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The case of double jeopardy on an ATV
By Larry Zirkle, P.E., Contributing writer -- Design News, October 21, 2002
Two teenagers (call them Bert & Ernie) were out for a joy ride on a four wheel (4W) ATV. They were on a gravel county road when they encountered a sharp curve. The ATV began to skid broadside slightly, and the lip on the ditch on the side of the road "tripped" the ATV. The ATV rolled, throwing off both boys. Bert, the driver, was killed, and Ernie had a broken leg and arm injuries. The insurance company wanted to know how fast they were driving.
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Analysis of skidding and rolling for an ATV is the same as for a car. The centrifugal force (Fc ) tending to overturn or skid the vehicle acts through the center of gravity (CG), and is Fc =WV2/(gr), where W = weight, V = speed, g = gravitational acceleration, and r = radius of curvature of the path of the CG. The friction force (Ff) from the tires resists Fc and has a maximum value of Ff=fW, where f is the coefficient of friction. At low speeds up to the point of impending skidding, Ff= Fc . Thus, at impending skidding,
V=(fgr)1/2
Measurements indicated that f=0.55, and r=51 ft. Thus, for skidding to occur, the speed had to be at least 20.5 mph, whether it was a car, a dump truck, or an ATV, as long as the coefficient of friction is the same.
When a vehicle begins to skid, it initially builds up lateral translational momentum (linear speed times mass). If it slides into an obstruction like a curb or the lip of the ditch, the bottom edge of the vehicle may stop moving laterally. Some energy will be lost during impact, but most of the momentum is usually retained. When the edge of the vehicle stops, translational momentum is changed into rotational momentum (angular speed times moment of inertia), and the vehicle rolls over if the lateral speed is large enough to carry it over. The change from translational to rotational momentum occurs due to an impulsive force on the outside tires created by impact with the lip. An impulsive moment is created about the CG in the rotational direction of the roll. This is much like a gymnast jumping toward the parallel bars and grabbing one, creating a bodily rotation. Since the ATV skidded only slightly, little translational momentum was generated. Momentum would have been only a small contributor to the rollover.
Tracks indicated little change in curvature at rollover, so that Fc was not significantly changed, and was also a contributor to rollover. Fc produces an overturning moment (hFc). "h" is the normal height of the CG above the ground. This moment is opposed by the moment produced by the weight (dW), where d is half the track width. At impending roll, these two moments would be equal. Thus,
dW=hWV2/(gr)orV2=dgr/h
We have noted before that if the static stability factor (SSF=d/h) is larger, the vehicle roll occurs at a higher speed, and is a design consideration. The above indicates a speed of 25.7 mph for rollover confirming that skidding would occur prior to rollover due to Fc. Normally, skidding would not allow Fc to overturn the vehicle, but the lip of the ditch provides resistance so that Ff can be larger than fW, resulting in rollover.
In general, analysis of rollover due to both lateral momentum, and Fc is more complex than indicated here. However, in this case, skidding can be considered a minor factor. It could be estimated that the ATV was traveling at least 25 mph prior to rollover. Additional considerations, such as the distance of roll and the distances the bodies were thrown, might allow a higher speed (but not lower) estimate, but are beyond the scope of this article. Also, as usual, a complete set of reliable evidence is not available, and you have to do the best you can with what you have.
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