The investigation of the longitudinal stability of hydrofoil craft

(1)

10JAN. 197Ç

ARCH1EF

D AT U M .

'.hee

Qnderad''

.er-nhche -1oqesCh0O DOCUMENTATIE :

Lab.

_{y. Scheepsbouwkwid3}

,

_{e hnische Hogeschool}

-yan de bouwkunde

NATIONAL PHYSICAL

LABORATORY

SHIP DIVISION

THE INVESTIGATION OF THE LONGITUDINAL STABILITY OF HYDROFOIL CRAFT

by

M. Krezelewski

A Station of the

Ministry of Technolog-v

DeIf

SHIP T. M. 212 March 1968

(2)

The investigation of the

longitudinal stability

of hydrofoil craft

by

M. Krezelewski

The program has been prepared to give a convenient tool to the designer when calculating the characteristics of longitudinal stability for hydrofoil craft, and to learn in what way these characteristics are affected by craft parameters.

This program can be applied to hydrofoil craft having surface piercing foils, fully but shallow submerged foils, or a combination of these two

arrangements

Thus,

it

cannot be used for craft equipped

with

both fully and

deep submerged foils since this configuration has no inherent stability0

In this program the equations of craft motions given in references (i) and

(2) are used, and are transformed to

a dimensionless form by using dimensionless

time t, defined as

VO

L1

whe'e V0 - craft speed

L1 -

horizontal distance between foils.

Then,

the equations of longitudinal moon for a craft flying above calm

water wiJ.1 be:

- - pgL1 B +T ₊ P B, fr + T1,

4' + P4' 4' = -- --

_. (2)

B1+ T+

1;+

B4'4'+ T14'

P141 4' g D J2

0)

...

(3)

where p increment of craft weight (positive when total craft weight increases)

D - weight of craft

g - acceleration due to gravity

-

trimming

moment

(positive bow up)

4'

trim angle

(positive bow up)

- vertical displacement of craft centre of gravity (positive _down)

x

-

horizontal distance between centre Af gravity and line of action of force _p

(3)

n = --D where as a = --dz

S1 = area of "I" foil

Z - increment of foil immersion CLI - lift coefficient of Il1 foil

CL1 - slope of the lift curve - load on bow foil

The dynamic stability cf the craft isdetermined. from its existing statical stability and from the negative real parts of the roots of the characteristic equations of motion f the craft. It is dependent upon the above foil parameters and furthermore upon Freude number _{'r =}

V0/V7

and transverse dimensionless radius of ration of craft = L1 /J» There are six further quantities having an influence on the longitudinal motion of hydrofoil craft:

h1 - vertical distance between craft CG and foil when it is fully submerged, and. half the foil immersion when it is surface piercing.

b1 - mean foil chord, and coefficients of added foil mass. - 7 (Lf\

CI

where f 2 + (. h)2

ho zh0/b

h0 - foil immersion b - foil chord

The influence of these six parameters upon craft stability is quite smell and in investigations of their effect on the longitudinal stability _{can be} neglected.

(4)

AD _aD FR N

ii

Kl = K1

K2

J

L1/J

HO

L,

O

OI

ç1 ZI = Zi

SI,

S2,,

S3, S)

are the real parts of the characteristic equation of craft's

notions:

s4 + a1 +

a2 S2

+ a S + a4 = O

...

(6)

ath MI, M2,

1:13, MLê

the inginary parts of these roots.

The roots are obtained.

by Lint s method.

When it is impossible to get these by this method, the

computer investigates whether the craft is stable or not.

Vlhen it

is stable then

in MI

and 1:13

values of 500 are printed. and. in M2

and M2+

the value -500 is

printed.

In the case of unstable craft the corresponding digit8 are

1000 and

-1000.

But in both the above cases the coefficients of equation

(6)

are printed

as

follows:-SI a S2 a2 _S3 a and SAj- = a4

Fthen the control

digit B7

= O then at the end of the printed results

there

are 12 undescribed values. They

are

the values of the coefficients of equations (i) and. (2). The

first

value means B, the second T,

third.

P and so on. Timing

VQhen _B7 = O

time of calculation is 2+

secs.

When B7

= I

mean time of calculation

is 12 secs.

References

(i) M. KREZELE'JSKI An Investigation of the influence of an unstable foil flow on the characteristics of longitudinal motions of

hydrofoil

craft.

