NACA RM L57A15 Statistical Approach to the Estimation of Loads and Pressures on Seaplane Hulls for...

7/27/2019 NACA RM L57A15 Statistical Approach to the Estimation of Loads and Pressures on Seaplane Hulls for Routine Ope

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RESEARCH MEMORANDUM

i ETATISTICALAPPROACHTOTHE ESTINLATION O F LOADSj 5.): &2.d,' . 2 3' \ j By Roy Steiner

AND PRESSURES ON SEAPLANE HULLS3 '",. FOR ROUTINEPERATIONS

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I -. . CLASSIFIED D O C U M E N T

1 ,. < Thi s material contains information affect- the National Defense of the Unlted States within the meanlng' ' of the espionage laws, n t l e 18, U.S.C., Secs. 19.3 and 794, he trBIyimiss1ono r revelation of which in any' .. manner to anunauthorized person is prohibited by law.

WASHINGTONMarch 27, 1957


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NACA I" L 5 7 A 1 5NATIONAL ADVISORY COMMITTEE FOR m O N A U T I C S

STATISTICAL APPROACH TO TRE ESTIMATION OF LOADSAND PRESSURES ON SEAPLANE WLLS

FOR ROUTINE OPERATIONSBy Roy Steiner

Available measurements o f th e seaway condit ions expected duringseap lane ope rat ion s are combined w ith exp erim ental data on the impactl oads exper i enced dur ing fu l l -sca l e and model t e s t s i n o r de r t o e s t im a tethe epeated oadingsofseaplanes or ongoperat ingperiods.Al thoughthe accuracy of th e re su l t s cannot be subs tant ia ted by opera%ional da ta ,t he na t u r e of t he va r i a t i on s t ha t m ight be expected i n t h e magnitudeand frequencies of hes e ap la ne oa ds and hu l l p r e s s u r e s f o r s e v e r a lassumed operations w a s r e f l e c t e d n h ee s t i m a t e d e s u l t s . These r e s u l t sind ica t ed tha t t he low l andingspeedsforant isubmarine-warfare seaplanesreduced t h e magnitudeof the l oads bu t th a t th e more f requent andingsand t a ke - o f f s r e qu i r e d f o r t he s e ope r a t i ons g r e a t l y i nc r e a s e d t he t o t a lnumber of l oads. The resul ts a l s o i nd ica t ed ha t nc reasedopera t ionsfrom the open ocean for a give n seap lane ype may have a re la t ive ly smalle ff ec t on th e magnitudeof the l oads o r pressures .

INTRODUCTION

The l oads developed on seaplanehul l sdur ing andings and take-of fsdepend upon a number ofseaplane and opera t ing facto rs such as h u l lconfigurat ion,descent peed, and sea con dit ion . The ef fe cto f h e s ed i f f e r e n t f a c t o r s on t h e l oads or hul l p ressures has been s tud ied in t hepa s t bymodeland fu l l - sca l e t e s t s under control led condi t ions, and th eresu l t s , such as t hose r epor t ed in r e fe rences 1 o 7, have provided hebasis fo r p re se n t methods fo r sp ec if yi ng maximum desi gn l oads.

With the rec en t app l ica t ion of sea pla nes to newer andextended ypesofoperat ions such as theant isubmarine warfare se rv i ces , a t t en t ion hasbe en cen ter ed no t on ly in the maximum l oads b u t al so i n some of th e more' de t a i l e dc ha r a c t e r i s t i c sof he load hi sto ry . For example, information


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on th e many load ing cycle s exp erien ced in these special iz ed ope rat ion si s of i n t e r e s t n a t i g u es tud ies . These studies, however,have beenhindered by l ack of inf orm atio n on t h e number of t h e d i f f e r e n t l oadsexpectedover ongoperatingperiods f or var ious se rv i ces .The purposeof th e presen t r epor t i s t o p r o v i d e a bas i s f o r e s t i -mating from a va i l a b l e t e s t data t he f r equenc ies and i n t e n s i t i e s of sea-plane oads and h u l lp r e s s u r e s o rg i v e noperat ions. Inasmuch as t h el oads and pressures are inf luenced by a number ofseaplane and op era tingf a c t o r s , it i s f i r s t ne c e s s a r y t o ge ne r a l i z e from t e s t da ta t h e s i g n i f i -can t e f f ec t s of t he se f ac tor s on t h e loads for con di t ion s of cont inuousrandom waves. The r e s u l t sa r e he nu s e d op r ov i de es t im a tes of t he l oadh i s t o r i e s o rs e ve r a l ou t i neope r a t i ons nva r i ouss e ac ond i t i ons . The

load h i s t o r i e s f o r t h e d i f f e r e n t s e a p l a n e u t i l i z a t i o n s are then camparedt o i n d i c a t e th e v a s i a t i o n s t h a t mightbeexpe cted and some of th e majorfa ct or s which cause these v a r i a t i o n s .

SYMBOLS

wave prop agat ion velo ci ty, kno tswave height, f twave length,c r e s t o c r e s t , f tnormal ac ce le ra t io n, f rom 1 g s teady-s ta tecondi t ion , g un i t ss ign i f i can t wave he igh t , def ined as theaveragevalue of t h e one-

t h i r d highest waves f or a givenperiodof ime, f tve loc i ty ,kno t spr ob ab i l i ty of exceeding a wave he ig ht fo r a given sea condi t ionp r o ba b i l i t y d i s t r i b u t i o n of wave h e i gh t f o r a given sea condi t ionp r o ba b i l i t y d i s t r i b u t i o n of norm al a c c e l e r a t i onmean-square wave he ig h tdens i ty ,s lugs /cu f ta c c e l e r a t i on due o g r a v i t y , f t / s e c 2


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NACA RM L 5 7 A 1 5 - 3Subscr ip ts :L landingpeedR r e l a t i v ee l o c i t y

GE2lERAL CO N SID ERA TIO N S AND METBOD

Duringeach anding and tak e-o ff, heseaplaneexper iencessevera limpactsofvarying ntensi t iesdep end ing on a number of fa ct or s su ch aswave height and slope,operat ingspeed, and seapla ne-h ullconf igura t ion.An exampleof the acc e le ra t i ons which occur for a seaplane anding n4-foot waves a t a landingspeedof 70 knots i s g iv en i n f i g u re 1. A s mayben oted i n t h i s t i m e h i s t o r y, h e a r ge s t l oad doesnotgeneral lyoccurdur ing he f i r s t impact butdur ing some subse quen t mp act.These esultsi n d i c a t e t h a t c o n d i t i o n s p r i o r t o landing are not necessar i ly a good indexof the l oad i n t e n s i t i e s b u t r a t h e r t h a t t h e l oad his to r ie s depend more ontheuncontrol ledcondit ions whichdevelop a f t e r h e n i t i a l i mp ac t. I tthus seems app are nt hat dat a ob tain ed under contr olled condi t ions f o rsingl e mpac ts may n ot alo ne ser ve as a re l i abl e ind ica t io n of the numberand in tens i ty of a l l l oads fo rivenandings .

Forextendedoperationsof a given seaplane, he t o t a l l oad h i s t o r yco ns is t s of a number of andings and tak e-o ffs , of th e ty pe i l lu st r at edi n f i g u r e 1, f o r d i f fe re n t wave condi t ions . The es t i ma t io no f h e o t a ll oad h i s t o ry fo r t h e s e a p l a n e r e q u i r e s t h e i n t e g ra t i o n of t h e l oads f o ra l l landings and ta ke-o ffs for the per io d of opera t ion be ing cons idered.Inasmuch as data are not ava ila ble f o r separate andings under a widevar ie t y o f s eacondit ions and f o r di f fe ren t seap lane ypes , it i s accord-ingly necessary t o es t ima te from ava i l ab le in fo rma t ion the in f luencesof th e se a and seaplaneparameters on th e l oads s o t h a t e x i s t i n g t i m e -h i s t o r y d a t a of t h e t y p e g i v e n i n f i g u re 1may be mod if ie d in ord er toes t ima te he l oads f o r landings notherseacon dit ion s. The estim atednumber and i n t e n s i t y of t h e l oads f o r gi ve n a nd in gs i n d i f f e r e n t seaconditions may thenbesimply summed t o a r r i v e a t t h e o v e r a l l l oad h i s t o r y .

For the present purpose of d e s c r i b i n g t h e r e a c t i o n s of a s e a p l a n e i nterms of app lied l oads or pr es su re s , th e magnitude and frequency of t h enormal acc e ler a t io ns , the m a x i m u m pres sures on the hu l l , the ave ra ge p res -sure and thewet tedareaareused. The normal acc ele rat ion sa re a measureof t h e fo r c e s of i n t e r e s t i n c o n s i d e r i n g t h e o v e ra l l s t r e n g t h of t h e sea-ple ne s t r uc t ure , whereas the pressu res and wet ted area de term ine the loca land t o t a l fo rc es on th e hu l l bottomwhich, i n t u r n , d e f i n e t h e s t r e n g t hrequirements f o r t h e h u l l .


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Sign i f i c ant Pa r ame te r sThenumber andmagnitude of t h e l oads imposed on seaplane hul lsdur ing landings and tak e-o ffs have been found from p a s t e x p e r i e n c e t o

dependon the f o l lowing sea and seaplane paramete rs:( a ) H u l l o r f l o a t c o n f i g u r a t i o n s u c h as p l a n f orm l o n g i t u d i n a lshape, and transverse shape( b ) Beam-loading c o e ff i c i e n t which depends on the we igh t of th eseap lane and h u l l s i z e( c ) Landingapproach or take-off condit ions which are normallyd e f in e d by t h e a n g l e o f t h e k e e l t o t h e w a t e r s u r f a c e (trim angle ) , a i r -p l a n e a t t i t u d e , and t h e v e l o c i t y of t h e s e a p l a n e e i t h e r i n r e f e r e n c e t ot h e w a t e r o r o t h e r a p p r o p r i at e r ef e r e n c e( d ) Seaway condit ions such a6 t h e wave s lope , wave propagationv e l o c i t y , and t h e o r b i t a l v e l o c i t y , a l t h o u g h t h e s l o p e and ve loc i ty vec-t o r s are normallyu se d i n c a l c u l a t i n g t h e l oads( e ) Aerodynamic l i f t which inf luences he seaplane s ink ing speed orv e r t i c a l v e l o c i t y( f ) Pil oti ng tec hn iqu e which would be expec ted to in f lue nc e theopera t iona l pa r ame te r s and the se , n u r n , a f f ec t he s eap l ane r eac t i onsA s w i l l be d is cus sed la t e r , no s imple method appe ared ava i lab le to

account f or t h e e f f e c t o f a l l the se va r ia b le s on th e l oads orh u l l p r e s -su r e s . It appeared, however, t h a t thepredomina t ing nf luencescould bee s t a b l i s h e d o a f f o r d a bas is f o re s t i m a t i n g , a t l e a s t , t h e g e n e r a l e v e lof th e loads and press ures and the f requ enc i es of occu r renc e for d i f fe re n topera t ions .Method

The gene ra l method developed in th i s pap er for es t im at i ng the loa dsor pr e s su r e s i s i l l u s t r a t e d n f i g u r e 2. A step- by-st ep example o f heca lcu la t ions nvo lved n e s t ima t ing an acce le r a t ion h i s to r y i s g iven i nappendix A.

