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Areas of Waterplanes and Other Ship-Sections

Waterplane : The horizontal plane which passes

through a floating ship on a level with the

waterline

Simpson's First Rule

The area between any three consecutive

ordinates is equal to the sum of the end

ordinates, plus four times the middle

ordinate, all multiplied by one-third of the

common interval.

TROPANG STABILITY

Group 3

3/8 h (a + d + 3b + 3c)

3/8 h (d + g + 3e + 3f)

Total area: 3/8 h (a + 3b + 3c + 2d + 3e + 3f +g)

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.

Simpson's Second Rule

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

THANK YOU

h/3 (a + c + 4b)

h/3 (c + e + 4d)

h/3 (e + g + 4f)

Total Area: h/3 (a + 4b + 2c + 4d + 2e + 4f + g)

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)

GOOD MORNING!

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