### Z

### 4've Çe2(

EXPERMEN1AL STUDY QN ACCELERATING AND DECELERATING SKIP MOTIONS

### ç

### .-

### 4ç*

### (isT

REPORT)### **

### **

### by Michio Nakato

,### Kuníji Kose

,### Sadarni Teramoto

### and Seiichi Shirnamune

Summary

In this report, the accelerating and decelerating motions of a ship are estimated from a practical point of view, using the

foiTt owing equation:

(m+m) V3T(1-t) -R.

At first, the added mass of the model ship (mi) is measurci by

forced surgi'g tests.

Next, operating the propeller, the forced surçng tests are carried out, and it is shown that both the model ship thrust T and thrust deduction factor (l-) are almost independent on

acceleration of a ship but ori J3 (=V./nD). Therefore the right

hand side of the above equation ma'1 be regarded as a function of

ship speed V, and propeller

### revolution n.

B this reason, theresult3 of the proDeller characteristics and thu thrust deduction factor, obtained by a kind of over/under-load tests at constant

speeds, can be used to estimate the accelerating and the decelerating

ship notions.

At last, putting rn, T and (1-t) into the above equation together with the resistance test result and integrating numerically,

the velocities during the accelerating

### and the dece1eratirig motions

are estimated.

Comparing these resi1ts with those cf the free running epriments,

they are in r good coincidence.

Some comments are also mentioned, as to the effective braking force and the side force acting on a ship hull at the ìiitial

stage of stopping.

Lab. y. Scheepsbouwlumde

### Technische Hogeschoi

DeIfL

### (i)

### * Presented at the J.S.N.A. conference on Nov. 11 at Osaka

### ** Hirosnrna University

### Maritime Safely Academy, Japan

### Mitsubishi Heavy Indistries, Ltd. (Post-graduate studeit

### at that time)

### ARCHIEF

F

(2)

INTRODUCTION

The stopping ability of ships was discussed by many researchers

for long time and Ehe results were sumniarized by Prof. Tani and

Dr. Fujii in the proceedings

### of the 2nd symposium

on shipmanoeuvrability held at Tokyo in l97O.

As to researches on accelerating an-9 decelerating motions of

ships, however, there are not many in this field. Akasaki and

Motora have studied about the longitudinal added mass of

### ships2'.

Harval.d has investigated about the thrust deduction factor etc4

but it is not easy to apply his results to the actual problem. Since a few years ago, authors have tried to estimate the accelerating and decelerating characteristics of ships by means

of the towjng tank experiments.

The method in this paper is based on the following equation

as commonly used:

### (m+m)T(l-t)-R,

(1)1iere ri : mass of a ship,

added mass of a ship in x direction, accaleration of a ship,

T : thrust,

l-t thrust deduction factor,

and R resistance of a snip at a steady speeds It is assumed that the equation is available for both a real ship and a model ship, even if the corresponding terms of the ship and its mode] shin are different from each other.

This first report, mainly concerning to the model ship,motions, consists of the following sections; in section 1 the basic

equation is discussed, in section 2 and ' the evaluation of each

term in th equation is treated, and n the last secton the

estimated results c'f model ship motions are compared with those

### of free

running tests cf the model ship, which shows a gcodcoincidence.

The application of this estimation to a real ship is not yet done, because some problems to be considerad still remain.

Some of them are such as the hydrodynamic similarity law cf flow field between a model ship and a real ship, and the ship engine characteristics in accelerating motions.

named T, which has a rather larger ratio of hull inertia force to propeller braking force, and another is a container named

ship C, whose ratio is rather small. The principal dimensions

of ships and propellers are listed in Table 1.

1. PRACTICAL ANALYSIS ON THE ACCELERATING AND DECELERATING MOTIONS

### (?n+m)T(l-t)-R

(1)Equation (1) is often used for the analysis of the unsteady

ship motions. Adopting this equation, the following two

assumptions are normally iniuded:

The resistance of a ship during an unsteady motion is able

to be separated into two parts. The first part, represented as

the added mass of a ship, is the resistance proportional to

the acceleration of the ship. The secend is the remainder,

represented as R, the rc'.istance of the ship at the steady speed.

Though the interaction forces between a hull and a propeller are to be chanced during an unsteady motion cf the ship, it is

able to be represented by the term (i-t) , which of course varies

with the propeller loading.

