Chapter 2-5 Center Of Mass for Vehicles and Their Effect on Rollover Accidents


Center of mass of a system of bodies is defined as the point where there is no moment about it. Namely, masses of all bodies in the system are balanced at the center of mass, like balancing playground seesaw. In a two dimensional rectangular coordinate system, center of mass in the direction is defined as

(2-5-1)

where is the mass of each body and is the corresponding distance from in the direction. After is determined, if Eq. (2-5-1) is reapplied to the system of bodies where this time is the corresponding distance from , then all the moments generated by each body mass should cancel out to get . This is a good check for the center of mass in the direction. Similarly center of mass in the direction is defined as

(2-5-2)

Center of mass is a very critical dimension in the vehicles that we ride in. It affects the stability of the vehicle while cornering. A loaded vehicle with a high center of mass, i.e. an SUV, might be more susceptible to rollover accidents than a low center of mass vehicle, i.e. a sports car, if they both have the same track widths.

Let us consider two vehicles for a rollover analysis during cornering with the parameters given in Table 2-5-1.

Vehicle Type Vehicle Curb Weight (Vehicle Plus Fluids), pounds Vehicle Curb Weight Center Of Gravity Height,Hv, feet Vehicle Track Width,T, feet Passenger In Riding Position Center Of Gravity Height, Hp, feet Number Of Passengers Riding In Vehicle Each Passenger Weight, pounds
SUV 4,000 2.5 5.0 3.0 6 200
4-Door Sedan 3,000 1.7 4.0 2.0 4 200

Table 2-5-1 Vehicle and passenger parameters
Center of gravity heights are from road level

The parameters given in Table 2-5-1 are typical ones for an SUV and for a 4-door sedan vehicle. Center of gravity heights are given from the road level. Track widths are defined as the distance between the two front tire thread centers of parallel wheels. For these vehicles, it is assumed that the front and the rear track widths are the same. Center of gravity of the vehicles loaded with passengers can be calculated using Eq. (2-5-1) where is the road level.

For the SUV:

(2-5-3)

For the 4-door sedan:

(2-5-4)

When a vehicle enters a curve on a flat road, the forces and accelerations acting on the vehicle whose tires have enough traction on the road are shown in Figure 2-5-1. The vehicle in Figure 2-5-1 is not sliding and it is in control, but it is starting to rollover.
















Figure 2-5-1 Forces and accelerations acting on a vehicle that is starting to roll

If moments of the forces acting on the vehicle are taken at the right tire interface with the road, following relationship is obtained.

(2-5-5)

where is the gravitational acceleration, 32.2 ft/s2 , and is the lateral acceleration of the vehicle given by . is the cornering speed of the vehicle in ft/s and is the circle radius in ft that the vehicle is trying to corner. For rollover to occur

(2-5-6)

where is called the vehicle’s static stability factor. The larger the static stability factor, it is less likely that it will rollover when we are cornering. For passenger loaded SUV vehicle in Table 2-5-1 and Eq. (2-5-3), the static stability factor is 0.96. For passenger loaded 4-door sedan vehicle in Table 2-5-1 and Eq. (2-5-4), the static stability factor is 1.28. The 4-door sedan is 33% more stable for rollovers during cornering than the SUV. Eq. (2-5-6) can be rewritten as

(2-5-7)

During cornering, speed of the vehicle has to be greater than for rollover to start occurring. For the two passenger loaded vehicles in Table 2-5-1, maximum cornering speed versus cornering circle radius on a flat road is shown in Figure 2-5-2.





Figure 2-5-2 Maximum cornering speed for vehicle rollover on a flat road versus cornering circle radius

For a given cornering circle radius, maximum cornering speed for an SUV is 16% less than a 4-door sedan.

Cornering speed can be increased or the rollover potential at a given speed can be decreased by introducing an inward facing bank (towards the center of the cornering circle radius) to the cornering segment of the road. Figure 2-5-3 depicts a vehicle cornering on a 10o banked road.


















Figure 2-5-3 Forces acting on a vehicle cornering on a 10o banked road

Gravitational and lateral acceleration forces acting on the vehicle in Figure 2-5-3 can be broken into components that are parallel and perpendicular to the banked road. Moments of these forces are taken at the right tire interface with the road to give the following relationship.


(2-5-8)

or for rollover to start occurring

(2-5-9)

For the passenger loaded vehicles in Table 2-5-1, maximum cornering speed versus cornering circle radius on a 10o banked road is shown in Figure 2-5-4.






Figure 2-5-4 Maximum cornering speed for vehicle rollover on a ten degrees banked road

A 10° bank on the road while cornering provides a 19% improvement in SUV cornering speed and a 21% improvement in 4-door sedan cornering speed.