Tentative results of the horizontal oscillation with a 4 meter model of the Britisch Bombardier

Report No.

_239.

LABORATORIUM VOOR

SCH EEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

TENTATIVE RESULTS OF THE HORIZONTAL OSCILLATION WITH A Ir-METER MODEL OF THE "BRITISH BOMBARDIER".

by

June 1969.

Tentative results of the horizontal oscillation tests with a k-meter model of the "British Bombardier".

by

G. van Leeuwen.

Suiiimary.

Horizontal oscillation tests were performed for four initial speeds with a model of the 50.000 ton deadweight tanker "British Bombardier", to determine the hydrodynamic derivatives of a non-linear mathematical model.

The test programme is given.

Tentative results are obtained without considering the correlation be-tween the measurements at the four initial speeds.

Introduction.

In pring of

₁₉₆₈

horizontal oscillation tests with a 1v-meter model of the tanker "British Bombardier" started. Originally the test programme was designed in such a way that the results of the tests conducted at one specified initial speed would contain the information needed for the determination of the hydrodynamic derivatives. Actually this means that the test programme should be repeated four times, i.e. for

_15.5,

12.b, 9.3

and

6.2

knots. As this would take too much time in which the facilities could not be used for other purposes, the test programme was curtailed in such a way that could be expected that the remaining pro-gramme could supply sufficient information.

For the determination of some non-linear derivatives however it was necessary to assume that the non-dimensional values are independent of the forward speed.

However the present report deals with the results of the separate tests, which means that some of the derivatives listed in tables II to IV are not definitive or have not yet a value at all.

-2-The test programme.

The test programme consisted of three parts i.e.:

I propulsion tests

II static- and oscillatory swaying tests III yawing tests

The propulsion tests vere performed to derive the additional model resistance and the number of revolutions of the propellor satisfying the condition of constant power during speed-loss simulation tests.

The static sway tests vere performed to determine all derivatives concer-ning combinationsof drift- and rudderangle, while the oscillatory swaying tests were mainly performed to determine the added mase in lateral

direction.

The yawing tests provided the remaining derivatives i.e. all coefficients concerning combinations of angular velocity, drift- and rudderangle.

In tables I and II a survey of the sway- and yaw tests performed is given.

Data procesing.

For the computation of the coefficients by a digital computer a least squares analysis is used. The pertinent Algol program is made in such a way that after the computation of the coefficients, their maximum contribution is compared to a given limit. If the contribution is less than this limit, the coefficient is supposed to be Zero while the remaining coefficients are computed again.

The tentative values of the derivatives summarized in tables III to VI are computed exclusively with the results of the tests performed with the speed which is given at the top of each column. As follows from the test programme in some cases the non-linear derivatives are determined for a very small range of the variable concerned or could not be determined at all. So in these cases the results of the other speeds will be combined and a new value of the non-linear derivative can be found by extrapolation.

2

-3-3

Final report.

The final report will deal with the results of the above mentioned combination of all information available. The coefficients derived

in this way will be used for the predictions of the various ma-noeuvres performed by the

"BrtLsh

_{Bombardier" on full scale.}

p indicates that test has been performed

TABLE I (sTATIC SWAY TESTS)

U actual speed U advance speed

L

=u

g

rtmber of shiplengths sailed during one period of oscillation.

Act.Speed 1.080 m, .864 rn,5 .648 mi .432 Fn.(act.Sp.) .172 .138 .103 .069 Adv.Speed 1.080 m15 1.080 rn1 .864 / i.o8o m, .864 .648 rn1 1.080 / .864 m1 .648 rn1 .432 m, Speed loss u' = O u'= -.20 u' O u' =-.40 u'=-.25

U'

O U7 -.60 u' -.50 u' -.33 u' = O

R.p.s. 12.38 11.95 10.29 11.54

9.85

8,34 11.20 9.53 8.00

_6.50

lvi

lvi

Ivi

ivi

ivi

lvi

T

lvi

ivi '

lvi

ivi

ivi

8°

+12° +13.8° .070 .139 .208 .239 .070 .139 .108 .056 .111 .i66 .191 .070 .139 .1o8 .239 .042 .084 .125 .143 .052 .104 .156 .179 .070 .139 .108 .239 .028 .056 .083

.095

.035 .070 .104 .119 .047 .093 .139 .159 .070 .139 .108 .239 combined drift and

rudder--tests

[I

9 18 27 36 9 18 27 36 9 18 2736 9 i8 27 36 9 18 2736 9 1827 36 9 18 27 36 9 18 27 39 18 27 36 9 18 27 36 +

pppppppp

ppp

pppp

ppp

pppp

-p =0 all rudderarigles Symbols:

v =-sin

*

L r

_=u.r

= L r U-U o u = U I o

s

TABLE II (YAWING TESTS)

Act.speed 1.080 .86)4

m

.6148 rn!8 .1432

rn15

Fn.(act.sp.) .172 .138 . 03 .069

Adv.speed 1.080 m1 1.080 m1 .8614 m1 1.080 Ifl/ .86)4 m1 .6+8 m1 1.080 m1 .8614 m1 .6148 m1 .1432 m1