The d i s t r i bu t i on of wave he ight s for a g iven ope r a t ion ove r a longperiodof imesuch as a year i s p r e s e n t e d i n f i gu re 2( a ) and the d i s t r i -butio ns of norm al acce lerati ons which would be expec ted for a given sea-plan e andi ng n waves ofc o n s t a n th e i g h ta r eg i v e n nf igu r e2 ( b ) . Fromknown o r assumed le ng th s of take -off and lan din gruns and t h e t o t a l numberof f l igh t s , he d i s t a nce ha t he s eap l ane r ave l s on th e waves i n g iven


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wave heights m a y bedetermined . These di st an ce s, when div ide d by anaverage wave len gth for the app rop ria te wave he ight , give an es t imateof t h e number of mpacts on waves of a givenhe igh t .Mul t ip ly ing hea p p ro p r i a t e d i s t r i b u t i o n s of a c c e l e r a t i o n s n f i g u re 2 (b ) by t h e t o t a lcurveswhich, when ummed, g iv e th e to ta l ac ce le ra ti o n h is to ry shown i nf i g u r e 2 (c ) .

' number ofmpacts forhe orre spon ding wave he ig hty ie lds a family of

A V A I W L E TIME-HISTORY MEASLIRENENTS OF SEAPLANEACCELERATIONS AND WLL PRESSURES

The avai l able ime -his to ry da ta on the seaplane acce lera t ions andhu l l p re s s ures whichform t h e b a s i s f o r t h e p r e s e n t s t u d y c o n s i s t o fful l -sc a le - and model- tes t resul ts obta ined from inves t iga tions conducteda t th e Lan gley Aeronautica l Laborato ry of the National Advisory Committeefo rAer onau tics . These dat aa red e s c r i b e d n h e o l l o w i n gsec t ions .

Normal AccelerationsMeasurements of the normal accelerat ionsexperienced during andingsi n given wave cond itions were obtained frommodel t e s t s in the sea p la netanks a t the LangleyLaboratory. The model ch ar ac te ri s t ic s and t e s tcond i t ions ( fu l l - s ca levalues) were as fol lows:

I Model IA I B C 1

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Landingpeed, kno ts . . .Wing loading,b / f t2 . . .Angle ofdead r i s e , deg . .Length-beam r a t i o . . . . .Weight, l b . . . . ; . . .

The cor res po ndi ng ful l-s cal e val ues of the hu ll beam and forebody engthof the modelswere 5 f e e t 10 inches and 50 f e e t 5 inches , respec t ive ly .The h u l l had hor izo nta l ch ine f la re and a basic angle of dead r i se of 20'.Both the dead -rise angl e and th e chi ne f l a r e were cons tan t fo r a d i s t a n c eof 21 f e e t forwardof th e s te p . Thebeam was a l s o c o n s t a n t o v e r h i sdis tan ce. The dead -riseang le hen nc reased o 68' a t the orwardper-pen dic ula r wh ile the beam decreased.

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6Time h is to r ie s of normal acc ele rat i on were a va i l a b l e fran about 60t o 160 l andings of the seap lane models f o r th e t e s t conditions summarizedi n t h e p r e c e d i n g t ab le fo r bo th 2- fo ot and 4-foo-t wave he i gh t s ( f u l l - s c a l eva lues ) . An inspe ct ion of the se esu l t s nd ica ted , however, tha ton l y

th e 4-foot-wave co nd itio ns were rep res ent a t iv e of th e wave height - lengthr a t i o s h/A whichoccur in out ineoper a t ions . Only th ed a t a o r h e4-foot-wave conditions were, t h e r e f o r e , u s e d i n t h e p r e s e n t a n a l y s i s .The sample time hi s to r y o f t he normal acce l e ra t io ns g ive n in f igur e 1was obta ined n a l anding run f o r one of th ese t e s t s .I n o r d e r t o o b t a i n a s i m p l e de s c r i p ti on of t he a c c e l e r a t i on da t a i nf i g u r e 1 f o r t he d i f f e r e n t l a nd i ng s pe e ds , t he a c c e l e r a t i on va l ue c o r r e -sponding t o each mpact w a s read from the time h i s t o r i e s a n d c l a s s i f i e dby acce l e ra t io n n t e rv a l s o f0.3g f o r each andingspeed. The re s u l tsa re g ive n in t he fo rm of p robab i l i t y d i s t r i bu t ions fo r t he th ree l and ings pe eds i n f i gu r e 3. These d i s t r i b u t io ns are usedsubsequently t o e s t i -

mate the normal acc el er at io ns fo r ot he r wave heigh ts and landingspeeds.Hul l Pressures and Wetted Areas

Measurements o f th e hu ll pr es su re s and we tted are as were obtainedfrom ful l - sca le t e s t s dur ing 64 landings and tak e-o ffs of a seaplane nwave heigh ts up t o about 2L f e e t . The testc ond i t i ons var ied f romnormal2landings t o s t a l le d a nd i ngs w i t h f l a p s e t t ings va r y i ng from ze ro t o f u l lf la ps . The ge ne ra lc h a r a c t e r i s t i c s of theseap lane and th e e s t condi -t i o n s a r e as fol lows:Landing speed,nots . . . . . . . . . . . . . . . . . . . . . . . 66Wing loading,b / f t2 . . . . . . . . . . . . . . . . . . . . . . . 40Length-beam r a t i o . . . . . . . . . . . . . . . . . . . . . . . . 6Operatingweight, l b . . . . . . . . . . . . . . . . . . . . . . 41,000Angle rise,e g 22-12. . . . . . . . . . . . . . . . . . . . .

The ful l -sc ale sea pla ne had a beam of 10 f e e t and an o v er al l forebodylength of 30 f e e t . The h u l l had hor i z on ta l c h i ne flare and a bas icangleof dead r i s e of 22z . The angle of dead r i se , hec h i n e f l a r e , and thebeam dimensionswereconstantfor a di s tan ce ofapproximately 10 f e e tforward of thes t ep .F o r heba l a nc eo f hehu l l o he forwardpe r pe n -d icu la r , he dead- r i se angle nc reased t o approximately 73O.

l o

From tim e hi st or ie s of press ure measurements taken on th e h u ll bottomo f the seaplane , da t a were obtained of t h e m a x i m u m pressure nea r t he s t ep ,the average pressures over he wet ted areas , and th e wet te d hul l l engt hsor are as for lan din gs and tak e- of fs in smooth water and 2-- foot waves.20


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NACA RM L57A15 - 7P r o ba b i l i t y d i s t r i bu t i on s w ere ob ta i ne d f rom t h e s e da t a i n a mannersimilar t o t ha t p r e v i ou s l y de s c r i b e d f o r t he m odel a c c e l e r a t i on m easure -ments. The re s u lt sa r eg i v e n nf i g u r e s 4 , 5 , and 6 f o r h e m a x i m u mpressure ,averagepressu res , and we t tedke e l e ng t h s , e s pe c t i ve l y . Itm a y be no ted tha t the cur ve fa i re d thro ugh the maximum pre ss ur e da ta inf i g u r e 4 doe s no t f o l l ow t he da t a po i n t s f o r t he h i ghe r p r e s s u r e s s i nc eit was con side red hat some of the andin gs were consid erably more sever ethan would be expec ted in ro u t in e op er a t io ns fo r t h e samenumber oflandin gs. The fa ir ed c u r v e n h e f i g u r e i s t he re foredashed a t t h eh igher va lues o nd ica t e he es t ima ted pressures fo r normal condi t ions .

ESTIMATESOFTHENFLUENCEOF SEAPUNE AND SEAPARAMETERS ON ACCEUXATIONS AND PRESSURES

The succes s ha t can be ach iev ed n es t ima t in g he oads and pres -sures fo r ex t end ed opera t ions dependson the success ob ta ined n account ingf o r t h e e f f e c t s o f t he d i f f e r e n t s e a p l a ne and s e a pa ra m e te r s on t he ba s i cr e s u l t sg i v e n n i g u r e s 3 t o 6. I n h i ss e c t i o n , h ea v a i l a b l e n f o r m a -t i o n on t h e e f f e c t s of t hes eparameters on the oad s i s considered. Fromthese consid era t ions of both s ingle param eters or group s of parameters ,r a t he r s i m p l e a d j u s t m e n t s t o t he l oa d h i s t o r i e s seem t o besuggested asa means of e s t i m a t i n g t he s i gn i f i c a n t va r i a t i o ns i n t he l oa d s f o r d i f f e r -e n t ope r a t i ons .

Seap lane-Hul l Charac t e r i s t ic sT e s t r e s u l t s have i n d i c a t e d t h a t v a r i a t i o n s i n t h e s e a p l a n e - h u l l

c h a r a c t e r i s t i c s ,s u c h as angle ofdead r i s e , length-beam ra t i o , o r beaml oa d i n g , ha ve s ubs t a n t i a l e f f e c t s on t he oa dsorpressuresdeve loped onth es e a p l a n eh u l l nva r io us wave he igh ts ( s e e r e f s . 4 t o 7) . An exami-na t i on of t h e r e s u l t s a va i l a b l e , however, i nd i c a t e d ha t he nd i v i d ua le f f e c t s ofchanges i n t he hu l l c o n f i gu r a t i on on t he oa dscouldbeapprox-imated by an a ppr opr iate acto r .Refe rence 4 , fo r example , in di ca te st ha t t he a c c e l e r a t i on s and p re s su r esvaryapproximate ly as f o l l o w s f o rg iven wave he ig h t s bu t d i f f e ren t deg ree s o f dead- r i se ang le :Dead-r iseangle,deg Acce le ra t ion (pe rcen t o f 20 dead- r i se ang le )

2071-0100

60 43


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8 NACA RM L37A15

Simi lar ly , reference 6 i n d i c a t e s t h a t t h e v e r t i c a l a c c e l e r a t i ons f o rgiven wave len gth s inc rea se by a f a c t o r o fabout 2 when t h e length-beamr a t i o i s changed rom 20 t o 6 . For hepresen ts tudy , it was t he r e f o r eassumed that s imp le adjustm ents of the load or p r e s s u r e h i s t o r i e s on t h ebasis of th es e re su l t s would bea de quate t o a c coun t f o r va r i a t i o ns i nhu l l conf igura t ions .

