation(U) givesthecarriagedisplacement-timecurvesveryclosetothetruevalues(seef=. 3),thisequationisusedto calculatethecarriagedisplacement.Thejetleavesthenozzlealonga straightlinewithan angulsrelevationa andfsllsaw~ fromthislineas a freelyfallingbody. Thetimerequiredforthestreamtotravelfromthenozzleto the carriagewouldbe se/V.

4Withthisknowledge,theheightofthe

pointof impactofthejeton he carriagebucketcanbe calculatedfrom~hefollow~ equation:

u2&t2=scsfna-~~Y = Sc StUffi- 2 j

Equation(19)canbe solvedas follows:A valueofandfromequation(U) thecorrespondingvalueof tc isvaluesarethenusedto establishcorrespondingvaluesofbymeansofthefollowingrelation

(19)

Sc ischosen,fomd. Thesetj d VJ

tc = tj+%

‘J

14

where,inthiscase,theinterpretationtobeisthesumofthethe of jeteffluxt~ andparticlesofwaterleavingthenozzleatthis

NACATN 3203

placedon t= isthatitthetimerequiredfortimeto travelthe

distanceSc. Thisrelation,usedin conjunctionwithequation(6),establishesthevalueof Vj. Thisvalueof Vj,whenusedwiththechosenvalueof SC)permitstheheightofthepointof impacttobecalculatedby meansofequation(19).Thiscalculationisrepeatedforothervaluesof Sc to covertheentirecatapultingstroke.

Thelateraldriftofthejetdueto sidewindsmaybecomea seriousconsiderationfora long-strokecatapultbecauseoftheincreasedsizeofthebucketrequiredto receivethejet. Thelateraldriftmaybecalculatedby equatingthesideforceduetowindonunitlengthof jettotheproductofmassofunitlengthandlateralacceleration.Theplausibleassumptionismadethatthelateralvelocityof driftisnegligibleincomparisonwithside-windVelocityj thereforethelateralaccelerationmeybe regardedconstant.Thelateral-driftequationmaybe writtenas follows:

Force= MassX Acceleration

or

Solutionfor aL anduseoftheequationforuniformlyaccelerated

motion,s = ~ at2,“givestheEUIIOUntOf sidedrift 8L as

(20)

InthisequationthedragcoefficientCD dependsprimari2yonReynolds“number.Fora Reynoldsnumberrangeof 10,000to 300,000,thecoefficientCD isalmostconstamtat 1.2andthereforeequation(20)reducesto

(21)

.

.—

.-

l!hi.sequationshouldbe satisfactoryforpracticalrangesof Jetdimeterandside-windvelocities.

NACATN 3203

PHYSICALCONDITIONSAFFECTINGJETFIOW

Themathematicaltreatmentofthecatapultsystemisbasedontheassumptionof idealjetflow,which,morespecifically,meansa jetthatcanmaintainitsshapeor integrityoverthecompleterangeoftravelfromthenozzle.Thedesignoftheparticularcatapultsystemunderconsiderationrequiresthatthejetbe collectedandreturnedby thebucketfora rangeof atleasth feet. Ithasbeenfoundthatthephysicalconditionsaffectingjetflow,suchas entranceconditionstothenozzle,nozzleform,nozzlesurface,andaerodynamiceffectsdown-streamfromthenozzle,createappreciabledisturbancestothejetandthequestionarosewhetheritwouldbe possibleto obtaina @O-footJetlengthofacceptableintegrity.Thepurposeofthissection,there-fore,isto delineatethesevariousphysicalconditionsandto showhowtheireffectsonthejetcanbenullifiedor,atleast,minimized.

Informationanddataonlong-rangejetswerefoundtobe veryscarcewiththeexceptionofmaterialonthejetsproducedby firenozzles.Itwasdecided,therefore,becauseoftheavailabilityof firenozzlesandof dataon jetsproducedby firenozzles,to initiatetheinvestigationof jetflowby studyingtheeffecton fire-nozzlejetswhenthesepreviouslymentionedphysicalconditionswereimproved.Forexsmple,bendingthehoseupstreamfromthenozzlewasfoundto decreasecon-siderablythemount of jetlengthhavingreasonableintegrity.Foranotherexsmple,cleaningandpolishingtheinsidesurfaceof a firenozzlewasfoundto increasetherangeofgoodflow.Thus,by theseandothersimilartestsa straightsymmetricalapproachtothenozzleanda smooth,polished,andfairedinternal.nozzlesurface,alongwitha smoothjointconnectingthehoseorplaypipetothenozzle,werefoundtobe essentialformaintainingthebestlong-rangeintegrityofa fire-nozzlejet.

