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96
BRITISH KINEMATOGRAPHY
Vol. 23, No. 4
Fig. 20. Strain pattern of the cross-section of a water-wave.
Scale Effects
The general formula for the wave resistance of geometrically similar bodies similarly immersed is of the form (for deep water) :
*-PJW(g)
• (10)
where / is the characteristic linear magnitude. R can be computed provided //c2 is constant. Thus, for a model ship to behave in water to the_correct scale, c must be proportional to \ /. This is expressed in Froude's first law :
Where two geometrically similarly bodies similarly immersed are behaving to scale in the same manner, then they are said to be travelling at " corresponding speeds." If the speed of the model is c and that of the real ship is C then :
c IT
where L and / are the characteristic magnitudes (e.g. lengths).
L/I is the scale of the model, and this can be otherwise expressed that the factor for reducing the speed to suit the model is the square root of the scale.
Thus, employing a scale of 1 : 12, a speed of 13 knots should be reduced to 13 13
J\2 3.46
= approximately 4 knots.
Of course, the reduced speed is that required to provide a correct reproduction of wavesystems, pitching and rolling characteristics. The illusion will not be correct unless the apparent speed of the model can be reduced
by a further factor of ^12 to give a correct linear reduction, e.g. in cinematography by increasing the camera speed by the factor v/lT.
Artificial Wave Production
There are two methods to consider. One is to direct artificial wind on to the surface of the water. The other is to use a mechanical wave-generator.
The requirements of a wave-generator are shown up by considering the motion required in the water to produce a wave on the surface (see Fig. 3). Another way of illustrating this is shown on Fig. 20, which shows the change in the shape of a series of planes (forming in still water a vertical and horizontal pattern) due to the passage of a wave.
! ; /
FLAT PLATE
Fig. 21. Action of an ideal wave-maker.
AXIS
Fig. 22. Action of a practical wave-maker.
The effect of wave-motion would therefore be produced by the use of a flexible plate immersed in the water as shown in section in Fig. 21.
The dotted lines show successive positions of the plate and it will be seen that the plate must flex as it oscillates, and that its axis of