If the righe hard side of the equation (1) does not depend on

the acceleratior of a ship, it is very convenient for the

practical treatments. Because this makes i+ possible to integrate

the equation, making used of the steady speed resistance R obtained from an ordinary resistance test, thrust T and thrust deduction factor (lt) obtained from various propeller loading

tests carried out behind the sNp at a constant speed, and the

added mass riS explained in the next section. Each term as

mentioned above will be discussed in se ion 2 and 3. The effect cf acceleration to the right hand side of equation (1) will be

also examined in section 3.

It is more converent to make an additional assumption that the added mass of a propeller during an unsteady motion is

neglected because it is rather small compared with that of a hull.

2 EXPERIMENTAL METHOD TO OBTAIN THE ADDED MASS '

To get the value of an added mass of a model ship, there are

two experirneril methods in a towing tank. One is to measure

the r:tions (position and velocity) after giving sorne force

(4)

after making some motion (known value) to the ship.

### 2.1 Experiment with u weight force

This is a kind of the former method. A model ship is

accelerated by a constant weight shifting along a piano wire setting to a towing carriage for its towing direction.

In this case the equation of the motion is,

### (m+rn) U+W±f-R,

(2)where W : a constant weight used to surge the ship,

and

### f

friction force of the guide wire.W and

### f

are both measureabie beforehand, so the right hand sideof equation (2) is all known values. Measuring the relative

velocity o the model ship to the towing carriage and using a

differential filter, the acceleration is obtained ccntinuously.

Hence, the added mass m can be found from the equation (2)

Usually the length of the guide wire is not long eough, so the test should be repeated till the desired speed is obtained. In the repeating tests the records o velocity u has to be

continued smoothly, and it cari be easily done by a little overlapping cf speed range in each test.

To get m accurately, the correct values of R and

### f

areindispensable, although the correct evaluation of

### f is a

difficult problem.

To eliminate the effect of the friction force

### f,

a pair ofsurging tests are carried out: in one test the weight shifts

forward and ir. anothcr it does backward. The trajectory of

this motion is shown in Fig. 2, taking the acceleration to

the abscissa and the velocity u to the ordinate. In the figure,

it is shown schematically that the dotted lines indicate the

ideal frictionless case, ¿ìd the solid lines do the test results.

Combining two tiectories of the ist and the 4th co-:inate

planes, for example, tH added mass of accelerating ship

### wi1i

be obtained without the fric-ion effect. The reason can easilybe seen from Fig. 2 or trom the equation (3) and (4) as follows:

### (m+rn)lj=W-f--Thi

(3)and _{(m+rnx) t}

_{=W+f-R.}

(4)
co-ordinate plane, and each bar above letters indicates its mean

value.

Eliminating the friction force

### f

from these equations, theadded mass can be obtained as the following equation:

### m=

### r{w-4R+R}/}(i)1-m.

(5)In Fig. 3, added mass thus obtained is shown. Because the

friction force f changes during measurements, the results are rather scattered, and from them it is difficult to find any

tendency of rn. against the ship base velocity u and the acceleration u.

2.2 Experiment with Planar Motion Mechanism (PMM)

This is a kind of the latter method mentioned in the beginning of this section and the procedures are as follows. Let a model

ship be fòrced a surging with a certain period by means of PMM, which is mounted on he towing carriage running at a constant speed, and then we can measure the forres required for the

surging.

It is the advantage of this method that the measured data is easily analyzed, and also that the tata contains no friction

effect.

Assuming that the change of ship resistance depends linearly

on the change of velocity at. or near the average speed, the

equation of motion in this case becomes,

### (m+r)l=P_(Po+R.l)

(6)where F : measured force,

resistance at a base speed

(carriage speed)

and R :

u is the additional surging velocity.

In this ease, u and can he written as follows, using a

amplitude of the surging and c : serying frequency:

### uac

CCSO)T,} (7)

and n

### 3

### lnú)t.

Putting the above equations into equation (6), we get,

(6)

Integrating both sides with the range of O "rt/, it becomes,

m+m_{X}

### r0)(FRO)dT.

2ac

In addition, if we integrate the equation with the range of

rt/2 'v 3ît/2u, R is obtained:

R =-

### f2°(F-Ro)dr.

(10)### U 2a

This is not so i-'portant and only be used to examine the validity of equation (6)

In Fig. 4 the added mass thus obtained is presented. The

frequency dependent character of does not seem to appear in such a low range of fiequency, nor the speed dependent character which is presented by Akasaki in this paper2.

