Last month I discussed the Consumers Union (CU) report indicating a tendency of the Mitsubishi Montero to roll over in certain situations during a test involving a simple double lane-change avoidance maneuver. I explained how the Static Stability Factor (one half the track width (t) divided by the height (h) of the center of gravity) is related to the tendency for a vehicle to roll over. This analysis assumed that the roadway was level with no slipping of the tires, but did not account for the several other factors that can contribute to rollover such as dynamic properties of the suspension, steering, tires, electronic stability control, etc. The CU test is intended to expose differences in vehicles due to these and other factors that are difficult to evaluate analytically.
Roll over can occur in many other scenarios, often involving skidding. One accident, coincidentally involving a Montero, resulted from the driver going to sleep, running off the road, and overcorrecting into a sideways skid, followed by a roll. The vehicle rolled four times before coming to rest upright. The driver sustained severe arm and leg injuries, one passenger was killed, and another passenger was treated and released. An analysis of the motion of the vehicle provides information about the speed of the vehicle when the accident occurred.
Skidding occurs when the friction forces are inadequate to offset the centrifugal forces. Shown below is the free-body diagram of the rear of a vehicle of weight "W" traveling with speed "v" along a path curving to the left with radius of curvature "r." We assume a state of impending tipping so that all the weight and all the tire friction is concentrated on the right side tires. The centrifugal force F = W v2 /(g r) is offset by the friction force "f" when there is no sliding and "g" is the gravitational constant. As v increases r decreases, the friction force increases. If the centrifugal force exceeds µ× W prior to tipping, the frictional forces max out and the vehicle begins to skid sideways. Thus, the relation
W v2 /(g r) > µW or v2 /(g r) > µ
defines the minimum speed that must exist for this to occur. On the other hand, if there is no skidding and tipping is occurring, summing moments about point P gives
h W v2 /(g r) > W t/2 or h v2 /(g r) > t/2
Thus, in order for tipping to occur before sliding,
µ> = v2 /(g r) > t/(2 h)
The value of t/(2 h) for the 2001 Montero is about 1.15, while µ is much less than 1.0, normally being smaller than the coefficient of friction in the direction of the path. Therefore, we would normally expect sliding to occur before rolling as in the case mentioned above. In the CU test, rolling occurred before sliding because of the dynamic effects of other elements such as the suspension, steering, tires, etc., and the nature of the test. Of course, highways are normally banked (called superelevation) in order to direct some of the centrifugal force normal to the surface of the highway. This increases the maximum value of the friction forces and decreases the tipping moment, reducing both the tendency to skid and to tip, depending on superelevation angle and highway design speed. Highways are designed using worst-case values for µ. Many cases like the one above involve vehicles going off the road onto slopes that increase the tendency to skid and tip.
Normally, skidding increases the radius of curvature of the path. This decreases the centrifugal force and the tendency to roll. Vehicles that are skidding will not usually roll unless there is some tripping mechanism such as a curb. This frequently happens as in the case mentioned above. Momentum and energy equations can be applied to determine the lateral speed required for tripping, providing more information that can be used to determine the original speed of the vehicle.