naca tm 1007 new method of extrapolation of the resistance of a model planing boat to full size

7/27/2019 NACA TM 1007 New Method of Extrapolation of the Resistance of a Model Planing Boat to Full Size

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/--~&..._-..--.., ----Q& -$.lzL//+_._-la -,.~.,, ..-. . . .,. +#t_:...,?.ADVISORY COliMITTEE FOR AERONAUTICSATIONAL

-No. 1007 :

. ..,mw TH3 R3SISTAtiCE:WTHOD O* EXTRAPOLATION OFTOMOD13L FLANING BOAT FULL SIZN

3y %. Sottorf.,,,,.i,.,,,Luftfahrtforschung ,Vol. Z6, No. 8, August 20, 1939 ,. ,,.Verlag v.on R. Oldpnbourg, IJiinchenund Berlin

..

.,.

,.WashingtonMarch 1942

,.,


2/22

. e.3 117601331 4142 ..--._.......... .i

.- ...

,.

NATIONAL ADVl~ORY-..OOiqMl~Y~%:@,R~ERONAUTICSCS........

T~CHN ICAL MEMORANDUM :NO.,1007--.---,....,....,..:.:..- .. ..;....NEW METHOD OF EXTRAPOLATION>,.....or A ItiODELpLANING ~-OAT

OF THE RESISTANCE,. :.!!iO FUiL SIZ3x,,,.,...,,.., Ijy W, Sottorf . ,,,....

SUMMARY .,

The previously employed method of extrapolating thetotal resistance to full size with ~3 (model scale) andthereby. foregoing a. separate appraisal of,the $rictionalresistance, was permissible for l+rge models and floa~sof normal size. But faced by the ever increasing sizeof aircraft afeexa.rninatio,nof the problem of extrapolat-ion to full size is called for. A metho~ is describedby means ofwhich, on the basis of an analysis Of testson planing surfaces, the variation of the wetted surfaceover the take-off range is analytically obtained. Thefriction coefficients are read from Prandtlls curve forturbulent boundary layer with laminar approach. Withthese two values a correction for friction is obtainable.

Worked-out examples indicate that resistance variat-ions analytically determined and those derived frommeasurements give a practica.1 approxirnatiOnO A formerscale series with the corrections applled to three re-sistance curv-es shows good agreement. The steyfrorn the10-ton to the 100-ton flyipg boat. with correction appliedis found to be not criti~al for extrapolation from a modelof customary size at the present timei, ..

., .. :NOTATION... ..,.,.. ,

Iiodel; subscript M ...

Full size: subscript H : - ~x~eues Verfahren der ~bertra.gung deq Modellwiderstandeseines Gleitfahrzeu~es au-f di,e..:a~p,tau.sf,iihru,ng.-lt:uftfahrt-forschung, vol. 16, no. 8, Aug. 20, 1939, pp, 412-18.,

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2

W resistance (kg) ,..

WN normal resis.tanc& (kg)WR frictional resistance (kg)T tangential force (kg)A hydrodynamic total lift = loading (kg)G gross weight (kg, ton)M moment (mkg)~

FDFr

3?r*

Rv

~11

2m

b~st

bnat

~Y

wetted area (m2)pressure area with Vee planing surface (m2),Froude number, referred to body lengthFroude number, referred to a length related to

the loadingReynolds numberspeed (m/s)speed component (m/s)length of,wetted area (m)average length of pressure area with Vee planing

surface (m)beam of pla?ing surface, (m)beam of float at step (m)natural beam of pressure area with Vee planing

surface (m)dynamic pressure (kg./m2)speeific weight (kg/ins)

t% acceleration of gravity (m/sa).

& .


4/22

NACA Technical Memorandum No&. 1007 3

k~ e~uivalentg-r-ii-nize (cm)Cf

fa

Pva

7s

friction coefficient from friction .measurementsfriction coefficient of the planing surfacederived lift. coefficient of the planing surfaceload coefficientdensity (kgsa/m4)kinematic viscosity (m2/s)angle of attack of the tangent to the horizontaldrawn at the point of the step in the centerline section (trim)angle of dead rise = slope of bottom plating atstep to the horizontal (concave Vee type dis-regarded)model scale

INTRODUCTION-1 ., ,,,., ~The ,&xtrapolatian of the resj.sta.nce~of a craft mov-

ing on the surface of the water, hence also of a float ,orhull f%w.m.mod.el.to -full-.siz-ejmay be done according tOFroude!s m~del method by the following formula

total resistanceof full size of model

frictional resistanceof model of full size.

