Page 40 - Introduction to Naval Architecture

28 SHIP FORM CALCULATIONS

GENERAL
1
It has been shown that:
(1) Odd ordinate Simpson's rules are preferred as they are only
marginally less accurate than the next higher even number
rule,
(2) Even ordinate Tchebycheff rules are preferred as they are as
accurate as the next highest odd ordinate rule.
(3) A Tchebycheff rule with an even number of ordinates is rather
more accurate than the next highest odd number Simpson
rule.

POLAR CO-ORDINATES
The rules discussed above have been illustrated by figures defined by a
set of parallel ordinates and this is most convenient for waterplanes. For
transverse sections a problem can arise at the turn of bilge unless
closely spaced ordinates are used in that area. An alternative is to adopt
polar co-ordinates radiating from some convenient pole, O, on the
centreline. Figure 3.6.

If the section shape is defined by a number of radial ordinates at equal
angular intervals the area can be determined using one of the

Figure 3.6 Polar co-ordinates