Further experiments of yawing effect on ahead resistance of ships

By

Keizo UENO, Kazuaki EGI, Kunihisa KONDO and Masanobu YAMAGUCHI

Reprinted from the Memoirs of the Faculty of Engineering

Kyushu University, Vol. XXIII. No. 3

FTJKUOKA JAPAN 1964

With the Compliments of the Author.

Lab.

y. Scheepsbouwkune

Technische Hogeschool

Dell t

Further Experiments of Yawing Effect on

Ahead Resistance of Ships

Keizo UENO

Professor of Naval Architecture

and

Kazuaki EGI,* Kunihisa KONDO't't and Masanobu YAMAGUCHI**

(Received December 11, 1963)

Abstract

In the preceding paper1) the authors investigated the effect of yawing on ahead resistance of

ships, carrying out resistance experiments on the three full tanker models artificially forced yawing,

and found that the ahead resistance increases with the increase of amplitude of yawing angle and yawing frequency, and also introduced the empirical formula calculating quantitatively the increase rate of ahead resistance of ships due to yawing. In order to obtain the effect of ship form on the increase rate of ahead resistance of ships due to yawing, we carried out resistance experiments on nine ship models with various kinds of forms, artificially forced yawing by just the same method as before1> at the Ship Model Experimental Tank of Kyushu University during the period between

May 1962 and February 1963. As a result, we found that, when ships' form, length, speed, ampli-tude of yawing angle and yawing period are given, the increase rate of ahead resistance of ships due to yawing can be approximately calculated, and also that the effect of yawing on the ahead resistance of ships is, roughly speaking, small for the bulbous bow form, and large for the Maier form, taking the middle value of the above two for the normal form.

1. Introduction

In the preceding paper° the authors in-vestigated the effect of yawing on ahead resistance of ships, carrying out resistance experiments on the three full tanker models (Block coefficients 0.785, 0.833 and 0.861

res-pectively) artificially forced yawing, and found that the ahead resistance increases

with the increase of amplitude of yawing angle and yawing frequency, and also in-troduced the empirical formula calculating

quantitatively the increase rate of ahead

resistance of ships due to yawing. In order

to obtain the effect of ship form on the

f The Brief explanation of this paper was pre-sented as the Contribution to the Resistance Committee of the 10th International Towing

rank Conference held in Teddington, England, on September 1963 in a subject "Some

Experi-ments of Yawing Effect on Ahead Resistance

of Ships (Continued)."

Navel Architect, Mitsubishi Shipbuilding and

Engineering Co., Ltd.

Naval Architect, Nagoya Shipbuilding Co., Ltd.

t* Student, Graduate Course of Naval

Architec-ture, Engineering Division, Kyushu University.

increase rate of ahead resistance of ships due to yawing, we carried out resistance

experiments on nine ship models with various

kinds of forms, artificially forced yawing by just the same method as before' at the Ship Model Experimental Tank of Kyushu University within the range of time between

May 1962 and February 1963. In the present

paper the above experimental results are stated.

2. Symbols and Formulae of Calculation

Dimensions of Model and Ship

L = length between perpendiculars of ship

in m.

¡ = length between perpendiculars of

mo-del in m.

b =breadth of model in m.

d =draft of model in m.

CB =block coefficient of model

Icb =distance of longitudinal centre of

bu-oyancy of model forward of midship expressed in 96 of ¡

= weight of displacement of model in

kg.

