Procedure of analysing the standard manoeuvre test of Kempf to obtain steering quality indices K & T

I

PROCEDURE OF ANALYSING THE STANDARD MANOEU#RE TEST OFIEMPF.TO OBTAIR STEERING QUALITY INDICES: K & T

The standard manoeuvre test of Kempf is. practisedin the

following

way as is well-known,

'

set a certain angle of heIn'(e.g. 15 degrees ) to starboard;

when ship's heading deviation has reached this angle to Starboard,

reverse the helm to the same angle to port; .

When the heading deviation has reached the same angle to port, reverse, the helm again to the same to starboard and so .on.

The principle of the analysis is to

find

those values of the

indices

K and T.with which the equation of motion of the first order may describe

an observed ship motion in the test. The

notation

used here is shown in

/ _{the attached figure (Fig. 11).}

a '

In taking up the analysis it should be noted that a ship usually

does not keep a straight course with a rudder apparently amidship (viz, sham by a helm indicator ) but makeSa certain slaw turning

by

reason of an

unsymmetric velocity field of single screw race, small missetting of a

rudder and some other miscellaneous factors'. Since the equation of motion

requires naturally a straight running for a rudder anidship, it must be necessary to make some correction upon an apparent (observed) helm angle

prior to put it into the equation. Then we put

4f)

observed angle of helm,

"residual helm, that is difference between )-H-j and

La9,

and may be considered as an unknown constant at the

beginning of the analysis.

into the equation of motion of the first order, we

Then putting obtain Integrating Setting the base course Oct

(1 )

7-

Ce7-the both sides from

f

= 0

t

a' f

da

4fa

cet

r-/ c 4-

/y dmit)

oa-p. 0

time origin at the start of a test, measuring c9 from the

and provided a ship is running straight prior to opening a

test, the initial conditions are

T

=

Kitt

crrt

-7-1(

(1)

( 2 )

^

g

0.

and

g

=

at ZL

'o

Then we get

4

Fig. / Notations

for Analysis of Standard

Manoeuvre of Kempf

( Numbers indicate successive periods during

a test)

because B

= 0

at these instants.

'fie"

and ti

a Grfrai(f) att may be obtained through a simple calculation

indicated later. Then unknown quantities in

these simultaneous equations are K and

dp

. They may be determined by

resolving these equations simultaneously. We call the K K in

after-half period in a test, writing simply /q)() .

Now applying the equation ( 2 ) at

r =

_te 2

g

te

Jtre +f ormio

ite

has been determined through the above procedure and

t

"lit) dt

may be calculated. We call this IC K in earlier-half period in a test,

writing simply

Ke

.

KG

and

Koa)

are more or less

different to each other by reason of speed reduction in a test and nonlinear

effect for steering quality indices. In usual cases it may be considered

that the mean value of

Kc:7

and

Kof,

is a representative K

of a ship that is tested.

Next applying Eq. ( 2 ) at

t = to'

and

we get

7-(6)

=

j

im0

1-

it to)

-(74'107

dt

14

1

/- 7

'Ito)

e

T =

_clt

b3(tat)

because

8

= at these instants. When carrying out the calculations,

it may be reasonable to use

/4.

for the first formula and to use

/(649

for

the remaining two.

_gao,

61/140() and ortfoff) may determined

°II the plotted curve of go.) that is obtained.

4 Lai') df may be caluculated as is discussed later. We call

the T obtained from the first formula T in earlier-half, period, writing

simply 74) and call the average of T's from the remaining two formulae T in after-half period, simply

TCO

. The mean value _of

TO

and

Tod)

may be considered as a representative T of a ship that is

we get

This is the fundamental equation for the present Procedure. Applying the equation ( 2 ) at

t

1-Z

and t

we get

Kirte1 arm

tel

at,t

_8e-

I

Xf

ea

_{arfri 10 eel}

7

tested.

tr.

.

._ The calculation of

f

4,d7jele may be carried out in the

following manner. A trapezoidal approximation is quite adequate for

_Sni(f)

. o

produced by usual steering gears; the emir of it does not exceed other

unavoidable errors. Then we get formulae of calculating

irt-ocea.)

co-as.follows; Jo No. of period in a test. ti 1

2 J

ti

/2

/

( r

tz)Z

2

) t

_{217'3 tz)}

--21(f2t13)]

₁₂₁

_{(r21473) 1. I}

-j-(t24-t5)/

417

!-(t27,

tt

_1-

21;tlft (t-4)

+ 121-

-21-(t2t.ti)

-4(4

t

(t

ti)/

-2(7

irz 1-t,)

4e4

fir)!

7". 13

I-4(4

t'

tr.

)

(to

r7)

t