Analysis of experimental investigations of the planing process on the surface of water

I

i

TI CflX CAL XgMOBANDUMS

NAT±ONAL ADVISOBY 00MMITTF

?5B AROAUTICS

ANkIYSIS 01' xP

IN!1AL IN

5TI(ATtC)NS 01' T

PLANIN

PR00 SS ON TB SUR1'A0 0?

By W. Sottorf

ahrbueh 1937 der Deut.chen LuftfahrtforachUng No. 1061

Wae)4ngt on

March 1944 TRM

DOCLJMt«

FILE I r

MAR 30 1944

NACA

_LIBRARY

LMLEY MEMORIAL_AERCNAUTICL

L&5OIATORY Langley Fie1d, V

Delft University of Technology

Ship Hydromechanics iaboratory

Library

Mekelweg 2 _{26282 CD Deift}

Phone: +31 (0)15 2786873 E-mail: p.w.deheer©tudelft.nl

i.

i

n-- NAP IONAL .4DVISOT OGUXI!TBE "OR LRONAUT lOS

TEOESXQAL MEXORIJDtTM NO. 1061. .AJALYSIS o

xxpu nrvzsTIGATzoNs

6i

Ta

PBOOESS ON TE3 SUBJAC 07 WATEB By W. Sottorf

Pressure diotributio.n arid. spray measu.venints were carried, out on reotangular flat and. Vbot.,tam planing

surfaces.

Lift, resistance, a4 centerofreesujro data

are analyzed and. it le shown how these values niay be

oomp-u.ted. for the pure planing procese of a flat or V-bottom surface o' arbitrary beam, load, arid speed., the

method being illustrated. with the aid. of an example.

SUMMARY

Plat

and. Vbottom ongitudinal1y straight planirig surfaces are investigated.. Por such surfaces the total resistance nay, for a given lift, be separated. into a normal and. frictional component. The analysia of thé tests leads to representations of the lift and. centerof-pressure position aS functions of the aapeot ratio of the pressure area with the Proud.e number, which characterizes the effect of gravity, aB parameter. While the fric-tional resistance coefficient Is equal to that given by Pran&tl for theturbulet boundary layer with preaeding laminar layer. Por high 3'roud.é numbers, for which the.

contribut ion of gra.vity. to the lift is negligibly small,

there is shown to be an..agreemerit between the planing

surface. tests' and. the Lift on flat airfoils on the under aide. The deviationà from the Wagner theory for short plates at large aspect ratios are considerable thougb,

justified by- the cond.itiona neglected. in the theory.

With the aid. of a working chart a number of practi-cal examleø are computed. that provid.e the answers to several important quastíon. Por the caøe of the flat plate the width of the plate, which is always the full yidth of the planing. surface hae an effect on the

re-istance-].oad. ratio in that the latter' becomes more

favorable rith increasing width.

tAnalyao oxperimentellei' Untorsuchungon fiber den

].elt-vorgang an der 3ahrbuch 193? der

2 ' N.Ø.L T No. 1061

With regarto

the

]oád.affebt ,ot 'ac0unt of the

impairr.ient in the aepect ratio there is an impairment in the rciBtaace].oad ratio with increasing load..,

1ith regard t the, efact of the speed., however, on account of thé improvement in the aspect ratio with increasing dynamic pressure above, the first reeistene maximun, there is an improvement'in the resistanceload, ratio zith increasing speed..

The teet for he.ac.leeffect sh6w that there'is

similarity of thè preestre eurface and. presure

d.is-tributionathát"th

ffet of the.écale. 1B.given only

by thQ d.epend.ne. of ta frïctioii coef1'1cfrxt 'on the Beynol,d.s numbq'. Ouiy forvery small d.ins1ons and.

loads of the planing surfacés does onsimiIarity occur In the' flow oond.itions because of the effect of surface t ene ion.

The Impairment In the resistanceload. ratio by the effect of the V bottom is a].Bo shown. With regard. to

the effect bf the width it is found Zo.r the V bottom that at rn,11 load. or,high dynamip preesu'ean. with 'he "natural width," :vhioh is ]ese than that of the p1aing

surface, .n optimum width oc1.trs which Is to be deter-mined for each particular case.

INTRODUCTION

when, with the

eve1opment of aircraft, the

invti-gation and. d.evelopment of seaplane floats 'were added to

thé'usual problems of he towing tank, theré was a lack of theoreticl as well as expérimental underlying bases for Ovaluatin.gtheteat results. A first expöriment with

a flat planing surface was carried. out in 1912 In nland.

at the lIillia,m Yroud.e Laboratory and. a report was

pre-sented by Baker and Il1ar (ieference i), who, however, did. not continue any further work of fundamental invest

i-gatlon. In order' to create a sufficiently wide basis, teste on planlng ,s'!lrfaces ha'ebéen conducted by the author since 1928 at' th.Rambüg Sh.p Conetuction

xperienta]. Inßtitute. Starting with testa' o a 1át

rectn.ular plañiug,B'rfe ybich served. for the tu_y of the planittg pocesa ánd.' its effect o the fli{

NAOA Ti! &o. 108]. 3 could. be furnished, to the moet inportaxit restions

arie-.-Ing for the oonstructoi and research engineer: namely, the effect of the beam, loading, speed., and. V angle on the resistance and. the effect of the sca'e in applying the model test resulte to tb6 fullscale design. Thsse

uestlone nay be answered. from the resulte of planing surface tests Insofar as the pure planing condition is being considered, this oond.itiou being ciaracterised. In a float by the breaking away of the vater at the step

and. side edges of the port ion of the bottom in front of the step and. also by the breaking of the water coxzta&b

at the stern, (See reference 2.) The results vere

partially published in the following years (reference 3). Meanwhile, sirias a theoretical treatment of the actual planing process that take all conditions luto account

does not appear possible, Wagner (reference 4)concerned himself with the limiting cases of the planing process (high.. speed planingneglecting gravity, and. infinitely.

small trin angles) and- by the application of the airfoil comparison, presented an approximate experimental method. that enabled him to determine the forces and. wetted sur-face of the flat plate with small aspect ratio aleo for finite trin angles. The comparison of the first teat

re-suits of the aut'hor with the Wagner theory showed that in the range of small aspect ratios rough agreement was ob-tained while for large aspect ratios the deviation from the theory was considerable. Wagner' aecrlbed.this

d.evia-tion to the effect of gravity. _{Sambraus (reference 5)} carried. out supplementary tests at higher speeds at the Prussian Bxperimentai Institute for Ship Constitution in

order to test the Wagner theory also with neglect of -gravity for higher aspect ratios. Prom his result

Sambraus concluded. that the Wagner theory ho-ida true at

high planing speeds for all aspect ratios. _Shoemaker (reference s) likevIe. extended the range of investiga-tion by totiing a series of flat and. Vbottom planing

surfaces in the SACA tank.

-Th the takeoff of a seaplane the lowspeôd. planing stage, during which gravity exerts a considerable effect,

la of oqua,l importance with the highspeed planing _stage. The analysis, preBented. in this paper, of all the

authorts own teats as well se those of Sambraus and

Shoemaker, leads to a clear explanation of the _{effect of} gravity rind, hence to the representations of lift, re-Bistance and center of pressure, and with the aid. of this

analysis these values may be numericall' determined. for flat ririd. Vbottom planing surfaces of arbitrary beam and.

4

ACA M No. 1061

arbitrary load.iug ad speed. for the cond.ition of pure planing.