170 Keizo UENO, Kazuaki Ei, Kunihisa KONDo and Masanobu YAMAGUOUF (Vol. XXIII,

g = gravitational acceleration

p =density of water in kg. m.4sec.2 ii =coefficient of kinematic viscosity of

water in rn.2 sec.-'

y = velocity of model in m. sec. V =velocity of ship in m. sec.' V3 =velocity of ship in knot F =Froude number

= Reynolds number

f = frequency of yawing per sec. T =period of yawing in sec. =1/f

6 Express liner (Medium bulbous bow) 7 Aeroplane Carrier (Large bulbous bow) 8 Destroyer form (Yudachi model) 9 Fishing boat model5 (Normal form) 10 Supertanker model (Normal form) 11 Supertanker model (Normal form) 12 Supertanker model (Normal form)

Table 1. X 100% Cs, =(C,F±C2F2)Kx 100%, wherb

K= +

(C,.,,,-C,,)

F=h'0 fViJ/.ao fLa0

F,, vv'jL V and also

Model _{Type of Ships} i b d icb

CB A S

No. (m.) (m.) (m.) (%) (kg.) (m.2)

1 Cargo ship (Normal form) 1.80 .239 .0912 -1.43 .583 23.09 .5300 2 Cargo ship (Small bulbous bow) 1.80 .260 .0913 -1.36 .598 25.59 .5570 3 Cargo ship (Normal form) 1.80 .242 .0876 -0.53 .641 24.50 .5400

4 Cargo ship (Semi-Maier form) 1.80 .246 .0898 H-0.66 .702 27.89 .5788 5 Cargo ship (Maier form) 1.54 .196 .0900 +1.66 .696 19.40 .3595

1.42 .196 .0600 -0.78 .655 10.78 .3168 1.50 .245 .0732 -0.47 .625 15.76 .4089 1.96 .182 .0518 -4.20 .434 8.77 .3479 1.20 .232 .1083 -3.30 .603 18.10 .4220 1.80 .277 .1108 +2.44 .785 43.35 .7391 1.80 .277 .1108 +2.44 .833 46.00 .7727 1.80 .277 .1108 +2.44 .861 47.55 .8022

Fishing boat model was tested at the draft with 27.7 % of d trim by the stern.

f,, = corresponding frequency

=f/L/g

r, =total resistance of model in kg.

=amplitude of yawing angle in radian

Cjm=frictional coefficient of model C,., =frictional coefficient of ship

C,,,=total resistance coefficient of model without yawing =r,/112.pSv2

Cmm= total resistance coefficient of model

with yawing

C,, = total resistance coefficient of ship

wi-thout yawing

4C,,,,= increase of total resistance

coeffici-ent of model due to yawing

4C,= increase of total resistance coeffici-ent of ship due to yawing

C = rate of increase of ahead resistance of ship due to yawing in %

K =coefficient of scale effect F = parameter

Ci and C= constants to be determined by the resistance tests of model with yawing

Formulae of Calculation

It is known from the preceding paper' that the value of C can be calculated by the

following formulae.

'=1+c1F+c2p=1+4

_C,,,,

3. Ship Models Tested

Particulars of nine models tested corres-pond to the numbers from 1 to 9 in 'Fable 1, in which the data of three tanker models

tested before' are represented as the Model No. from 10 to 12. As shown in Table 1,

we took five cargo ship forms with various

kinds of block coefficients, among which two

are normal form, one small bulbous bow form, one Maier form and one semi-Maier form, and also took an express liner form with a medium bulbous bow, an aeroplane carrier model with a large bulbous bow, an ex-destroyer Yudachi model and a fishing boat model.

All models are made of wood with their surfaces varnished, and they are provided with no rudder and no bilge keel. As the tur-bulence stimulation devices, piano wires of 1 mm. diameter were fitted on model sur-faces at the stations of 1/20. 1 abaft the lead-ing edges of the models.