As to th values of mr, they are quite coincident with that obtained from Prof. Motora's chart.

3. EXPERIMENTS ON THRUST AND THRUST DEDECTION FACTOR DURING ACCELERATING AND DECELERATING MOTIONS

Tho'igh it will be proved in the latter part of this section,

the thrust coefficient and the thru3t deduction factor t do not depend on the acceleration of ship motions, but depend on the apparent advance ratio

### J=V6/nD.

So if data of and t versus the wide range of J8 as

Fig. 5 and Fig. 6 are provided, it is useful to estimate accelerating and decelerating ship motions.

The data of KT and t are obtained by means of over/under-load tests in which the loading of the propeller varies considerably. 3.1 Over/under-load tests of propeller and flow fields under

propeller reversing

The over/under-load tests here stated are carried out with

sorne combinations

### of the ship

speed and the propellerrevolution n. During the test, the model ship is attached to

the towing carriage with the dynanorneter, and she runs at a

constant speed with a constant revolution of the propeller. Thrust T, torque Q and the force F acting to the hull are measured under a constant speed. The relation of forces is

expressed as follows:

(9)

From this equation, Fig. 5 and Fig. 6 can be drawn. In the

figures, the dotted lines show tii open characteristics of the

propeller and its àbscissa is not

### J.

but J=V/nD. it is seenfrom the figures that KT and (l-t) can be reqarded as the

function of

### J8.

Fig. 7 shows the observed flow fields during the over/under-load

tests under propeller reversing. In these cases, the ship is

advancing, while the propeller is reversely revoluting.

From the figures, it is found that if the apparent advance

### J8

of two ships is equal to each other, the flow fields of the shipslook like similar, even if V and n are quite different and also the flows around hulls are much turbulent. This is the reason why KT and (l-t) are well arranged by apparent advance ratio J.

One more remarkable fact is that the propeller reversing race is stronger in the starboard side than in the port side (clockwise

turn of the propeller corresponds to ahead in this case) , and it

may produce a force at the stern directed to the port side from the starboard side as shown in the last seLion.

### 3.2 Open test results of propellers

The propellers used in the experiments are tested in the whole range of advance ratio J, as shown in Fig. 8. Fiom te results

of over/under-load tests and these operi charts, ship wake factor

w can be obtained and is shown in Fig. 9 in the form uf (l-w)

where

### lWVa/VsJ/Jsi

} (12)

and JVa/nD.

Fig. 9 is available to estimate KT or thrust T, but it lacks a little bit the accuracy in some negative range of J.

### 3.3 Effect of acceleration on propeller thrust and thrust

### deduction factor

In section 2.2, the forced surging test using a PMM was

mentioned. In this time the tests are agai:i held ji.'st as the

same manner adding a rotating propeller attached to the hull.

The equation in this case is,

### (r,H-rn)F+T(l-t)-(Ro+Ru.u) .

(13)(mfm)

(B)

With Taylor expansion the thrust term becomes;

### T(l-t)=[T(l-t)I0+[T(l-t)Ju+[T(l-t)l.

(14)Putting equation (14) into (13), the following equation is

obtained:

### F+[T(l-t) lo -R0={ (rn+m)-[T(l-t) l}+{R-[T(i-t) l}i, (15)

where suffix "O" indicates the steady value at a steady speed and suffix "u" and "" indicate the partial differential

coefficients with them each. Equation (15) can be integrated

with the same procedure as equation (8) and the following equation is obtained corresponding to equation (9).

### (m+mx)-[T(1-t)]--

### f

### F+ET(1t)10-Ro}dT.

### (16)

2ac

### i

'O (ç;)If the right hand sides of equation (16) an (9) are equal,

the contribution of [T(1-t)] must be zero and then the term

[T(l-t)] has no relation to the acceleration .

The integration of the right hand sides of equation (16) and

(9) can be carried out directly by some electric circuit.

