Question

A wind turbine has blades 50m in diameter and an overall height (to the highest point) of 125m. If it has four blades instead of three, create four equations modelling the height of a point on the tip for each of the four blades.

Answer 1

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )

Blade D : H(θ) = 75 + 50 sin( θ + 270° )

Explanation:

Given data :

Diameter of blade = 50 m

overall height = 125 m

The four blades : Blade A , Blade B, Blade C, Blade D all moves in same direction hence they make 90° to each other.

Lets assume The blades are standing at θ with the horizontal

The four equation modelling the heights :

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )

Blade D : H(θ) = 75 + 50 sin( θ + 270° )