AP AP Fig. 1. MODEL i MODEL 2 Fig. 2. MODEL 3 Fig. 3. q qi q _fp 9 FP ,rp r4 AP

172 Keizo UENO, Kazuaki En; Kunihisa KONDO and Masanobu YAtAnucRE (Vol. XXIII, p AP P P MODEL 4 Fig. 4. (q MODEL 5 Fig. 5. MODEL 7 Fig. 7. Th MODEL 6 Fig. 6. 2 91 F-p q34 _fp PP FP

4. Test Results

The range of yawing amplitude a0, yawing

frequency 60f/min., towing velocity y and its corresponding Froude number F tested for each model are represented in Table 2. Namely, towing experiments were carried

out for each model artificially forced yawing

by just the same method as

before"

for three or four

values of a0 and four values

of 60f/min. as indicated in Table 2, and the amount of total resistance rt was

mea-sured. In Table 2, the cases of a0=0 and 1=0 correspond

to the case of the model advancing without yawing. All measured values of r were converted into those

for the standard tempera-ture 15C, using Dr. K. E. Schoenherr's frictional

for-MODEL 8

Fig. 8.

MODEL q

Fig. 9.

mula for plates, while those resistance ex-periments had been carried out at the various values of temperature of water within the range of 8C-16C. The experimental values

of rt/z for each model were expressed as the contour curves for test values of a0 and 60f on the base of F, as shown in Fig. 10-S Fig. 28. Table 2. Model No. Yawing amplitude (a0 in degree) Yawing frequency (60 f/mm.) Velocity a in (rn/sec.) Froude number (Fa) Constants C1 C2 1 0 1.46 1.96 0 20 30 40 0.20-1.35 0.05-0.32 0.60 166.0 2 0 1.50 2.00 0 20 30 40 0.20-1.35 0.05-0.32 1.30 91.5 3 0 1.40 2.20 0 20 30 40 0.20-1.35 0.05-0.32 1.20 144.0 4 0 0.95 1.50 2.00 0 20 30 40 0.20-1.31 0.05-0.31 0.30 216.0 5 0 1.50 2.00 0 20 30 40 0.20-1.15 0.05-0.30 3.21 82.1 6 0 1.50 2.00 0 20 30 40 0.20-1.55 0.05-0.42 300 25.0 7 0 1.50 2.20 0 20 30 40 0.20-1.55 0.05-0.42 1.00 104.0 8 0 1.67 2.07 0 20 30 40 0.20-3.20 0.05-0.73 8.40 -54.0 9 0 1.70 2.10 0 20 30 40 0.20-1.70 0.06-0.50 4.00 60.0 10 0.90 63.0 11 0.90 63.0 12 0.90 63.0 AP FP

174 Keizo UENO, Kazuaki Ei, Kunihisa KONDO and Masanobu YAMAGUORI MODEL 4 20 60-°

f

41 5 o 010 OiS 020 025 030 F Fig. lo. 'I o 010 015 0.20 025 0.30 Fig. 11. 20 15 "o 10 s o 0.10 MODEL 2 a'.= 20' 601- 0 = 20 30 40 Fig. 13. F-fl (Vol. XXIII,

1

j,.

0.15 0.20 025 030 20 15 t'o s MODEL -I i.qo 601 0 20 =30 40 r-..

/

/

/

/

..

//"

/.'/

/

10 5 20 lo 010 015 020 0.25 030 O -30 40

;

-MODEL 3 &.- 2.2 60* O 20 -30 40 Fig. 14. S, 5 _---. 010 0.15 0.20 0.25 030 Fig. 15. 010 0.15 0.20 025 030 F Fig. 16. /1 15 MODEL 4 D c.= 0.qY 601 - O /'I/ - =20 =30 -40 _{,/ ,/} 10 5

---:7---t;,

.7- -72v 7-o 15 _{MODEL 3} o 1.= 1.4 C _6Q:

176 Keizo UENO, Kazuaki Eoi, Kunihisa KONDO and Masanobu YAMAGucIJI (Vol. XXIII, 20 15 20 O MODEL 4 c4 2.0 600- 0 20 30 40 15 _MODEL 5 20 o MODEL 6 &. 1.5' 600 O 40 0.10 0.75 0.20 0.25 0.30 010 0.20 030

-F

Fig. 19. Fig. 21. 0.40 a w 0.75 0.20 025 0,30 010 015 0.20 0.25 030 Fig. 18. Fig. 20. 40 30

o 010 0.20 M0OL '7 Ct. -7.5. 60,'= O -20 -30 = 40 60,' O 20 30 0.30

-Fig. 22. 040 60f- O 20 -30 40 3° 10 O 0.10 0.20 0.30 loo 60 14° 20 O MODEL 7 it.- 2.2 Fig. 24. 010 030 0.50 R Fig. 25. 1i 0.40 0.70 010 0.20 0.30 0.40

-i;

Fig. 23.