This fact is examined to ship T in the case that a=5Ocm,

co=n/lO and ît/2Orad/sec and

### n=7.67rps.

It is found that thecontribution of [T(1-t)] took nearly zero within the experimental

errors. We can treat tb2 accelerating and decelerating ship

motions as quasi-steady problems. Also from the fact that

equation (9) and (16) are equal each other, rn,. can be obtained

from either tests ith or without a propeller.

Lj, _{ESTIMATION OF ACCELERATING AND DECELERATiNG SHIP MOTIONS}
Though the right hand side of equation (1) is a function of

J3, it can he regarded as a function of V6 unless n changes

continuously. In cases of accelerating and decelerating motions,

the revolution n reaches in a shorter time to the steady state

than the ship velocity V8. Assuming n changes stepwise, in each

state of

### n,

equation (J.) can be written as;(m+rn.) '3=T(l-t)-f1EG(V8) (17)

Integrating equation (17) with known n, equation (18) is obtained:

### ()fVl dV1T1.

(18) G(V3)

### t

where suffix "O" means an initial value and "i" does a final

values.

To estimate the accelerating and delerating motions of a

ship practically, the following procedures are recommended:

To estimate rn from the experiments mentioned before or

from Prof Motora's chart.

To obtain T and (l-t) from over/under-load tests within the required range of J or from a sister ship data.

To obtain R from resistance tests or estimation formula.

To put them into equation (13) and to integrate it numerically. The example of estimated results are shown in Fig. 10 and 11.

in the figures, dotted lines indicate the estimated results and solid lines do the experimental results respectively. They are in a good coincidence.

### 4.2 Stopping motion of a ship

Asuminq a ship is sailing with a normal speed, whciì some accident happens and the quarer-iaster wants to stop her as fast as possible, what will he do? Crash astern? Or once slow and then switching to full astern? There are two kinds of answer

half and half.

To solve this question, the braking forces of . ship under a

positive V and negative n are measured and plotted in Fig. 12. It is apparent from the figures that a stronger effective braking

force

### KT(1-t)n

is always accompanied with by a hig1er reverserevolution of a propeller. Consequently, the coLrect answer to

to question is "full astern sooner in any cases". But it must he remembered that these results are only valid in cases when the ship is kept on a straight course

### ifl

general case of crash astern, some side force and moment are produced as swn in fig. 13, and the ship will turn herhead and will drift. It should be investigated more in detail

together with many other problems. CONCLUSION

Practical treatment of equation (1) and a simple method to obtain the added mass in the equation accurately under

accelerating and decelerating ship motions are presented.

(10)

on the acceleration in comparatively slow ship motions and the values obtained by over/under-load tests are valid.

Using thus obtained T, (1-t) and R obtained from

resistance tests, the accelerating and decelerating motions of a ship can be accurately estimated from equation (1)

In model tests, it is verified that the higher the reversing revolution of a propeller is, the stronger is the effective

braking force and that it is independent on the ship speed. An

example of side force acting on a ship at a crash astern is shown.

Authors would like to express sincere thanks to Prof. K. Nornoto

and others who have collaborated with them in various stages of

this study. A part of this research expenses were supported by

Ministry of Education of Japan and numerical calculation was carried out by TOSBAC-3400 and HITAC-8700 of Computer Center of

Hiroshima University.

REFERENCE

H. Tani & H. Fujii: On Crash Astern of a Ship, proceedings of the 2nd symposium on ship manoeuvrabilitv, Tokyo (1970)

S. Akasaki: On the Virtual Water Masses of Ship while Turning, Journal of the Society of Naval Architects of Japan, Vol.70 (1942)

S. Motora: On the Measurement of dded Mass and Added Moment of Inertia for Ship Motions (Part 2. Added Mass Abstract for the

Longitudinal Motions.), Journal of the Society of Naval Architects

of Japan, Vol.106 (1960)

SV. AA. Harvald: Wake and Thrust Deduction at Extreme Propeller

### Table i Particulars of model

1__-1800 1200 600 V ( 1ec) 1.4Fici.

