The banking angle for a curve of radius 400 ft for a speed of 60 mi/h should be approximately?


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Please show solutions. Thanks :D


Banks in Center Line, MI



Answer (1):

Dean

(For banking with no side forces on the car)
Use feet for all:
velocity (v) = 60 mi/h = 88 feet per second
radius (r) = 400 feet
gravitational acceleration (g) taken at 32.2 (feet/sec)/sec
centripetal acceleration = v² / r = 19.36 (feet/sec)/sec

Assuming radius centre on the left, draw the point representing the car C of G on the right. From the point draw gravity acceleration vector (to scale) vertically down (32 (feet/sec)/sec)
From the same point and horizontally to the right draw (to scale) the centripetal acceleration vector (19.36 (feet/sec)/sec.
Draw in the resultant, a line normal to this resultant gives the banking slope, and the angle (a) from horizontal can be calculated from:
a = inverse tan ( 19.36 / 32.2 )
a = 31.016°