Page 259 - Introduction to Naval Architecture

244 PROPULSION

(6) After passing the last pair of posts the ship must continue on for
some way and then turn for the return run, reaching a steady
speed before passing the first set of posts. This may involve a run
on of several miles and an easy turn to minimize the drop in
speed associated with turning.
(7) The displacement must be accurately obtained by measuring the
ship's draughts and the density of the water.

If there were no wind, current or tide, one run at each power setting
would theoretically be enough and the speed through the water would
be the same as that relative to land. In any practical situation a number
of runs are needed in each direction so that the results can be analysed
to remove current and tidal effects.
Determining speed through the water
It is usually assumed that the current and tide effects will vary with time
in accordance with an equation of the type:

V T = ao + a] t + a 2 t 2

where ao, a r and a 2 are constants.
What concerns the ship is the component of tide along the ship's line
of transit on the measured mile. This is to be understood when tide is
mentioned. Suppose four runs are made, two in each direction. Two
will be with the tide and two against. Using subscripts to denote the
speeds recorded on the runs:

V l = V+ ao
2
F 2 = V- ao - aj ^ - a 2i 1
2
F 3 = V + ao + aj % + a 21%
V 4 = V— ao - &i % - a 21% 2

where Fis the speed through the water and the runs are at times zero
and ti, % and %.
The four equations can be solved for the three unknowns and the
speed relative to the water found. To illustrate this take the simple case
where the four runs are made at equal time intervals. In this case tj can
be taken as t, t% as 21 and % as 3t. The equations become:

V l = V+ ^
2
l/ 2 = V"— ao — aj i — a 2t
V 3 = V + ao + 2a x t + 4a 21 2
V 4 = y-a 0 - 3a 1 *-9a 2 < 2