Onthebasisoftheseresults,a nozzleof 3-inchdismeterwasdesignedandtested.Theprofilechosenforthisoriginaltestnozzlewasbasedon considerationsof accelerationofthewater,minimumboundarylayer,andpsrallelflowatthenozzleexit.F@re 6(a)showsaphotographof a jetproducedby thisnozzle.ThehprovementinjetintegritybecauseofbetterentranceconditionsandnozzXedesignisapparentwhenfigure6(a)iscomparedwithfigure7,a photographofa jetproducedby the5-inchnozzleaboarda NewYorkCityfireboat.Thefire-nozzlejetis seento divergeimmediatelyuponleavingthenozzleintotwoseparatestresmswhereasthejetinfigure6(a)ispracticallynondivergentthroughoutitslength.A studyofhigh-speedmotionpicturesofthessmeJetas infigure6 disclosedthatvisualobservationoftheestablishedstresmsmdstillphotographs(suchasfig.6)giveapessimistichpressionas compsredwiththestreamduringthefirstfew

16 NACATN 3203

secondsofoperationbecauseJetsprqyaccumulateswithtimeandthere-foreobscuresthesharperstresmboundariesthatwouldotherwiseappear.Thesprayshowninfigure6(b)hasaccumulatedduringanoperatingperiodofabout8 seconds,whereasthetimeofoperationofthecata-

pultconsideredhereinis approxtiatelyonly2* seconds.Wher

evidencethata relativelysolidcoreexistsinthemidstofthissprayisindicatedby thefactthat,ata distanceof 300feetfromihenozzl~thejetcutsa narrowtrenchonly6 or8 incheswideintheturf.

.

*

Smallernozzlessimilarto this3-inch-dismeternozzleweretestedstillfurtherinorderto determinetheefficiencyofthejetasafunctionof distancefromthenozzleby recordingtheloadsimposedbythejetona flatplatebymeansof a smallstrain-gagetypeof dyna-mometerandcomparingtheseloadswiththetheoreticaljetimpactforces.Theresultsofthesetestsareshowninfigure8. TheseresfitsindicatethatallJetlossesforthesesmalljets,includingshocklossescausedby theimpingementofa Jetona flatplate,averagedlessthan5 per-centfora distanceupto about125jetdiameters,equivalentto aboutone-fifththescalecatapultingstroke,andwerenegligibleforthegreaterdistancestested.

Thepurposeoftheprecedingtestshasbeentohelpdeterminewhetheritispossibleto throwa jet400feet.withsufficientintegritytobe caughtandreturnedby a bucketatthatpoint,butthesetestswere .performedonlywithequipmentutilizingsmall-scalesizesandsmall-scalepressures.Theresultsgainedfromthesetestsarepromising;however,thereremainsthequestionofwhethertheserestitswillstillbe valid .whenscaledupto full-size.Theconibinationof jetsizeandnozzlepressurerequiredby thepropulsionsystemisbeyondcurrentengineeringpracticeas farascanbe determined,butthereisnoapparentchangeinthephysicalconditionsupongoingto largerandhigher-velocityjets.‘I’lierelativespraylossesofa jetdueto airfrictionontheoutermostsurfaceofthejetdecreaserapidlyasthejetdiameterincreases.Inreference1, dataaregivenonhowfara “good”streamcanbe thrownby

a firenozzle.Thesedataareshowninfigure9 andindicatethatagoodstreamcanbe thrown270feetin stillairwitha firenozzle2 inchesindismeteroperatingat250poundspersquareinch.Thisfigurealsoindicatesthattheobtainablehorizontalthroworreachofthegoodstreamincreaseswithbothnozzlepressureandnozzlediameter.It seemsprobable,therefore,thata largernozzleandhigherpressurecombinationmaybe usedto obtaina satisfactoryjetwitha lengthof400feet.