178 Keizo UENO. Kazuaki Eut, Kunihisa KoNDo and Masanobu YAMAGUCHI (Vol. XXIII, / 00 MODSL 8 el.- 2.OT 60 80 20 o 010

7

0.30 60f O 20 =30// I/I

'j

¿f /1/ o 050 0.70 0.10 020

-J

0,30 Fig. 28. Fig. 26.

,

/

50 40 MODEL q &.- 2.1 "30 20 10 60f 20 3 0 -40 7 0.40

5. Analysis of Test Results

0.50

As the experimental results, the values of

Tt/L for two definite values of a0=1.5 and

2.0', and for three values of 60f=20, 30 and 40, summarizing six cases per each model, were obtained by interpolation or

extrapola-tion from Fig. 10'=-Fig. 28 and also the values

of ri/ for the case of each model advancing without yawing were represented on the base of F in Fig. 10=-Fig. 28. Then, from these experimental results, the values of

can be calculated for the above six cases of each of several velocities of model and thus obtained values of C,,,,,,JC,, were plotted on the base of 60F=60fLs0JV for each model as shown in Fig. 29-'Fig. 37. In these figures

the mean lines through the experimental

spots will be able to be approximately ex-pressed by the following equation

Cmm

= - C1F+ C2F2

C.s.n

The values of coefficients C1 and C2 in the above equation determined from these mean

lines for each model are indicated in the

right-hand columns of Table 2. Using these

values of Ci and C2, the values of rate of increase of ahead resistance of the models due to yawing calculated by the following

g D. ol. 1.466Ú440 =.q6°601= 40 s O a s. 0 a o MODEL 2 o ci, 1.5' 60f=20 2.0' 60= 20 A o,=.5' 60f=30 a o(,=20' 60f=30 n c4=1.5' 60f=40

i

s.=2.0' 60f=40 MODEL 3 o c/.= 14' 60f=20 c/.=2.2' 60f=20 &.1.4' 60i=30 £ _{c/.=2.2' 60f=30} a o',=t4' 60=40 c4=2.2 60=40 A A S Fig. 29.

is

o0 A jO A A u I 2 3 60#Lci, ULIf

-o _11.20F+744F2 L D A u A 4 a _s oc 3

60F

60kc*. Fig. 30. O 3

60F

6OfLcÇ Fig. 31.

180 Keizo UENO, Kazuaki Eai. Kunihisa KoNno and Masanobu YAMAGUCHI (Vol. XXIII, 1 2 3

60 F

60#L V o c4=1.5 60f=20 60+=20 o(.=1.5° 60/r3Q * o.=20 60f=30 a c4=I.5 60/=40 oÇ=2.0 ó0/=40 1+3.21F82.1F2 a MODEL 6 Fig. 32. MODEL 5 Fig. 33. Fig. 34. £ 3

60F

c1. A ,-_R__ \1o.3F+216F2 £

60F

60Lc1, 4 o 1.5 60f20 o(.=2.0 60f 20 oÇ=f.5 60=30 c<.=2.0 60/=30 o c4=1.5 6O40 o,.=20 60/=40 MODEL 4 o c/.=15 60/= 20 o/.= 20 60f=20 c4= 1.5 60/=30 £ c.= 20 0f=30