Operational ParametersA number of va ri ab le s which in flu en ce th e l oads, such as t r im angle ,forward and sinkingspeed, and f l i g h t a t t i t u d e a t t imeof anding, m a ybegroupedunder operationalparameters .Al thoughcon sidera ble work hasbeendone i n t h e p a s t t o d e f i n e t h e e f f e c t of t h e s e v a r i a b le s on t h el oads ( r e f s . 2 and 3 ) , no s imple methods fo r ap pl yi ng he re su l t s d i re c t l yt o t h e p ro ble mofes timating he oads and pres sures for rout in e ope ra-

t i on s were evident .Fo r example, th ea v a i l a b l e da t a on the e f f e c to ftrim angle on the l oads genera l ly r epresen t f i xed trim condit ions, suchas a t r imangleof 3'. Discussionswithpi lotshave ndic ated, however,t h a t v a r i a t i o n s of a t le a s t 22' f rom the de sire d trim angle would beexpected a t t h e i m eof he n i t i a l impact fo r a given anding. naddi -t i on , on ly l i t t l e c o n t r o l i s had o ve r he t r i m angle forsubsequentimpacts, and con sid era ble more trim -an gle var iati on s would beexpectedf o r he ba lan ce of t he and ingrun . No s implecor rec tio n would appeart o a c co u ntfor hese r im-anglee f fec t s . Data obtained from t e s t s of afu ll- sc ale se ap lan e were examined f o r the re la t ion shi p between acceler -a t io n and s inkin gspeed ; he esu l t sa reg iven n igure 7. I n t h i sf igur e , t he va r i a t ion of acce l e ra t ion wi th i n i t i a l sinkingspeed i s shownf o r he s uc c e s s i ve m pa c t s f o r 20 l andings i n approximate ly2--footwaves. It i s evident from the s c a t t e r of p o i n t s n f i g u r e 7 t h a t h ei n i t i a l s i n k i n g speedb y i t s e l f i s not s imply re la ted to the magni tudeof t he acce l e ra t ion , even fo r a givenseaplane and f o r a givenseacondi t ion.

12

Although it seemed imp ract ica ble o acco unt for he ndiv idua l ef fec tsof t r i m angle ,s inkingspeed ,orseaplaneat t i tude on th e l oads f o r r o u t i n eopera t ing condi t ions , a fu r the r cons ide ra t ion of t he da t a from the fu l l -sca l e - and model -seaplane t e s t s i nd ica t ed tha t t he ov era l l e f f ec t s o f t hesevar i a b les were inc lud ed in the acce l e ra t ion and press ure da t a of f i g ure s 3t o 6. It alsoappeared ha t heseva ria bl es would have similar e f f e c t son otherseaplaneopera t ions . No fur theradjus tments of t h e b a s i c d i s t r i -b u t i o n s n f i g u r e s 3 t o 6 f o r t he s e pa r a t e e f f e c t s o f t r i m angle,sinkingspeed, o r f l i g h t a t t i t u de were, t here fore ,considerednecessary.Flight speed has a marked inf lue nc e on t h e magnitudeof the l oadsand pressures f o r individual wave impacts.Both th eo re t i ca l and exper i -

mental da ta i n d i c a t e h a t h e o a dv a r i e s as V2 f o rge om e t r i c a l l ys i m i l a r


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NACA m ~ 5 7 ~ 1 3 - 9impac t s ( r e f s . 2 and 3 ) . For opera t ionso fd i f f e r e n ts e a p l a n e s nd i f -ferentseacon dit ion s, however, ge om etr ica ls imi l a r i t y i s notobta inedbetween the impacts f o r eachoperation, and undercondit ionswhichincludedboth smooth- and rough-water andings, th e ac ce le ra ti on s havebeen ound t o increasewith andingspeed a t r a t esvarying between Vand V . For ough-water andings, i n which a t l e a s t h e n i t i a l impactusual ly occurs on th e forwardslope of t h e wave, a high r a te of i nc reaseof the l oad with andingspeedappears t o r e s u l t from the inc reasedve loc i ty of the hu l l pe ne t ra t io n int o the wave due to t h e component ofseaplaneveloci tynormal t o th e wave fr on t . A su ff ic ie n t number of t e s t shasnotbeen made t o es tabl i sh an average or r e p r e s e n t a t i v e r e l a t i o nbetween the oad s or pres sure s and the hor iz onta l spee d for a l l impactsof r ou t i neo p e r a t i o n s ndi f fer en t wave condi t ions . An i nspec t ion oft he model t e s t da t a i n f i g u r e 3 i nd i c a t e s t ha t t he a c c e l e r a t i ons i nc r e a s eapproximately as VI m3 fo r and ings n&- fo ot waves. Although t h isv a l u emay notapply t o a l l opera t ions n o the r wave condi tions , it i s usedhereas the ba s ic re l a t io n between seaplanespeed and the acce l e ra t io ns orp r e s s u r e sf o rd i f f e r e n t s e a p l a n eut i l i za t io ns . Some mo dif ica t ion w i l l bemade t o t h i s r e l a t i o n l a t e r t o accountfurther f o r d i f f e r e n c e s i n seacondi t ions .

2

Seaway ParametersThe seaway parametersnormallyr equ ir ed i n t he a na l y s i s of t h e l oadsand motions of a sea pla ne are he wave slo pe s, wave pro pa ga tio n ve loc ity ,and the o r b i t a l v e l o c i t y of t h ew a t e rpar t ic les . There i s i n s u f f i c i e n t

i nf or m at ion i n t h e l i t e r a t u r e on s e a c ond i t i ons ( r e f s . 8 t o 11, f o r exam-p l e ) ode f i nes i m p l y h e s e h r e equa n t i t i e s . I t i s necessa ry , he re fore ,t o det erm ine some para me ter which may beused t o approximate the inf lue nc eof these acon di t ion on theseap lane l oads. Since it w a s i n d i c a t e d nth ep r e v i o u ss e c t i o n h a t h e l oads var i ed as a func t ion of V ( i n h i sana lys i s V i s t akenas he and ing peed) , it w a s con side red hat somemodi f i ca t ion to t he va lue of the andingspeedcouldbeuse d t o i nc l u dethe nf lue nce of theseacon dit ion . The ge ne ralp r oc e du r e ofo l low w a sindica ted from an inspec t ion of t he da t a on normal a cc e l e r a t io n fo r d i f -f e r e n t wave heig hts which showed th a t th e magnitude of th e ac ce le ra t io nsincreasedwith wave he igh t. It i s a l s o known t ha t hep r opa ga t i onve l oc -i ty in cr ea se s w i th wave height for g iven values of s lope due t o t h eincreased wave l en gt h ref . 8 ) . It a ppe a r e d , he r e f o r e , ha t he nc r e a s ein normal acce l e ra t io n cou ld be r e l a t e d to t he wave pr opa ga t i on v e l oc i tyt o account f o r va r i a t io ns in wave he igh t .

I n o r d e r t o r e l a t e t h e wave p r o p a g a t i o n v e l o c i t y t o t h e loads andpressures , it i s f i r s t ne c e s s a r y t o de t e r m i ne t he d i s k r i bu t i on of wavehe igh ts and the ang e of wave slo pe s. From th is nf or ma tio n, he wavelengths and th en the pro pa ga t io n ve loc i t ie s .may be computed, s i n c e t h i sv e l o c i t y i s r e l a t e d d i r e c t l y t o t h e wave l eng th .-


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Wave heights .-Considerable nformat ion i s avai lable on thecondi -t i o ns of t he sea i n the formof s t a t i s t i c s on s i g n i f i c a n t wave he i gh t swhich des igna te t he average he igh t o f t he h ighes t one- th i rd of th e wavesf o r a givenper iodof im e see , or example, r e f s . 8 t o 11). Separatesamples of t h e s e d a t a when summarized a s p r o b a b i l i t y d i s t r i b u t i o n s( f i g . 8) appear t o f a l l roughly nto hreegroups which repre sent hesea c ond i t i ons n s he l t e r e d r e a s , e e i de o f i s la nd s , and th e"open ocean. It She l t e reda r e a s as usedhere epresent akes and nea rlylandlockedbayswhich are prote cted from the la rg e waves and swe llsgen era te d n he open sea . Lee s id e of i s l an ds r e f e r s ow a t e r n a i r -dromes a t i s l a n d b a s e s o r t o bayswhich a r e r e l a t iv e l y open t o t h e e f f e c tof waves from th e openocean. The open ocean i s , as the erm mpl ies ,wa ter of t h e oceans away from any she l t e reda r e a . In order t o obta inan ind ica t ion of the average condi t ions whichmightrepresenteachgroupof d a t a i n f i g u r e 8, an averagecurve was f a i r e d t h r o u g h t h e d i f f e r e n tse t s of p r o b a b i l i t y d i s t r i b u t i o n s of s i g n i f i c a n t wave h e i g h t s i n t h ef i g u r e .

I1 11

I n or de r t o a pp l y t he s e da t a on s i gn i f i c a n t wave he igh t s t o t h eproblem of e s t i m a t i n g t h e h u l l l oads or p res sure s a r i s in g fram a l l landingo r take-off mpacts , i t i s necessa ry o conver t he r esu l t s g iven by theaveragec ur ve s i n f i g u r e 8 t o a form givin g the more deta i led nformat ionon t h e d i s t r i b u t i o n s f o r a l l wave hei gh ts. The method f or us in g h e da taon s i gn i f i ca n t wave he ig h t s t o approximate th e d i s t r i b u t i on s o f a l l waveheights i s descr ibed nappendix B. Br ie fly , he method involves f i r s tes t ima t in g the dis t r ib ut io ns of th e root-mean-squarevalues of wave he ig ht sfrom t h e d a t a i n f i g u r e 8 and t he n t r a ns f o r m i ng t he s e d i s t r i bu t i ons t od i s t r i b u t i on s of t hehe igh t s o f a l l waves. The r e s u l t s are given i nf i g u r e 9.