### i

_{Resistance curves of model ship}

### tf\

\___### I--i

'N### i

_{\\}

'1(\ _{\\}

- with trict0ti
r ,ct,one ss(raat)
### Fig. 2 uu trajectory (forced surging

### cxperirrent with constant force)

-0.6 R(g)## //

/ o shp T (WT21.2°C) A ship C (W.T.11Q C)/### /1

S h o T S h p C### Huti

L (rn) L+'0O ¿812 8 Cm) 0.701 0.632 d (rn) 0.270 0.216 ( 0.689 (381 CB 0.810 0.578LCB(°/o) 2.O7Fore 2.60At.

r ropeU'°r

section Aero-oïI Aro-foit

Z 5

### 6(x2)

D 0.1207 0.1414 RA. 9° 58 00 B.T.R. 0.647 0.480 EAR. 0.575 0.850 P.R. 0.730 1.055 BR. 0.189 0.200a a u L s 0.3 4c car, 0.5

### -t

'tFig. 3 Added mass of ship T obtained Fig. 4 Added mass of ship T

by force surging (const. force) obtained by forced

surging (const. motion)

'

925rpm.

### \

o55

480

t 300 "

- - - ooen 1e't result

-i -OB -t4
-04
*5
-0 -04 0
- trom MtOr2S ct'.rt
u
/
o
*
Jt
4 CB', U -12 -08 -0.4
- -545rpm._{480}
a
(ship T

Fig. 5 Over/under-load tests c'su1ts of propellers

12i(1-t) u a . A 0 CO 0 s 1151 A 2 cm u 0.4 0.8 12 -1T -0.a -04 i Or -, from Motors's cbrt o -A 335 o

- -- - open test resu(t

o carraoe speed 0.5 0.5 Ki-0.4 2

### /

0-.110 orn seca O. (ship C o 04 08 i7Fig. E) Thrust deduction faetos obtained, by over/under-load tests of pr'pellers

I

### -o

J11 0.4 08 1.2 s -505 rpm.### i

235 -08 (ship C t 0.4 Kr### -.

### j'

_{-s}0? o 485rpm. Csr T ) A

_{T25.prn.}-505r.Orri. 04 o

_{-}L-235 ° 480 o a 4

### £ p

-655rpm u-680 a-300-6rpm. 4-Q,4QQ

A.ODratn rA ce .rsrd p.cptIIfl c.c. ot cOent

### I

çJ y. tt'_{I}

### \

_{.t/}

_{)}

_{j,}

0.8 0 3'
'b LO
*1.2 (1-w)
$-5rpr. o
-300
s
ithp T
Ct
A!_{a}

_{e}O o o

_{- 1$}O 480 -: - -o o 04 O 2

### /

C do-,n c,t "s,,, ?ce,c,'r V 12 O' I/Fig. 8 Propeller open test rerults

s A A .-05'p.rn L-335 A 0.8 £ 04 o.773! l=480rprn. .i-O.800

Fig.' "i Observed flow fields under various propeller loadings under stopping (ship T)

I? 't-fl) A (shp C ) - 04 0 GA C! Cs-p C :' o 5r.prn, 4 335 - no' -04 0. G. & t2

Fig. 9 (l-w) obtained by over/under-load tests of propellers

(13)

N5cOrrL j: -0.61' 0

o o

### -

V- .-20 1.0 -O O °_{0}o 0 0 0 0 r.o riaured - strnated

Fig. 10 Comparison of accelerating and decelerating motions between estimated

result and experimental result (ship T)

-T -5-A-A.. n V('spc) .û

### ¡---o-

---_s1,,,' -20### ._9-3

/ -70_{:}(ship T 10 20 30 ?(Sec) --20 -40 -t}fl° (ship C

Fig. 12 Effective brake forces of propeller during stopping

-5

### rig.

il Comparison of accelerating and decelerating motions between estimatedresult and experimental result (ship C)

-u- --u-a-- - .- - T1_4SOr(n

### '..'

T(-665rt'm) - .---S ---S----60 - - 90 0Nc) ,_{i-- - esIm.ld}-£ m5iir01 I--(onr --- 30 --O .A-A - T-5m.pmn.) g _

_{Iv}

### 600')

-A -665 s p r!,. -1. 0 r. pm -20G (14) TOFig. 13 Measured for:es and moments at the initiai stage of

stop-ping motions (ship T)

-_-meaçurtd ---eslirnateO __d- - - -T(kg).c) 2.0 C I --S i--- estirralei --