oÇ=1.5 60t=40 o(.=2.0 óOf-=40

is

1.4 1.3 1.2 1.1 1.0 0!? £ La 'a a O /+3F25F2 O O . 2 3

1.5 12 1.1 o 4A.AOA

lo

000,__0

* 09 601=40 =2.2°O01=4O o cI.=16T601=20 .=2.0T60=2Q ¿ 4=1.ó7601=30 a s(=2.o76o1=30 o c=1.6Y601=40 o(.=2.OF601=40 a e A A o ..ul a 04 u MODEL 8 A AS o MODEL Fig. 35. 3 60F .. 601Lo' u Fig. 36. o c.=1.7 60h20 rJ.=21 601=20 £ c.=1.7 601=30 £ t42.1 £O1r3O o c4=1.7° 601=40 oL=2f 601=40 Fig. 37. o £ u o 3

60E-

60#Lc(. o i F- 104F2 1+8.40E- 54.QF2 1+4F60F2 3

60F

.6OLoÇ

182 Keizo UENO, Kazuaki Eui, Kunihisa KOSDO and Masanobu Y&MAOIJCHJ (Vol. XXIII,

Fig. 38.

xl00%(C1F±C2F2)xl00% Strictly speaking, the values of 60F should be different for each model, but those values arc roughly considered to be in the range

between about 0.3 and about 0.7. It is seen in Fig. 38 that, in the range of 60F=0.3-0.7, the increase rate of ahead resistance of mo-del due to yawing indicates the largest value for a destroyer model having a finest form, next successively lower values for a fishing boat model, a cargo ship model with Maier form, an express liner form wtih a medium bulbous bow, four cargo ship models, an aeroplane carrier model with a large bulbous bow and a lowest value for a supertanker model having a fullest form. However, it must be noted that what is mentioned above can be applicable only to the case of model ships, but not to the case of actual ships, because in the latter case the values of pa-rameter F and also the coefficient of scale effect K are different for each type of ships whose size and service speed are different.

6. Application to Actual Ships

If length L, service speed V and type of

0.2 0.4 0.6 0.8 1,0

60F= V4!t. 6O?JE a'. Fig. 38.

any actual ship are given, the value of coef-ficient of scale effect K for the ship can be calculated, by using any appropriate friction line, for instance, Dr. K. E. Schoenherr's friction line, model dimensions corresponding

to the type of the ship represented in Table 1 and rt/L-v//gl curve of the model advan-cing without yawing. The value C of the increase rate of ahead resistance of the ship who advances at the speed V yawing with arbitrary amplitude 00 and frequency f, can be evaluated, using the value of K obtained above and also the values of C1 and C2

cor-responding to the type of the ship represented

in Table 2.

As examples, the values of C of the vari-ous types of ships calculated by the above mentioned method for two values of yawing amplitude a0=1 and 2, and for several

va-lues of yawing period T in sec., assuming the

length of actual ships L be as in Table 3, are represented in the figures from 39 to 47.

In Table 3 the service speed V8 and Froude

number F corresponding to V are shown. The values of C in the right-end column of Table 3 represent the approximate values of the increase rate of ahead resistance of ships due to yawing at the service speed ranges

for the amplitudes of yawing angle ± i

degree and for the corresponding frequency. In the preceding paper1> the authors tcok,

as an example, the case of a 180 m.

supertan-ker with block coefficient 0.80 advancing at a speed 8 m./sec., yawing with the amplitude ± i degree and the period 30 seconds,

ac-cording to the late Dr. G. Kempf's report2 for

the tankers, and indicated that the value of

C calculated by the authors' method was

about 3 %.

The values of C of the other

various types of ships obtained by the

pre-sent experiments at the service speeds for the

yawing amplitudes ± i degree and for the same corresponding frequency fV'Ljg as the above tanker example are shown on C base in Fig. 48 and on V/VgL base in Fig. 49, and also the approximate mean values of C are represented in Table 3. It is seen in Table

3 that the effect of yawing on the ahead

resistance of ships is small for the bulbous

bow form, large for the Maier form and

takes the middle value of the above two for the normal form.

q

80 70

100 . I Ccrgo shLp 100

t Nor mo.) form)

Remarks:

L = Length of ship in m..