Wave slo pe and pro pa ga tio n ve loc ity .- The inf orm atio n n ref ere nce 8i nd i c a t e d t ha t a wave he igh t - le ng th ra t io of l :7 i s a t h e o r e t i c a l limitt o th es t eepness o f a wave a f t e r which t h e wave would bre ak .S ince hewave cha ra ct er is t i cs depend on th e wind ve lo ci ty , le ng th of open area o rfet ch , and the du ra t io n of th e wind, th e waves go through a cycleofbuildup and decay.Dur ing hese ycles , he h/A values may varyovera rangeof 1:7 t o about 1:120 with a probable range of 1:20 t o 1:100.

If two waves exist,bo t hha v i ng an h/A of 1/40 bu t he waves are1 foot and X) fe et hi gh , th e wave leng ths would be 40 f ee t and 800 f e e t ,resp ect iv ely . The prop agat io nve loc i ty fo r he se two waves would be8 .5 h o t s and 38.0 h o t s 8s computed by th e fo rm ul a fo r tro ch io da l waves( r e f . 8 )


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wherec wave pr op ag at io neloc i ty ,no t s

A wave length, f tIn o rd e r t o account f o r th e e f fe c t o f th i s inc r eased wave p ropaga t ionv e l o c i t y f o r increased wave he ights on the oad s or pres sures , he prop a-ga t ion ve loc i ty . was added to the l and ing o r t ake -o f f speed to ob ta in there la t ive speedbetween theseap lane and the waves a t time of mpact. Fora givenseaplane it w a s fu r the r cons ide red ha t he mpac t s are geomet-r i c a l l y similar . For th isc o n d i t i o n , h eacc e le ra t ion s would bepropor-t i o n a l o V2 where, as has j u s t beennoted, V i s e q u a l o h e sum ofthe seaplane speed and th e wave propag ation velo city, or

The data frommodels A, B, and C werecons idered in de ter min ingw hether t h i s r e l a t i o n c ou ldbeused i n approx ima t ingavai labledata. Thecomparison was l i m i t e d i n n a t u r e s i n c e d a t a f o r o n l y 2- and 4-foot waveswere av ai la bl e and t h e h/A val ue s f o r the twowave heightscovered adifferent angewi thonly a sma ll sample i n a comparable ange. The d a t aindi ca ted ha t he oreg oing e la t io n oug hly approximated th edata . There la t i on was used, herefore , and assumed to be su ff ic ie nt ly re pr es en ta -t i v e ' t o be extended t o 40-foot wave heig hts .Since a range of wave height-length r a t i o s e x i s t s i n t h e d i f f e r e n tsea con di t ion s , h is same rangemustbecons idered in ob ta i n in g an averagespeedof wave propagatio n. The range of he ig ht -l en gt h at io scons ide reda r e 1: 20 t o 1: l OO as shown in able I. T h i s a b l egi ve s he wave leng thsand thep r o p a g a t i o nv e l o c i t i e s o rdi ff er en t wave he igh ts and h/A r a t i o s .The velocities were computed by the formula g iven previous ly .It may be no te d th at se ve ra l va lu es of wave len gth s and pro paga tionv e l o c i t i e s a r e o m i t t e d from t a b l e I fo r the h ig he r and longe r waves.These omissions were made f o r two re as on s. Fi rs t, hi gh waves with longwave len gth s seldom oc cw . Second, di sc us sio nsw i t hp i l o t s n d i c a t e dtha t lan din gs would normally be made p a r a l l e l t o t h e wave c re s t s when

t h e wave le ng th s become s ev er al times the span of the seaplane.Sincethe seaplanes under considerat ion were of t h e bomber or t r a n s p o r t t y p e swi th re l a t i ve l y l a r ge wing spans , he wave l eng ths o f 300 f e e t or moref o r t h e smaller wave he igh t s and p rogres s ive ly longe r waves f o r th ehighe r wave h e i g h t s were omi tted. The ta b lecon ta ins , he re fo re ,o n l ythe va lues of wave l e n g t h s for t h e d i f f e r e n t wave heights which are con-s i d e r e d i n t h i s a n a l y s i s .

-


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The pro pag a t io n ve l oc i t i e s l i s t ed in t he lower h a l f o f t he t a b l ewere a ve ra ge d t o g i ve t he a ve r a ge p r op a ga t i on ve l oc i t y f o r t he d i f f e r e n twave he ig ht s. The seaverageveloci t ies were added t o h e a n d i n g s p e e d sand p l o t t e d a ga i n s t wave h e i g h t s i n f i g u r e 10 t o o b t a i n t h e r e l a t i v ev e l o c i t y i n k n o t s . It may be noted from f igure 10 t h a t t h e r e l a t i v eve l oc i t y i nc r e a s e s r a p i d l y w i t h wave heig ht up t o a he igh t o f 1.5 orx) f e e t . Becauseof theomiss ionof he onger wave l e n g t h sf o r hehig her waves, t h e re l a t ive ve l oc i t y t he n i nc r e a s e s a t a much lower ra te .

"he di s t r ib u t io n of normal acce l e ra tions fo r a given andingspeedand wave he igh t may then be mo dif ied for othe r wave hei gh ts by t h er e l a t i o n

o r

where th e s ubs c r i p t R r e f e r s o e l a t i v ev e l o c i t y . f h ed i s t r i b u t i o nfor 4-foot waves i s considered as t he ba s i c d i s t r i bu t i on o f a c c e l e r a t i ons ,t he d i s t r i b u t i o n f o r 8 - f oo t waves, f o r instance, can be ca lcu la t ed by th er e l a t i o n f o r g i v e n p r o b a b i l i t y l e v e l sVv2

*8-2R4

where t h e numbers used as subsc r ip t sde sig na te he wave heig hts . "hisprocedure w a s u sed t o o b t a i n t h e d i s t r i b u t i o n s of a c c e l e r a t i o n s f o r t h edi f f er en t wave heig hts shown in f ig u r e 11.

SUMMARY OF CONDITIONS AND ASSUMPTIONSThe fol lowing condit ions or assump tions were i n t roduced or d i scussedin the p rec ed in g sec t io n and a re used i n t h e subsequent analysis:(a) Data from t h e fu l l - sca l e seap lane and t he seap lane models onnormal acce lera t io ns , ocal pressures , we t t edme a, and averagepressuresareconsideredcomparable t o da t a expected rom rout ine ope rat ion s und er

s imilar seaplane and seaway conditions.


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NACA m ~ 3 7 ~ 1 3 13( b) The ef fe c ts of operat ionalparameterssuch as trim angle ,s inkingspeed, and f l i g h t a t t i t u d e a r e i n c l u d e d i n t h e b a s i c d i s t r i b u t i o n s and i t

i s assumed tha t the se var ia ble s w i l l have s im i la r e f fec t s fo r o the r s ea -p laneop era tio ns and seaway co nd itio ns.(c ) The eff ec t o f airspeed on the l oads may va r y fo r d i f fe r en t

landing peeds and op era tio ns from V t o V2 . In h i s n a l y s i s , h eeffec to f and ingspeed i s takenasapproximately V l S 3 as shown by thed a t a from th e model t e s t s .

( d ) Dis t r ibut ions of l oads fo r d i f fe ren t s eap lane -hu l l conf igura t io nsmay be accomp lished by adjusting he magnitu de of he l oads by an appro-pr ia t e fac to r de te rmin ed from resea rch on th e e f fe c t of the parameters .( e ) Thewave heights are assumed t o b e a Gauss ian d i s t r ibu t ion w i t ha narrowspectrum and th e di s t r i b u ti o n of wave hei gh ts i s given by ( se eeq. ( u), appendix B )

h22 "00 ""-Qh) r e y2 dY

J o y2( f ) The effect o f the sea para met ers may be repr esent ed by an

hinc rease n and ing peed so t h a t n a VR where VR i s e q u a l o h elandingspeed of the seaplane plus he average speed of propagation ofth e waves f o r a given wave height.

2

(g) Thewave hei gh t-l eng th rat ios of importanceare from 1:20 t o1:100.( h ) The seapla ne i s la nd ed nt o he waves except when t h e wavelength i s sev era l im es he wing span. For t h e long-wave c ond iti on s,the seap lane i s la nde d p a ra l l e l t o t h e wave c r e s t s .( i )The e ff ec t of wind on the anding spee d i s neglected.

ESTIMATION OF LOAD AND PRESSURE HISTORIESEst imat ion of Dis t r ibu t ion of Accelera t ions for

Assumed OperationsI n o r d e r t o estimate t h e t o t a l l oad hi s t o r ie s , th e method f o r ca lcu -l a t i n g t h e a c c e l e r a t i o n s as d e s c r i b e d fo r f i g u re 2 was a p p l i e d t o several

.


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14assumed operations. Table I1 gives he ypes of a i rplanes , engthofmission assumed, range i n speed,angleofdead r i se , and sea condi t ionsinves t iga t ed . The l oa ds on t h e pa t r o l bomber and thesupersonic bomberwere i nves t iga t ed fo r and ing speeds o f 70 and I 20 h o t s , anglesofdeadr ise of 20 and 40, and sea condit ions which varied from 50 percent oft he a nd i ngs n he ope nocean t o as l i t t l e as 0.01 percent . This l a t t e rcondi t ion m a y be c l a s s e d as an emergency co nd it io n rat he r tha n a des igncondit ion. The landing peedsof heant i submar ine-warfare ( ASW sea-p l a ne a r e 40 i d 80 knots, and 90 per cen t of he op era tio ns were assumedt o o c cu r i n t h e o penocean.

I n a dd i t i on , it w a s assumed that eachseaplane would op era te for1,000 f l ig ht ho urs and thoseseaplanes anding a t 70 knots, 120 knots,40 knots ( A S W ) , and 80 knots ( ASW would require,fo rea ch combined tak e-off and landing, a d i s t a nc e o f 10,000, l 3, OOO, 4,000, and 6,000 f e e t ,r e spec t ive ly . It was also assumed that he ASW se ap lan e made 20 t o30 l andings per miss ion, whereas he other seaplane ypes made onlyone land ing per miss ion.