.. . . .- ._. ._


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4 NACA. TechnicalMem.orandurn i?o.1.OC?

when temperature and density differences between tankwater and sea water tire disregarded.,..,Theknown factors are: the recorded model resi&t-

ance wM, the scale A, and the density p of thewater.

Uncertain to define so far. were:1. The coefficient of friction,,of the, model cfM>

according to figure 1, which fluctuates co~siderably inthe low range of Reynolds number depending upon whe,therthe boundary layer is fully tur%ulent or has laminar ap-proach. On the other hand-, the surface of the. mode.l maYbe considered as being technically smooth.,, ,,..

2. The- coefficient. of friction .fo.rf!al,l,~ze cfH which is affected by roughness, es caused by joints,rivets, or coats. .of paint, whence .Wa.nu,facturing qualityand maintenance condition also assume ,considerable im-portance (reference 1).

3. The desired speed affected by the pressure dis-tribution along the planing bottom locally, and the aver-age of which in consequence varies from the forward speedof the float gear v (reference 6).

Unknown factors remain:... .,. .,. The. gize of wetted area. l?,. which changes withspeed and trim and whose prediction by test would intro-duce abnormal complications.

The last reason in particular and the fluctuationsin the low range of Reynolds number cited under (1) haveled toward the selection of such.a great model scalethat the results vary from the true values merely withinthe limits of accuracy customarj in such model tests, orwithin about 5 percent even with disregarded scale effect,that is, by assuming

(2)The converte~ rnodelvalua ii higher than that for fullsize, hence includes a margin (reference 2)..,

. . ,...


6/22

NAGA Technic iil.Memorand,umo. 1007 5,, .>... _,, ,.(h the more iec-~ntlylarifiediant fl!Yi%gOat$~hOW-

ever, (reference 3,)..,theRse of corresyondi,ngly large mod-els would involve un,wan.te,dexpense and:difficulties i,n.testing, hence the conversion from model of normal size(b St = 0.300 m) (11.8 in..) needs to be reexamined on thebasis of improved knowledge. The study is restricted tosteady hydrodynamic processes.. ..,,,... . ..

NEW METHOD : . . ,.,

Figure 2 illustrates inthe usual manner the variat-ion of load, resistance, and trim of a 10-to,n flyingboat as Qbtained according, to the specific method or, onthe lasis of the data from the general toying method (ref-erence. 4), and converted to, full size by the use of

For the region of pure planing an investigation. of afamily of flat rectangular planing surfaces under geomet-rically similar test conditions has given similitude ofpressure areas and moments. (reference 5.), that is, alsosimilar pQsi.tion,,o:f,he resultant water ,force, provideda lower limit of:beam, of.model, loca,t,edat about bst = 0,150 to 0,200 meter depending on loading, is not ex-ceeded. Thus the, application of th.e$oregoing momentconversion affords the same trimforfull size and model

.,. .,.%. x .=, UN ...,-Now, visu,,aiize the ;~o,rebody~ottomofthe floa.tre-placed by a lon,gitudina~ly straight bof-tornof con~tant?,

The subsequent arguments are based ,on.this assumption,alth~ugh the investigat%on of float famil,$ei disclosed .also a slight change in the trim with the shale.,. .


7/22

6 NACA .~echni,c.al Mem.oran.dum.~o. 1.007,.

beam b~~ and c.o.nstantangle of .d.ea,drise $ c.orre.spond.ing to the main. step. ~~Then then ormal resistance .of thisplaning surface in region III (fig. 2)

w~ ,= A tan a . (3),.is approximately equal to the normal resistance of thefloat, if the total resistance is divided in normal andfrictional resistance

ii =w~+wR (4)Hence the ve,riation of the norma.lresistance \?N conver-sion of which with ~3 is justified, can he plotted infigure 2. An extension in the zone of the first hump -zone II - repre~ents merely a rough approximation for N because of the profound effect of the forebody curvatureand of the stern. The w~ curve has, howsever, as isseen, the same chara.uter as the converted t?H curve.The formation of the hump is therefore decisively deter-mined by the variation of the trim m, At the start ofzone II NN and ~~H are practically Coincident, hencethe proportion of >{R cannot be considerable (whereby itshould he remembered that WN merely represents an ap-proximation). .,.,

The frictional resistance Of the substitute bottom - .is computed with the helpof the test data of flat andVee planing surfaces, for which the frictional coeffi-,cients Cf are known from (reference 5):. .,

w W A tan a = ~.~ T . cfl F ~yii Cos cc,.

