Can someone help me please with this problem? (Modeling) solve each problem. 67.

Question

Can someone help me please with this problem?
(Modeling) solve each problem. 67. Design of Highway Curves When highway curves are designed, the outside of the curve is often slightly elevated or inclined above the inside of the curve. See the figure. This inclination is the superelevation. For safety reasons, it is important that both the curve's radius and superelevation be correct for a given speed limit. If an automobile is traveling at velocity Vin feet per second), the safe radius R for a curve with superelevation 0 is modeled by the formula g(f+ tan 0) where fand g are constants. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

Explanation / Answer

Q1.
as given R=V^2/(g*(f+tan(theta)))

theta=3 degree

g=32.2 ft/s^2

f=0.14

V=45 mph=66 ft/sec

then R=66^2/(32.2*(0.14+tan(3)))=703.1 ft

hence nearest foot is 704 ft (for safety, radius should be on higher side).

Q2.

if V=70 mph=102.667 ft/s

then R=102.667^2/(32.2*(0.14+tan(3)))=1701.3 ft=1702 ft

Q3.part a with theta=4 degree:

R=66^2/(32.2*(0.14+tan(4)))=644.41 ft=645 ft

hence radius decreases

part b with theta=4 degrees
:

R=102.667^2/(32.2*(0.14+tan(4)))=1559.3 ft=1560 ft

hence radius decreases with increasing theta.

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