Examples - Tire Cornering Stiffness Calculation
When the tire is orientated at an angle to the direction of motion, a steering force occurs perpendicular to the plane of the tire. This force does not vary linearly with the tire slip angle, but the relation is nearly linear for small slip angles. The nominal cornering stiffness is equal to the side force in pounds divided by the slip angle in radians for small angles. For larger angles the rate of increase of perpendicular force with increasing angle falls off as "saturation" is approached. The program handles this in a standard manner for all tires. A Typical value for the cornering stiffness per degree of slip angle is approximately 16-17% of the load on the tire.
Tire cornering stiffness properties are input separately to allow the simulation of tire damage--a damaged tire which has lost its pressure will have a substantially lower cornering stiffness, perhaps 20 percent of that for an undamaged tire. Under-inflated tires will have somewhat lower cornering stiffness than those of properly inflated tires, but far greater than seriously damaged tires.
The following example demonstrates the calculation procedure for the tire cornering stiffness. Assume you have a 4000 lb. vehicle with 60/40 weight distribution. Per original SMAC, the cornering stiffness would be calculated for a neutral steer vehicle as follows: (note that for m-smac, the inputs can be entered as positive or negative)
For front wheels, CSTF(1),CSTF(2) = 4000*0.60*0.50*0.165*57.29578 = -11345. Lbs/rad
For rear wheels, CSTF(3),CSTF(4) = 4000*0.40*0.50*0.165*57.29578 = -7563. Lbs/rad
The inputs in Default (EDSMAC compatible) units are as follows:
For front wheels, CSTF(1),CSTF(2) = 4000*0.60*0.50*0.165 = 198. Lbs/deg
For rear wheels, CSTF(3),CSTF(4) = 4000*0.40*0.50*0.165 = 132. Lbs/deg
DISCUSSION: Moment of
Inertia