(In Polish.) Z.N.P.G. BOXI, 1966.

(2) M.

EEWI

Theoretical prediction of hydrofoil craft responses to the

longitudinal

excitments in smooth water,, (In Polish.) To be published in Z.N.P.G-. BOXIII, 1967.

(5)

Al23'5

17:P

LI)ND2N 11/12/67

IO

22 2CJ)

_{f1,29 ,R3,24,25,R6,R7}

30 JF fl7

2 TT-fN 1542

0

R.fl c.1,C,r,3, Ct,C5,r,6, n7, C, r

65 ÏE'D V1,'12,y13

72 PINT"

T{E INVFSTIO\TII)N F T1E

Lr)NOIT1)F"tLt'

S0 DRINT '

ST\RILITY 2F

YDRI)FOTL 621\FT NI)." AF

90 PRINT

122 PRIN1'

110 PRINT"<D=" 1,

"D="A2,"FR="A3, "N="A4, "1<1

'5

122

PRINT "

13fl RINT

142 1F 1=" THFN3Ifl

1 5

P?JNT "N", "HI)'', "rn1F'',

''orF

i", ''z i"

162 PRINT

17g

LFT ('4

1fl

LET A/!=C1

19

FI)R I-1

TI) C3+1

200 P2INTt'i,

210

GI)SUfl 15

22'

LFT V(I)í4

232 LYT 4

_C1+i*C2

2 NEXT T

252

PRINT

260 PRINT "N","'',

tt,t?t,I9tt

270 LET 2=23

2,0Ç GI)SIJF3 1390 292

21NT

_''M''

.300 GI)S112 1461'I

305 L.T í4=4

310 IF

i2=0 THEN

320 PR INI "K i", "HI)", "I)1E.", "I)ME i",''

7j"

330

PRINT

34

LE'r

352 LFT í54

36 _{F22 1=1 TO 26+1}

370

PRINT 5

32

OOSH1

1540

392 LR.T 'I(I)=A5

400 LFT A5=C4+T*65

¿12

NEXT I 4211 P2INT

43 _{R-TNT''Kl'',''5 1'',''M i'',''S2'', ttv')tt}

442 _{LRT 2=26}

452 GI).}P

139

460 PRINT "Kl.', S53tt, t3t, 54tt, "í4''

472 _{r9!Jf 1460}

475 _{LFT (5}

40 IF

J3 =0 THEN 650

490 _{PRINT "K2","HI)", ''I)HT'', "OMEÌ'', "}

_i''

500 PPI1T

512 _{LET t=6}

522 LET 46=67

530 F22 1=1

TI) 29+1

540 P2INT A6,

552

GOSIJP, 1542

563 LET V(I)=P.6

570 LFT 46=67+I*6R

(6)

o0 NEXT T 59(71 PRINT 600

PRINT ''l<)'',''",''\i'',

''S2'',''M2''

610 LET P=09 620 GOSTiR 1390 630 PR TNT "(-<9'', "53", ''MO", ''54'', "M'i" 640 Gr)SUR 1460 650 GO TO 2690 1390 PRINT

140 FOR I1 TO R

1410 PRINTV(T), F'(I), 9(1), 3Cl), 9(1) 1420 POINT 1'43 NEXT I 1144g PRINT 1'i50 RF.TIJRN 1460 PRINT 147fl

FOR I1 TO R

1400 PRINTV(T), 5(1), T(i),LJ(T),T(l) 1490 POINT 1500 NEXT I 1510 PRINT 1520 PTINT 1530 RF.TJ0N 1540 LET G=4+(1Pui)*A6 1550 LF.T 01=1/(A1*A2) 156° LEi G2j)Lt+(1-A4)*A5 1570 I.T G3=1A4+A/i*46/ 1500 LET G41-1\/-+t/4*5 1590 LFTG5=1/(c2*A3t2) 1600

