Hydrodynamic derivatives as a function of draught and ship speed

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TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANICA Rapport No. 477

HYDRODYNAMIC DERIVATIVES AS A FUNCTION OF DRAUGHT AND SHIP SPEED.

Prof. ir. J. Gerritsma

Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg 2

Delft 2208 Netherlands

januari 1979

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s

Contents: page

Summary i

Introduction 2

Model dimensions and test conditions 2

Experimental results 3 Conclusions 5 Acknowledgement 5 References 6 Tables 7 Figure 1 15

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2 L,. 5 1J 7 C' IC) 3

i

4. b / S C' 30 o 5 o 7 g o 40 i 2 J a 5 6 7 8 9 50

i

2 3 4 o G 7 uj_ ) h i a

clj fui'

"iij ) L

dubbe1zi.jdig)

'2

Hydrodynamic derivatives as a function of draught and ship speed.

Prof.ir. J. Gerritsma

Summary.

Forced oscillation experiments in sway and yaw have been carried out with a 10 feet model of the Series Sixty for five loading conditions and three forward speeds.

The experiments included the bare hull condition, as well as the modelequippedwith rudder and propeller. In the last case rudder angle tests hake been carried out, in addition to the determina-tion of the yaw and sway derivatives.

The various hydrodynamic derivatives are given in tabular form and the data inc1ude the corresponding straight line stability

roots.

(enkeizijuig)

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--ij--9 5 6 / 3 9 20 i I b G 9 9 :30 2 3 4 5 U 8 9 40 b G 8 9 50 I 2 3 4 5. 6 7 8 9 hi -' blanco cij f e r introduction.

--2-(dubbelzijdig) 3

To study the influence of draught on the steeriñg qualities of ships a series of Planar Motion Mechanism (PMM) testh have been carried out for the determination of the hydrodynamic mass and damping of low frequency harmonic swaying and yawing motions. The testSihave been carried out with a 10 feet model of the Series Sixty, block 0.70 in five different loading conditions and three

forward speeds.

In addition, static tests have been carried out to determine rudder- and drift angle forces.

To show the influence of rudder and propeller on the magnitude of the various hydrodynamic derivatives, the experiments have been carried out with the bare hull, as well as with the model

equipped with a rudder and a running propeller. The propeller revd-lutions correspond to the ship propulsion point according to one particular model scale value and the ITTC friction extrapolation line. In the experiments the:ranges of the various variables have been chosen to enable the determination Of the linear hyd.rodynamid derivatives.

In the near future a similar series of tests will be carried out to include the influence of restricted wate.r depth.

In this report the international Towing Tank Conference Standard Symbols 1976 hàvè been used.

Model dimensions arid:.:test conditions.

The main dimensions of the ship model and the propeller are given in Table 1, whereas the rudder cohfi tfn: is shown in Figure 1.

The static and P.M.M. tests have been carried out at three forward speeds, corresponding to Froude numbers F = 0.1, 0.2, 0.3; the considered loading conditions are summarized in Table 2.

The friction correction applied to simulate the "ship propulsion point" has been calculated by. using the ITTC 1973 friction extra-polatòr: 0.075 C\7 - (log Re - 2) ¿ (1) (enkelzijdig) OC. 1. _{L,'ìP í:(} _1i.

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I.::

:::i:.

'.C''I

The friction corrections, as calculated for the zero drift- and rudder angle condition, are summarized in Table 3, assuming a model scale 1 60.

The corresponding propeller revolutions are given in Table 4 for the consideréd three' forward speeds. These values have also been used in the P.M.M. and the static tests.

The static rudder angle tests have been carried out with zero drift angle ( = 0) and the following range of rudder angles:

o o o O O o o I

= -21 , -14 , -7 , o , 7 , 14 and 21

The static drift angle tests have been carried out with zero rudder angle ( = 0) and drift angles:

û .10 O ,O ,,O O O

p -

-i

-::)

, -J, J

,

3,5

The P.M.M. tests are carried out at four circular frequencies: w = 0.1, 0.4, 0.7 and 1.0 rad/s.

These values correspond to the following maximum dimensionless frequencies:

wL

= -- _{= 5.6, 2.8, 1.9} for respectively:

3.. Experimental results.

The sideforces Y and the moments N, as measured in the P.M.M. and static tests, have been reduced to dimensionless 'derivatives

Y', N', Y', etc.

y y r

The dimensionless form of the various derivatives correponds to the dimensionless force and moment:

N '-J 1) 'J 'J D .) () ) Fn = 0.1, 0.2 and 0.3. 3 'J 1 2 3 b 6 7 b n 50 I 2 3 4 5 6 7 8 hi n h J. ali co

ci,j fer

o and 7 U) Y, Y ½pUL-2 pp and N' _½PULL pp

For the presentation of the values for (Izz - Ni)', the radius of gyration for all of t'he considered conditions has been taken as.:

k =

0.25L

zz _pp

The static rudder ang.le tests show an almost linear relation of

--31

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Cori ecei or. ov .l.g :o

1:Trkar

tbun oidoi'b7oo1iul)

i-

----

-2 side force and moment with rudder angles up to 14 degrees for the considered speed range.