Inadditionto theprecedingconsiderations,otherfactors,suchasairentrainment,dissolvedair,andcavitation,mayinfluencejetflow;properprecautionarymeasuresshouldthereforebe takentoguardagainstadverseeffectsthatthesefactorsmaycause.

K

.

.

.

NACATN 3203 17

Inregardto airentrainmentreference2 statesthattheeddieswhichwhirloutofthemainstreamareimmediatelyretardedanddis-integratedby theresistanceoftheair. Furthermore,voidscausedbyseparationofwater@articlesarefiediate%ff~ed withafi” A PoorJetshowsremarkablequalitiesto setinmotionandcarryalonglargequantitiesof air. Thesestatements”indicatethatan initiallypoorjetcontainstheseedsof itsowndestructionby airentrainment.Thenozzlemustthereforebe sodesignedthatJetdivergenceandjetrotationsreas smallaspossible.Sucha nozzleis describedinthesectionentitled“NozzleDesign.”

Theamountof dissolvedairinwateris showninreferences3 andktobe a functionoftheairpressureonthewaterad thelengthoftimethewaterisexposedtotheair. Thedissolved-airproblembecomesimportantasto itseffecton jettitegritywhenthepressureishighandtheexposuretimelongenoughtoproducenearlysaturatedconditions.Ifthiswater,whichis saturatedwithairathighpressure,isallowedto flowfromthenozzleasa freejetatatmosphericstaticpressure,thejetbecomesextremelyturbulentowingto theescapeof airfromthestreamboundaries.

Fromreference3,thefollowingequationisgivenfortheirdthl.rateof abso?@ionof airinwater:

where

% liquidfi3mcoefficient(0.6%to 2.35ft/hr)

CE saturationathighpressure,poundspercubicfoot

c saturationat atmosphericpressure(0.0015lb/cuf%)

s interfacearea,squarefeet

t time,hours

m weightofgas,pounds

SinceCH variesalmostdirectlywiththepressureP, thisequationmaybe written

18.—.—

NACATN 3203

.

where

P pressureonair

‘atm atmosphericpressure

Fromthisequationitcanbe seenthatthetimeof exposureofthewatertotheairandalsotheinterfaceareashouldbe heldto a min5mmn.Fora shortperiodof exposuretheairdissolvedwouldprobablybe unimpor-tant. Forlongexposuretime,however,thedissolvedairis hportaatand,ifa longexposurecannotbe avoided,suitablemeckical meansofseparatingtheairfromthewater,suchasa diaphragm,mustbe used.

If sharpedgesortooabruptchangesofcurvatureoccurina nozzle,theresultingIowpressurecancausecavitation,andthatwouldbe verydetrimentalto jetintegrity.Thenozzleshapesdescribedinthenefisectionhavebeendesignedsothatconditionsfavorableto cavitationdonotoccur.

NOZZLEDESIGN

Thepurposeofthissectionisto describethedesignof a nozzlewhichwilldelivera nondivergentjetwithuniformcross-sectionalvelocity.Inreference5,calculationoftherequirednozzleshapeismadeby meansoftheexactanalogybetweenthepotentialfluidflowdesiredandthemagneticfieldthatiscreatedby twocoaxialandparallelcoilscarryingelectricalcurrent.Theelectromagneticsolutionisappliedto fluidpotentialflowandoneofthestreamsurfacesischosenasa flowboundary.A familyofthesecontractingpassagesisdeveloped(seefig.10},andsurfacesa toh givecross-sectionaltbroett-speeddistributions,boundarylayerbeingneglected,thatareuniformtheoreticallywithinone-fifthof 1 percent.Thedistributionsbecomelessuniformfortheoutercones,butvariationsfromuniformityarestilllessthan1 percentevenfortheoutemst one. Essentially,thesamethroatuniformitieswilloccurinthecaseofrealfluidflowasinpotential.flow,provided-theupstreaflowisuniformandtheboundarylayerismaintainedverythin. Theboundary-layerthicknessisexpectedtobe lessthan0.004inchfora nozzlewitha 7-inchthroatdiameter.As anaidinthedesignofa nozzle,figure10andtableI arepresented,thedataofwhicharetakenfromreference5.

