Hudson's equation

Hudson's equation

Hudsons Equation is an equation used by coastal engineers, enabling them to calculate the maximum weight of an object that can be moved by a wave (of a chosen size.)

Rip-rap

This rock armour is sometimes used in Hudsons Equation. The boulder size is crucial to the stability of the rip-rap under storm wave impact. The equation is as follows:

(3= cubed)

W= D.H3 ___________ (divided by)

K(d-1)3 Cot Aw Tem

W= Weight of the boulder in tonnesD= Boulder density (given at 2.8 tonnes per m3)H= Height of the storm waveK= Stability co-efficientA= Angle of rest (usually 45 degrees)

To calculate the equation

E.g
* = multiply

Wave height= 3m

Measured Boulder

L= 1.64m, W= 1.2m, D= 0.9mVolume= L*W*D= 1.8m

Weight= volume*densityW= 1.8*2.8= 5 tonnes

W= 2.8*27 / 2(1.8)3*1 = 6.5(27=3 cubed)

Therefore a boulder must be above 6.5 tonnes to not to be moved by a 3m storm wave. Our boulder of 5 tonnes will be moved by a 3m wave.


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