Simpson's Rules (Ship Stability)

Simpson's 1st rule

Also known as the 1-4-1 rule (after the multipliers used ).

A r e a = h 3 ( a + 4 b + c )

Simpson's 2nd rule

Also known as the 1-3-3-1 rule, Simpson's second rule is a simplified version of Simpson's 3/8 rule.

A r e a = 3 h 8 ( a + 3 b + 3 c + d )

Simpson's 3rd rule

Also known as the 5 - 8 -1 rule

A r e a = h 12 ( 5 a + 8 b − c )

Use of Simpsons rules

Simpson's rules are used to calculate the volume of lifeboats, and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used.