Turn On Flat Surfaces
If the bank angle is zero, the surface is flat and the normal force is vertically upwards. The only force keeping the vehicle turning on its path is friction, or traction. This must be large enough to provide the centripetal force, a relationship which can be expressed as an inequality, assuming the car is driving in a circle of radius r:
The expression on the right hand side is the centripetal acceleration multiplied by mass, the force required to turn the vehicle. The left hand side is the maximum frictional force, which equals the coefficient of friction μ multiplied by the normal force. Rearranging the maximum cornering speed is
Note that μ can be the coefficient for static or dynamic friction. In the latter case, where the vehicle is skidding around a bend, the friction is at its limit and the inequalities becomes equations. This also ignores effects such as downforce which can increase the normal force and cornering speed.
Read more about this topic: Banked Turn
Famous quotes containing the words turn, flat and/or surfaces:
“A sturdy lad from New Hampshire or Vermont who in turn tries all the professions, who teams it, farms it, peddles, keeps a school, preaches, edits a newspaper, goes to Congress, buys a township, and so forth, in successive years, and always like a cat falls on his feet, is worth a hundred of these city dolls. He walks abreast with his days and feels no shame in not “studying a profession,” for he does not postpone his life, but lives already.”
—Ralph Waldo Emerson (1803–1882)
“And thou, all-shaking thunder,
Strike flat the thick rotundity o’ the world!
Crack nature’s moulds, all germens spill at once
That makes ingrateful man!”
—William Shakespeare (1564–1616)
“But ice-crunching and loud gum-chewing, together with drumming on tables, and whistling the same tune seventy times in succession, because they indicate an indifference on the part of the perpetrator to the rest of the world in general, are not only registered on the delicate surfaces of the brain but eat little holes in it until it finally collapses or blows up.”
—Robert Benchley (1889–1945)