(5)

But then it is S.lSO necessary to insert into the formulaas area the wetted area of the float-equivalent planingsurface, that is, t,he area which has the identically de-rived lift coefficient as the float: ,x The approximation is the c.l,os,erhe @ore nearly thefloat bottom ahwead of the step re~embles a longitudinallystraight ,fli.t,ee planing surfec,e, a..sexemplified by. theDVL:sta:nda.rdfloat,,. .Y At small m, if N !Z A. .


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NACA .Te clin i.tml;. .,Memoandum .No;Q07 7-. ..,. ,.,. . . . .,, .,. c,Jj ,~:... .,- -, ......&CL ab~q (6)

This. lift coefficient depends only on the aspect. ratioZ/b and.on the Froude number., .,*=*

The flat planing .surface equivalent to the float, in con-sequence , can be predicted from figure 3.X In the eventthat the pressure areais Vee shaped the procedure is asfollows: The size ofthe pressure area follows similarlyto the method for the flat surface; then, with allowancefor the angle of dead rise $ the calculation proceedsaccording to

CB tm t~. andCos 79a b b r* = J-

The wetted area which in this instance is substan-tially different from the pressure a,rea is estimated fromreference 5 at (fig. 5);Case. 1) loaded width:,b, .,,if tan d


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a IJA.CATechnical. lTemorandtiin~?0.-~07tan t9 lmCase 3} loaded widthi-bnat , if.........,.... . ... 4 tan ccT

,,.,and, 2ita.n Y.=3:_b. z 10.nat

Then the insertion of > == tan T94 tan a givesnat

and / .. -;4tnat = CG C09 d~nat q a. \.,.. 11 RI= b2b nat nat

henceL (b + bnat)F=,- . .2 Cos d.-

,. . .

Case 4) loaded width: bnat if

Then:

.

(8)

tan 8 tm4 tan a %-

and tan Y 21 c io.= b --bnat

~=+~.

,.,.,, .

(9)


10/22

NACA Technical MemoY?aM~@i. NO. 2@7.. 9......,.Ilicases1 and2--the-water emerging ~~n the -forward,.,.-....2contour 0$ the we.tt.edarea and pass,ing as .plVmes.along

the surface covers almost {he whole width of...the.surface,so that 1 must he inserted as length in th,e determina-tion of F and R. In case 3 t~e limit of spray wettingi$approximatel,y indicated by the dashed line, averaged :by th,e solid line. In case 4 an increase in planing sur-face width puts the edge portions clear of the water,The limit value is tan Y = 10.Since the frictional resistance for the whole take-off run is to be determined, the variation of the wettedarea F over the whole speed range i% necessary. Forseveral points v in zones II and III the wetted area is

computed as before. In addition, the following threevalues of wetted area (fig, 2) can be plotted for v = O.FI = forebody bottom = greatest possible pressurearea is the ,start of the first curve of wetted area forthe equivalent planing surface. This area shows only theslight falling off up to the first hump;- while beyondthis speed the area, despite the rising dynamic pre%sure,remains almost constant, because of the decreasing angleof attack, until at aro~nd 20 meters per second the angleof attack, kept constant by elevator, has reached m = 5when the area diminishes rapidly.Between Fa = FI + afterbody wetted area and the endpoint of zone II the second curve denotes the addedwetted afterbody bottom surface, and the third curve in-dicates the wetted side area, the wetting of which ceasesat around 12 meters per second according to flow observa-tions; F3 represents the total wetted area in rest posi-

tion.The second hump speed, which is attributable to addedfriction at the afterbody bottom surface, occurs when, athigh dynamic pressure and low residuary load, the width ofthe wedge-shaped pressure area originating from the Veebottom falls short of the width of the float at the step /.(.bnat< b.st). The propor,t,~on of the frictional resistance

produced by the pressure area to the total frictional re-sistance $s small shortly before the get-away. This elim-inates $n general the task of effecting the more cumber-some division of the frictional resistance. portions in

