Determine the height of a capsule/pod above the ground after 25 mins.

Question

The diameter of the "Eye" is 135 meters and each rotation takes 30 mins. By first developing a suitable model to represent the rotation of the "Eye", determine the height of a capsule/pod above the ground after 25 minutes.

The London Eye is a major tourist attraction in London, England. During a ride on the "Eye", the rotation can be modeled using a periodic function.

State any assumptions made in determining your results.

Answer 1

This is difficult to explain without a drawing.

 

Let d = diameter of the Eye = 135 m

      r = radius of the Eye = d/2 = 67.5 m

      t = 25 min

 

assume ho = 1 meter above ground for loading at initial theta = 0; or &theta = -90^o

 

1 rev = 360^o/30 min = 12^o/min

 

θ = (12^o/min)*t

 

   h = ho + r*(1 + sin(θ^o + θ))         General Solution

 

at t = 25 min

 

h = 1 m + (67.5)*[1 + sin(-90+ 12*(25) ]  = 34.75 m above ground after 25 min