Page 204 - Practical Ship Design

170 Chapter 6

@ = 3.4 + 0.5 LA

For the speed/length ratio, Froude introduced two different constants and 0,
whilst a third, 8, was later added by Baker.
@ relates the speed of the ship to that of a trochoidal wave having a length of
u/2

The speed of such a wave is J(g / 2n) x 1 / 2(V)”3

Jm
@= V = 0.5846 Vk/(A)’l6

@ relates the speed to that of a wave of length L/2
V
A
15 = = 0.5822 Vk/(L,)1/2
J( g I 2n) x L / 2
@
Some useful inter-relationships between 0, and F, are given by:
= @ x @”*

@ = 3.545 F,

8 relates the speed to that of a wave of length Cp . L

A more fundamental definition of 0 than that already given is:

R, x 1000
=
Ax02

Froude wanted to use R, /A which is the total resistance per unit of displacement
weight in identical units, but because the value of this ratio increases quite rapidly
at high speeds he divided it by O2 and multiplied it by 1000 to avoid small
numerical values. The rather peculiar denominator D in eq. 6.13. can be derived as
follows: