Page 190 - Practical Ship Design

156 Chapter 6

6.2 RESISTANCE AND SHIP MODEL CORRELATION

6.2. I The classical treatment of resistance

Resistance is the force that the ship overcomes as it moves through the water. The
classical treatment of resistance is outlined in this section and is followed in the
next section by an outline of the present day treatment of resistance.
In the classical treatment of resistance, this is divided into two components,
which are governed by different laws, so that they can be separately extrapolated
from model to full-scale ship size:
(i) the skin frictional resistance, which is governed by the Reynolds’ number,
and
(ii) the residuary resistance, taken mainly to be wavemaking, which is
governed by the Froude number.
In the following paragraphs use will be made of the resistance coefficient C.
This is related to the wetted surface S, the speed V, and the mass density p by the
following equation:

R = 1/2. C. p. S. V2 (6.1)
The coefficient C is given two types of subscripts. The first of these refers to the
subdivision of resistance with t = total; f = frictional; r = residuary; w = wave-
making. The second subscript distinguishes between model resistance = m; and
ship resistance = s.
In the classical treatment, the skin frictional resistance coefficient of the model
is calculated based on the coefficient of friction applicable to a plank (flat plane) of
model length and having the same wetted area as the model. This is then deducted
from the total model resistance coefficient to establish the model residuary resist-
ance coefficient.

At a constant Froude number the residuary resistance coefficient remains the same
for the ship as it is for the model, so there is no need for a suffix to indicate “model”
or “ship” in this case.
The ship frictional resistance coefficient C,, is again calculated using the
coefficient of friction applicable to a plank, this time one of the same wetted area
and the same length as the ship. This is then added to C, to arrive at the total
resistance coefficient Ct, of the ship.

ct, = Cfs + cr (6.3)
It should be noted that the use of friction coefficients based on a plank for both model
and ship implies that the skin friction is independent of the shape of the lines.