$. ,


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10 NACA TeChn3cal Memorandum I?.oA1007

the nat < bSt zone. Since in this zone the wetting ofthe afterbody bottom-surface is the cause of the hi%hfrictional resistance, we introduce one-thirdof the,afterbody bottom surface; and for the determination of theReynolds number & we put one-third~f the afterbody length from main ~tep to second step,wiih cOrresP~;~~ng:,hange from rein and extending to .vtake-off. measure is to be considered as an expedient, for the wet-ting of the after%ody area subject to:the spray water ef-fect is physically:unlike the wetting.of a pressure area. Unknown quantities remain the actual surface- dimensions,the densityof wetting, and the rate of spray -impact.However, -since only the difference of the friction coef-ficientsof model;andfull size is involved in the con-version process, the error is presumably allowable..,. i .

In the range of the first hump the total residuaryresistance exceeding the analytically,.defined frictionalresistance is interpretedas normal resistance, becausein this instance~ as.already stated., the forebody curva-ture and afterbodyeffect cause a discrepancy betweenanalytically defined and true normal resistance. To de-termine the frictional resistance the partial areas Fl,F ~s and F3 are therefore combined to Qbtain the inter-polated total wetted area F, whereby assuming,,

t = F COS ~ ::; .: ,%stFollowing the determination of the area to be enteredin equation (5) for the frictional resistance, the sole .lacking cf! value is read from Prandtlfs curve for tur-

bulent boundary layer with laminar approach (fig. 1).

0.455Cf = _ 17C0(lOg R)2-~ R

.

which, according to reference 5, covered all planing sur-face experiments satisfactorily.x .The following exceptional case is cited: too small amodel (bSt ~ 0.15 m) is unsuitable for exploration of the(Continued on p. 11)


12/22

NAGA !I!e.chnigalMemorandu.a::No,.1007 11~K$: WR cuive four full size. with implicit maximums andthe curve of the analytical total resistance as the sumw is obtained in this manner, the differenceWN + WRof which with respect to the WHctlf,Ve ,.o.nver.t,edaftermeasurement is due to the scale effect -.provided $tfully corresponds to the actu,al resistance..

.Eaving thus e$tablisbed the si~.ilarity of the numer-ically defined and,:the converted t~t,~~ resistance through-out the take-off range considered the correction can beapplied. ~~ ., . . .,.,

As correction for the friction..( Cf,M )-cf. H FH~ v@2

is to ,he deducted according to equat~on (1). The Reynoldsnumber for full size is according to the model lawRE = RM AW~ (11)

In figure 4 the correction. factor )(cfM - cf~ is\M Mplotted against RM.y with A as parameter.

The reduced WH curve , also shown in figure 2, isalmost coincidentwiththe theoretical W-curve in the -region of: pure planing as expected, ,,(Continued fro~ p.10) ,,.first hump because of anticipated dissi,milarityof flowcondition, although it-can be used under .certain.circum-stances in the region of pure planing and in the regionpreceding get-away. .l?hen, however, the Reynolds numbersbecome so small, as a result of the small dimensions,that they generally fall in the range ~M


13/22

i2..

NACA Te.chnic&l Memorandum Me;007

EFl?E~TOF ROUGHNESS. .

Figure 6 was taken from ref.eren.ce 7which deals withscale experiments over the whole speed range inclusive offull size. An unexpected departure is noticed in the up-per speed range, where the full-scale resistance exceedsthe converted mo.dei resistance.. The higher resistance isattributed to the effect of rivet heads and laps, althoughn.o analysis is given. .,

The increase in roughness (figure 1) for the fullsize can be defined according to Schlichting (reference 1)if the equivalent grain size ks resembling its surfacecondition iis experimentally ascertained. Since G5ttingenreports on systematic tests with plate roughness, such asoccurs on the bottom of a flaat, a r e available, the leastroughness of SchlichtingIs study and the grain size towhich the tests refer will. be checked by a rough calcula-tion.