NOTATIoeT

A total lift load. (kg)

Aìyn dynamic lift (kg)

stat static lift (kg) G total weight (kg) W resiBtance (kg) normal resistance (kg) frictional resistance (kg) S :po:peller thrust (kg) Z to'ring pull (kg) N normal forces (kg) T tangential force (kg) 3 V static displacement (m ) load. roduction (kg)

Mhst mouent about the lateral axis through step (t,ail-ing edge for flat surface, after end. of keel for Vbottom surface) (mkg)

y speed. Cm/e)

mean velocity of the water along the planing

surface (rn/B)

mean vertical velocity of the mass of water

dis-placed. (in/s)

roude number referred to a f ixd. dimension of the body

Ca* =

b lift coefficient of the pianiig

eurface

derived, lift coefficiint

of the planing eurface

A. cBa ₌ A e

- -

_{load, coefficient} -.2

_Dq,

Cf, Cf1 _{friotiona], coefficient} - lih St Cmh Y b4 load, coefficient moment coefficient

p/2 v.

d.yuamio preoeure (kg/m2) p - d.enaity (kg

/in4)

'1 specif,o weight '(kg/m5)

V

kineaatic

vieooeity (ma/e)

L0.& TM NoS. 1061 5

r' =

v/h11v)n1

'rou.d.e nber tefexred. to a length correepond.ing to the load

R . vi/i, Beynolda namber

= Planíñg Number1 reeletanceload ratio

'A

Cat

?b

load. coefficient

ca lift coefficient of the airfoil

S S

e N.LcL&

:

No. 106].

P PdYXZ.3 at.at .re.Bsue,(kg/in2)

mean pressure on "pressure area (kg/rn5)

mean length of wetted surface Cm)

mean lenth of pressure area for Vbottom planiiig

surface (nc)..

distance of center of preasure from trailing

edge

of planing

surface (in)

-local elevation (in)

Y ,stted auiface, also pree sure areá for flat

plan-ing

surface (in5)

projecion of pressure arca for Vbotom planing

surface (in2)

7

wing

area

(in2)

b

beam of planing surf ace

b5t 'beam of float at step (in)

bnat

natural

width of

pressure area for Vbottom

sur-face (in)

o distance of fountain from tiailing edge of

plan-ing surface (m)

ti im

X scale of model dead. rise angle

NACA TI

No.. 1061

XPEE IMNTAX -PROCEDURE Measurement of the Porces

Heaeurementg were mad.e on the lift, reeistance, and. noment about a lateral axis. The threecomponent measuring gear is schematioa].Ly shown in figure 1. The resistance tension vire leads forward. from the point

Po, through which passes. the axis of the model head, to the dynamometer. The resistance rneasuremnt -is made by means of a recording pen and. coarse weight, the

spriig- force being. determined from the recorA of the spring extension, the -spring having been previously calibrated. A constant weight serves to maintain the tautness of the tension member. The calibration wire,

in addition, takes up by means of a stop the inertia force that is set up on the model on braking the tow-ing carriage. At equ..]. distances from po there are attached. the vertical tension wires leading to the moment beam. With the aid of a sliding weight the moment appl-ied to the model and hence the trim angle may be varied. At po there is attached. an ada.itiona].

vertical wire that leads to the unloading beam. By

varying the size or the p-osition of the eliding weight the load on the model is reduced so that the remaining weight corresponds to the loading desired. One of the reversing wheels is formed aS a gear wheel and. to this

io attached. by means of a. coupling, a winch by moans of which the model at the end. of each test run is lifted from the water in order to remove it from the following waves and. utilize the time of the return trip of th carricige for quieting the water surface.

At the start of each test run the. model is reL. leased only when the 'dynamic lift is sufficient to -S.

avo1d. an undercutting of the leading edge of the plc.n ing surface.

The draft and trim of the model were determined. from two draft Bcales attached. to the wheels of the

moment- -ba1anca.- - The setting for a given trim angle is obtained by displacement of the sliding weight of the moment balance and. reading of an angleindicating device. Damping when required. is exerted at the d.ynamometer

lever (damping of lon.gitud.inal oscillations) and at the slide of the moment balance (damping of vertical

-8 -

iL M NO

-1061

The relative a.r velocity at the location of the

model Is, on account of the closed, carriage and two air

scoops, practically equal to zero so that the air

re-aistance of the inode]

,s ngeliglbly email aleo at high

speed.s.

The measurements are therefore purely

hydrody-iianiical,

The preliminary testa were conducted. with flat

glass platee In -order that the forward boundary line of

the wetted surface might be determined.

This boundary

line under ail speeds, loads, and trim angles had. the

shape of a very flat arc.

In -the subsequent teats

there 'rere therefore employed plates, some of aluminum

and. some of wood, glass etrips being inserted at

one-quarter width so that the mean value of the wetted

length could be read off.

In the case of very wide and

V-bottom surfaces several glass strips were used.

The model was su8pended. without crowding so that

all the errors in measuring the draft, trim, and. lougi-'

tu.d.inal displacement of the mode]. were negligibly smäll.

insofar a they were not eliminated by the calibration

itself or by having the vires run on circular segments

where required.

Pressure Distribution Measurement

Por' taking the pressure distribution measurements

the planing surface was provided, with about ninety

measuring stations which were arranged in thrQe longi-'

t-u.&inal sections and. a number of transverse sections.

Pigure 2 shows a measuring station in. cross section.

The free opening of the orifice is 2 mIllimeters In

diameter.

The glass tubes over the orifices ae held.

fixed in position by means of a short pipe construction.

In taking the measurement the planing surface is held

fixed at the trim determined during the resistance

measurements, the measurements being cond.ucted with the

water surface smooth.

The heights of the water columns

are marked,

It was checked to see whether there was a

poible interference effect of adjacent orifìcês by

closing the QrifIces 'with plasticine in the cheek runs

an& keeping oiily- one orifice open.

o apprecia.ble

dif-ferences were observed.

Check measurements with 1

millimeter free opening of the orlfiâes showed, on

.a-count of the stronger throttling of the liquid column.a,

a smaller fluctuation.

jCA TM :No.

I Oi

9

Yor obtainin

the preasurs distribution, lt was

- necessary ,to make aeverar test- run

at each trim, angle,..

alight speed. differences which 'àìéäted. th61áad.ig on

the adjusted plate bei.ng foun4 unavoidable.

The

meas-iiring accuracy is to be estimated at about

5.pereent

of

¿h.

THEOETICALBÁSÍS 01'

STS

l'or a surface in steady plaxiflg motion on a quiet

frictionleas fluid. surface (fig. 3) the Bernoulli law

may beapplied. tg all the streamlines including the

d.iytd.ijg stréamiine.

.

L.

+ +

g z = constant

(i)

The pressure

p

is assumed 'to. be composed. of the

static pressure

_stat

due to the weight of the fluid.

and. the portion

_Pd.y

due to the dynamic effects.

The

staic lift is therefore'

stat = COB

_(LfPstat

dl'

(a)

an1 for a flat rectangular planing auifaae may

approxi-maely be set equal to

-2

(3)

64

(os v'

" / I

4

if the wetted length

Z

le determined during the teat,

it being assumed. that the rise in level at the

neighbor-oo& of the plániúg eiirfàoe 18 -obnstant.

-The dynamIc lift is

10 .NLC1 TX No. 1.061

and.acôórd.ing tó the momentum law is equal to the time rate. of change. of momentum of the .aBB of vater involved.

d. (in

y0)

dyn

dt

The total lift of the planing surface is thus

A

_A2tt

_{+ Myn}

In the case of a iscoue fluid the streamlines

and. velocities, in spite of the bound.ary layer occurring, agree approximately with those of the frictionless flow, differing only in the appearance of an ad.d.itional

tan-gentia]. force T.

Owing to-the effect of the finite width there is set up at the edges a áross hoy with lateral pressure drop which for sufficiently large values ).ead.è tÖ a separa-tion of the water aleo at the aide edges.

In the pure planing phase .haracterized. by- the separation cf the water at the trailing and. aid.e edges of the planing surface the resistance of a flat surface

as i'ol1 as of all surfaces that are longitudinally straight and. without twist is given by

Y = + = A tan a + T

cas a.

Thè normal resistance

= A tan c (8)

is proportional to the loadand. the trim angle but in-dependent of the speed, while the frictional resistance

---- T = Of1

q. (8a)

COB (L

-is proportional to the wetted surface and. the dynamic pressure1 the friction coefficient Cf1 being a function

(5)

1,2

and.

