Apparatus Rollovers, Part 8: More on the Friction Circle


In last month’s article, we discussed the fact that too much lateral g-force will likely cause a low center of gravity vehicle to break traction with the road and spin out instead of rolling over.

A vehicle with a low center of gravity may spin out while rounding a curve because there is only so much grip available between the tire and the road surface. The available tire grip is equal to the drag factor of the roadway. If the driver’s speed and steering angle create a g-force on the vehicle that is greater than the drag factor of the road, the tire will break traction and the vehicle will lose control. This concept is better understood as “the Friction Circle.”

When discussing the friction circle, we must remember that a driver can use all of the available grip in the lateral (side-to-side) direction while turning, longitudinal (front-to-back) direction while accelerating or braking, or some combination of these directions. As long as the combined g-force does not exceed the available grip of the road, the vehicle will hold its grip on the road.

Last month, we examined a vehicle that was traveling through a curve that had a radius of 320 feet. We assumed that the vehicle was traveling through this curve at a steady speed, meaning the driver was not using any braking or acceleration. Because the driver was not using any grip in the longitudinal direction (braking or accelerating), all of the grip was available to use in the lateral direction (side-to-side). But what happens if the driver accelerates or brakes while rounding the curve? In that case, the driver would need to use some of the available grip in the longitudinal direction as well as the lateral direction as he rounds the curve. If this combined g-force exceeds the available grip of the road, the vehicle will break traction.


To best examine this, let’s use the friction circle to examine a common scenario. Let’s assume that a vehicle is rounding our 320-foot curve at 59 miles per hour (mph). Based on our previous calculations, they are just at the edge of the friction circle. As the driver rounds the curve at 59 mph, there is 0.74 g pushing on the side of the vehicle. As the drag factor of the road is 0.75, there is almost no g-force left to use in any other direction so there is no room for error. However, our driver feels the excessive g-force pushing on his body, realizes that he is riding on a razor’s edge, and panics. When he panics, he slams on the brakes and decelerates the vehicle at 0.4 g in the longitudinal direction. Now what?

When we combine the lateral and longitudinal g-force, we discover that the driver just put a combined force of 0.84 g on the vehicle. As there was only 0.75 g to work with (because that is the drag factor of this dry road), the driver is now outside of the friction circle. As a result, the tires break traction, and the vehicle loses control. This is why you may have heard that you shouldn’t apply the brakes while rounding a curve.


So, how do we prevent this scenario? Fire apparatus operators must understand that they cannot operate their vehicles anywhere near the edge of the friction circle. If the driver is rounding a curve at a speed that places so much lateral g-force on the vehicle that he is just at the edge of the friction circle, he will have no g-force left to use if he needs to brake or accelerate. Fire apparatus operators must learn to slow down and reduce the potential g-force acting on the vehicle prior to entering a curve. To enter the curve too fast and suddenly realize that you need to slow down is a recipe for disaster.

Also remember that a fire apparatus would have rolled over long before the driver came close to using up all of the available grip from the road. As we have discussed in previous articles, once the amount of lateral g-force exceeds the rollover threshold of the vehicle, it will roll over. Since most fire apparatus have a rollover threshold of around 0.5 to 0.6 g, the fire apparatus would have rolled over at around 50 mph. This 50-mph speed also assumes that the driver was driving the apparatus at nearly 100 percent of its capability, which is completely irresponsible. Fire apparatus operators should strive to drive at speeds that place minimal lateral g-force on their vehicle to reduce weight shift, liquid slosh, and the chances of rolling over.

Fire apparatus operators must understand that there are limits to the speed at which they can operate the vehicle. These limits are set in stone by the dynamics of a moving vehicle. No matter how good you think you are or how long you have been driving, you will not be able to exceed the limits of science.

CHRIS DALY is a 22-year police veteran, serving as a patrol supervisor in West Chester, Pennsylvania. He has served 29 years as both a career and volunteer firefighter, holding numerous positions, including the rank of assistant chief. He is an accredited crash reconstructionist (ACTAR #1863) and a lead investigator for the Chester County (PA) Serious Crash Assistance Team. Daly is a member of the Fire Apparatus & Emergency Equipment Editorial Advisory Board. Daly has also developed an emergency vehicle driver training program called “Drive to Survive,” which has been presented to more than 22,000 firefighters and police officers at more than 500 emergency service agencies across the United States.

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