The estimated l oad h i s t o r i e s f o r s e ve r a l of t he s e ope r a t ions a r eg i ve n i n f i gu r e 12 as the cumulat ive f requency dis t r ibut ions of acce le r -a t i on . An i l l u s t r a t i v e example of t hep r oc e du r efo res t ima t ing he l oadh i s t o r y i s given i n appendix A fo r opera t ion A of t a b l e I1 f o r 70 knotslandingspeed, 20 angleofdeadrise, and a mission ength of 11 hours.Es t imat ion of Maxi mum Pressure Hi s to r i e s

The pr oc ed ur e fo r es t im at in g th e di st r ib ut io n of th e maximum orl oc a l p r e s s u r e s f o l l ow s t he i de n t i c a l s t e p s u s e d i n e s t i m a t i ng t he a c c e l -e r a t i o n h i s t o r i e s once t h e d i s t r i b u t i o n s of pr e s s u r e s f o r d i f f e r e n t waveheights and landingspeedsa rede te rmined . n h i scase , hepressured i s t r i bu t i on ob t a i ne d fromf l i g h t t e s t s o f t h e XPBS-1 s e a p l a ne ( f i g . 4)w a s used as a b a s i c d i s t r i b u t i o n f o r a wave heightof 2 f ee t .T h i sd i s t r i b u t i o n i s p l o t t e d as thecurve or2-fo ot waves of igu re 13. Thedi s t r ib u t io n of p re ssure s fo r t he o the r wave he igh t s shown in th e f igurew a s obta ined f rom t h i s d i s t r i b u t io n by assuming th a t fo r a given seaplanethe p ressures va r i ed as the velo ci ty squ ared , where ag ain it i s assumedt h a t t h e v e l o c i t y i s t h e r e l a t iv e ve lo c i ty between the seap lane and th ewave. It s hou l dbeno t e d ha t hepressure doe sn o tva ryexac t ly as t h eacce l e ra t ions , bu t it w a s f e l t t h a t t h e same relat ionscouldbeused asa f i r s t approximation.

The est imated cumulat ive frequency dist r ibut ions of m a x i m u m pressuresn e a r t h e s t e p f o r 1,000 f l i g h t h o u r s o f h e o p e ra t io n s i s te d n t a b l e I 1f o r landingspeeds of 70 knots (40 kno t s f o r t h e ASW a i rp l ane) and 200dead- r i se ang le a re g iven n f igure 14.


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1-5Local Pressures a t a Location Forward of th e St ep

In con s id er i ng the pr oba bi l i ty d is t r ib ut i on of maximum pres suresa t a point forward of he s tep , it i s necessary t o know th e va ri at io nor change in th e pr es su re as maximum pre ss ure moves fo rw ard wi th we tteda rea and the p robab i l i ty tha t the po in t unde r cons ide ra t ion w i l l bewettedduring an impact. The v ar ia ti o n of th e p re s s u re as thewe t teda re a moves forward i s shown in f ig u r e 15 as t h e r a t i o of t h e maximumpressure a t a given point on th e ke e l t o the maximum pressure a t t h estep.Thiscurve i s based on pressuredataobta ined on models i n t h eLangley mpact b a si n ( r e f . 12 ) and checked by a l imited amount of f l ightda ta .F igure 15 ind ica te s ha t hep e a kpres sures a t a point ,say2> percent of he keel ength forward of th e s te p, would onlybeabout35 percent of the magnitude of t h e peakpressures a t t h e step. The f r e -quency of th ese oa ds depends, however, on th e pr ob ab il i ty of th i s lo c a -t i o n be ing we tted .

The p rob ab i l i ty o f we t t ing d i f fe ren t kee l l eng ths of t h e XPBS-1 sea-plane during landings i n smooth water and i n 2- - foot waves w a s giveni n f i g u r e 6. Since no a dd i t io na l da t a were av a i l ab le fo r he h igh e r waveheights , hreeaddi t iona lcurves were es t im ated fo r 5 - , LO-, and 20-footwaves and ar e shown as dashedcurves in f i g u r e 6. These l a s t threecurvesare con sid ere d to be on ly ver y rough est imates based on th e judgment ofengineers who haveconducted f l ight t e s t s of seaplanes.

12

The fol lowing procedure was used to es t im at e th e d i s t r i bu t io n ofl o c a l p r e s s u r e s a t a pointforward of t h e s t e p , say a t 25 percen t o f heke el en gt h. The d is tr ib u ti o n s of maximum pr es su re f o r di f fe ren t wavehe igh t s ( f i g . 13) weremodifiedby the va lue obta ined from f i gu re 15 t oaccount f or hedec rease npres surefo rward of the s te p . The p ro bab i l i tyva lue for each curve as obta ined in the p reced ing s tep was then modif iedby the appropr ia te va lue f romt h e c u rv e s i n f i g u re 6 t o r e p r e s e n t t h ed i s t r i b u t i o n a t h e p o i n t u nd erconsiderat ion. The res ult ingcurves werethe n mu lt i pl i ed by th e number of impacts expected i n each wave he igh tand s m e d t o o b t a i n h e o t a l d i s t r i b u t i o n . The r e s u l t s are shown i nf i g u r e 16. The distribution of maximum pressures a t t h es t e pfo ro p e r a -t i o n A a t 70 knots and 20 angle of dead r i s e i s inc luded i n f igure 16for comparison.Es t imat ion of Tota l Pressures or Forces

The t o t a l p r e s s u r e o r f o r c e on t h e h u l l i s t h e p ro d u c t of the ave ragepress ure and the wet t ed area. The d a t a i n f i g u re 5 i n d i c a t e d t h a t t h eaverage pressures f e l l roughly in to three groups depending upon th e ex te nto f hewet ted area. Averagecurves fo r the p re s su res for wetted areasof 0 t o 13 percen t , 13 t o 40 per cen t, and over 40 percent of he forebody


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16wereg iv en i n f i g u r e 5 . These d a t a are fo r op er a t io ns in smooth waterand up t o 2a - fo ot waves f o r a seaplane having approximately 20 angleofdead r i se and anaverage andingspeedof 66 knots. For g r e a t e r waveheights , it was assumed, as i n he c a s e of t hea c c e l e r a t i on , ha t hep r e ss u r es would i nc r e a s e i n p r op o r t i on t o t he s qua r e of t h e r e l a t i v eveloci ty. From a knowledge of theaverage wave len gt hs , he d i s t a nc et raveled through these wave len gths , and th e pr ob ab i l i ty of wet t ing givenareas o r keel lengt hs from f ig ur e 6, a curve may be derived by fol lowingthe p rocedures no ted in t he p re v io us sec t ion t o g i v e t h e t o t a l p r e s s u r eon the hu l l . The r e su l t s f or fouropera t ions are g i ve n i n f igure 1.7.

2

DISCUSSION

Limita t onsThe data ava i l ab l e fo r t he p resen t s tudy were ob ta ined from t e s t si n which th e models or seaplanes reduced speed during anding by a ct i onof the drag force s . The r a t e of de cel era t ion for he model wi th a landingspeed of 120 knots w a s approximately 1.25 t imes he r a t e o f dece l e ra t ionf o r th e model with a 70-knot landingspee d. The hi gh er r a t e of deceler -at io n would presumab ly reduce he ntensi ty of t h e l oads f o r t h e l a t e rimpacts. Some fu rt h er m o d if ic at io n might be needed when th e presen t da t aare app l ied to sea pla nes which decelera tequickly, such as those wi thr e ve r s i b l ep r ope l l e r s . It appears, a t t h ep r e s e n t time, t h a t any modi-f i c a t i o n t o t he p r e s e n t d a t a would a t l eas t con sis t of red uci ng the num-

be r o f a cce l e ra t ion s to acco unt fo r t he r educed andingdistance.In r egar d t o t he p r e s s u r e d a t a , t he r e i s t h e p o s s i b i l i t y t h a t t h eba si c di st r ib ut io ns of maximum pre ss ur es (f i g. 4 ) and t he va r i a t i on o fthe maximum pressure as it moves forward (fig. 15) may notbe as w e l ldefined as t h e d i s t r ib u t io ns of acce l e ra t ions . These p ress uredata wereobtained on seaplanes or t e s t modelswhere it was ass ure d tha t a s t e planding w a s made. It i s po ssib le, however, th a t some impacts fo r ou t i neop er a t i on s , es pe cia l ly in th e la rg er wave heights , may occur bow f i r s tor w i t h he ke e l pa r a l l e l o he wave s l ope . The e f f e c t of i nd ve r t e n timpacts o f t he se t ypes on t h e d i s t r i b u t i o n o f t h e maximum pressure a tt he s t e p o r a t a point forward of he s tep i s not known a t t h i s t i m e .

Comparison of D is tr ib ut io ns of Normal Ac ce le ra tio nsAn in sp ect io n o f t he d i s t r i b u t io ns of normal acce l e ra t ion g iven inf i gu r e 1 2 f o r some of the op era t io ns l i s ted in t ab l e II i n d i c a t e s e v e r a lin teres t ing and probablyunexpe cted esul ts . The cum es epre sent in gthe four opera t ions wi th anding speeds of 70 h o t s and 20 angle of


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dea d r i s e a r e ve r y s imilar al though he operat ions varied from 0 . 0 1 per -cent of t he la nd in gs in th e open ocean t o 50 percent of the andin gs nthe open ocean.For he andings in h e openocean, th e ar ge waveheights ha t might be encountered (see f ig . 9 ) would be expected to p ro -duce rathersevere oads .Severe l oads a renot nd ica t ed i n f i gu r e 12 ,however, f o r two re as on s.F i r s t , it was previously assumed that,be c a us eof the l ong wave len gt hs as so ci ate d wi th he hi gh waves, land ings wouldg e n e r a l l y b e pa ra l le l o he wave cres t .Th i sassumpt ion ends o e l i m -in a t e from the pre sen t an aly s is the inf req uen t la r ge waves whichmightbeexpected in th e openocean. A s hasbeenpreviouslyn ot ed i n f i g u r e 10,th e ef fe c t of omi t t ing hese high waves i s t o r e d u c e t h e r a t e a t whicht h e e l a t i v ev e l o c i t y VR in cr ea se s or waves above 1.5 t o 20 f e e t .S i n c et h e a c c e l e r a t i o n s a r e s c a l e d i n p r o p o r t i o n t o t h e s q u a r e of t h e r e l a t i v ev e l o c i t i e s , t h e l oads would incre ase s low ly for wave hei gh ts gre a te r tha n20 feet . Second, 25 t o 50 percen t o f t h e and in gs o r hese ourope r a -t i on s were assumed t o occur in h e ee si d e o f s l a n d s. Wave he igh ts upt o 15 o r 20 f e e t may occur in th es e se a co nd i t i on s and would producemostof th e arg e l oads exper ienced neachoperat ion . On the bas i s of theser e s u l t s i n f i g u r e 12, i t would appear th at op er at i on s n va rio us combina-t io n s of seaway co nd iti on s would haveonly a l imi t e d e f f ec t on th e l oadh i s t o r i e s o f s imi la r seap lane ypes .

