Simpson's Rules (Ship Stability)

Simpson's rules are a set of rules used in Ship Stability and naval architecture, to calculate the areas and volumes of irregular figures.^[1]

Simpson's First Rule

Simpson's 1st rule

Also known as the 1-4-1 rule (after the multipliers used ).^[2]

$Area = \frac{h}{3}( a + 4b + 2c + 4d + 2e + 4f + g )$

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.^[3]

$Area = \frac{3h}{8}( sum.. of ..products )$

Simpson's Second Rule

Simpson's 3rd rule

Also known as the 5 - 8 -1 rule^[4]

$Area = \frac{h}{12} (5a + 8b - c )$

Use of Simpsons rules

Simpson's rules are used to calculate the volume of lifeboats,^[5] 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.^[6]

References

1. Ship stability for Masters and Mates (PDF). United Kingdom: Elsevier Butterworth. p. 69. |first1= missing |last1= in Authors list (help)
2. Rhodes, Martin (2003). Ship Stability for Mates/Masters. United Kingdom: Seamanship International.
3. Subramaniam, Capt. Harry. Nutshell series - Ship Stability III. Mumbai, India: Vijaya Publications.
4. Donkum, Enkhuizen, Van. ShipStability. Dokmar publications. ISBN 978-90-71500-15-2.
5. Kitching, Capt. R.C.E. Introduction to Ship Stability. Canada: Starpath Publications.
6. Stability and Safety of Ships. USA: The Society of Naval Architects and Marine Engineers. ISBN 0-939773-61-9. |first1= missing |last1= in Authors list (help)