Althoughnomeasurementsofnozzleefficiencyweremadeonthepotential-flownozzle,dynamometertestsofnozzlesoftheoriginaltestshapeindicatethatthecoefficientof dischargeof suchnozzlesapproaches1.0.Itseemsreasonableto expectthatthepotential-flownozzlewill .giveasgoodresults.

.

NACATN 3203 19

Theinflowrequirementsarefairlysimplebutveryimportant.Theflowapproachingtheentrancetothenozzleshouldbe parallel,shouldbe ofuniformvelocity,andshouldhavea minimumofturbulence.ArIYappreciablerqtationaboutthejetcenterlineintheapproachflowwouldbe disastrous.Becauseoftheconservationof @w momentum,anyrotationalvelocityintheapproachflowwouldbe greatlymagnifiedinthenozzle,withtheresultthatthejetwouldtendto expandowingto centrifugalforceas soonas it isclearofthenozzle;esrlyjetdisintegrationwouldthenoccur.A fairedtransitionsectionforconnectingthenozzleto thestraightapproachsectionshouldgivesatisfactoryflow.

Cavitationinthepotential-flownozzleisnotexpectedsincetheoperatingpressurerage lieswellabovethevaporpressureofwater,andtheuseof a smoothpolishedfinishofthenozzlewaterswfaceshouldpreventlocslpressuredropsdueto a discontinuityof surface.

Reference6 statesthatstainlesssteelofthe18-8chrome-nickeltype,usedeitherasa forgingor asa layerweldupona mild-steelbase,isbestforoperationundersevereconditions.TheworkinglifeofnozzlesusingthismetalhM exceeded2 yesrsof continuousoperation.Thismetal,ifusedinthecatapulting-systemnozzle,shouldhaveaworkinglifemuchgreaterthan2 yearsbecauseof theintermittentusageofthesystem.

BUXET DESIGN

Theenergyofthestresmistransmittedto thecsrriageby thecatchingandturningofthewaterofthejetin a bucketattachedto theresrofthecarriage.It isknownthatma~ thrustefficiencyisachievedby a bucketthatcanturnthejetthroughalmost1800andtherebyobtainmaxtiumcarriagethrust.Thebucketmustbe sodesignedthatitcanreturnthisjetefficientlythroughoutthemaximumcatapultingrangeof 400feet. Overthislargerange,however,significantverticalandlateraldisplacementstothejetcanoccuxbecauseoftheeffectsofgravityandof sidewinds.Theseeffectsofgravi~andof sidewindsona long-rangejetmadeit hpossibleto adopt,withoutinvestigation,theinformationavailableregardingimpulse-turbinebucketdesign,theonlyothersystemutilizingpowerderivedfroma jet-bucketconfiguration.Thetipulseturbineisessentiallya completelyhousedmultiple-bucketshort-rangejetsysteminwhichthepointofcontactis quitepreciselycontrolled.

A summationoftheseconsiderationsindicatesthatwhatisneededfora bucketisa concentratingdevice,suchas a cone,thatcancollectthedeviatedandexpandedjetanddeliveritto a turningsectionwherethecollectedjetisturnedthrough1800formaximumenergytransfer.

20 NACATN 3203.

A testpro~a wasarrangedtherefore,whereinvarioussmall-scalebucketshapesweretestedwithregardtopropulsiveefficiencyoverscalejet

—.

rangesby recordingthebucketloadsintroducedona smallstrain-gagetypeof dynamometerandcomparingtheseresultswiththetheoreticaljet-impactforces.Sketchesanddimensionsofthebucketsinvestigated

—

areshowninfigureU. Jetshavingdiametersatthenozzleof1/2inchand1/4inchwereusedintestingthesebuckets.Figure12 showsthepropulsiveefficiencyofthesebucketsplottedagainstjetlengthfor ,thetwonozzlesizes.A studyoftheinformationon impulse-turbinebuckets(references6 to8) inconjunctionwiththesetestsindicatesthattherearethreefmportantbucketdesignparameters,namely,theratioofbucketwidthto jetdiameterb/d,theamgleof approachofthejettothebucketsurface,andtheconditionofthewettedbucketsurface.Theseparametersareveryimportantasregardstheefficiencyofanybucket.Theratiob/d isespeciallyimportantinbucketdesignbecauseof itslsrgeeffectonbucketpropulsiveefficiency.~pulse-turbinebucketdesignindicatesthattheskinfrictiondevelopedby abucketanditscorrespondingener~ lossisa functionofthisratio.Toolargea ratioresultsinexcessivelossesthroughskinfrictionwhereastoosmalla ratioresultsinanoverflowingbucketwithitscorrespondingloss.Figure13 showstheincreaseinbucketefficiencygainedby decreasingthisratiofrom12to 6. Thisratiowasdecreasedby increasingtheJetdismeterfroml/4inchto1/2inch.Theefficiencygainwasoftheorderof9 percent.