5 For the static drift angle results linearity of the sideforce is good för drift angles up to 7 degrees (the maximum value being g tested). The moment - drift angle relation becomes slightly non

linear only for Fn = 0.3, loading conditions larger than 60%

i and drift angles exceeding 3 - 4 degrees.

2

3

4 The hydrodynamic derivatives, as determined for the PMM and static

tests are summarized in the Tables 5 and 6. It should be noted

that y-'ç and N:, refer to static values, whereas Y' and N'

corres-y y

pond to the dynamic PMM results. The differences between the two

20 sets of values is rather small, indicating that the frequency effe

in determining Y, and N are not very important.

The derivatives have been used to calculate the s:traightline G stability roots os.. andai

The equations of motions for sway and yaw with the rudder fixed in the neutral position are given by:

2 3

5 N - N + (I - N.)'' - N'r'

8 The stability roots, as derived from (2) are:

9 40 i 2 3 4 = 5 6 7 where: 8 9 50 i .3 B Y (I - N.)' - N' (m - y.)' + - N - rn)' hi bianco cij fer ai =

e;i pagin.c:n (2, 4, 3 r) 1.nc oi (op cj -2 -)

= O r r

-B ±T/B2

-

4 AC

2A

-B - T/B2

-

4 AC

2A

A = (m-Y.)'(:I

-N.

y zz r C = N r - rn)' - Y N

rv

(2) ts 5 6 7 8 (dubbelzijdig) _{(enkelzijdig)}

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2 4 o 'I O 9 .t C J 9 a 4 5 7 3 9 20 -t 7 3 4 5 S '1 n 9 30 i 9 -j 2 3 4 5 6 7 8 9 50 i 2 3 4 5 6 7 8 bi o bianco cijfer

In the Tables 5 and 6 two sets of stability roots are given, corresponding to the static - and dynamic values of Y, N and N respectively.

The differences between the "static" and "dynamict' stability roots

:smal1,

_{as can be expected from the small differences between the}

static and dynamic derivatives, already mentioned.

Conclusions.

From Tables 5 and 6 it may be concluded that the influence of for-ward speed on the various hydrodynamic derivatives is small as compared with the influence of the loading condition and trim of the model.

Forward speed and loading condition have only. a small influence on the values of the stability roots, with the exception of condition lIA (trim by the stern):

iñ the bare hull condition all of the roots have positive values except for the trim aft condition.

With rudder and running propeller there is a positive straight line stability in all cases considered, except for the 40% loading condition, and the 60% loading condition at a Froude number

-Fn = 0.10.

Because of insufficient propeller thrust the 40% loading condition could not be investigated at Fn = 0.30, but this speed is not realistic for the considered hull form.

Acknowledgement.

The experiments and the data reduction have been carried out by R. Onnink and J.B.M. Pieffers.

(dubbeizijdi g) Li; . (7 'L O -J7) 1y.r cc; fr (c;« -. cc :

.a

c 7 --5'--(erìkelzijdig)

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. o-c ÎTaa: orko 3:o:: L2)

6. References.

[i]. F.H. Todd, G.R. Stuntz and P.C. Pien,

Series 60 - The effect upon resistance and power of variation in ship proportions.

SNANE 1957.

[2] W.P.A. van Lammeren, J.D. van Manen and M.W.C. Oosterveld,

The Wageningen B-screw series. SNAME 1969.

()

ccc:;i (o . )

--6-

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R 3 4 b 6 9 tC 2 3 4 5 G 7 8 9 50

i

2 3 4 5 6 7 8 hi ,-f Model Table 1 Ma in Dimensions o

j

(9 2.

c) IYc,

-:- A-

)--;:-r:-,'

Hull form: Series Sixty [i]

L = 3.048 m PP iC B = 0.435 m 2 T = 0.174 m at 100% loading condition :3 4 C = 0.700 G LCB = 0.46% fwd L /2 at 100% loading condition

i

PP 9() Propeller: B Series NSMB [2] .1 D

=0.122m

'5 4

P/D

=1.00

o (5 _AE/A = 0.55 'I z

=4

h lanco

cijfer

- 2

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J

Table 3: Friction correction for model scale 1: 60.

