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Question
Answer in Brief:
Part of a racing track is to be designed for curvature of 72m. We are not recommending the vehicles to drive faster than 216 kmph. With what angle should the road be tilted? By what height will its outer edge be, with respect to the inner edge if the track is 10 m wide?
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Solution
Given:
The radius of curvature of the track = 72m
Maximum speed = 216km/h = 60m/s
Width of the track = 10m
To find:
- The angle the road should be tilted by
- Height of the outer edge wrt inner edge
Solution:
The angle of banking of the road is given by
`tanθ = "v"^2/(rg)`
`θ = tan^-1("v"^2/(rg))`
θ = `tan^-1(60^2/(72 xx 10))`
θ = `tan^-1(3600/720)`
θ = `tan^-1(5)` = 78.69°
The height of the outer edge of the road is given by
`sinθ = h/w`
h = w sinθ
h = 10 × sin(78.69)
h = 10 × 0.9805
h = 9.805m
- The angle that the road should be tilted is 78.69°.
- The height of the outer edge is 9.805m.
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