The reverse spiral test as applied to large ships

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THE reversed spiral test, which was first made public in 1966 at the

Nordic ship technical meeting in Malmö, has since been applied to a variety of ships in full scale trials, model tests and analog

simula-tions. Consequently experience has been gained with respect to the use-fulness and reliability of the method. Recently results have been obtained

from a number of very big ships,

where this method is of a special in-terest, because of the time saved in

its application.

It may be relevant here to give the theoretical bnckgrourid of the test method. The linerised equation con-necting rudder angle and rate of turn

for a ship is:

TiTi

[+8_

-[;

+ (I)

Where O is the rate of turn and the rudder angle. The terms k, rl, rl, and

T3 are constants as long as linearity may

be assumed.

1f is constant, the equation will be

reduced to:

(2) As is known, the ship's steering

characteristics are non-linear outside a

limited area. As, however, the rudder

effect generally is a linear function of

the rudder angIe, the non-linearity is due to the forces acting on the ship's hull as a consequence of the ship's turning.

Therefore, equation 2 must be re-written as follows:

(3)

If the ship is being steered to a certain

rate of turn, , measured on a rate

gyro, then 8 will only indicate the small

steering movements which are

neces-ppr

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n

sary in order to maintain this

con-dition. Then:

i rT

-

j [rz 8(t) + 8(t)] dt - 6 (4)

Where 6 is the mean value of the ob-served rudder deflection. From this is

obtained:

60=H(4)

(5)

Thus H () indicates the rudder angle, 6, as a function of rate of turn, ,/', i.e. the rudder angle necessary in order to balance the forces acting on the ship's hull as a consequence of the ship's turning.

This definition of the

- 8 curve

also makes a single valued function of

in cases of unstable ships. It further means that a spiral test will normally need only one run instead of two, and at the same time it ensures that the

individual points are obtained

consider-ably faster than by the previous method. This difference is due to the

fact that the helmsman brings the ship

into the desired rate of turn by active

steering instead of passively waiting for

the ship to stabilise

its rate of turn

at a fixed rudder angle, which in the

case of marginal stability theoretically

will take an infinite time. Thereafter

it is only a question of maintaining an already obtained balance and of reading the rudder angle.

A further advantage is that the points need not be taken in any specific order,

but may be taken at random as sailing conditions permit. This implies that

interference from other traffic or land

obstruction during a test does not mean

that the test has to be started all over

again as is the case by previous method;

at least if stability of the ship in

ques-tion is not known beforehand.

Recently a comparison was made

be-tween the traditional spiral test and

the reversed test

on a

supertanker

(365,000 t fully laden displacement). The

Lab.

_{y. Scheepsbouwkunde}

Technische Hogeschool

Deift

comparison was made in a light

ballast condition of approx 130,000 ton displacement and the results of the two tests are shown by the curves of Figs. i and 2. The points in the reversed spiral

test, Fig. i are taken in random order, because navigation at the time of

measurement did not permit excessive excursion from the given heading. The

maximum excursions from the given

heading were held within -45 deg

and +30 deg and the total test time

was slightly less

than 45 min. The

points of the normal spiral test, Fig.

2, were taken in the order shown

by the arrows. The test was broken off

in the middle of the second run

(be-cause of traffic interference), by which

time two hours and ten minutes had

elapsed from the beginning of the test.

Both results clearly show the very

good stability of the ship. The ship was stable even in its fully laden condition,

but only a few points of the curve

were taken in this condition and only by the reversed method. The curve of Fig. 2 shows the characteristic hysteresis effect which always results when

in-sufficient time is given for steady-state conditions to be reached. The outgoing

branch to SB, where the ship has just passed zero rate of turn, compares favourably with the results of Fig. I.

lt may reasonably be expected that the

outzoing branch to P, if it had been

taken, might have done the same. The

pnints in Fig. I for the larger values

of rate of turn suffer to some extent in the same way, because of the re-strictions imposed by navigation

re-quirements.

The values for = 0.45 deg.f sec. SB and = 0.475 deg./sec. P clearly show how rudder angle increases as

ship's speed drops from the initial 15 k

in order to maintain constant rate of turn. Even the end values shown are nrobably not steady-state values but

the turn had to be altered by then. Similarly the value of 8

ing to 0.4 deg/sec SB should probably be slightly larger than indi-cated.

Between = ±0.2 deg/sec, steady-state values have definitely been reached, and a true figure

for the

stability of the ship can thus be ob-tained.

When applying the reversed spiral test to very big ships, care must be

taken that steady-state conditions have been reached when readings are taken. Particularly in autopilot control, which was used during the test reported,

con-stant rate

of turn

is reached very

quickly, and immediately after, a quasi-steady mean value of rudder angle can

be observed. This does not, however,

imply that steady-state values of ship's

speed ahead and of drift-angle have yet been reached. Certain simulator

tests reported seem to indicate that if points are taken too quickly in the case of an unstable ship, a smooth

curve may be obtained, which slightly

Fig. 2 Result of the normal spiral test, showing the hysteresis effect

exaggerates the degree of instability of

the ship.

If testing time must be kept to a minimum, it is recommended that

points are taken in random order with a preference for low values of rate of turn to be dealt with first. Thereby, settling time to the steady-state con-dition is kept to a minimum because both drift angle and speed drop are small. Also random points are not as

likely to give a smooth, but erroneous

curve.

This programme can frequently be

combined with normal sailing and vir-tually no extra sailing time is necessary.

Usually, not many points for high

rates of turn are necessary and may, if

convenient, be obtained from turning circle tests. This does not imply that

excessively long times are involved in getting steady-state conditions. Rate of

turn is controlled very quickly and

subsequently speed ahead and drift angle converge in an exponential way

1754rn SHIPPING WORLD AND SHIPBUILDER NOVEMBER 1968

Fig. I Result of the reversed spiral

test for the fully loaded condition

towards their final values in accordance with the fixed rate of turn. The

temp-tation to read the rudder angle as the

quasi-steady value immediately after fixed rate of turn is obtained should

be guarded against.

In the case of the conventional spiral test, rate of turn converges driven only by the free balance of forces towards its final value, and speed and drift angle must then follow. For

d H()

small values of . the convergence

d

is very slow, at zero value the time taken is infinite and in an unstable

region there is divergence. This is the condition at low values of rate of turn.

At the higher values of rate of turn,

d H()

where . always has a reasonably

d

high value, the two methods are com-parable in time, because the time taken for speed and drift angle to settle

pre-dominates.

I

s

90-90 RPM, z 20° z

INITIAL SPEED ILOGI IS EN.

:

EN EN.

DRAUGH T F 27 II34 - -DRAUGHT A 32 '/z' I OISPL. 29,053 TON 1(15 EN. I STARB'D. t ?/seC. 5 '4 '3 2 I 1 2 3 4 '5

ANGULAR VELOCITY (deg./sec)

IS EN X PORT

- IS'

IO EN X RUDDER ANGLE

s - 20°

NOR BALLAST CONDITION -SHAFT R. P M. 90- 90

INITIAL SHIPS SPEED ABOUT 15 KNOTS

BY LOG) -RUDDER SETTING 0° 10° - - STARB D. - 0/sec ' .4 '3 '2 I .."° '1 '2 3 1

-

-

ANGULAR VELOCITY (deg/sec.)

PORT . BASE COURSE 210°

- SEA STATE 3

SWELL 3,.,4

15'