When BLOODHOUND SSC reaches the end of each run Andy Green will turn the car around to face the new course for his return run through the measured mile. The minimum turning circle that Andy’s steering will allow is 240m in diameter.
Calculate the maximum speed that will be the safe to turn the car at. Above this figure the front wheels may understeer. The diagram below will help your calculations.
The mass of the car is m kg.
The reaction force from the desert surface is N newtons.
The lateral grip of the wheels on the desert is F N which is calculated at 0.4
Give your answer in ms-1 and mph.
If the mass of the car is m kg and its speed is v ms-1 and it is moving in a circle of radius 120 metres, then its acceleration is v2/120 ms-2 towards the centre.
There is no vertical acceleration, as the car remains on its wheels, so N is 9.8m. The lateral grip produces the centripetal acceleration towards the centre:-
F = m.v2/120
So mv2/120 ≤ 0.4 x 9.8m
Putting the figures in gives:-
v ≤ √ (120 x 0.4 x 9.8) = 21.68 ms-1 or 48.49 mph.
The turn should be made at a speed below 49.5 mph.