By way of example let the surface length be 1 = 1 mand the speed- v = 30 m/s, which is a condition %eforeget-away; With v = 1.3 x 10-6 m2/s we get R = 2.3 x107 and for it

Cf = 0.00266smoothThe least roughness was observed on plates with sphericalsegments resembling f~at rivet heads of 2.6-millimeterheight. and.8-m-illimeter di-ametprspaced at 40 millimetersover the surface (,plate XIII, ks = 0.0$9 cm). The rela-tive roughness is t/ks = 3-.23x 103 and hence.,,.(Continued from p. 11) ...the boundary layer, it is justified to effect the correc-tion for friction in such a case on the basis of the tur-bulent boundary layer curve

....,. -..,,

~f = 0.455-..(log ~)2.58as confirmed by the close agreement between measurementand conversion on two similar models 0.15 and 0.3 m width(not included herein).

. .-.- .- .-. ----


14/22

NACA TeChniCalMemOrandurn Nol 1007 13. . ,.,.,. .Cf &-o,o63,-that- is-;-137-ti@rcent-=roughn es,s.,increase.rough ... .

,.The roughness produced by sand of 1,35-rnillimeteraverage grain s$ze on the varnished surface has with

ks 1 :,45x lo2a= 0.222 centimeter ,atk.s,,,

Cf = 0.0106,rough that ls,3OO-percent-roughness increase,from which the profound effect of roughness at high plan-ing speeds becomes apparent.$In a check test on,a standard nodel float of 0.3-meter beam, the results of which arereproduced in figure7, a quantitative check on the model was made, particular-ly respecting the potential resistance increase prior tolift-off due to the effect of spray water on the after-body bottom areaiThe upper half of the diagram shows under a constant50-kilogram load the planing number of the first hump

w6 = ~ plotted against the trim a for three modelconditions: smooth model, afterbody bottom roughened byc,oat of sand of 1.35-millimeter grain size, and the wholebottom roughened.

It is seen that afterbody roughness alone has prac-tically no effect, since at the first hump only the ex-treme tip of the afterbody is loaded. The effect of fore-body roughness is, on the other hand, considerable. Theresistance increase is greatest at sma~l m because ofthe greater wetted area; at CL = 9,50 as expected at thehum~, the increase amounts to 41 percent. .,The lower half of the diagram shows the conditionshortly before lift-off at a 10-kilogram load and 15.5meters per second .speed. The three afore-mentioned modelconditions are now augmented by a fourth, forebody alonesmooth, Here the increased resistance caused by after-body spray with increasing a over the condition fore-body alone, is plainly apparent,, While the increase intotal resistance due to roughness of afterbody rises by115 peroent at a = 9,5 - the greatest angle obtainablefor qarly lift-off - this percentage of roughness even ofthe forebody is o n l y 50 percent.


15/22

.

.

14 NACA Techni6al Memdra-ridurnNo* 1007

Inserting one-third of the afterbody surface and:one-third .of the afterbody length for computing the factorCf as suggested in the present report? gives.,accQrding to..Schlichting a cfrough of0*015. The same value is ob-tained from the measurement at a = 9.50 On the smoothmodel agreement between theory and test prevails ata= 7*50. In other words, the assumptions iegarding sizeand length of wetted ,afterbody bottom area are confirmedat the high trims aiined at for purposes of quick get-away.

so , even though the correction dealt. with inthepresent report yields in the zone of the second hump adeduction, full attention should be given to the factthat resistance increases attributable to roughness effectcan materially impair.the get-away power of.hi.ghly loadedseaplanes. x

RECAPITULATION O.l?CONVERSIONMETHOD

. 1.2.3.

4,.,

,.,.w~ =, ~ A=, i and a are plotted against a..,wmax II-w max i.1~ and ~min are marked.

Zone 111, condition of pureplanihg, IS res!ricted onthe basis of flow observations (in general Close upto vm,ax1, to rein). . ..,, .,.max I2 is chosen as origin ofthe ordinate, sta+~..,. ,.as the final ordinate.. . .,

5. The equivalent. pressure area FD ,and the wetted areaF of the planing surface are determined for aboutthree points in zone III, pure planing, andonepoint-at The angle of dead risernax 1. ~ .of theplaning surface hereby corresponds to the angle of,,

~P~rkinson arrivesat the same conclusion in an article(reference 9) published while the present r~port Was beingprinted, wherein, on the basisof a study on a model fittedwithrivet he~ttsi the increase due t9 roui%hness of lowerroughness density is defined acCOrdihgly - loweh (40 per-cent). ...,, .,.


16/22

NACA gechnical Memorandum No* 1007 15,.,,.,,

6.