P = 80 m

çorrospoud.iug to

65 kg/m2

surface loading,

NACA TX No 3dì

11

of the

eynold.e number

R = vs/v

an& d.epend.1.ng on .the.

turof the bound.ary lay-ex' .as..,wa13aa...qnthe

rough-ness o

the su.rface.

.R.SULTS

di

ÌEE TESTS AND APPIiIOAT IONS

(A)h flat P1anig Srface

(i) iethiì

f''he' reliminax'y Tests 'with Plat

Planing Suzface

l'or the pre1iminár. tese on the flat rectangular

planing surface average re1at.ons were chosen with

re-gerd. to boam1 load., and. speed.

ligure 4 shows a

loax'ithiiic plot of the beam at step

b3't

as a

func-t1.on ¿f t1p f.ying boat weight

0',

or

G/2

in the' case

o

t

tijnf1oa

seaplane, the load. coefficient

_Ca'

bing taken as pars.metei.

Select.ng' from'the thean raÊ.ge

a.beam 'bSt

- 1.800

meters

and. with

G = 5.18b t

and.

c'

0.889,

furthermore a mean airfoil lift

= Ca P q. = 1296 kilogralnB,1

.nd.èpendent of the trim

anglo and. assuming.a model scale X = 6,

then the model

beam is

bst = 0.300 mete?, the corroepoud.ing weight

G = 24 kilograms

and. the hpdrod.ynamic load, at

y = 6

meterß pr second. - an aorago speed. in the spoed. range

in which tho se.plane float executes 'a puro 'planing

motión -

18 kilograxnB,

then

= 0.109

and.

3.74

The trim a2xg].e range of interest 10

a.

2°

'to 100.

Resiatanbe,' inoment, center of preesure,- and. static

2.L t. On figure 5 -are plotted the nonaimons lonal values

C,

Crn',

i/b,

7,,/t,

and.

_Astat/A

a

functions of

u.

Tan

.

r'oprosents the lower

lug' value of the re-

-si'a'1' 'ôfroTh

'

'..i

ccrrdimg-to eq.uation

(7) the fr±ctional resistance

NR,' 'on the assumption

of frictionloss flulod., becomes zero,

Since with

12

NAOA.TM No.1061

por.'tlonof:th.reaie±ance

V

to the total resistance

Y

rapIdly d.eoreas-s on account of the øtrong1

deceas-Ing wottod. area

7,

as

ay be seen fromthe trend of

¡/b,

the

curve approaches asymptotically the value

tan

> 100 may be replaced approximately

by

tan &.

Another -asnptoteis the axisof ordinates

since

P

andhence.

_R

approach infinity aS

-

0.

The position of tho minimum lying between the asymptotes

is d.otormned. by- ther.atioof..tho frictional to the

total rosiatance.

Por avorago

onditions this position

lies botwoon

40 an60

Proaaure distribution and. character of flow. Pigure

6 shois the measured pressure d.intrib.tLon and. the flow

picture for tho anglos

40,

6, and.80.

The etanation

point liös nóar the 1eading. edge of the wotted. surface.

The groatost portion0f the watoretroam flowing up is

thus d.oyiatod. downward whiJ.e the portion.of the water

lying shoed. of the etagnattòù point le pro3eóted. forward.

& spray.

The maximum prouro, measurettat the

stag-nation point remains considerably below tho stagstag-nation

preesuro, .It is présumod. that the ful). stagnation

pres-sure occurs within..sD narrow a rango that it does not

show up in the measurement.

On account of the sharpedge boundary. of the

plan-ing suriaco the flow at tha trailplan-ing edge already begins

to separato at.

Qmp.aratiToly low speed and the water

continuos its downward. mótiøn !ohlnd. the plate, thus

forming a dopreBs ion wh ich is l.mito

sideways by two

wave tzains coling. from the sido edges o

tho plan.iug

surface,

Th

wave tral.ne mGet.bohind the planing

sur-face in tha plane of symmetry, and .at 'the point, of int

tersect ion the water spouts up In the manner of a fountain.

The tan8voree pressure drop producoe a cross flow

which £or a sufficient speed. leadB to the.eepara.tion. of

the water also at the side otges.

The separation' :bog1n

in the forward. region of tho pr

suro area evéll

t t.he

smaller spoods.,. on account of the rlative1y high

pros-eur.e or pressure. drap that occiira there, and. with

tn-cz'easig speed continues toward the reax'

Te ide :spray

rises steeply near tesurfco and thòn spread.a out

I

NACA TI! No.

13

aenter of pressure. Zf the trai1irg edge of the

planing surface is chosn as .the. axle about which

mpmente are taken the moments on the planing surface,

according to Dlgure 7 aró

G i

4Z'i

N

nder the aotiói'of the app].ied inome

at the left

of the equation the p.lanlng suifaoö trims to an angle

a

or which the hy&rodrnainic moment at the right Is

equal to the applied moment.

A plot of the moment.

coef-ficient

mh*

ahovethe vriatlon of the moment with

the. angle

a,

The greater the tr.m angle

a

the

smaller Is the increment

tNj

In the moment required.

to change the trim angle by an

.mount

a.

The ratio

Cmh

= i/b

Ca'

gives the position of the center of pressure If

A IB

assumed to be approximately equal to

N.

According to

the curve in figure 5

Lp/i = 0.77

with a tendency to

decrease as the angle a decreases.

The moment of the static lift determined according

to formula (3) Is

Matat

As-tat

.1

COB

BO that the di8tanceof the center of pressure is

L1,

- Aetat.

or

_T

0.333

The moment of the aerodynamic lift

> Aj.yj * i COB

a,

u ii i

i i i. I Iiii .. 11 IiI I

-14

N..LC.L.TIt !1o. l06l

and the d.istance of the. center .o, pressure > 0.666.

if

a

triangular pressure distribution with the maximum lift at the lead,in edge is apprximae].y aswned., since

accord.ing.tO

the measured presure distribution the center of pressure lies always ahead. of the center of pressure

of a triangular. presv.re. d.istributibn tha lever arm of which 'trould be 2/3 ;- .

'rom equatiou (io) and. (ii) the:following may be said. about thecenter of preseurO travel: With

in-creaoin trim angle (A and. y being .conetant) the ratio of static to total lift _Astat/. decreases and p/2

increases, as is confirmed. by the preliminary tests. Withincreasiñg speed (i/b and a. constant) the dynamic lift increases with the dynamic pressure while the

static lift remains ooatant. The ratio of the latter to the total lift therefore decreases and

correspond-ingly ip/& inoreasee.

(2) osults of tho Tests with Planing Surfaces

(a) Lift

The lift

A

by

analogy with the similar expression

used. in aerodynamics may be expressed. by the equation

A = a*HBI q

In tho case o the airfoil the lift coefficient ca.

in the nid.dle raige of the angle of attack and. for small aepoct ratios, is proportional to the angle of attack

and the d.orivative dea/da. = oon.stant if i/b = constant.

If, for the experimental range of angles, the same as-sumption is made for the planing surface (reference 7)

thon

c-

=Ca.a.

da.

A0A T14 No. 106].

15

where the derivative Is replaced by

Inorder

o

eliminate

a.

as parameter, as would.be couvenentfor

a suitable representation of the lift coefftàlènt, it is

therefore written

0a. =

A

(13)

-

The test carves of fIgure 8 show that for the region

of high 'roude numbers

the assumption is sufficiently

justified as a practical working hypothesis.

Deviatipns.

from the straight line'law may be ascribed to the gravity

effect as will be further clarified below.

If, in

fig-ure 9

c

is plotted, as a function of the aspect ratio

/b

(reference 7), then from the foregoing considerations

the Froud.e number

wi].l be the parameter.

The

family of curves gives the results for all the lift

coef-fioiente öbtáined. from the 33 test series indicated on

the figure,

T-o bring oùt more cleàrly the scattering

of the points, since the plótting of ath test points

would. oomplicatè. the digram, fIgure 9a ahow the values

for the test series 2, 14, and.

