You want to design an oval racetrack such that 3200 lb racecars can round the tu

Question

You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 104 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle necessary for the racecars to navigate these turns at 104 mi/h and without the aid of friction.

You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 104 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle necessary for the racecars to navigate these turns at 104 mi/h and without the aid of friction.

Explanation / Answer

v = (22/15)*104 = 152.53 ft/sec
For no friction, = arctan[v²/(R*g)] = 36.01°

Anet = [(v²/R + g²] = 32.36 ft/sec²
Af = Anet*sin = 19.02 ft/sec²
Ff = m*Af = (3200/32.2)*Af = 1890.18 lb along the slope.
Fr = Ff*cos = 1529 lb

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