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]

${\displaystyle Area={\frac {h}{3}}(a+4b+c)}$

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.^[3]

${\displaystyle Area={\frac {3h}{8}}(a+3b+3c+d)}$

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. p. 70.
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)