2 to 33with

= 374

the constant value.

-Al]. valuesare well represented. by

the heavy averaging curve.

In figure 9h the lift coeffieient values

correspond-Ing to the tests of Sambraixê (reference 5) have been

pl'otted.

The wetted. L&ug

i

on the determinationof which

the a,cca.racy of

ca.

main].- deèn-d.s had .to be obtained.

by photographic meawurement-s' in:. the Sambraus teat-ø'- since

thehigh epeed. carrt'age

.id not- permit direct

obsrva-tion.-. 8-mce the Z.örward. bound.aryof the pveeure area

at high dynamic preseur"ea and.- sm1'aas,-.euch as were

mostly assumed. by Bambrauo, fluctuated. greatly even for

an almost smooth water surface,..(.øae'Seo. II,. 4 of ref.-.

erence-5) directobservationa as made in thetets 14 tho

ESVA tank, in whib.the f1uotiatione maybe well averae&,

are more reliable.

The scattering, must be greater the

-shorter the wetted. length-that is, the smaller the

as-pect ratio o

the planing surfaos.

Taking theec

condi-tiona into consid.erdtlon.it is poBeib1e.t speak of a

reaoön.ble agrB'ement between the two serles of tests

with the exoopt ions of tests 2,

3, and. 4 the coefficients

.of which aro about l5percant higher.

he c.ef'icients..

16

:AaA. LH No. 1061

higer.on1y.in the smallest aepect rio.-range

/b.:0.7

to 1.2, areo for the medium aspect ratto range

Z/b

12 tá 2.5, ánd. becomé somewhat leso

t the maximum

'as-pect ratiG i/b

3.

In figure 9c there are similarly plotted the

coef-ficients of the testa byShoemaicer (reference 6).

In

the Aniorican teste the

atted length was obtained by

mirror observation of the spray coming off- at the sides.

This method, too, cannot lay claim to the same accuracy

as the determination -by direct observation of the

for--

ward. contour ofthe ressute area through a glass

tr-ip

insert ed in -the p].ate.

Gorresponding1

there is a con'

siderable scattering of the values for smal]. asp

ect-ratios

i/b <.1. the valueslyingon the average below

those of the ESTA measurments so that in this range

the latter values average approximately those of Sambraus

and- Shoenaker.

At ]arge aspect ratios the measurements

agreevorye1l ance in this range an error inthe

determination of the votted-length only slightly affects

the value of the lift coefficient.

-For Proude nuxnbera

8.5

the offèct of gravity

Is negligibly small and the lift coefficient

ca.

&eterminod by the empirical euation

-C. = 0.845

₍₊₎

-3/2

In theprevious section it was established

that-the fraction-of that-the -static displacement increases with

d.ecreaszg trim anglo or Increasing- aspect ratio.

The

ourvos jith &iffeent

parameter therefore d.lverga

in tho d-ireotion-Iñ increasing

-

i/b.

--

-. As a limit- of the pure planing condition - that is,

when tho sHee of the planing surface begin to bo wotted.

at--the stopthere is obtained--a straight lino passing

through the family of curves

-.

--- 0.375

-

-= 0.94

Et)-

(if-q

_'!)

yh1h at the samo t.me connecte the miiums-f the curvos,

(14)

NACA T1 No. .1061

1'?

CompariBoL wjh t)e flat latC

etre.- The

-wiu.tiiune'te'±ì1ed. out by

i'nter tr.eference 6) on

flat p1ate of various àspect ratlos povi4e a means of comparison between the 1aning e;faceand ai airfoil. In the table are given the coefflient of the total

--. :, CN COB ß

lift. cooffiofent in tjeir _ca.tot as a

furct ion of - Z/b I for.d. = 1:0°. Jom the pressure

measu.rementÇfig. 23 nWinterIs..raper) therp is ob-tained. by integratIon,for

95O

_{the. presaure} d.istributionon te topand bottom slds, the ratio of lift on the two sides _{Abot/Atop or}

AbOt. 0.38 Lt0t -

()

If for the angle-of-attack range considered tlie above re.ation in the absence of pressure d.istribu.tioi meas-urenent ct small angles of attack le

_BBSIØd

onatant

with change in angle of attack and. aaect ratio, then tha.stnIght. line IÙ figure

9b-CcL

0.91)

(17).

giveB the change in the lift oefficlent on the bottom sid.e of the flat rectangular plate in a.r.

ormulaa.

(14) and. (17) .d.iffer -on.y by the value of. the const.nt

and that to such-a email extent that the lift coeffi-cienta in air aud. water may b6-.sat& bo agree ae long ac the Dffoct of gravity is nogligible.

18 ACA 1UNo. 1061

i4 Rectangular

1st.e in kir

Comparieon with the theory of Wagner and. the re-suits of Sfiinbraus. On figure 9b lu plotted. the lift

coefficient, c according to the Wagner the.ory for the

short plate. The ourve, which Was obtained. by neglect-ing gravity, le to be compared. with the curve iron

formi.1a (14) for which the effect of gravity is negli-gibly small. In the range of email aspect ratios the

theoretical curve lles about 20 percent above that ob-tamed, from the test resulte where, however, lt le to be noted. that in the theory, on the assumption of in-finitely email angle of attack .&bOt hae been set equal

to 0.5 Atot; whereas, for finite angles of attack the

pressure ¡neasurements of Winter give

the

ratio of

formul-a (16). A com-plete. agreement between test and.

theoy is therefore not to be expected. n the

neigh-borhood. of 1/b = 2 the turvee Intersect and diverge with increasing aspect r.atio.

In the case of long planing surfaces (i/b 3)

there is good experimental agreement with the flat air-foil in air (under the assumption Cabot = 0,39

whereas the Wagner theory- of the short plate does not agree zith the test results also for planing cond.ltione

for which the effect of the earth's gravity is negligible.. -(The theory of the long plate gives greater deviations

from the experimental results as shown by Sambraus.)

P

Q.&Om

28 m/e,.

a1OÓ

1/b _Ca,tot .: 0.5 0,576

325

1.27 666' .520 '2.93 i . 14 .80 .468 2.64 1.03 1.0 .41.2 2.32 . Ì5 L.51? .338. 1.91 .745

.2

300 1.69 .66 2 . 8.6 / 2'37 1.34 .522 7.48 .155 .875 34]..

NACA

fl sc-.. 1Ó61

1g

-Thoconclsions of S

byais on the long flat

plan-1±giirfaàs (5uimar'y pøtnts i t

3.

ii -reference 5) thae

find. no coñf1rmatio

while poi

tcbe

e.--.---...

mentad. by the statement that at high Proud.e numbers

'

the Lift in ,the inveetlgat.ed. range at oonBtant aspect

ratio vß.rios linearly with the

rirn ángle

iit tb.t with

decreasing

rotide number thé 1ifí coeffic1.eit as a

suit of the increaèing, favorable, effect' of gravity

increases so that

d.Ca*/&

&bea not remain oonstnt.

b-)

eeistance

ProLi formu1, (8a) tere is. cbtaind. for- the friso.

tional coefficient

cf.t

_R/

q.

When plotting

Cft

as a function of the Re'nOl&s number. R

vl/

arid,

corn-paring i:ith the resulte c-f pure friction meaauremens,

the fo11oring points -are to be noted.::

1. The normal resistance

W

obtained, by

subtract-in

f.ron the me.oure.

is, in the

rago of minimum resistance- d

about the sa3nO magnitude,

an4 'for higher trim añgies, -couaid.erably1ager than the

frctiona1 resistance

Since the scattering

con-tribution of the measurement on

W

is removed., the

scattoring of

Cft

must be relatively largo and. in

Oreases th' i..rxcreasing trim anglo.

11n the

resentetio

herochoßen -the Proud.e number

= v/Jg(A/)

±úproportionalto the epée&ad

in-versely proportS.ona]. to the sq,úare root of a d..ifl!

which increases with increasing lift; n&nel, the length

of anedfe of the water cube in correspondence with the

hysica]. interpretation..of the'Pr.oude number.

