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Waterplane : The horizontal plane which passes
through a floating ship on a level with the
waterline
TROPANG STABILITY
Group 3
The area between any four consecutive
ordinates is equal to the sum of end ordinates,
plus three times each of the middle ordinates,
all multiplied by three-eights of the common
interval.
a. The rule can be used when, and only when, the
number of ordinates is four, or four plus some
multiple of three ( 4, 7, 10, 13, 16, etc.)
b. The area is found by multiplying successive
ordinates, including the ends, by the multiplier
1, 3, 3, 2, 3, 3, ... ,1, adding the results together,
and then multiplying by three-eights of the
common interval.
Example: Given are 10 ordinates (a,b,c,d,e,f,g,h,i,j)
Common interval is BN
The formula is : 3/8 BN (1a + 3b +3c + 2d + 3e
+ 3f + 2g + 3h + 3i + 1j)
Use Simpson's First Rule to find the area of a waterplane which has th ff. half ordinates, spaced 12 meters apart: -1.7, 5.9, 7.0, 5.2, 1.3, meters.
Find the area of a waterplane, using Simpson's Second Rule. The common
interval is 15 meters and the ordinates are: - 0, 9.0, 13.3, 14.7, 12.8, 7.5, 0.6 meters.
a,b,c,d,e,f,g are ordinates; the
length of the strips
Divide the plane or half plane
into strips with equal width
a.) It can be used when, and only when, an odd
number of ordinates are taken.
b.) The area is found by multiplying successive
ordinates by the multipliers 1, 4, 2, 4, 2, 4,...,1
Example. Given are 11 ordinates ( a,b,c,d,e,f,g,h,i,j,k )
BN as the common interval or width
Formula is : BN/3 (1a + 4b + 2c + 4d + 2e + 4f
+2g + 4h + 2i + 4j + k)