LET G6ClA).4G5*7t9

1610 LET G7\4*R3*R5/A0t2 1620 LOT G0(1_A4)*R4*R6/43-r2 1630 3F.T G0=G0/G7

1640 LET R5=(A4 I )*(A6+(A5A6)*141)*!1*A4/G

1650

LET R6(C1A4)(1-46)4G102)/G

1,60 LET R7((J4-1)*(1A6)*A4)/(G*R5) 1670 LFT P0( A4 1) *( (5 1) *G1+G3) */( G*R5) 1600 LET H1=1+(1+G0)*07 1690

LET -t22*G5

1700

LET H3G*A1/A3?2

1710 LET 4=C44-1+A/I-G0)*G7 1720 LET M5=(C1_A4)*CA5_1)*A/4+(4+(1_Aí4)*02)*2*2*R1)*G5 1730

LET H6=(G2+Cii)(6-1)MA2A'i)G5

1740

LET M7/7

1750

LET H0=L5-1)*06

1760 LET H9=(P6-1)*G6/G1 1770

LET K5=1+((1A4)?2+42)G7*472

1700

LET i6=(G4(1R2)2A2*R1)G6

1790 LET K7=(A5-1-4-03/G1)*06 1000 LET G91*<5-7*(-{4 101fl

LET K1(R1K6+H2<5T*O7)/G9

1020

LET X=(1<7+-{2K6+H3<5K4H9H5H8H6H7)/G9

0030 LET 1<3(H2*K7+H3*X6M5*H9M6*H0)/G9 1040 LET K4=(H3*K7H6*!--{9)/G9 1050 LET 7=K3/K2 /1060 LET F=K4/<2 1.70

LET L0

1009 LET N1K1-7 1090 LET N=i-<2F'*M 1900

LET Z1=<3F*M)/N

2

(7)

19l LET F1</?,N l91 L1'T '11=7-71 192fl LET "u1=!P,S('11)

1'S

LET M2=F-F1 193fl LET .1=RS(12) 19 LET 7=71 195g LET F=Fl

l6

LET IL+1

l97 IF L>l(fl THEN lin

1Qn

TE .11> (1.flfl5 THEN 1Sfl 1Q9(' TE 12> c.nn5 THEN

1Efl

2flPfl

_EflJR

252r ne TFR7=n THEN 2(3 2311 LET PCfl=X2 2(2 LET fl(T)

23'

LET H(I)='3 2.n31

(fl

T) 2'1

2n32

LET P1X2

2fl33 LET 2l=X4 2n3/i )..ET .1=X3 2nl4 LET 7=M 215n LET F=N 2n6r G1)S! 252n

2(65

IF P7n

THEN! n92 227r LET (I)=X2 2nçr2) LET

T(T)=X4

2fl9 LET (I)=X3 (3fl Tfl 21'1fl LET Sl=X2 21193 LET Ti=.4 9119 _LET _J1=X3 213fl Gfl T

221

2l1C IF 1<fl THEN 91911

2i2 IF R2<11 THEN 2i9 21311 IF <3<11 .THEN 21911 2l'n TE <4<11 THEN 21911 21511 IF (H3*H2-H3)*R3-K/,*Vi9<fl THEN 21911 2155 IF 117=11 _{THEN 2172} 2111 LET O(I)=5011 2170 LET T(T)=51111 2171

r1)T11 2lfl

2172 LE1 111=5('11 2173 LET T1=511

2iR

GO T3 25

21911

IF

ì7 HEÑ 2242 2195 LET OCT)=111fl 22112

LET T(I)=1020

92115 IF P711 THEN 2242 92111 LET P(I)=(l 22211 LET (T)=KP 2232 LET S(J)=K3 224rn LET IJ(I)=H4 22/41 co in 7252 22/42 'FT 111=111112 22/3

LET T1=132

224

LET P1=H1

22/5

LET .r1<2

22/«- LET S1=K3 2247 LET Ui=H4 22511 iF 117=2 THEN 22911 22eY F2INT 25,R6,77,2s 3

(8)

L;

227fl

PRINT

229(

RETMRN

229(Z

PRINT"T'P C{(\RcRTERISTICS flF THE LDNGITLTDINL STrILITY"

93fl _PRINT'S (W

Hyr)nr'Fr)IL CF(FT N1." AF

2.31(

PRI\T

22P)

pjï

233 PIT '<D-''f\ I , "'D="2, "FR". "N=''A4,

'!< I =''P5 23IJ PRINT

K2"P6, "J:j7

5( _PRINT

236rn

PRINT "f(V', "m.1,',

"r)MEl',,

'7J'',

"si''

238g

PRINT

5,R6,R7,R,1

24P1fl PRINT

2'i1(

PRINT "11',,

''C2'

'fl',

IÇ'