The number

chosen by Sambraun

P

v/.v-g.b

'which fulfills its

pur-pose as regard.e coneiderations of similarity, increases,

however, iiith d.ecreasing wi4th

b1

a1so, for exampie.

when,be vetted, length remains .conatant with ß.eceaaiùg

load..

_{This representation is not suitable for the wórk}

under ccnidi'on.

I

1he-

flg, 9b)

is used. for the Sambtau'teats, it,appear,e that- the latter

only- slightly exceed. the

P

bangt. o

our own tes'te. in

spite of .higher.test -s;ees on-account of the

applica-tion o± narrower p.lates,

- - . -.

20 NLL TM No. -1061

- :. 2. The. acatteri.ng j.e izcreaeed. by

.tke.

!act that the

me.8UrOd vala-of 4he vttpd qurf ace P-. !1ucuat.es more the -smaller the, ya].ue of 3 - that -te. t.he. i.argei the

angle , .. -.

- ...

3.. The xater thrown uj in front as spray parti4lly

vets the bo.tt eif ace and. d.eòxeaBea the iesietance

(reference 4)... TbJÏ thrust a.nnot'bø d.etermin.ed. and. is

thu uot .ako.n into acczun,t. .

The total pressure surface is used in the compu-tation as the wetted.surface in spite of the fact that

the .d.iroction of motion oftbe vater partiçies at the urfaco ahead. of the stagnation line is forward. and. in

the aid.o régfons haB a eid.e

component.-The high preaeurerogiois

uperpoeed. on the frictions]. boud.ary 1-ayer,vit.h the rqßult of ad.ecaaaee

in speed. so that vm-<.-v, hia-d.ee.reaao in speed. ieot

taken into account.

The Reynold.s law asSumes geometrical similarity

óf- the. flov his requirement e not eat j.sf ted. since. it

is possible, that tha.wottüd. length J .and. hence also

R ma.be..conant for, .v,ar,ious..load.s; whereas the trim

angleand. honce the presau ánd. ve1ocit istri.button aro d.ifÍ'orent.

In figure 10 are plottea. the cur'es for the erips

of tests 2. to-33. It -may be seen that In--spito of 'the

above restriotions the valu.os. of

o

arero].ati'veiy

veli ropresontod.. by ho puvo givon by. Prand.tl

(refer-ence 9) for the turbulent bdund.ary layer with reoed.ing

laminarlayor. . . -.

e = -, 0,455 -. 1700/R

(log (16)

if'it'.s taken' into accout that thecattering that ind.er1ios the'Praúd.tl curve ia-likewise not small.

The rn'éasuiementB vere partly cond.uoted. in completely

quiet vater: namely at: the beginning òf the tests an& after long intervals and. pütly in water yitli a alight

-amount of motiòn. The relative'y mal1' scattering le

RACA TN Ro. 1061

21

eing].e stable form of.the boundary layer exista.

This

ie of paricula importanoe for -th-e -model t:est Binde

the larger portion of the towing test occurs within the

range of Beynold-ø ni1mbers 4tu which there might possibly

have been two boundary layer conditions and henoe

fluo-tuatione in the fribtiona1 relBtafl.CeB up to about 100

percent.

oreynold.s

mber

the surface tension

at mean pessura

:.

=

20 - 50 kg/ms

(19)

results in the wett.ng of the sid.eo of .the planing

sur-face, thereby producing -a cQnsiderable Increase in the

resietanee..

Under these conditions spray no longer

oc-curs.

The condition for the occurrence-of 6he pure

planing process

s therefore, according to formula (15-),

f...

\.-o.375

c

<

an,d,:accoi'd.ing to formula (is),

Pm >20:- 50 kg/ms.

In the towing test, for

consider-able intervala d.uing the t-a]e-of f process,

p<20_-50kg/m

if the e cale of the model le made too small; then the

model resulta are no louger .traneferable to full scale.

The test series 31 to 33 belonging to a single scale

series lie In this range and partly also In the test

series 10 and 11, for-which, reason In the latter case

the

Cf1

values risa unstead11y with decreasing mean

pressure (increasixig

and.

_s)..

That these values -cf

li-e in the range of the curve for turbulent

bound-ary layer le physically noi justified and. may be

con-sidered as an accidental resu3t.

(c)Ceterof'piaflure

The fun&axaental obseratione pteously made on

-

'the effect

f- the

athTsgrávlt

bn the position of

the center of pressure are confirmed in the family of

curves (fig. 11) which shows

as.-a function of

l/)i

with the Proude number

as parameter.

or Proud.e

numbers greater than 8

0.8 oonstant.

Both with

decreasing r and. with Increasing aspect ratio

(if

_V

< 8)the center of pressure moves in the

22 NAD1 T14

o. 1Sl

(3) Application of ths ReSulta to the Determination

of the Sffact of the Beam, Load., Speed., and. Scale

in the Range of Pure Plating

In the following paragraphe a number of

i].uetr.-tive examples will be computed. asregarda lift,

resist-ance,and. center of preestre and. thereby a number of

important questione with regard. to the planing problem

will be clarified.

In the following diagrame therefore

it.. addition to the nwneri«ò.11y computed: carvee there

will also be lnd.icated the test pointe obtained from

measurement so that the extent of agreement of the families

of curves in, the wor]cing charte wi1

become clear.

There will first b.ö described. the proce-d.ure for

the numerical computation.

Let there be given tbewid.th

b

of a flat rectangular planing' surface, the lift

A,

and. the planing speed.

y

and. hence aLeo the Proud.e

numbor

I

= 'v/.Jg (A/'Y)1'.'

1t is req.uirad to find, the

resistance-load ratio ratio

and. the moment

coeffi-cient

cmh*

aafunctionsoí' the trim angle

a,

Oorre-sponding to a number of suitably chosen

i/b

values

there are determined from figure 9 for the parameter

1'

the lift coefficient

ca,.

.Prom the eq.uation

-arca-

A

there is obtained. the trim angle

a,

The.Reynolda number

is

C, i/b b3 q.

The corrosponding frictional coefficient

c'

is taken

from fi&ure 10, the curvefor turbulent bound.ary layer

with preceding laminar layer and.

y.

i' b2

E

=-R _{A b A}

is determined,

Therefore

I

&A.L T1No

1061

2

?urer,- fo' the intersection point of the

c

curve

and. ti b: iiit Ig'

'f

j1aning in f Igte 9

thèa are detrinined. the corrénponding apoot ratio and.

uimiting angle, réspectively, at which the character of

the f].-ow changes.

The d.ottea

ort Ions of the

i1lu.tra-tlon. curves apply tò con-d.it'ion.-e for vhicti the pure

planing procese has not yet been reached 80 that it may

be expeted. that the

eaeurement reeul-tTs ezceed. the

oteeiu1t on aòòunt of additional resistances.

3rôm f.gu±- 13.

/-

1A similarly detérmined. and.

with HhStpA

= -

-Xi.st

-

.L

b

Cmb..

_(j/y)1/3

-

b (A/Y)'/o

(a)

ffct of the Width

Por the interpretation of the teat results on floats

it is -of importance -to determine how., the resistanceicad.

ratio and. moment coefficient vary with the wtd.tb for

constant load. añd. planing speed..

-Pive flat rectangular planing surfaces of various

.widtis, in comparison with, the Initial test with

plan-lug surface

A,

were investigated. according 'to the

following test schedule:

figure 12. the reel tance and. mcixnen.t coeÍ'ficieit

and.'

_{cmh* '-computed. from .the,nieasured. values have}

been plotted. as f.nctione. of

a.

with

b

_{as parameter.,}

U ...

Planing

surface

Test

num

-ber

. b .. -.

kg'

.. C

-'vmJe

. --. :

0.600

1ff

0.0272

6 -

3.74

- 2

_{- 23}

- 50Ò

18

.0392

6

3'74

1].-- -

24

. .400

18

-.0612

6

.3.74

j

2+25

.300

18

.1090

6 - .