V3 = Service speeds in knots.

= Froude numbers corresponding to the above service speeds.

C = Rate of increase of ahead resistance of ship due to yawing in %. 9-80 70 C) 60

t:

30 20 10 10 15

-

vs Fig. 40. 2 Cargo sh)p

Soo.)) bo.t boos bo)

20 1 140 19 20 21 .264 .278 .292 about 2.7 2 140 19 20 21 .264 .278 .292 t' 2.8 3 140 17 18 19 .236 .250 .264 'f 3.9 4 140 15 16 17 .209 .222 .236 'f 4.5 5 140 15 16 17 .209 .222 .236 6.5 6 7 230 280 25 30 26 31 27 32 .271 .294 .282 .304 .293 .314 ', 4.3 2.2 8 70.71 28 29 30 35 .547 .567 .586 .684 " 4.7 9 28 13 14 15 .404 .435 .466 t' 4.8 10 180 13 15 17 .159 .184 .208 't 3.8 11 180 13 15 17 .159 .184 .208 'f 3.3 12 180 13 15 17 .159 .184 .208 3.0 20 is - vs 10 Fig. 39.

184 Keizo UENO, Kazuaki Eoj, Kunihisa KONDO and Masanobu YAMAGUCUI (Vol. XXIII,

u

60 50 40 30 20 10 Io Is vs Fig. 41. 20 /0 15

- vs

Fig. 42. 20 100 90-80 70 60 i 50-40 30 20- lo-o 100 10 BO 70 u 40 30 20 lo o 0. 10 15 vs Fig. 43. 5 C,rgo ship (t1ae,-20 25 y5 30 Fig. 44. 70 20 6 (Md,n oI bo 30 40 35 100 80 70 4 Cargo sip CSem-Nri

20 25 30 35 vs Fig. 45. 20 s o 40 (J 30 120 w 8 lO 12 14 vs F ig.47. - Jo o 20 q Fheg boal (Nereol f oro, 16 25 30

--

vs Fig. 46. to 75 20 30 40 35

186 Keizo UENO, Kazuaki Eoi, Kunihisa K0NDO and Masanobu YAMAOUOHI (Vol. XXIII,

Cargo (ha(er)

Ltner -Cargo (Se,n(-Moer) (f1d(um O1)r) i, Fig. 49. £ â. + a o ..__Cargo + o ¿

/

(Jornwi)

A3

±6

_N

¿ a F?sh(ng b0at Cargo 2 (Sni)L6.oLb)

i

Carrier (Large buLb)

Q r r r r r r i i 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

u

3 Fshing L boct a U Cargo + (Sona)L bu)b) Car-go (Norma)) o o .._Tarrier (Norma)) A a A 2 Cargo_(Norna[)t Carrier (Lar9e bu1) -1 0.5

6

O.7 0.8 Fig. 48. 8 Cargo (Maier] o

7-s X o, Tanker ,, Cargo (Semì-Maier) ;.-- e

/

Destroyer \L) 8 X Detroyor

of rate of increase of ahead resistance of

ships due to yawing, and we found that,

when ship form, length, speed, amplitude of yawing angle and yawing period are given, the increase rate of ahead resistance of ships due to yawing can be approximately calcu-lated, and also that, roughly speaking, the effect of yawing on the ahead resistance of

ships is small for the bulbous bow form,

large for the Maier form and takes the mid-dle value of the above two for the normal

form.

for their cooperations in the experiments.

References

K. Ueno, J. Ucno, T. Hosoda and M. Maeda:

"Some Experiments of Yawing Effect on Ahead

Resistance of Ships", Memoirs of the Faculty

of Engineering, Kyushu University, Vol. XXII, No. 1, July 1962.

G. Kempf: "Running Resistance Tests with

Models of Full Form", Proceedings of the Ninth

International Towing Tank Conference, Paris,