Simpson's Rules (Ship Stability)

For Simpson's rules used in numerical analysis, see Simpson's rule.

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)
This article is issued from Wikipedia - version of the Monday, March 21, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.