3.74

3

26

.225

18

.1940

₃₇₄

-- ..,?? - 18 -

435p

.

374

24 NL0A T No. 1061', the cònt&n'uou cu.r"vee'

iYing

th c.oefflcients deteriain

by compu,t.ation.' The ex'apJe-show .that !nth.e case of the f3t platø for which -the 'u1l wU.th contributes to

the 1i,fA the opt imui rßBiStancßlOe4 .rtio becomea. con-t-inu,ously more favorable with increasing w.d.th and.

de-creasing aspect ratio or wetted area,

In the range of small wid.the the' .impairmn çf the

rat.io due, to the ,increaeing effect. of gravity .ecr0ases.

tf the pure planing process discontinues, bowever,tha ratios again:1ncrea.ee.o account of the ad.d.ttional edge

resistances.

As limiting value of the width at the' steps of sea floats there is given ij figure 4 for the wide float

the value bt

..4 (GJ'Y)1'3 'and. forths narrow float

bBt = 0.7 (G'/Y)J. If for the 'tests under considera-tion, according to the assumptions of the preliminary test, the displaced weight at rest- is chosen as G' = 24

kilograms, then the beams corrèsponding to the beam at the steg in,.the moel are biarge =..O..4 meter and

ba11

'0,2 meter. For 'thoGe values there are obtained. the optimum load.resiat.nce ratioo o' 0.122and 0.154, r the difference amounting to 26' percent.

he effect of he 'beam où the' trim anglo becoma

cter if the

.ng].&"is det'ermiuedas function of 'the

beam for constant cmh*. or t1e previously mentioned limiting beams there is obtained é. difference of about 5 percent.

he beam of the planin.g 'surface has a great effect on the in'tensity of the spray. Since the lift coeffi-dent decreases with decreasing aapet ratio; that is, with increasing beam, there, is a reduction in the d.is' placed volume of water and in thé 'wetted side length, at whih the spray ésc'apes. The axsnt by which the

spray formation may dife'r in the t'wa previously de-fined' limiting beams may be seen from figure 13 where the tro models are equally leaded and bavé t1ie same

speed and trim angle.' Figure 14 sh'ows, for the example given, the ratio of the static displacement V to the

tota]. lift V ?/A as a function of c and. it may be

sécu that for the two limiting caser the ieplaced. volume ci' iater' of the narrow flo't exceeds that of

'I

N&OA Tu No. 1061 25

in thIs connection the position of the d.epress ion behind, the planing surface is aleo of significance. In

the first ana. second-pa t.ofthe takeOff process of

"a eeap1aie the aten lies .behl.nd. the fount-a'i on' the:

vater thus relieving the load.' on the for ebod.y and., on

accoi.i òf the Bmá].'l Lnit,a1 ti1m'of'the f.oat' resultiu

in a egaÌve trim bp' te atein,'there.. i even set 'up a

thrist that owere the resis'anoe(referénce 2).

he aitance

c' of'the fountain behind, the

rai1--ing êd.ge 'was meaauréd. in tests 22 to 27 aa well as in. a speoiaJ. test vith..p].aning.surface

A using a l°a

corresponding to the takeoff process. I. fIgure 15

the values + e are plotted, against the trim angle . It may be seen that + e,. is practically independent

of .... ao'that thepoeiti'on of the f Òuntain with change

in t±.im angle is Bhift ed. in hó same sense' as the c6n-tour of thewetted. surface.. The value of + o is

approximately proportional to:

V

and, b

'1 + e 1..8Z* b (20)

as may be &erived from figure 151.

'(b) Eff'oct'Df Load.

It. will nov be determined how, for a given beam

and. speed, the resistanceload. rati,o and,, the moment

coefficient vary with the loá.d.

Por constant seed. and.' a large ra'úge o loa&s,

tèsta were conducted. on planIng surface i accord.Ing

to the following test achedu1e:

expression given by Wetnig (reference 12) of the

fountain distano does not agree with the results obtained by the author and. not published, at the time and is

there-fore not taken into account here. Planing áurfaca Tßet n-u.m ber

b'.

.

'kg'

...

' . "rn/s

-18 '' 0.3' _{iO 0.0218 10 6.90} - A 19 .3. . .5 ''.0545 10 5.90 -. '16 .3 0 "

.lÓ9'' .10

. 20 .3 100 .218 10 4.70 21 .3 150 .327 10 4.38

26

r :'

NACA TM No, 106].

_

Ia. -figure l6.temeasued.-valu-os; ' and.-.

cj

are

p1ottod. aainet '

wnitli

b5

p

ametbr aid. the

theprfca1ly compued, ci.ves are a,lso 811CWL.

I

may be

seen that

or sivalj. and. averge load,e tb

reeistancç..-load, ratio inoreasen coxaidezaly witi ipereaoing load.

on account bf the ipairment of the aspect ratio.

In

&oubl1ug the -load.1.for eamp1e1.frorn

5 to 50.. kilograms,

opt.:

tzcreases. by 25. percent .

&t. very ]a.rgo loa.s the

impairment' is slight on account.of.theiu

easing-of-fect o' gravity.

-

i

"Choc2 'cf the re1tibn

ca/&

cOn'stant

in. the

investigátéd, range for higher

nujnbers.- In figure

for toste 16,' 18, end. 19 the wetted. Iength-

1

have

been plotted. again.-et

and. emade to intoÌ-eeot the

straight linos

0.3, 0.6, and. 0.9 metbr,

corrre.

sponing to the aspect ratios

/b = 1, 2, 3.

The

0a

values are also plotted.. 'Tbese lie on straight linos

,which pase through the origin - that is, in the range of

numbors,within whiçh tts.effect -of gravity may be

entirely or approximatoly neg1cted.

d.ca*/d.r

= constant

and. thus the assumption iin.ß.r1ying forni1a (12) is

justified..

(c) Eff

tof.th

speed

-The t&to--off d4agra.in of a seaplane showe two

ro-sistanco znaximune, the f iret in the sango of the transi-.

tion frox the floating to the planing cond.tion, thcr

second. boforo the get-ava.

It will now bo itvostigated.

to what oxtont the formatipn of, these maximwns depend.

on the stern of the float.

This qiestion may bo

an-everód. with the aid. of the planing siirf'aco which is

equiva1ont to the longitudinally straight forobody;

a larger speed range with conßtant

beam and.

load. the rosiatanee and moment coeffiionte wore con-.

Plotting c and. _cnih i.e functions of a. with

V as IDaranleter, figu.re 1?, there le found the type of

relation familiar from float iuve8tlgations. Lt low

speeds c increases approximately linearly with a.,

the puro planing procese not yet occurring. With in-creasinC speed the resistance increases, particularly

o at sLlall trim angles so that a maximum resistance is Boon obtained, at moderate trim angles. After exceed-ing the maximum the resistance 'again decreaeos with In-creasing speed. A second. maximum therefore does not appear In the case of the planing surface and. the ap-peararice of auch a maximum for the float Is to be

as:crlbod. to the wetting of the stern by the spray. In

the plot, figure 18, g1vig c and.

ch

as functions

of Y. the formation ot' the first maximum is brought but.Titb particular cleariese. The indicated boundary curveof the pure planing condition:shows that the

latter occurs before the maximum is reached. Resistance snd. moment maximums lie, as aleo In the case of float tnvestigutione, at about the same speeds, so that the greatest trim angle coincides with the resistance maxi-mum if the p].anIngsurf.ce planes free to trim.

llheroas, with decreased. speed. the résistance-load

ratio increases on account oÍ the impairm.ønt of t,ho aspect ratio -and on noglecting gravity there would be obt'a1'nod the up ercu.e

te affect of

gravity in the lower speed range Is to de'crea'sè the re-eista.nco to such an. extent that with tho second curva branch a rosietance maximum occurs. By support of the

stern tho maximum in a float may bo considerably affected as explained, in reference 2. Planing surface bm

Ag

-°B

A

0.3

.50

0.436.

