PHYSICS Cars and Their “Cornering” Ability

The term cornering describes, without, numbers a cars ability to go fast around a curve. The physics of a flat curve has a built in cornering limiting factor. This factor is the centripetal acceleration. The centripetal acceleration can be found from

Where a_c equals the centripetal acceleration, v equals the car's velocity around the curve, and R represents the radius of the curve. A curve that as a posted speed limit of 25 ^m/s and has a radius of 50 m requires a centripetal acceleration of 6.5 ^m/s². In terms of g's this is 0.66 g's, (^6.5/9.8 = 0.66 ).
The centripetal force needed for a car to make it around a flat corner supplied by the friction between the car's tires and the road. This value is described in magazines such as Car and Driver as the car's lateral acceleration. To find the car's lateral acceleration, a car turns a circle of a given radius. Then it accelerates slowly until it begins to slip to the outside of the circle. This is the point where the friction between the tires and the road have exerted the maximum amount of friction. The cars maximum lateral acceleration can be calculated from the formula for centripetal acceleration shown above.
The curve decides how much centripetal acceleration is needed to safely navigate the curve. It decides it by the velocity the curve is going to be traveled and the radius of the curve. Use the equation, V²/R.

In the example above the curve requires 0.66 g's to make it around without slipping. If the car's lateral acceleration is greater than or equal to the curve's calculated centripetal acceleration then it will go around the curve without slipping. If the lateral acceleration of the car is less than the centripetal acceleration then the car will slip to the outside of the curve until the radius is big enough to allow the curves centripetal acceleration to be equal to the car's lateral acceleration.


EXAMPLE #1
1. A curve has a posted speed limit of 25 mph, 11.16 ^m/s. The curves radius is 40 meters.
• With what centripetal acceleration can a car travel around the curve without slipping?

This means that a car can travel around the curve without slipping if the tires exert a frictional force of 3.11 m/s², 0.318 g's. In car and driver this frictional force is described as the "lateral acceleration." The limiting factor is 0.317 g’s for this curve.

EXAMPLE #2
While traveling down a road at 25 ^m/s, a car needs to negotiate a curve of radius 19 m. What centripetal force is needed to make the curve and what will happen if the friction between the car’s tire’s and the road is not equal to or greater than the needed centripetal force needed for the curve.
SOLUTION

3.36 g’s! There are no passenger cars that do this. The car will not make it around the curve. The driver will have the wheels turned but the car will continue to slide. If the curve were banked, the car would slide to the outside of the curve until the centripetal acceleration needed to negotiate the curve equals the centripetal acceleration the car can exert. Suppose the car can exert a centripetal acceleration of 0.88 g’s. Then;

Therefore R = 72.47m. The car will slide outwards along the banked curve until the radius of the turn equals 72.47 meters. Or until a fence stops the car.

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