The curv es for ope ra t ion A wi th a landing speed of 120 knots( f i g . 1 2 ) i nd i c a t e a nappreciable ncrease n hemagni tudeof he l oadsa t a givenfrequency as compared wi th op er ati on A wi th a landing speedof 70 knots.Forexample, 100 acc ele rat i on s of4.2g or greater would beexperienced for op era t io n A (70kno ts) , whereas 100 acc ele ra t ion s of 7.7go rgr ea te r would beexper i enced oropera t ion A (120 knots) .This ncreasein th e magnitudeof the l oads by a f a c t o r of 1.8 i nd i c a t e s t h a t t he s e a -plane andingspeed has a s i g n i f i c a n t e f f e c t on t h e l oad h i s t o r i e s .

A comparisonof the oad his tory for he ant i submar ine -warfare sea-p l ane w i t h t he o t he r l oad h i s t o r i e s i n f i g u r e 12 shows the combined effectof thereduced andingspeed and the f requ ent ake-o f fst h e ASW type of op era tio n. The lower peed educes hel oads. The inc rea sed number of an di ng s n 1,000 hou rshowever, in c re as e s th e to ta l number of loa ds o suc h anseaplane i n th i s type of opera t ion might be exp ected tof a t i g u e f a i l u r e .

and lan din gs formagnitudeof t heof opera t ion,e x t e n t t h a t aexperience a

A comparisonof t he d i s t r i bu t i ons o f no r m a l a c c e l e r a t i ons f o r ope r a -t i o n s A i n f i g u r e 12 f o r 20 and 40 d e a d - r i s e a n g l e s i l l u s t r a t e s t h eef fe c t of t he change indead- r i seangl e on th e l oads. The magnitudeofthe acce l e ra t ions fo r t he seap lane wi th 40 angle of dead r i s e hasbeenreduced t o approximately 70 percen t o f t he va lues fo r t he seap lane wi th20 angle of dead r ise.


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18Comparisonof Dis t r ibu t ion s of Hul l Pressures

The d i s t r i b u t i o n s o f h u l l p r e s s u r e s i n f i g u r e s 14, 16, and 1-7 followt h e same g e n e r a l t r e n d s f o r t h e d i f f e r e n t o p e r a t i o n s as hasbeennotedf o r h e ac ce le ra t i on s . The inf luenceofboth he educedpressures or-ward of th e s t ep and th e lower pro bab i l i ty of w e t t i n g a point forward oft h e s t e p i n a given mpact i s r e f l e c ted by th e r educedpressures and f r e -quenciesof igure 16 as compared with hoseof f i gu re 14. It i s notedtha t the percent o f wet ted a rea has a l ready bee n taken in to account ind e f i n i n g h e average h u l l p r e s s u r e s n f i g u r e 17. For o the ropera t ionsi n which the seap lanes may have dif ferent forebody areas , he curves i nf i g u r e 17 would b e sh if te d upwards or downwards in p ro p or ti o n t o t h er a t i o o f the f o r ebody a r ea s .

Estimateshavebeen made of the f r equenc ie s and in t en s i t i e s o fsea-p lane no r mal a ccele ra t ions and hu l l p r e s su r e s f o r d i f f e r e n t ope r a t ion sby use of procedures i n which t h e e ff e c t of many of the param eters whichi n fl u e nc e h e s e a pl a n e r e sp o n s e w ere i n c l u d e d s t a t i s t i c a l l y i n t h e a v a i l -a b l e e s t d a t a . A lth ou gh d a t a are not available fram se rv iceopera t ionst o check the r e su l t s ob ta ined , he endenc ie s no ted n he e s t ima ted l oadh is to r ie s o rd i f f e r en ts eap laneu t i l i z a t ionsappe ar eason able . Thee f f ec t s o f nc r eased and ing and t ake - o f f speeds f o r d i f f e r en t ope r a t ionswere r e f l e c t ed in inc r ea se s in bo th the number andmagnitude o f t h e loads .The lower landingspeedforantisubmarine-warfare seaplanes ended t oreduce hemagnitudeof he maximum l oads, bu t th e more f requent andingsexpec ted f o r th i s type ' o f s e r v ic e inc r ea sed the to t a l number of loadst o s u c h an e x t e n t h a t f a t i g u e f a i lu r e s may be expected. It a l s o appearedt h a t an increased f requency of opera t ion f rom th e open ocean f or s i m i l a rtyp es of sea pla nes may have a r e l a t i v e l y small ef fe c t on th e magnitudeo f t h e l oads and pressures .Langley Aeronau tical Laboratory,Nat iona l Adv isory Committee f o r Aeronautics ,Langley Field, V a . , December 26, 1956.


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APPEND X A

SAMPLfC CALCULATIONS

The procedure and calculations f o r es t im at ing the normal acce le r-a t i on s fo r th e pa t r o l bomber f o r ope ra t ions A with a 20' de ad -r ise an gl e,a landingspeedof 70 knots, and a lengthofmissionof 11 hours i s workedout s t ep by s t ep n he fo l lowing pa ragraphs as an i l l u s t r a t i v e e x a m p l e .From table 11, 25 perce nt of the andi ngs are i n s h e l t e r e d areas, 23 per -c e n t a r e i n l e e s i d e o f is lands, and 50 pe rc en t a r e in th e open ocean.These perce ntage s and the cur ves of f ig u re 9 must be used i n combinationt o o b t a i n t h e d i s t r i b u t i o n of wave h e i g h t s f o r t h i s t y p e of opera t ionand presumably f o r a re la t ive ly ongper iodof ime . I n this example,1,000 hours w i l l be assumed.

The t o t a l d i s t r i b u t i o n of wave he i gh t s fo r th i s d i s t r ib u t i on i sobta ined n he o l lowings teps and pre sen ted n abl e 111. The proba-b i l i t y of e q u a ll in g or exceedinggiven wave hei gh ts are obt ain ed fromthe f igures fo r each sea con dit ion for he samewave heightssuch as 0,2, 4 , 6, et c . These val uesofprobab i l i ty are given i n columns (l), ( e ) ,and ( 3 ) of t ab le 111. Next, the pr ob ab i l i t ie s n each column arem u l t i -p l ied by the prop ort io n of landings neachseacondit ion,0.25,0.25,and 0.50 fo r he sh el te re d ar ea , ee s id e of is land , and th e open ocean,respe c t ive l y . These adj us t edp ro b a b i l i t i e sa r egi ve n n columns ( k ) , ( 5 ) ,and ( 6 ) of the ab l e . Adding these h ree columns y ie ld s h e o ta l d i s t r i -but ionsgiven i n column (7) ; th e d at a n columns (4) t o (7) are p l o t t e di n f i g u r e 18.

In re la t ing the behav io r of the s ea p la ne to the wave he igh t s , theinformat ion given n f igure 11 f o r t h e d i s t r i b u t i o n of a c c e l er a t i o n s f o rgiven wave heights i s used.Since it i s i m p ra c t i c a l o have a n n f i n i t enumber of curves i n th is f i g u r e f o r a l l f i n i t e wave he ights , it must beassumed tha t the curv e for 2-fo ot waves d e s c r i b e s t h e d i s t r i b u t i o n ofacc e le ra t ion s in wave he ights from 0 t o 3 f e e t , t h e 4 - fo o t c u rv e fo r3- t o 5-foot waves, th e6-footcurve o r 5- t o 7-foot waves, e t c . It i sn e c e s s ary , h e r e fo re , o c a l c u la t e h e p ro p o r t io n s of t h e d i s t r i b u t i o nof wave heights given i n f i g u r e 18 t h a t f a l l in to each of the brackets .T h i sca lcu la t ion i s presented i n t a b l e N; theprocedure i s as fol lows:The pr ob ab il i t y fo r th e upper and lower limit of each bracket i sdetermined from figure 18 and giv en i n column (1)of table N. Successivesub t rac t ion of the p robab i l i t i e s g ives the p ropor t ion o f the waves(column ( 2 ) ) in th e br ac ke ts of wave heigh ts (column ( 3 ) with an approxi-mate meanwave heightfo r he bracket (column ( 4 ) ) . These m e a n valuesof wave heightsshouldcorrespond t o t h e wave he ig hts i n figure 11. Itshould be noted ha t column (2 ) to ta ls 1. 00.


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The p r o ba b i l i t y d i s t r i b u t i o ns of a c c e l e ra t i on for t h e 2-, 4-, 6 - ,e t c . , f oo t waves are obtained from figure 11 and g iven in t a b l e V( a ) .Each o f these curves , however, rep res ent the dis t r ib ut io n of acce lera t io nsi f a l l landings were m a d e i n a given wave heig ht . These pr ob ab i l i t ie smust be modi f ied by the propor t ion of landings in each wave he igh t fort h i s o p e r a t i o n as w a s determined 5n table IV (column ( 2 ) ). These calcu-l a t i o n s are performed i n ab le V ( b ) . Summing columns (1) o (9) oft a b l e V(b) g i ves the p ro ba bi l i t y d i s t r i b u t i on (column ( 1 0 ) ) of the acce l -e r a t i o n s f o r t h e t o t a l o p e r a t i o n .