5 2.63 2.92 31 _.3

ß0

.302' 6 3.16 3.5 31 .. .3 . 50 .222 .7 . 3.69 4.09 31 . .3 .50. . .170 8 4.21 4.67 31 .3 50 .134 9 4.74 5.28 A. . . 50 . .109 - 10 5.26

5.4

A .3 50 .075? 12 6.32 7.00 31 .3 .50- .0556 3.4 7.38 8.18 31 .3 50 _.0:424- 16 8.44

9-5

f,, NAOA.TH N6. 1061 27

In figure 20 the values of ,

/b, and.

obtainod. from the measured values are plotted. aan.pt

a. uith X as parameter. Planing surface i. within

b = 0.600 meter is the widest of all surfaces

investi-gated.. For the scale comparison the fullscale design was c flying boat of beam b = 2.400 meters with A

= 9216 kilograms and. G = 12,288 kilograms p = i).

The planing surface with b = 1.200 meters and A = 1152 kilograms, G' = 1536X2= 3072 kilgrane correspond.e to

the design o' a normal twinfloat seaplane (X5 = i).

Plan

ing

sur

face Toat number 'ull .Pul].-acab flying boat scalo bwin float e ea-plane bm CB Akg Xp 1 2.400 0.109 9216 3,74 16.96 2 1 1.200 .109 1152 3.74 12 1 28 4 2 0.600 .109 144 3.74 8.48 2L 2,25,29 8 4 .300 .109 18 3.74 6.00 3 30 .0.66 5.33 .225 .109 7,6 3.74 5.20 4 31 16 8 .150 ,109 2.25 3.74 4.2 5 32 24 12 .100 .109 660 3.74 3.46 6 33 32 16 .075 .1.09 .281 3.74 3.00 28 b:oA .Th Cd.) Xffect of the-Scale

It ji1l now be investigated. to what extent

simi-larity a:pDliee a regar.e the pressure eurface8 and. centerofpressure position and. whether tho scale ef-fect is given solely-by the dependence o tho frictional

ooeficiont on the eyno1d. number. Byinvestigatin.g a family Of planing surfaces thi,s question may be

an-s'vereci for the Case of the-pure planing process.

Sixplane rectangular plan.ng surfaces of various

beams îcro investigated. accord.ing to the. following test schedule:

RACA III Ro.'. 1061

The. contixiuous curves show .the ar1at ion of the values obtained, by coinputat ion vhic were' determined.

for all conditions for which p

>

50

kg/m2.

At smaller preseures at which, ¿n account f the effect of surfacc

tension', the pure planing process has diecontin.ued. the d.8tetinat ion of the restet'anoe 'is not poas

ible.'

In this

case the dotted curves ahoy the 'ai.ation in the maas

ured.-va1uea. '

Thó

values d.etermined. in

the

séries

of tests

for

the aspect ratio

/b

and. the moment coefficient

_c,ht

arrange these14"as i

euch a manner t.at no regular

deviation, rom .an avèraging cur' through the, test points (thia cui-v,e has. not

béend.rayn

one

diagram)

can be

established. -

that in

t'ha pure planIng prqceea there

is conplet'e siini1.aitr of wetted. sfaoe

and. momnts and

hence also of pressure ditr.b'jtion,. The sim±larity still -holds in"bhoaa'ranea i which the urface tension exerts an effect on the planing condition.

The resistancéload' iatios become more favorable with increasing size o!. planing surface on account of the decreasing-resistance coefficient, a shift in

opt

tot-ar,d email angles taking place. On acco.unt of the

fact that

ct

ia' approximately constant :.1n the range

B i

5X106

the ratios ar _{practica.1y equal fo}

average scales. With further decrease the resistances

strongly Increase o-n account of the eff@ct of the

s'u.r-face t;Bion, with' Opt

gkifting,,c.onaid.erabr'.in the

direction

ô!

_{higher angi,es,..}

-T]ieimpairme't

for eq,ual

Cmh,

i/b, Ei!1d.

'for, the flying boat and. twin float seaplane is given"

in the following table:

r. '

g boat

400

ni win floa b'= 1.

!lyin

b.= 2.

2 '

7.2'

'4

122

se,aplaie

200

m

erc.nt.

''2'

3.8'

'4

l0.5

-

5.33'

21,8

8 32; 12

16

107

18.5.: 10.66 30.6 '16 ₄₂

24

90

.30

'&CA TU No. 106L

The above Ligured Ehow that teats .wItb. mod.eli of

too sall' ascale

(b < o.&) auch as were mainly

conducteà. in Exgland.,for eùmp2e,'(referoncie io) and. In It.&iy, (reference 11) since the, beginring of flo,at in-vestigations,, cannot: be used. or the. determination of

the. resietance, aince the additional resistances arie ir& under the effect af .he sirfaoe tenion canot .be de.

ternined., Also in the case of somewhat larger .mod.ele the difference in the ratios between model and. full -scale design is s141]. considerable.. L transfer of the -od.el test reeult according to the method. here given to the fullscale design is practically impossible on account of thd.1ffidu1ty d.ur.ng the teät i'n

d.etermin-Ing the vetted. ares b moasuremeüt,' rt la 'only after

the construction oVtowIn tanks with high carriage velocitlés that têsta ön large so.Ìe models became

posible. for which, even with no ac'couñt being takénof

the

cale effect - that is,vith te ésumption:

W = w X3 or _E CM

and. or _{emhE = (21)}

results are, obtained that deviated from the true values only ulthin the accuracuival 'In passing from the model to fullacale computatioLna.

The ebove example shows that in passing from the

model to.the fullscale de.sign..accord.ing .to formula (21)

one je on the safe side. On account of the additional

rouhnese and, wave effect (ref erenc'e 13') which occurS

part icularly in the case of riveted sheet bottom of the fu11cale design the actual differences' bétween the

resistance computed. from the rnodel.and. the true one are

smaller than given In the prevlou8 table as is ehown by scale tests conducted on families of floats (references

l an'd.' 15).1

1The-possibili'ty should. be noted that In th model of very large scale the dIffeience of the fric.tion

coeffi-cien.t of the model and ful].ecale. design la so small that on account of the roughness' 'and. wave effect te

re-sistance o the f.].lscale design. may be higher than that obtained. from The model com'putatipn but does not

come Into c'onstd.erat&on in the case of the usual scales

NAOA. Tu ITo,- 1061

(B) The VBottom P1antn Surface

(i) aslc Equatl.one and, Determination of the Lift, Resistance, and. Center of Pressure

or a longitud4nally Gtralght Vbottom planing

sur-face the reaultaxi:t brma]. force on one side is acoord.ing

to figure 21

2 2 cos

or the tota]. normal force

A

Ca =

COB ¿'

The lateral componente Q balance out.

The production of the lateral speeds corresponding to the lateral components Q for equal lift and. other-wiae equal conditions, particularly equal effective beam results lxi an additional exit loss and. hence an increased. resistance uhich corresponds approximately to an increase in the load, and. la equivalent to a lilt increase from

A to Ii = Alcoa . That this actually represents a

usefu.l approximation is also shown by the analysis of the further tests. There -is therefore set

N.

₌ A

a COB. ¿

h.-)

(23)

3'or the length there is taken the mean length 2

of the ed.geshape surface 7 the forward bounding line of'the preseure-aroa --in -oorre-pondence to teat

measurements being taken as a straight line, and. e.

atagnat.oa of ccnatant hight along this line being

32 GÂ.T! No. 1031

and. at the outer edge of the planing surface

- btafl

4 tan a

Tho full beam of the Vbottom planing surface contributee to tio support as long as

' o. or and therefore If

btan

4tanci

tane

b

4tanct

tane

b -

4 tan

>_rn

4tana

b

the natural beam bnat of the pressure surface le boloti that of the beam b of the planing surface and.

tane bnt - 4 tan a.

(25)

(26).