7.

8.

. . ,.dead rise of-thefloat b-ottornat the first step withno allowance for concave Pee planing bottom at thebow. With the inclusion of the three initial pointsatv= O and. of the end point at start 1? canbe plotted with respect to v.

One-third of the afteibody bottom area is assumed asarea in zone IT in the central third of this zone,while at either side the decrease to the predeter-mined area is linear.

For the determination of the Reynolds number thelength of the equivalent wetted area

serves as length Z in zones 11 and 111, and one-third of the length of the afterbody from main stepto the second step in the central third o.f zone IVrectilinearly decreasing to the adjoining junctionpoint and to zero, respectively-The correction is applied according to equation (10)and deducted from WH,

EXAMPLES OF CONVERSIONS

TO identify the effect of increasing gross weight onthe scale effect the conversion of the example for figure .2 to 100-ton gross weight is carried out in figure 8 whereW/G is plotted nondimensionally as (l?r) 0 % = 60kilograms and GH = 10 tons in comparison. It is seen -especially in the separate plot of the friction @orrectionfor 10 and 100 tons - that the correction is subject to a.relatively small incree.se during the jump from 10 to 100-ton gross weight. . ,,,.-

One of Schmidtrs


17/22

16 I?ACA Technical Memorandum No. 1.007..,, . .. ,.friction and the trim with a slight dependence on thescale, The applied correctf~rirings ,the results ofmodel and full size in good agreement,

.!..

Translation by J. Vanier,National Advisory Committeefor Aeronautics, ..: -

.,.

REFERENCES ~~:

d1.

,2.

-3.

d 7.

Schlichting, H.: Experimental Investigation of theProblem of Surface Roughness. T.Il. No. 823, ~ACA, ,1937.Sottorf, Walter: fi~.erden Einfluss, des Modellmass-

stabes bei der, Unte.rsuchung vo,n I?lugzeugschwimmern.2, Flugtechn. Bd. 22.,Heft 24, 1932- ~~ -lob

awl

1w~1&/\ \ W8 No+ con-e. fed.- \,/ \\ i / w- t i N+kR-ret tea

,..

h0aF Side

q

F&gure 2.- Div$sion of resistance, identification of qream and correc-S t $pb f or friction on a flying boat of

G = 1000Okg, bst = ls651D0

.A ,, ------- . . . . . . . . . . . . . . . . . . . ,, . . . . . . . . . . ., .- . . . . ...-. -


19/22

.-

ma TechnicalMeieorandumo.1007_ ,,,I

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745,, +3273m..-?;, .,..

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$25-...L -. .- . .

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20/22

. NACA TeohnicalL?OLV5

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-(/00!!

Memorandum No. 1007 Ifigfl.4, 5

I

I I

.,@9

Figure 4.- mrrection factbr (cf~+-cfa) plotted against model Rqnoldsnumber & with scalQAas parameter..

v

Figure 5.- Pressure area and wetted area on vee.type planing\.

-

surface.


21/22

MACA ToohnicalMemorand~Xo. 1007. . . .. . mm- . . 1

pi~. 6.. Data from EIvW* scaletests with the Sin@pore II C

.@-+Qw-,

m+ - GH-fOUOCi7kgG - fOOOO kg

o , I I , \ t I!.2 3 5 6 / 83+Fj.gu.re 8.. Comparieonofcorrected re-eis~nce curves of a flyingboat on raising the gross weight from10 tO 100 tons.

J :-LL4

figure 7.-.~fecofof roughness on thereei8tanc6 ofa modelfloat.0,3 mbeam at hump speed and before getawq.

4f5-

;

/ ..>ANotcorrecfed[ +,>,L Af / ..>----- --

A

-1

/ ~ Correcfed- ,< ;,51

Q!O

Q05

Figure 9.- Correction of.a,resistvcecurve ascertained witi fillscale 111 and two models fromSchmldt18 scale series.

: _... ~~orrecfedfOrfrJ~iofl,/ /,L-5

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22/22

. .. .. . I-.

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IDO NOT REMOVE SLIP FROM MATERIAL

Delete your name from this slip when returning materialto the library.

NAME MS

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INASA Langley (Rev. May 1988)

IRIAD N-75

naca tm 1007 new method of extrapolation of the resistance of a model planing boat to full size

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