In o r d e r t o c o n v e r t t h e p r o b a b i l i t y d i s t r i b u t i o n t o a cumulativef r e que nc y d i s t r i bu t i on , ha t i s , th e number of acce lera t io ns grea ter hana given va lue , t he d i s t ance t r ave l ed on the water and t h e wave le ng thsmust beconsidered. It was previously assumed that 1, 000 f l i gh th o u r swould be cons idere d and 10, 000 f e e t would be t rav ele d on the wate r f o reach ake-off and landing. If thea ve r a ge e ng t hof l i gh t (11 hours)i s used, 91 f l i g h t s would be m a d e and 9lO,OOO f e e t would be t rave led onthewate r . Th i sd is ta nce assumed speeds above t h e "hump" speed of t h eseap lane) .T h i sd i s t ance i s subdiv ided n todis tan ce ravele d n wavehe igh t swi th ing i ve nbr ac ke ts n column (1)of t a b l e V I . Ino r de r t ode term ine he number of impacts ( i f i t i s assumed t h a t e ach wave cau sesan mpa ct), he distan ces must be divid ed by the aver age wave len gth(column ( 2 ) ) fo r h e wave heig htbracke t sus ed n he abl e. These aver-agesaredetermined ram nformationsuch as g iv en i n t a b l e I . The num-b e r of impactsby wave he ig ht s are gi ve n n column (3) . The to t a l ofthese mpa cts give s he number 7,414 expected i n 1,000 hourso f f l i g h tf o r h i s ope r a t i on .

The product of t h e t o t a l number of impacts ( t o t a l of column (3 ) i nt a b l e V I ) and th e p r ob ab i l i t i e s i n column (10 ) of ta bl e V(b) i s t h ecumulat ive f requen cy dis t r ibut ion of normal accelera t ion expected for thecondi t ionsspec i f i ed and i s g i v e n n h e l a s t column i n ab leV ( b ) .Thi sd i s t r i b u t i o n i s g iven i n f i g u r e 12 as opera t ion A f o r 1,000 f l i gh t hou r s ,landingspeedof 70 knots, and 20 angle of dead r i s e .


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NACA RM L57A15APPENDI X B

ESTI MATES OF WAVE HEI GHTS

21

Considerable nformation i s avai lable on thecond i t ions of th e s eain th e formof s t a t i s t i c s on s ig n i f i ca n t wave he igh t s which des igna te theaverageheight of theone - th i rdhi gh es t wave he ig ht s. For many purp oses,such as fa t ig ue s tud ies , more de ta i led nformat ionon wave he ig ht s i srequired .Thisappendixdescribes a method foru s i n g h ed a t a on s i g n i f i -cant wave he ig hts to app roxi mat e the prob abi l i ty d is t r ibut ion of a l l waveheights .The approachused in the fo l lowing ana lys i s can be d iv ided in tot h r e eteps: namely,(a ) Re la t ing the s ign i f i ca n t wave he igh t fo r a given sea condi t ion

t o the root-mean-squarevalueof t h e wave he igh ts(b) Determ ination of th e d is tr ib u ti o n of th e root-mean-square wavehe igh t f rom the d i s t r ib u t io n of the s ig n i f i ca n t wave heigh t s

by means of step ( a )( c ) D e r i v a t i o n o f t h e p r o b a b i l i t y d i s t r i b u t i o n of a l l wave heightsfrom th e d is tr ib u ti o n of th e root-mean-square wave heig htIn th i s pa ra grap h , the re la t ion between th e s ig n i f i ca n t wave heigh tand t h e root-mean-square wave he ig ht i s deriv ed. The s i g ni fi ca n t wavehe igh t H i s def ined as

03

H = 3la P(h)dhwhereh heightf waves

P ( h )p r o b a b i l i t y di s t r i bu t i on of wave he ig ht s or a givenseacondi t ionand a i s defi ned by theexpres s ion

$=larn( h)dh


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22 -1 NACA RM L57A15It i s clear f rom equat ions (1)and ( 2) ha t H i s theaveragevalueoftheone- thi rdhighest waves.Before any fu r the r ca l cu la t i on s can be made,it i s ne c e s s a r y t o s pe c i f y t he d i s t r i bu t i on of wave he igh t s fo r a g ivensea condi t ion P( h ) . Forpresentpurposes, it w i l l be assumed th a t P (h )i s given by

P ( h ) = 2hh22e h2-

where h2 i s t h e mean-square wave he ig ht .Thisdist r ibut ionhasbeenusedwithsuccess in o t he r nve s t i ga t i ons ( r e f . 11) t o represent wave-he i gh tda ta and has a t h e o r e t i c a l b a s i s . S p e c i f i c a l l y , i f t hes eahe i gh ti s assumed t o be a Gauss ian dis turbance wi th a narrowspectrum, it canbe shown th at th e di s t r i bu t i on of wave heights tend s toward the di s t r i bu -t iongive n by equat ion ( 3 ) . Inasmuch as t h e sea he igh t m a y genera l lybeconsidered t o have a narrowspectrum, t h i s assumptionappearsreasonable.Subst i tu t ingequat ion ( 3 ) in toequa t ions ( 2 ) and (1) uccess ive lyy ie ldsthe fo l lowing r esu l t s :

-

For the lower l i m i t of n t egra t ion of equation ( 2 ) f o r t h e s i g n i f i c a n twave height- /2

a = 1.05(h2)and

- 12H = 1.41(h2)

Equation ( 5 ) may thusbeused t o convert measured v alu es of H t o t h e i rassocia ted a lues of (2) I t i s a l s o used d i r e c t l y o dete rm ined i s t r i b u t i o n s of (z) frommeasured di s t r i bu t i on s of H, t h e i s t r i -but ion of (z) being ivenimply by th eo l lowinge la t ion :

1/21/ 2

112

f [(z)]1 . 4 1 f ( H )where f ( H ) i s t h ep r oba b i l i t yd i s t r ib u t ion of s ig n i f i ca n t wave he igh t s .


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For a gi ven sea condi t i on def i ned by a val ue of si gni f i cant wa($/2hei ght H or aval ueof r oot - mean- squarewavehei ght , t hedi st r i but i on of wave hei ght s i s gi ven by equat i on3) as

-P(h) = =eh2h2

The pr opor t i on of waves exceedi ng a gi ven hei ght f or t hi s case i s t hgi ven by 2P*(h) = e h2

--I f t he quant i t y h2 var i es f r om day t o day or l ocat i on and, t her ef or e,must al so be descr i bed by a pr obabi l i t y di st r i but i on, t he over al l pr ot i on of wave hei ght s exceedi ng a gi ven val ue i s t hen gi ven by

wher e f [(h2 1 i s t he di st r i but i on of r oot - mean- squar e wave hei ght .Thus, conver t i ng di st r i but i ons of si gni f i cant wave hei ght t o over al ldi st r i but i ons of wave hei ght consi st s of t wo st eps:- / 2

( 1) Appl i cat i on of equat i on 6) t o det er m ne t he di st r i but i onf(S)I2 f r om di st r i but i ons of s i gni f i cant wave hei ght s H

( 2 ) Appl i cat i on of r esul t ant di s t r i but i onft i on (8)I n or der t o i l l ust r at e t he appl i cat i on of t he f or egoi ng pr ocedur e,i t i s assumed t hat t he si gni f i cant wave hei ght has t he f ol l owi ngdi s t r i but i on:


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T h i s d i s t r i b u t i o n was used in r e f e r en ce 11 i n t h i s c o n n e c t i o n and wasfound t o approximate same ava il ab le da ta on s i gn if ic an t wave hei ght s .However, it may not have a gene r a lapp l ica t ion . It i s , by coincidence,the same dis tr ibution assumed ea r l i e r t o a pp ly t o d i s t r i b u t i o n s of wavehe igh t P ( h ) f o r a givenseacondit ion. The d at a of reference 11, f o rexample, al so gi ve a mean-square value of wave height- 2 of 60 f o rda ta o r he open s ea .Subs t i tu t ing a lue s o f H, H2, and f(H) erive dfrom equations ( 5 ) and ( 6 ) in toequa t ion (9 ) y i e l d s h e f o l l o w i n g d i s t r i -b u t i o n o r (?)12 where the im ple rnota t ion of y i s s u b s t i t u t e df o r

-

Subs t i tu t ing equa t ion ( 10 ) in toequa t ion ( 8 ) y i e l d s t h e f i n a l r e s u l t f o rt h e o v e r a l l d i s t r i b u t i o n of p ea ksexceedinggivenvaluesof h

where it may i n t u r n be shown from equation ( 5 ) t h a t

Eva lua t ions of the n te gra ls def ine d by equa t ions ( 8 ) md (11)havebeenperformed md form the bas is f o r t h e d e r i v e d d a t a on d i s t r i b u t i o n s ofwave he ig ht in f ig ur e 9.


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NACA RM L57A15 -REFERENCES 251. Edge, Philip M . , Jr.: Hydrodynamic Impact Loads i n Smooth Water f o r

a Prism atic Flo at Having an^ Angle & D e a d Rise of 40'. NACA TN 1775,1949

3. Mayo, Wilbur L. : Analysis and Modif icat ionof Theory f o r ImpactofSeaplanes on Water. NACA Rep. 810, 1943. (Supersedes NACA TN 1008.4 . Kapryan, Walter J . , and Wein stein, rving:Effec to f nc re a se i nAngle of Dead Rise on th e Hydrodynamic Q u a li t ie s of a Seaplane Con-fig ur at io n nc or po ra ti ng High Wing Loading. NACA RM ~ 5 6 ~ 2 1 ,956.5 . Whitaker,Walter E., Jr., and Bryce, P a u l W . , Jr.: E f f e c t o fanIn cr ea se in Angle of Dead Rise on the Hydrodynamic Character is t icsof a High-Length-Beam-Ratio Hull. NACA TN 2297, 1951.6. Parkinson, J ohn B . : NACA Model Invest igat ions ofSeapla nes i n Waves.

NACA TN 3419, 1953.7. Carter , Arthur W . : E ff e c t of Hu ll Length-Beam Rat io on th e Hydro-dynamic Character i s t ics ofFlyingBoats i n Waves. NACA TN 1782,19498. Bigelow, Henry B . , and Eamondson, W. T . : WindWaves a t SeaBreakersand Surf. H. 0. Pub. NO. 602, U. S. Navy mdrographicOf f i ce , 1947.(Repr inted 1953. )9. Burt, W V., Anderson, E . R . , e t a l . : A S t a t i s t i c a l Studyof WaveCondit ions a t FourShel tered Areas. S.I.O. Wave Rep. No. 69(Contract No.NObs 2490),Scr ipp s ns t . ofOceanography,Univ. ofCal i fo rn i a ,Oc t . 1947.

10. Brauer, H.: Measurement andObse rvation of t h e Seaway a t the Light sh ipFehmarnbel t. Univ. of Michigan T ra n sl at io n or B u r . Aero.) , B u r .Aero. , N a v y Dept . CGD-633 , 1946.

