Chapter 25 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
(251)
where is the mass of each body and is the corresponding distance from in the direction. After is determined, if Eq. (251) 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
(252)
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 251.
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 4Door Sedan 3,000 1.7 4.0 2.0 4 200
Table 251 Vehicle and passenger parameters Center of gravity heights are from road level
The parameters given in Table 251 are typical ones for an SUV and for a 4door 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. (251) where is the road level.
For the SUV:
(253)
For the 4door sedan:
(254)
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 251. The vehicle in Figure 251 is not sliding and it is in control, but it is starting to rollover.
Figure 251 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.
(255)
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
(256)
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 251 and Eq. (253), the static stability factor is 0.96. For passenger loaded 4door sedan vehicle in Table 251 and Eq. (254), the static stability factor is 1.28. The 4door sedan is 33% more stable for rollovers during cornering than the SUV. Eq. (256) can be rewritten as
(257)
During cornering, speed of the vehicle has to be greater than for rollover to start occurring. For the two passenger loaded vehicles in Table 251, maximum cornering speed versus cornering circle radius on a flat road is shown in Figure 252.
Figure 252 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 4door 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 253 depicts a vehicle cornering on a 10o banked road.
Figure 253 Forces acting on a vehicle cornering on a 10o banked road
Gravitational and lateral acceleration forces acting on the vehicle in Figure 253 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.
(258)
or for rollover to start occurring
(259)
For the passenger loaded vehicles in Table 251, maximum cornering speed versus cornering circle radius on a 10o banked road is shown in Figure 254.
Figure 254 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 4door sedan cornering speed.