Thea@proachangleofthejettotheimpactsurfacewasfoundalsotohaveanimportanteffectonbucketpropulsiveefficiency.Pelton,inhisdevelopmentofthePeltonwheel(reference8],foundthattheimpingementofa jetontheedgeofhiscuppedbucket,ratherthaninthecenterofthebucket,increasedtheefficiencyconsiderably.Thisefficiencygainwasduetothejethittingthebucketwherethejetpathandthebucketsurfacewerenearlyparallel.Fromthispoint,thejet,followingthebucketcontour,wasledgradudlyintoa 170°reversalratherthanreversingabruptlyaswasthecasewitha directcentraljettipactonthebucket.Thebestpossiblejetentranceistangentialto thebucketbutithasbeenfoundthatdeviationsfromthistangentialentrancecanbetoleratedup to cloutl~”becauseoftherelativelysmallenergylossesinvolved.

Theconditionofthewettedbucketsurfaceisan importantconsid-erationalso.Theidealbucketsurzaceisonethatisas smoothandhighlypolishedas isfeasible.Sucha surfacereducestheerosiveactionofhigh-velocityjets,eliminatestheturbulenceandpossiblelocalshockeffectsresultingfroma discontinuityof surface,andreducestheskinfrictiondevelopedby thebucket.

.

NACATN 3203 Z?l

So faronlythedesignconditionsapplicableto anytypeof ~et-bucketsystemhavebeendescribed.Themagnitudeoftheverticalandlateraldeviationsgivena long-rangejetby theactionofgravityandof sidewindsmustbe determinedbeforeanydesignforthecatapuJ.t-systembucketcanbe reached.The”vertical.deviatioriisa functionofthejetvelocityandnozzleangleandmaybe calculatedfromequation(19).Figure14 showsthepointof impactofthejetonthebucketthroughoutthemaximumcatapultingdistanceforthecaseofthefacilityundercon-sideration.Thiscurvefurnishesthevertical-jet-displacementinfor-mationnecessaryforthisparticularbucketdesign.Thelateraljetdisplacementcausedby sidewindbecomesof significancewhenthecatapultingdistancessrelongandwhenthecatapultsystemisnotprotectedfromthewind. Figure15 showsa ty@.calIateral-displacaentcurvefora jetof givendtiensions.Themathematicaltreatmentofthisproblemhasbeendiscussedinthesectionentitled“MathematicalDevelopment”(seeequation(!21)).

Figure16 showsseveralviewsofa modelbucketsodesigned.astoincludeallthediscusseddesignconditions.Thevariationinefficiencyofthisbucketdueto lateraldisplacementandva@ationinjetlength

of a &inch jetareshowninfigure17. Thesecurvesindicatethataproperlydesignedbucketwillhavean efficiencyrangeof78to 98per-cent,dependinguponwherethejetstrikesthebucket.Theaveragejet-bucketlossisconsideredtobe 15percent.

Themorerefinedbucketdesignshownin figure18makesuseof anelliptical-cross-sectionalconeratherthanthecircular-cross-sectionalcone.Thisbucketresultedin someweightsav~.alongwithproducinga morecompactbucket.Althoughno efficiencytestsweremadeonthisbucket,itwasfoundto giveverysatisfactoryresultswhenusedinaworkingmodel.