2/-3

PRINT fll,N1,S1,T1»Jl

R51

PRINT

RZi6fl

PRINT HI,,H3»-M,H5

2i7)

PINT H6,H7,HF,H9,K5

2F

PRINT !KA, <7 2L9ci

PRT'T

25D(

P'T

251(2S 1fl T )A9P

252(

LET

T/2)?2-E

253R

IF X<i TREN 259fl

25r)

LET X1SflR(X)

'55(

_{LET X2-?/2-'<1}

256m

LET X3=-T/2+XI

2571

LET X4=ø

25R Gr) TI) 262m

259g

LET X'=SI)R-X

R6

LET X2-7/2

2r,1

LET X3<'

'6'fl

ÑFTJRN

263fl

DíTA 2,fl. I)6,

.,

I). 5,

1, 1

,

2 56,

2

26/4( 1)4T(\

266I) U)ATÇ 1,1,1

269

END

HE CH4RÇCTFRISTTCS (W THE LI)NGITUDINE\I. ST6RILITY (W

_{iYDI)FI)IL CR4FT Nr).}

6

'<D= 25

'fl

FR 2

.5

<i= I 1<'- i _.J=

.56

H'fl I)'4T I)MEI TI

-6.25

-.666667

P

-2.95fl34

11 SR S3 M3 c;/4

37313

-2.95fl34

-I.9(35

1.i51I7

-1.91235

I)96fr?

¿i.16667

6.25 3.92625 E-/i

_{6.52P95 E-2}

i. 16667

_{.7311 E-3}

I)

_1.15732

6. 3 R99

1fl.R'i

(9)

2640 DATA .129,1.Ç122,.0666,.0606,5.72,6.39,1

2650 DATA .3,. 1, 5 . 5,. 5, 4, 0 5, 5

Al2345 9:49 LONDON 12/12/67

THE INVESTIGATION OF THE LONGITUDINAL STABILITY OF HYDROFOIL CRAFT NO. 2

K2/ HO _OME _OME1 71 0 _-8.33333 _-.333333 .06 _.03 .5 _-6.94444 _-.722222 .024 _.036 1 -6.25 _-.666667 0 _.04 1.5 _-5.33333 _-.633333 -1.71429 E-2 _{4.28571 E-2} 2 _-5.55556 _-.611111 -.03 _.045 2.5 _-5.35714 _-.595238 -.04 _{4.66667 E-2} RD= 25 <2= N .3 / .4 AD= .06 1 HO -5.25 -6 FR= 2 J= 2.56 OME -.666667 -.666667 N= .5 OMEI 0 0 K1= ¡

n

.04 .04 .5 -6.25 -.666667 0 _.04 .6 -6. _-.666667 ₀ _.04 .7 _-5.25 _-.666667 0 .04 .8 -4. _-.666667 ₀ _.04 N Si Ml S2 M2 .3 -2.52717 1.06471 -2.52717 -1.06471 .4 _-2.84719 _.633803 _-2.84719 -.633803 .5 _-2.95034 _.347313 _-2.95034 -.347313 ? .6 _-2.84598 _.636267 _-2.84598 _-.636267 .7 _-2.52538 _1.066 _-2.52538 _-1.066 N S3 M3? S4? M4 .3 -1.90602 1.45903 -1.90602 -1.45903 .4 -1.90049 1.45349 -1.90049 -1.45349 .5 -1.90035 1.45117 -1.90035 -1.45117 ?.6 -1.90097 1.45346 -1.90097 -1.45346 .7 _-1.90675 _1.45934 _-1.90675 _-1.45934 / 1.5 2 2.5 Kl -8.33333 -10.4167 -12.5 SI -.833333 -1 -1.16667 Ml 0 0 S2 .04 .04 .04 .5 7.27921 500 22.9382 -500 -2.95034 .347313 -2.95034 -.347313 1.5 -1.1174 1.14345 _-1.1174 _-1.14345 2 _-.945892 _1.12678 _-.945392 -1.12678 Kl S3? M3 S4 _M4 .5 _50.4666 ₅₀₀ _33.6368 -500 1 -1.90035 _1.45117 -1.90035 -1.45117 1.5 _-4.94635 _1.3612Lj -4.94635 _-1.36124 2 _-7.42527 ₀ -5.23257 0

Kl HO/ OME OME1 ZI

.5 -4.16667 -.5 0 .04

(10)