* Propeller emergence 9 _{_**__Insuf.f:icien.t propellerthr.ust}

bi

o blauco

cijier

_{. 8}

-rfr _;bL.o

_1:';

2 ₎ Test nr. loading condition displace-ment m3 TA m TF m LCB % L pp I 40% 0.0647 0.076 0.076 +1.33 ii 60% 0.0971 0.110 0.110 +1.12 lIA 60% 0.0971 0.141 0.080 -2.05 iiI 80% 0.1294 0.143 0.143 +0.84 IV 100% 0.1618 0.174 0.174 +0.46 F n

friction correction in Newtons

loading conditions I II lIA III IV 0.1 0.49 0.57 0.57 0.65 0.74 0.2 1.64 1.91 1.91 2.18 2.45 0.3 3.34 3.90 3.90 4.45 5.01 F n Test number I II lIA III IV 0.1 4.38* 3.96* 3.96 4.16

4U6

0.2 9.06* 8.50* 8,48 8.58 9.06 0.3 16.87* 16.51 19.17 20.20 2 3 4

Table 2: Test Conditions.

8 9 40 2 3 4

Table 4: Propeller revolutions (n/s) P.M.M. and static tests

(model values) b 6 7 8 9 50

i

2 3 4 5 6 7 8 G 7 3 9 o 2 3

î

J G 'I 3 D. 3 4 L. (3 'i 3 30 3 b G 'f

(dubbeizijdig)

_{(enkeizijdig)}

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2 4 O 30

i

2 3 4 b G R 9 40 1 2 3 4 5 6 7 8 9 50

i

2 3 4 5 6 7 8 q

bi'

o

hi a co

cij fer

(:

':'.'

7,

': ::

O" -J

Table 5 a: Hydrodynamic Derivatives (*i0) for F = 0.10

(no rudder and propeller); k/L =

0.25

Loading condition I II ITA III IV - - - - --N

-

-470 800 1080 1255 1750 +N 150 250 130 450 720 (m-Y) ' 680 1150 1120 1700 2310 -Y' '' - 460 710 900 1100 1500 V -N 1 5

3.

21 38 V -N' 156 240 150 462 720

(I-N) '

38 65 64 96 134 -N' r 50 130 130 178 200 -Y r 2 8 1 23 41 (m-Y ) ' r 377 475 500 630 810 '.4, stat. +0.513 +0.073 -0.411 +0.142 +0.318 +2.494 -2.711 -2.562 -2.597 -2.383 +0.551 +0.109 -0.227 +0.226 +0.392

}-2.516

-2.670 -2.585 -2.588 -2.348

-2-

- -9]

--(dubbeizidig)

(enkeizijdig)

'1 20 3 f;

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'J G b 'j 7 I' s e 9 40 2 3 o 5 7 8 s 50 TI 2 3 4 5 6 7 8 t-'

bi

o

hia1co

cii Ler

. 10

-- (2

Table 5 b: Hydrodynamic Derivatives (* i0) for = 0.20.

(no rudder and propeller); k2/L = 0.25

Loading condition I II lIA III IV

Yc

- - - - --N - - - - -+Y 490 850 1120 1345 1800 160 300 150 500 750 (m-Y.) ' y 710 1180 1120 1720 2360 -Y' 460 860 1020 1190 1700 V -N! 2 12 12 28 43 V -N' 170 30.0 175 460 770 V (I -N.) ' ZZ r 37 65 61 91 129 -N' r 80 160 160 220 310 -Y! r 9 37 13 60 68 (m-Y ) ' r 390 540 4.20 700 850 a' 1 stat. +0.289 +0.111 -0.577 +0.115 +0.088 -3.059 -3.080 -2.951 -3.029 -2.994

-li

+0.364 +0.104 -0 439 +0.131 +0 141 :JdY11. -3.088 -3.082 -2.995 -2.969 -3.000 (duhbelzijdig) _{(enkeïzijdig)}

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i j 4 5 6 7 'J 2 3 b ..1 7 9 30

i

2 3 ¿I. 5 6 7 8 9 40

i

2 3 4 5 6 7 8 9 50

i

.2

3 4 b 6 7 8 9

bi

o hi ai ico

cii fer

'..

