Last month we discussed an accident involving a four wheel (4W) ATV that rolled while making a curve on a gravel country road. Two factors that cause rolling were involved in this case:

1. Lateral linear momentum due to skidding combined with impact with an obstruction; and

2. The overturning moment due to centrifugal force.
Another common cause for rolling in ATVs is the overturning tendencies due to the weight force (W) and dynamic forces when traveling on a slope. Even though this was not the situation in the case considered, it deserves consideration, and has some interesting aspects.
With reference to the accompanying figures, specifications for the 4W are: W =746 lbs, h=24.9 inches, L=49.3 inches, and d=21.5 inches. Since the rollover started on a level surface, W was not a factor in this accident. However, W is a factor for ATVs traveling on a slope since on a steep slope, W can produce an overturning moment. In order for this to occur the line of action of W, acting vertically through the center of gravity (CG), must pass outside the envelope of the tire contact points with the ground. This track envelope is square for a 4W ATV, and triangular for a threewheel (3W) ATV, as shown. For an ATV traveling at a constant speed transverse to a slope, a vertical line through the CG would have to pass outside line AA, shown in the figure, for W to cause a rollover. For a 3W, the vertical line through the CG would have to pass outside line BB. The 3W ATV has a smaller track envelope than a similar sized 4W ATV. Since the CG is forward of the rear axle, and the envelope is narrower toward the front, a rollover would occur with less slope for a 3W than with a 4W.
The occurrence of rolling depends not on W but on geometry. W would only determine the rate at which rolling occurs. For a 4W with the specifications given above, a static analysis shows that rollover due to W would occur on a slope of 40.8° or more when traveling transverse to the slope. For a 3W with the same values for h, L and d, and for which the CG is a distance c = 29.6" from the front, rollover would occur on a slope of 27.4° or more, much less than for the 4W.
For a 4W traveling transverse to the slope, any steering will only increase the distance of W from the envelope, decreasing the tendency to roll due to W. However, for a 3W traveling at an angle "á" to the horizontal in the plane of the slope, a geometric analysis shows that the distance "m" of the CG from the envelope in the direction of W is given by:
m=cd/[Lcos(á)+dsin(á)]
From the figure, m obviously decreases as á increases, reaches a minimum value when m is perpendicular to A'A', and then begins to increase. Thus, there is a critical value of á at which the 3W is more likely to overturn due to W. For the 3W specified above this angle is 23.6°. Further geometric analysis shows that the slope angle (Ö) at which rolling would occur for a given á is:
Ö=arctan{(c/L)(d/h)/[cos(á)+(d/L)sin(á)]}
Thus, Ö is determined by the static stability factor (2d/h), as well as a factor (c/L) related to how far back the CG is. For the critical value of steering given above, Ö=25.4° is not much different than the value for á=0°. This vehicle should not be ridden on a slope with an angle greater than this.
Of course, steering also introduces centrifugal forces as discussed last month in addition to W. If you get headed downhill at á=25° on this 3W, and start a turn back uphill, the combination of W and dynamic forces assure disaster. It's little wonder that you don't see many 3W ATVs around anymore.