Page 195 - Introduction to Naval Architecture

RESISTANCE 181

will be less. Whilst it is convenient to picture two wave systems
interacting, in fact the bow wave system modifies the pressure field
around the stern so that the waves it generates are altered. Both wave
systems are moving with the ship and will have the same lengths. As ship
speed increases the wavelengths increase so there will be times when
crests combine and others when crest and trough become coincident.
The ship will suffer more or less resistance depending upon whether
the two waves augment each other or partially cancel each other out.
This leads to a series of humps and hollows in the resistance curve,
relative to a smoothly increasing curve, as speed increases. This is
shown in Figure 8.4.

Figure 8.4 Humps and hollows in resistance curve

3
This effect was shown experimentally by Froude by testing models
with varying lengths of parallel middle body but the same forward and
after ends. Figure 8.5 illustrates some of these early results. The
residuary resistance was taken as the total measured resistance less a
calculated skin friction resistance.
Now the distance between the two pressure systems is approximately
0.9L. The condition therefore that a crest or trough from the bow
system should coincide with the first stern trough is:

The troughs will coincide when JVis an odd integer and for even values
of N a crest from the bow coincides with the stern trough. The most
pronounced hump occurs when N = 1 and this hump is termed the
main hump. The hump at N = 3 is often called the prismatic hump as it
is greatly affected by the ship's prismatic coefficient.