6 K2 SI MI 52 M2 0

-.'39849

1.22176

-.489849 -1.22176 .5 -.943294 1.3198

-.943294

-1.3198 ¡ -2.95034 .347313 -2.95034 -.347313 7 1.5 -3.67179 0

-1.30203

0 2

-3.77705

0

-1.06777

0 K2 53 M3 S4 M4 0

-4.36063

.631099

-4.36063

_-.631099

-3.90905

.834375

-3.90905

-.834375

1 -1.90035 1.45117 -1.90035 -1.45117 1.5 -2.36558 2.59166 -2.36558 -2.59166 2 -2.43041 3.28235 -2.43041 -3.28235 TINE: 9 SECS.

170

PRINT"KD", "HO",

"OME", "OME1" "Z 1"

170 PRINT

170 LET A=A1 180 LET A1=C1

200 PRINT

Al,

220 LET VI)A1

230 LET A1=C1I*C2

260 PRINT"KD",

"S 1", "M1","S2","M2"

290 PRINT"l<D", "S3", "M3", "S4", "M4"

305 LET A1=A

320 PRINT"AD","HO","OME","OrvlEl","Zl"

340 LET

=A2 350 LET A2=C4

370 PRINT A2,

390 LET V(I)=A2 400 LET P2=C4+I*C5

430 PRINT ''AD",''S1","M1'',''S2","M2"

460 PRI NT "AD", "S3", "M3", "S4", "Nl 4"

475 LET A2=A

490 PRINT "FR","HO",

"ONE", "ONlEl","Zl"

510 LET AA3

520 LET A3=C7

540 PRINT A3,

560 LET V(I)A3

570 LET A3C7I*C8

600 PRINT "FR'',"S1","M1","S2","M2''

630 PR INT "FR", "S3", "M3", "S4", "M4"

2650 DATA

(11)

Al2345 10:01 LONDON 12/12/67

THE INVESTIGATION OF THE LONGITUDINAL STABILITY OF HYDROFOIL CRAFT NO. 2

KD= 25 AD .06 FR= 2 N .5 K1= 1 K2 I J= 2.56 KD RO OME ON1E1 ZI AD HO OME OMEI 71 .04 -6.25 -1 0 .04 .06 -6.25 -.666667 0 .04 .08 -6.25 -.5 0 .04 .1 -6.25 -.4 0 .04 .12 -6.25 -.333333 0 .04 25 -6.25 -.666667 0 .04 30 -7.5 -.555556 0 3.33333 E-2 35 -8.75 -.47619 0 2.85714 E-2 40 -10 -.416667 0 .025 45 -11.25 -.37037 0 2.22222 E-2 Si Nil _S2 _M2 FR HO OME OMEI ZI 1.5 -6.25 -.666667 0 .04 2 -6.25 -.666667 0 _.04 2.5 -6.25 -.666667 0 _.04 3 -6.25 -.666667 0 .04 AD SI Nil S2 M2 .04 _-1.296 0 -1.14518 0 .06 -2.95034 .347313 -2.95034 -.347313 .08 7.2771 500 27.1636 -500 .1 -1.13754 2.10004 -1.13754 -2.10004 25 -1.90035 1.45117 -1.90035 -1.45117 30 -1.8998 1.79988 -1.8998 -1.79988 35 -1.89906 2.09242 -1.89906 -2.09242 40 107.656 500 129.165 -500 25 -2.95034 .347313 -2.95034 --.3473313! 30 --2..95204 1.37762 -2.95204

-1.37622

35 -2.95303 1.91439 -2.95303 -1.91439 40 9.70217 500 45.7044 -500 KD S3 M3 S4 M4 AD S3 M3 S4 N14 .04 _-7.69983 0 _-4.41513 ₀ .06 -1.90035 1.45117 -1.90035 -1.45117 .08 50.4666 500 50.4551 -500 .1 -1.7738 2.38726 -1.7738 -2.38726

(12)

lINiE:

9 SECS.

BYE

*** OFF AT 10:08

LONDON 12/12/67.

FR

Si

Ml S2 M2

1.5 -2.4663

0

-1.8559

0 2

-2.95034

.347313

-2.95034

-.347313

2.5 6.48297

500

19.6944

-500

FR S3 M3 S4 M4

1.5 -7.62672

0

-3.86762

0 2