Somecaremustbe usedintheselectionofthematerialtobe usedforconstructingthebucket.Theexperiencegainedintheconstructionof impulse-turbinebucketsisavailableforthispurpose.Reference6statesthatthematerialusedforhigh-headbucketsiscaststeel,themediumgradesofcarbonsteelbeingpreferred.Eeat-treated.aUoysteelisusedto a ltiitedextentbutthepracticalprobleminconnectionwiththismaterialisthedifficultyinheattreatmentfollowingfieldrepairsby welding.An increaseinbucketlifehasbeensecuredby thelayerweldingof 18-8chrome-nickelstainlesssteelorotherhardfacingsinthebucketbowlswhichareafterwardgroundsmoothto trueshape.Theprobabilityof fatiguefailureoccurringinthepropulsion-systembucketisverysmallduetotheintermittentusageexpectedofthecatapult.Consequently,a higherdesignstresscanbe usedinthisbucketthaninthecaseofthe@ulse-turbinebucketwheretheprobabilityof fatigue

22 NACATN 3203

failureoccurringismuchgreaterduetothecontinuousoperationoftheturhine. Itisalsoexpected,becauseofthislowfrequencyof catapultoperation,thatthepossibilityofdsmagedueto cavitationoccurring

smalland,hence,-canbe neglected.

ADDITIONALDESIGNPROBLEMS

Onedesignproblathathasnotbeenpreviouslymentionedisthatof controllingtheflowofwaterleavingthebucket.Thewaterreturnedby thebucketpossessesa largeamountofpowerthatcouldbedamagingtothepressuretankfoundationsandtrackinstallationsandinjurioustopersonnel.Figure19 showshow%hisreturn-watervelocityvariesoverthecatapultingdistance.Thecurveshowsthatthereturn-watervelocityvariesfrompracticallyinitialjetvelocityatthestarttoaboutone-thirdthejetvelocityattheendofthecatapultingdistance.A practicalwayto disposeofthisreturnjetisto inserta shallowreturn-watertankbetweenthetracks.A systemofraisedlaterallouversisplacedoverthistank. Thebucketshouldbe sodesignedthatthereturnwaterisconcentratedanddirectedthroughtheselouversandintothetankasthecarriagemovesthroughthecatapultingdistance.Thereturn-waterener~ isdissipatedinthistankwhereuponthewaterbecomesavailablefor’re-useinthesystem.

.Thedesignofthewatertankmustbe givencsrefulconsideration.

Ithasbeenshownpreviouslythattheintegrityoflong-rangejetsdependsuponsymmetrical.inflowtothenozzleandtheavoidanceofdissolmdairinthewaterunderhighpressure.Thewatertank,there-fore,mustbe sodesignedthattheseconditionsaremet. Figure1 showsa tankdesignthatmeetstheseconditions.Thewatertankismadeupofa verticalcylinderjoinedbymeansof a 90°elbowto a horizontalcylinder.TheexhemeendofthehorizontaltankcontainsthepotentisJ.-flownozzlealongwitha transitionsectionbetweentheupstresmnozzlefaceandtheinteriortankWSU. Theupperendoftheverticaltankcontainstheconnectionleadingtothehigh-pressureairsupplyalongwitha diffuserto distributethisairequal~acrossthewatersurfaceofthetank. Theflowofwaterthroughthenozzleiscontrolledbymeansofa quickopeningandclosingvalveplacedoutsideandovertheendofthenozzle.Theairflowintothewatertankiscontrolledbya valvelocatedbetweentheairdiffuserandthepipeleadingfromtheairtank.

Symmetricalinflowtothenozzleisachievedprimarilybymakingthehorizontaltankandverticaltankof suchvolumethatallthewaterdischargedis initiallylocateddownstresnfromtheelbow.Withthisarrangement,noneofthewaterthatpassesthroughtheelbowduringa

.

NACATN 3203 23

catapultstrokeeverreachesthenozzle.Tominimizetheturbulencegeneratedinthewaterinpassingthroughthiselbow,turningvanesshouldbe provided.By usinga largecontractionratio(ratiooftamkcross-sectionalareato nozzlearea),thevelocityofwaterflowthroughthetankisheldto a lowvalueascomparedwiththewaterflowthroughthenozzle.Thus,theturbulenceofthewaterupstreamfromthenozzleisheldto a mintium.Thiswatertankcanbe operatedin sucha mannerastominimizetheproblemof dissolvedairby ventingthewatertankto atmosphericpressureuntilimmediatelybeforea catapultstrokewhenthehigh-pressureairwillbe admittedto thetank.