Table 5 C: Hydrodynamic Derivatives (* i0) for F = 0.30

(no rudder and propeller): k/L =

0.25

Loading condition I II lIA III IV -Yi . - - - - --N - - - -+Y 640 1090 1300 1535 2050 230 390 26.0 680 990 (m-Y.) t ₇₈₀ ₁₂₅₀ 1300 1850 260'O V

-Y'

_y

640 1090 1210 1520 2000 -N! y 1 1 1 35 14 -N' 230 360 .260 630 980 (I -N.) ' ZZ _r 46 65 74 101 149 -N' r 120 190 185 260 335 -Y! r 15 70 10 110 190 (m-Y) ' 4.10 560 430 760 940 oj stat. +0.141. +0.04.0 -0.442 +0.206 +0.229 -3.464 -3.495 -3.027 -3.127 -2.764 a'

_li

dyn. +0.141 -0 020 -0 387 +0.148 +0 237 -3.464 -3.461 -3.013 -3.091 -2.757

(dubbeizi.jdig)

_{(erìkelz:ijclig)}

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3 G 3 -1 3 6 3 9 30 3 o 8 o 40 I 2 'J a J 6 8 9 50 2 3 4 5 G 7 8 9 -1

blanco

L:

(duhhelzi.jdig)

Table 6 a: Hydrodynamic Derivatives (* 10) for Fn = 0.10

(wtth rudder...nd propeller); k/L = O 25

-.12--

-1-(enkolijdig)

Loading condition I II lIA III . IV -Y 115 163 170 210 225 -N -48 -75 -73 -93 -86 450 820 1180 1250 1800 +N 140 280 78 382 600 (m-y.) ' 700 1183 1143 . 1717 2267 -Y' y 450 800 1044 1312 1700 -N! . y -ii -9 -17 -6 19 -N' 113 190 75 313 525 V (I -N ) ' zz t 47 72 62 103 126 -N' r 77 148 161 233 305 -Y! r -4 0 -10 12 21 (m-Y ) ' r 420 610 450 . 710 855 cT]' H 0.271 0.193 -0.722 -0.C38 -0.041 G2 _} stat. -2.713 -3.006 -3.035 -2.949 -3.077 a ' 0.151 -0.011 -0.632 -0.165 -0.081 a2' } dyn. -2.589 -2.786 -3.005 -2.863 -3.000

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i

2 3 4 5 6 7 8 9 10

i

2 3 4 5 G 7 8 9 20

i

2 3 4 5 6 7 8 9 30

i

2 3 4 5 G 7 8 9 40

i

2 3 4 5 G 7 8 9 50

i

2 3 4 5 6 7 8 9 blarco bi. o cij fer

Cor:eces on ovoxigo ri ck ochtermarge (bu.ten ordbonJiii)

Table 6 b: Hydrodynamic Derivatives (* 10) for F = 0.20

(with rudder and prorel1er); kÌL =

0.25

-2-o iìiZ i:í.c cil op

- 13 -. Loading condition I Ii lIA III IV -y 94 160 170 H 175 195 -N -48 -75 -83 83 -100 500 910 1280 1460 1930 143 265 58 375 580 (m-Y.) ' 735 1100 1060 1594 2138 V -Y' 503 917 1300 1527 1987 V -N -8 -6 35 24 39 V -N' 125 262 50 437 675 V (I -N.) ' r 47 70 50 78 100 -N' r 87 167 185 272 327 -y r 2 13 13 66 74 (m_Yr) ' 360 494 307 577 733 a' } stat. +0.086 -2.691 -0.088 -3.116 -1.271 -3.555 -0.392 -3.753 -0.270 -3.621 o''

li

_dyn. +0.014 -0.099 -1.209 -0.349 -0.199 -2.624 -3.1.11 -3.543 -3.805 -3.685 (dubbei.zijclig) _{(enkeizijdig)}

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C orrectie en over:ge an e ;;'. de eche::marge (bui.ten onderbroen iijn)

eOJ. )-J

jß

o btlZ) 1..J u1c* c.! (00 ej.;r

Table 6 C: Hydrodynamic Derivatives (

i0) for F

= 0.30

(with rudder and propeller); k/L =

0.25

Loading H condition I II ITA III, IV -Y - 215 243 255 285 -N - -110 -118 -138 -173 +Y - 1210 1640 1800 2420 +N - 330 120 432 610 (m-Y.) ' y - 1283 1210 1810 2343 -Y' y - 1175 1550 1675 2225 y H -16 10 28 80 - 333 110. 533 767 (I -N.) ' zz r - 83 55 102 118 -N' r - 230 ₂₄₅ ₃₀₈ 403 - 20 0 60 90 (in-Y)'' - 510 440 665 790 ej i stat. - -0.301 -1.139 -0.433 -0.506 - -3.416 -4.605

_3375

-3.623 ej - -0.275 -1.086 -0.256 -0.292 } dyn. - -3.414 -4.583 -3.449 -3.699 i 2 3 4 5 6 7 8 9 lo i 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 .9 30 1. 2 3 4 5 6 7 8 9 40 i 3 4 5 6 7 8 9 50 i 2 3 4 5 6 7 b1 M bL JO

cij fer

- a4-

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Rudder Profile NACA 0018

Figure 1: Rudder configuration

Propeller z

=4

2c.3

-

15 -D = 0.122 m. P0/D = 1.00 AE/A0 0.55