(27)

In contrast to the flat surface for which, with increased. beam of the planing surface the aspect ratio o the

proa--sure area also becomes more favorable, since the trail-ing odo of the plantrail-ing surface Is always utilized. to ita

b b _bnat (24)

Prom £igue 22 the length of the pressure area a!t

the keo]., equa]. to the maximlim wetted. length, is

CA Tillo. 3.061

33

full extent,

in the case of the

V-bottom

surface there

a

imitig"baaw

bnat of thepressur-e area

vhioh.i

.t

the samp jme the most favorable beam of the planing surface for the given load relations. The

portions of the planing surfce lyingou.teide of the pressure area aro wètt,ed bythe spray which is rotar.ed.

on the surface and. so increa.ses the resistance. They aro therefore, without being utilized. for tho support.

of tho surface, the cause oZ ad.d.itional resistances which aro larger themdre..the width of the planing sur-face exceeds the natural wiath of the pressure area.

In the case othe a:eaplane float this condition occurs according to figu.r.e 23 before the got-away. Since in the outer free bottom strip of width (b

-a pozorfu]. spr-ay is directed. b-ackw-ard., the stern of one

float is aleo wettod. and. under certain conditions such largo additional resistance may be set up that in epito of the small residual loading of planing bottom the total resistance of the aircraft attains the valio of the pro-pollai- thrust and. take-off is impossible.

The

assumptions

required. for the numerical

determi-nation of the friction coefficient ori the size of the

wetted. eurface $' and. the Reynolds number R obtainod on tuo basis of test. observations are the following figuro 23a.

Cceo i) loaded beam: b 1f

Caso 2) loaded beam; b _bnat if

co s !

tane

_<IR

4tana.

b

tane

4 tan a. -. b I _1m tanò

Ri'--, whòre. -=-+

.

(28).

D. . b

4ta31

aae- a)Gad..ed. b.eaz b

21

and.

tanY=

10

34

NAOAN ITo. 1061

iero is then abaine

and

sothat

Y fr u (b + bnat) -2 cos I 1

Caeo 4) load.od. beam: bnat if tan

4tan

b

and. tan?

<10

bbnat

(bnat+

(so) cos 'j u

In casos i and. 2 the water escaping from the forward oontoir of the wetted surface and the water running along the surface as a film covers almost the entire width of the surface so that is to be used. in the determination

of P and B. In case 3 the limitj of the spray water wetting is given approximately by t1e dotted curve. In

caBe 4 no further wetting of the edge portions occurs with further increase inwi&thof the planing surface. The limiting valu.e is for tan ? 10

(29) bnat i A

J C

COS ¿ q.a bnat 'n a t

t.

In figure'24 the computed coefficients

and

are plotted. against

with

as parameter;

the values of

_Cah'

being gi'ven by the dotted. curvas.

The computed. curves are..contlnuous.

Very. goo1aroement

io ohaurn between the computed and. test. values, of. c,

the, as,sumtion lying at th.e..bsis .of 'foru1a (23) thus

being .eonftrrned..

_{0.ly .i. thcase of th'e sharpest}

V

botton &o

the test 'a1ues. at 5mall .trim angleB. shöw

any &eyiation. from

ho'genera1 shape of th.e,curve

since

in this case the Btatioa,lly d.1eplace&.vo1u.me.f water is

practically equal to the entire lift so that in spite

of free side edges the process is more like that of

f.oating than that eI. planin.g.

CorreBpo1dingJ.y.the

pres-sure .drop at th9 sides ii small, and. heñee the.spray.

for ati&n'.weak.. The .ress,tn i-e- stroug1y keeled and

there is formed. a short distance behind. the planing

sur-face a low fountain extending over some distance.

The

spray development then increases up to a V angle of

beS-t%Ieen 1000 and. 132°.

_{With fwrther increase in the angle,}

howevor, there is a strong decrease in the Spray.

Planing

arface

n'u.m-

Teat

ber

A C3 _Vm/a A

2&25

1800

18

0..09.

6

3.74

.7

34

i.60°'

- 18 -

.109

- .

3.74

I50

.8

.109

6

3.74

36

132°

18

.109

6 .

374

10

..

37

100°

.

18

.109

6

3.74

NACA TH No. 105).

:35

(2) .App4qation of the EeBU1tB for the Determ.ination of

(a) The Effect of the V angle

-1heeas, the impact forces in take-off and. land.ing

decreiae with thcrease ±n 'V. angle of the f]oat'. the

re-aistance increases.

The d.epend.ence of the resistance on

the V angle will now be found..

Four rectangular planing surfaces of various V

angles and. constant beam were investigated. according to

e

-36 HACA M No. 1063.

The añgle of in1iimum resistance apt increases with increasing V angle. The ConflOOtixLç-Btr'aight line

opt

has according' to the aesumption made iñ the compu-tation the same trend as on increasing the load, of a flat surface (fig. 16). Por .accord.ing to figure

24 thore is an' increase in the drag with V angle given by

100 1 + 40

+ 622

(31)

0

-- In the formula for the flat plate'if. i is

re-placoci. by . there is obtained

Cmht =

b (A/'Y)1"3

The agreement of the computed and experimentally .etprnined values of Cm is very gaod. up to medium

V ancles; at larger angles for constant Cmb* the

difference remains less than'1° so that heie tQo. a sufficiently accurate determination of the trim angle is possible.

(b) Zffect of the Beam

In the takeoff of a seaplane the wi'd.th of step of the Vbottom float, on account of the small residual load and. the high dynamic pressure exceeds the natural width of the bottom surface under pressure, in contrast to the flat bottom for which the full beam at step in

the pressure area is utilized. The most fAvorable width of tho bottom depends therefore on the load and. the

d.ynaLic pressure.

'or the purpose of testing these conc.lusions plan-ing surfaces with two Vbottom anglos and. various beams were tosted. according to the following test schedule:

t

In figuree 25 to 28 the measured. values of _are

connected. by d.otted. curves and. cmh* plot-tea against .

The continuous curvos give the results of the computed.

valuas.. _{The differences between the two aro indicated.}

by arrojs. Since beyond tha limiting curve, (fig. 9)

no nro planing condition is set up, the computed curves

aro also dotted. - Good agreement is obtained between the planing process determined. from the diagram and. that from

the observed appearance of the free planing condition. In a comparison of the values of -e for pure plan-ing conditions it is found. thai; the test values _are

always somewhat below the computed values but otherwiao the curves are similar. This is probably to be as-cribod. to the fact that the mean flow direction on the ad.ditiönal wetted areas does not agree with the d.iroo.-tian, of travel so that the resistance -isincreaaed. _'ozt].y by a component of the additional frictional resistance. In spite of this for most purposes the numerically com-'

e6value* ara sufficient

(greae

ff e ice

Lc = 0.025).

An optimum beam which is obtained. both oxperimon-tally and. by computation in the above example lies botwoon the two mean beams, the experimental valuo being somewhat higher than the computed. value.

III U

I uI

Planing

e ur f a ce Test .um-ber - . e3 - -c .

-y1

-12 38 1500 _{0.150 18 0.435 0.142 6 3.74} 13 35 150° .30 18 .109 .142 6 3.74 14 39 150° .472 18 .044 .142 6 3.74 15 40 1500 .772 18 .0164 .142 6' 3.74 12 43 150° .150 50 .435 .071 10 5.26 13 44 1500 .300 50 .109 .071 10 5.26 14 45 1500 _.477 50 .0431 .071 lo 5.26 15 46 150° .772 50 .164 .071 10 5,26 1? 36 132° .390 18 .109 .142 6 3.74 18 41 132° .444 - 18 .0498 .142 6 3,74 19 42 132° .730 18 .0184 .142 6 3.74 16 47 132° .150 50 .435 .071 10 5,26 17 48 132° .300 50. slog .071 10 5.26 18 49 132° .444 50 .0431 .071 10 5.26 19 50 132° .730 5Ö .0164 .071 10 5.26 NACA

1t !io. 1061

₃₇