CONCLUDINGREMARTIS

Fkomthestudiesreportedthehydraulicjetcatapultappearstobesatisfactoryforacceleratinga 100,000-~undcarto 150milesperhourandtobe cheaperthantheothertypesconsidered.Wdel testsandotherinformationindicatethata satisfactoryjetshouldbe obtainedovertheindicateddesigncatapultingdistanceof &OOfeet. Designrequirements,suchas provisionoftanksandvalvesto operateat therequiredpressure$preventionof erosionandcorrosioninthenozzleandbucket,controlofthereturn-waterjet,sndsoforth,offerproblems;butitappearsthattheseproblemscsnbe handled.

~

LangleyAeronauticalLaboratory,NationalAdvisoryCommitteefor.Aeronautics,

LangleyField,Vs.,January17,1951.

24 NACATN3203

REFERENCES.

1.Crosby,EverettU.,Fiske,HenryA.,andForster,H.Walter:HandbookofFireProtection.Ninthcd.,NationalFireProtectionAssoc.,1941,figs.1134,1136B,and1137%.

2.Howe,J.W.,andPosey,C. J.: CharacteristicsofHigh-VelocityJets.Proc.ThirdHydraulicsConf.}Univ.I-, Studiesinllug.Bull.31,1947,pp.315-332.

3. Brown,F.Barton:AirResorptioninWaterTunnels.Rep.NO.N-62,ContractNOrd-9612,Bur.Oral.,NavyDept.,C.I.T.,March1949.

4.Adeney,W. E.,andBecker,H. G.: TheDeterminationoftheRateofSolutionofAtmosphericNitrogenandOxygenbyWater.Phil.Msg.,pt.1, ser.6,vol.38,no.225,Sept.1919,pp.317-337;pt 11,ser.6,vol.39,no.232,April1920,pp.385-404.

5.“Smith,Ri.chardH.,andWang,Chi-Teh:ContractingConesGivingUniformThroatSpeed.Jour.Aero.Sci.,vol.I.1,no.4,Oct.1944,pp.356-360.

6. Quick,RayS.: ProblemsEncounteredintheDesignandOperationofImpulseTurbines.Trans.A.S.M.E.,VOI.62,no.1, Jan.1940,pp.15-27.

7. Lowy,Robert:EfficiencyAnalysisofPeltonWheels.Trans.A.S.M.E.,vol.66,no.6,Aug.1944,pp.527-538.

8. Durand,W. F.: ThePeltonWaterWheel.I - DevelopmentsbyPeltonandOthersPriorto 1880.Mech.Eng.,

vol.61,no.6,June1939,pp.447-454.II- Developmentsby DobleandOthers,188otoDate.Mech.Eng.,

vol.61,no.7,July1939,pp.511-518.

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Sequenceofoperationsduringa catapultingstroke.

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FLw= 3.-Comparisonofperformancecurvesobtainedby integrationwiththoseobkin~ byanapproximatemethodwhichassumesthejetvelncityconstantatitsaveragevalue.

10(D I

NACATN 3203 29

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Figure5.-Carriage~rformancecharacteristics.Averagejetvelocity,633feetpersecond;nozzleara, 0.23.25squarefoot;carriageweight,100,OOOpounds.

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NACATN3203 37

Figure11.- Sketchesofbucketsusedinpreliminarytestsof jet-catapultreturnbucket.

NACATN3203.

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180(

60

.a o I .2 .4 .6 .8 I 1.0Lateraljetdisplacement,in. I

0 10 20 30 hoJetlength,in. 504

Figure17.- Variationof returnefficiencywithjetlengthandwithlateraljetdisplacementof circular-cross-sectionconicalreturnbucket.

~-inchjet.

.— -

—

15°

.

.

.

curve.

scaletI \mo,ooolb/fi

Urd.tload

————————— ——. — —-----————- ———— ———- --- ->\\

+

3°

L

Figure18.- Sketchshowtigfinalshapeandloadingdiagramof jet-returnbucket.

?.t’i!

\

/’

.—

r Velooityof setrelativeto carriage

\

-x -7 ,).

Retorn-natcr velocity relative to ground

v— ‘—! ,

f

Cerriege velocity

I I I I I I t I I J

40 00 120 160 2co 240 2&l 320 36o 400Catapnl~lng❑troke,ft

Figure19.- Variationofreturn-watervelocityrelativeb groundthrough.ou’tcatapultingstroke.