physics of car slip centripetal?

Question

the tires of a car are more likely to slip on gradual curves than tight ones.

true or false? why?

Answer 1

Generally speaking, an automobile would be more likely to roll over in a tight turn as opposed to a gradual turn.

At the heart of the laws of motion lies a vehicle's center of gravity, the point at which an object's mass is in equilibrium.

The center of gravity is the single point through which all of the forces affecting a vehicle— from braking and accelerating to turning— act. And its location, especially its height off the ground, is crucial to understanding a vehicle's stability on the road.

A car, like any moving object, has to obey Newton's first law of motion. Once it's moving, inertia will keep the car's center of gravity traveling in a straight line with a constant velocity until a force such as friction makes it change speed or direction. Yet even when a car heads straight, the load on its four tires— which cling to the pavement with postcard-sized patches of rubber— can change radically.

Accelerating, for example, shifts the bulk of the load to the two rear tires. This presses the driver back into the seat and reduces the weight on the front tires, thus diminishing their ability to change the direction of the vehicle.

A car with a short wheelbase (the distance between the front and back tires) and a high center of gravity can be made to lurch forward and backward so violently that it does a somersault end over end.

Front somersaults in modern vehicles are rare, but lateral somersaults— rollovers— are not. Vehicles most often roll over when drivers attempt to execute a turn. Because the car's center of gravity keeps moving in a straight line, the only way to change direc-tion is to turn the front wheels. (In all but a few exotic vehicles with four-wheel steering, only the front tires are steerable.) As the tires turn sideways against the direction of travel, they create a lateral force that is opposed by an equal force— sometimes known as centrifugal force— in the opposite direction, which propels the car toward the outside of the turn.

As with acceleration and braking on a straightaway, turning causes the load of the car to shift toward the two tires on the outside of the turn. In a left-hand turn, for example, the load increases on the passenger-side tires, especially the one in front. As long as some weight remains on the inside tires, the car will stay upright. But if you end up with no weight on the inside tires, they'll lift into the air,

Drivers are rarely aware when the inside tires become weightless in a tight, fast turn because the tires may be less than half an inch off the ground. But at that point, anything at all— a gust of wind, an outside tire hitting a pothole or a curb or the soft shoulder of a road— can flip the car over.

A vehicle's springs, shock absorbers, and tires can help control these forces, but in general, the tendency to roll over can be quantified by a simple ratio. That ratio is found by dividing the height of the vehicle's center of gravity into half the distance between the centers of the two front tires (called track width). The higher the ratio, known as the static stability factor, the more likely a vehicle is to stay on its feet. This makes perfect sense: A wide, flat piece of sheet metal is harder to flip over than a tall, thin metal cylinder. But the implications for car designers aren't always obvious.

Vehicles with the lowest centers of gravity— less than a foot off the ground in some race cars— are very stable. But they are useless on anything other than a smooth racetrack. If most cars were designed like race cars, Lopez says, "every time you went to the supermarket, you'd have to call a tow truck to pull you off the speed bump." So, over the course of a century of car manufacturing, a compromise has emerged: Most cars are built just high enough to clear road obstacles yet with a center of gravity low enough— about 20 inches off the ground— to prevent most rollovers.

SUVs, unfortunately, tend to have a center of gravity five or six inches higher than that of passenger cars and a track width that's about the same. According to figures compiled by the NHTSA, one popular 2001 model SUV has a track width of 58.6 inches and a center of gravity 27.53 inches off the ground. The best-selling passenger car by the same manufacturer has a track width of 61.9 inches and a center of gravity 21.7 inches off the ground. The numbers may seem similar, but they combine to give a static stability factor of 1.06 for the SUV and 1.43 for the passenger car. Statistically, that means that the SUV has a 37 percent chance of rolling over in a single-vehicle crash, whereas the passenger car has only a 10.6 percent chance of rolling over. For the SUV to be as stable as the car, its track width would have to be 20 inches wider than it now is.

Answer 2

False.

If you look at a plot of tire slip angle vs. cornering force generated (for a constant weight applied on the tire), you see that at first, as you increase slip angle, the cornering force rises in a linear fashion. As you continue increasing slip angle, you eventually reach a point around 12 degrees of slip (meaning the tire is pointing in a direction 12 degrees away from the direction it's traveling in) where the cornering force stops increasing linearly. It goes up a bit more, then as slip angle increases more still, the cornering force actually goes down. If you go far past 12 degrees of slip angle, the cornering force drops off dramatically, and you're essentially out of control.