We previously described an accident in which a Montero ran off the road, went into a broadside skid, and rolled four times. We have discussed the static stability factor (SSF) and the speed necessary to cause a vehicle to roll due to abrupt turns without skidding. However, this case involved a sideways skid. Thus, the friction force in the tires could not offset the centrifugal force of the turn. In investigating this case, we want to determine what caused the Montero to roll.
In a skid the driver has little control. The vehicle just skids in the direction of the velocity vector until friction forces stop it. (Forever if you are skidding on ice or hydroplaning.) Once the skid starts, nothing the driver does will cause the vehicle to roll. Something must have happened during the skid to change the dynamic situation.
What happened? We can discount impact with a low flying UFO since there was no evidence of such a collision and there were no reported sightings. The friction force was the only unbalanced force causing a tipping moment about the center of gravity (CG) of the vehicle. Evidently, something caused the tire friction to increase enough to roll the car. This could happen when skidding onto a surface with a higher coefficient of friction (mu) such as the shoulder of the road. Also, sideways pressure on the tires could have caused the tire bead and the wheel rim to separate, at least partially deflating the tire and increasing mu. Checking the tire pressure could check this. Also, there is frequently grass or other foreign objects between the tire and the rim when this happens. The vehicle could also have slid off the road onto a slope, increasing the tipping moment. Frequently, such a rollover will occur because the tires hit some immovable object such as a curb or ditch, stopping lateral motion of the tires. This stops the translational motion of the vehicle and causes it to begin to rotate about the point where the tires hit the obstacle. Since evidence points toward the latter situation, we will examine the lateral speed that would cause rolling.
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Equation in action |
The diagrams indicate State 1 of the vehicle just after impact with a fixed obstacle, with a horizontal speed V, and State 2, where it is rolled to a position where the center of mass is vertically above the point of contact "A" with the obstacle. State 2 assumes zero rotational velocity and represents the marginal condition for rollover. To determine the minimum speed of skidding V required for rollover, we equate the kinetic energy (KE) of the vehicle just prior to State 1 to the change in potential energy (PE) in State 2. Thus:
KE = 0.5 I u2 = PE = W (c - h)
I is the mass moment of inertia about point A, W is the weight, h and c are the vertical distances to the CG in States 1 and 2 respectively, and v is the State 1 velocity of rotation. This ignores energy lost during impact, and assumes pure rotation about point A.
Using conservation of momentum about point A to calculate v in terms of V:
W V h / g = I u or u = W V h/( g I )
Substituting this expression for v into the first equation, we find that
V2 = 2 (c - h) I g2 / (W h2)
This equation determines the minimum speed of skidding for rollover. Note that as the track width (t) is increased (increasing c), the minimum speed required for rollover increases. Alas, we again find that vehicles like the Montero are more likely to roll than those with a lower SSF, another reason to trade your SUV.