Fishing Craft Technology

Unit 3 - Design procedure

3.3. Simpson’s I^st rule

These rules are widely applied in Naval Architecture. They are a special case of the Newton’s cotes rule.
Let us deduce a rule for integrating a curve Y over the extent of x. It will be convenient to choose the origin to be in the middle of the base 2 h long having ordinates Y1, Y2 and Y3. The choice of origin in no way affects the result.

Assume that the curve can be represented by an equation of the third order.

This is the generalized form of the first rule applied to areas. The common multiplier is 1/3 x the common interval “h” and the individual multipliers are 1,4,2,4,2,4,2,4,1
The rule is one for evaluating an integral. It is equally applicable to any integration using Cartesian or polar co-ordinates.
It is suitable for 3, 5, 7, 9, 11, 13 ... etc ordinates