11. Mathewson, Alice W.: A p p l i c a t i o no fS t a t i s ti c s o h eP r e s e n t a t i o nof Wave and Ship-Motion Data. Rep. 813, David W. Taylor Model Basin,Navy Dept . Feb . 1955.12. Smiley,Robert F.: A Study of Water PressureDis t r ibu t ionsDur ingLandingsWith Spec ia l Refe re nce to a Prismatic Model Having a HeavyBeam Loadingand a 30' Angle of D e a d Rise. NACA TN 2111, i g70.


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26

TABLE I . - HEIGHT, LENGTH, AND PROPAGATION VELOCITY OF WAVES( a ) Wave le ng th , A, f t

h/A

1/20 20

1/308000080 200 1200/40 1, 200oo0000/ 50

800 600000040000

5001/60

Values of h of -1 400007

I

( b ) Wave propagationve loc i ty , c , knotsI Values of h of -

h/A 1 101/20 19. 05. 93. 40. 4. 91/ 30

13. 4/10020. 82. 0/80 27. 43. 28. 00. 4/60

29.8/30 26. 92.49.04. 7. 5/ 4023. 2

2026. 932. 838. 0


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Aim lanePa tr ol bomber(Operation A )

Patrol bomber(Operation B )

Supersonic bomber(Operation C )

Supersonic bomber(Operation D )

Antisubmarine warfare(Operation E )

Speed,knots70 and 1M

70 and 120

70 and120

70 and 120

$0 and 80

TA B U 11.- ASSUMED OPERATIONSAngle of

lead r i se , deg20and 40

20 and 40

20 and 40

20and 40

x) and 40

Length ofl i ssion, hr11

11

9

9

5

Sea condit ion

25 percent, she l t e red area25 percent, l e e s i d e of i s l and50 percent , open ocean65 percent , she l t e red area25 percen t, l e e s i d e of i s l and10 percent , open ocean50 percent , she l t e red a rea49 percent , l e e s i d e of i s l and1per cen t, open ocean50 percent ,she l t e red area49.99 percent , ee s ide of i s l and

. 01percent, open ocean10 percent ,she l t e redarea90 per cen t, open ocean


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TABU3 111.- COMPUTATIONF D STRI BUTIONOF WAVE HEI GHTS

IWavele ight ,

f t

0246a

10121416182022242628303234363840

Pr o b a b i l i t yShel tereda rea

(1)1. 00

.082

.0076

.0008

.000095

.000012. 000018

.0000004

Lee s i de3f i s l and( 2 )

1.00.24,067.02.0066.0022.00078.00026. 001.00004.000015.000006.0000023. 000001

Openocean

( 3 )1.00.61-351.9. O

.056033.ox)

.013

.0086* 0057-0039.0026.0018.0012. 009.00063.00045.00032.00023.00016

T

0.25.0205. 019.000003,0002.000024.00000045. 0000001

1.25 x ( 2 )(5 )

~ ~~~ ~~

3.25.06.017.005.00165

.000065

.moo25. 00001

.0000037

.00000057

.00055

.000195

.0000015

.00000025

~ ~ ~~

0.50* 3050 175.095* 05,028. 165. 01.0065,0043.a1285.00195.0013. 009. a 0 6.00&5.000225.00016.000115.00008

.0003 15

L .000.386. 194. OO.052.0286.0167. 01.0065.0043.0028500195.0013. 009

.0006. a045

.000225

.00016.000115

.00008

.000315


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Wavehe igh t ,f t

03579

1217-52535

TABLE I V. - PROPORTIONOF WAVES OF G I W N E I G H T SP r o b a b i l i t y

( 1)1. 00

- 275- 135* 07* 037.017- 0055.00107. 00018

Frequency( 2 )0.725

.14

.065* 033.020. o n 5.00443.00089. 00 18

Wave he igh t ,f t(3 )

Mean wavehe igh t , f t(4

2468

101-5203040


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w0TABLE V. - COMPUTATION OF DISTRDLJTION OF ACCELERATIONS FOR AN ASSUMED OPERATION(a) Probab i l i ty of exceeding given accelerat ion by wave height with 100 percentoperation assumed f o r each wave height

(b) Proba bi l i ty of exceeding given accelerat ion by wave height for percentageof assumed oper atio n n eac h wave height

I I Wave height , f t 11g units 2n, 4 10

(1) x 0.725 (5) x 0.0204 ) x 0.0333) x 0.0652) x 0.140 0.020.033.065.14.7251

.coo7800105600143a1182co28286. 5

. 0400059401001 .00188OO270600403005601305 .O&050025

.014802376 .0082O 2%02275. a 5 5* 042.091.174.4205

7891011

.m0%6 .coo3000396000468.COO143 . 00010800132.0000396 .000038

0.0115.00874.0 0 9 6.a2668, 00138.coo621.coo276.0001104.000&37.0000161

.X213

.000647.000323.coo151.COO0665.0000284

.712 x 10-3

.0828

.0196

.00160

0.00018. I48 X 10.0972.0594.0353.0198.0106.a3522.00252. 1 1 5.a0522.030216

1.000000.6086.2672.ogd.0295.00896.000585.00219.000161.0000326.000000216.00000655


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NACA RM L57A15 31

T A B U VI . - COMPUTATI ONOF NUMBER OF I MPACTS FOR AN ASSUMED OPEXUTION

rave height, f t

0 t o 33 t o 55 t o 77 t o 9

g t o 12.512.5 t o 17.517.5 t o 2525 t o 3535 t o -

Tota l s

Cota l d i s t an ce t rave led Xr o b a b i l i t y of wave height( 1)

660, 00127, 0059,10330, ooo18,10010, 004, 00

800100

910,000

iverage wavelength , f t( 2 )105180240320400480550750

1,000"-"

b n b e r of waveso r impacts( 3 )6,290

70624894452281

7,414


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= I 2 n d i m p a c tT i m e

Figure 1.-Tracing of time his tor y of normal acce lera tion for land ing of model in 4-foot waves.


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NACA RM L57Al5

(a ) Wave he igh t .

33

I

( b ) Accelera t ion.

( c) Accelera t ion.Figure 2.- Three basicelements f o r e s t i m a t i ng t he load f o r a seaplane .

"


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34 NACA RM L57AI-5

Landingspeed,knots

0 2 4 6Normal acceleration, n , g un i ts

Figure 3 . - Pro ba bi l i ty of exceeding given normal accelera tions f o r t h r e ed i f f e ren t and ingspeeds . Da ta from models A, By and C. )


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"NACA RM L57Al5 35

M a x i m u m p r e s s u r e , I b / s q in .Figure 4. - Pr ob ab i l i t y of exceeding given m&imm' p re s s u re s n e a r ' s tepof fu l l -sca le seaplane anding i n approximately2-foot-waves.


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36 NACA RM ~ 5 7 ~ 1 5

ni I \G r e a t e r than 4 0I 18 12 16 2 0 24 28A v e r a g e p r e s s u r e , I b /s q in.Figure 5.- P r o b a b i l i t y of exceeding given average pressure on f u l l - s c a l eseap lane for di f fe rent va lu es of wet ted =ea .


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NACA RM L57Al5

1.0

IO "

IO"c--.-00

0n

c

I

37

I 30

.\

\\\

\

\ \A-\

L e n g t h o f k e e l ,p e r c e n tFigure 6 .- Pr ob abi l i ty of exceeding given wet ted kee l lengths on fu l l -sca le seaplane for di ff er en t wave he ights .


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.

-.

-

-

-0 I 2 3 4 5 6 7 8 EI?Sin k in g speed , f t / s e c u2

Fi g m e 7.- Varia t ion ofnormal acceleration with sinking speed a t impact for fu l l - sca l e seapl ane . u

w03

I


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NACA RM L57AI-5 39

I o

Io- '

to-*src.--.-nnQ

0

2IO-^

IO-

I IIII

I

Iv e r a g e u r v e s

3S i g n i f i c a n t w a v e h e i g h t , H, tFigure 8.- D i s t r i b u t i o n s of s ig n i f i ca n t wave he ig h t s fo r s eve r a l areas.


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40 NACA RM L57Al5

Figure 9. - Average di s t r i bu ti on s of wave heigh ts .


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40 6 0 80 100 I20 I40 I60 I80 200R e l a t i v e v e l o c i t y , k n o t sFigure 10.- Rela t ive ve loc i ty of seaplane and wave p rop aga tio n vel oci ty f o r four landing speeds. fi


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-

-

-

-

-

-

-

-! I I I I I2 4 6 8 IO 12 14Normal accelerat ion, n, g un i t s

15 2 0 3

NACA RM L57Al5

\40


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NACA RM L57AI-5 43

Figure 12.- Frequency of exceeding given accelerat ion in 1,000 f l i g h thours f o r s even ope ra t ions .


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44 NACA RM L57Al5

1.08

6

4

2

IO "8

6i1

90 120 I50 180 210Maximum p re ssu re , ib/sq i n .Figure 1 3 . - D i s t r i b u t i o n o f maxi mum pressures f o r l andings i n constantwave he igh t s .1


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NACA RM L57Al5

\\\t

45

Operations, table I I2 0 d e a d r i s e70 knotspenceon,A 5 0B I O

ID 0.01. -0 knots- 90 r-

Maximum p r e s s u r e , I b / sq i n .Figure 14 . - Frequency of exceeding given maxi mum pressures a t s t e p in1,000 f l i g h t h ours f o r f i v e o p e r a t i o n s .


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1.5

1.0

- 5

0

Figure 15.- Ratio of maximumK e e l

pressu re

IO 2 0l e n g t ha h e a d o f s tep ,p e r ce n t 3 0

t o maximum p re ss ur e a t s t e p as wetted area moves forward. *52EIU4

ul


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48 NACA RM L57A15

IP e r c e n tw e t t e da r e a X av . p r e s s u r e , Ib /sq in .Figure 17.- P r o b a b i l i t y of exceeding given t o t a l pr e s s u r e s i n 1,000 f l i g h thours.


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NACA RM L37A-I-5 -' C 49

Figure 18.- Total distribution f wave heights with contributing distri-butions for operation .

N.4CA - Langley Field, Va

~~ - -


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NACA RM L57A15 Statistical Approach to the Estimation of Loads and Pressures on Seaplane Hulls for...

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Transcript of NACA RM L57A15 Statistical Approach to the Estimation of Loads and Pressures on Seaplane Hulls for...