Speed loss

U' =

O u'=-.20 u' = O u' =-.140

_u'-.25

u' =0 u'=-.60

uT_.50

u-.33

u'O

R.p.s. 12.38 11.95 10.29 11.5)4 9.85 8 314 11.20 9 53 8.00 _6.50

r*

2u/*

r' r r' r' . r r . r ' r y r _.. r .05 5.03 .037 .05 .10 3.53 .053 .10 .019 .06 .019 .075 .019 .10 .15 2.87 .065 .15 .20 2.147 075 .20 .0148 .16 .0)48 .20 .027 .12 .02 .15 .027 .20 .012 .08 .012 .10 .012 .012 .20 .25 2.20 .013 .10 .013 .125 .013 .013 .25 .30 1.99 .060 .2)4 .06. .30 .033 1& .03 .225 .033 .30 .015 .12 .015 .15 .015 .015 .30 .35 1.83 .oi6 .1)4 .016 .175 .oi6 .016 .35 .140 _1.70 .070 .32 .070 .140 .039 .2)4 .03' .30 .039 .140 .017 .16 .017 .20 .017 .017 .140 .50 1.51 .079 .140 .079 .50 .01414 .30 .01414 .375 .01414 .50 .60 1.36 .087 .148 .087 .6o .0149 .36 .0149 .145 _.0)49

.6o°

.70 1.2)4 _{.096 .56 .096 .70 .0514} .142 .0514 .525 .05)4 .70 driftangle(deg)0 14 8 12 0 14 8 12 0 14 8 12 0 14 8 12 0 - 14 8 12 0 14 8 12 0 14 8 12 0 14 8 12 0 14 8 12 0 14 8 12 rudder

°PPPPP

PPPPP

P

PPPPP

p p p angle

l2p

p p _{p p p p} (degrees) 18 p

2)4p

P p p p _p

36p

p

ppppP.

P

PPPPP

p p

p indicates that test has been performed. _{O tests only performed atS}

6

TABLE III.

Mass coeTicien-ts * lO5

TABLE IV.

Lateral force coefficients *

T

-Advance

speedU

o

1080m,

s

864m,

s

.648

m,

s .1432 m, s

l'-N:

Z r +1142 +1143

+138

+129

r

-66

-46

-53

-64

M'-Y:

X

_-2267

X

+2230

X

_-38

_X

_-31

X X X X Advance

speedU

o

1.080

m,

s

.864

in,

s .6148

m,

s .1432

m,

s

Y'

o

-13

-15

- 20

- 114

+ 214 +31 +1414

+ 63

Y' tS uu O O o X -i'rri

-1828

-1731

_-18514

y'

-iTo

-782

-808

_-685

+232

+225

+256

+344

-15

-18

_-49

X -15143

-1732

-1335

X

- 8614

- 928

_-1065

X

+ 211

+ 179

+ 193

X

y'

_ouu O o o _X

y'

-866o

_-7530

_-10239

_-9307

y'

+2843

+2594

+3157

X -i-1189

+ 325

+893

0

T

'ABL IV (continued)

5

Lateral force coefficients * 10 Advance speed U

1.080

.8614 s .6148 m, s .1432 n/ s

-8-Y, vr 6 X +200 +386 X Y, vvvll o O +3688 X

Y,

rvv-u X X X X Y, 6vvu y, vr óu o X X X X X X X Y' vrr o -17143

-2171

X

y

rrr +10149 +361 +535 o

y,

6rr o o

-128

O

Y,

vrru y, rrru

yt

órru X +2951 o X +928 +5140 X + 1535 o X X X 6 +250 o

-201

o rcS 6

-69

-25

+82 O

-53

o _313

_-166

o o +52 X

y'

v6óu +250 X X X y' ró óu o o +226 X 5ä6u

-72

+50 +1014 X

Y,

6 6uu o o O X

8

TABLE V.

Moment coefficients * lO5

-9-Advance

speedU

1.080 m1 s .8614 m, s .6)48 m, s ,1432 m, s N' o 0 0 0 +3 0 -8 -8 -18 N' o O O O X N' _-1415 147)4

₄₉₉

₄₈₎₄ N' _-259 -.2140 -2)48 -258 io6 -112 -127 -151 N' ou O O O X N' _1498 -578 X N' ru -260 e-206 -217 X N -.90

-90

-113 X N' ouu O O O X N' virv -835 -622 0 0 N' _{-2735 -2198} -2368 X _2614 -565 428 -227 N' vrO X -130 -11)4 X N'

mu

0 0 +3688 X N' rvvu X X X X N' Ovvu O X X X N' vr Ou X X X X N' vrr O +141)4 +388 x N' rrr -18)-t -305 -2)41 -125 N' Orr

-70

-96

-i614

-62

N' vrru X X X X

9

TABLE V (continued) Moment coefficients * 10

TABLE VÌ Lon,itudina1 force coeffiient. Advance speedlJ0

1.080

m,

s

.86k

m

"s

.6148 m1 .1432 m, s rrru N' rru N'56 ±6T3

+396

O 0 0 O O O 0 O +1439 0 O

+22

0 O O O

-33

O 0 0 O 0

+15

O O O 0 O X X O

-32

+17 X X X X X Advance

speedU

o 1.080 m, s .8614

m,

s

.6148

m,

s

.1432

m,

s

-206

,105

- 51 ₁₆₉

X'

-132

- 140

-25

+ 148 -1141

_-137

_-151

_-182

X'

uu

-148

-141

+ 5 + 'T

X'

+2060

₊₂₁₀₉

₊₂₀₅₇

X X'6 -

37

-71

-6

-53

X, X o

+119

-+105

-+102

-

-X' 14141

-366

₊₃₁₁

-136

(w&s 7203)

10

TABLE VI. (continued)

Longitudinal force coeffidients.

X means: no information available; the coefficient concerned will be estimated or derived from the results of other speeds.

Advance

speedU

1.080 m, s .861 m,

s

.618 m, s .1t32 X' rru -361 +26 +112 X X -123 -86

i68

-.290 XI uuu -23 -25 -3

-T

x

vru X X X X X' róu -70

-i8

+126

x

XI Svu +121 +105 +102 X X' u -111 -110 -105 i148