How to Calculate a Vehicle Roll Over
by Richard Rowe
Where vehicles are concerned, center of gravity (balance point) has two relevant parts: the longitudinal (where it falls between the wheels) and the vertical (how far it is from the ground). When the CG's vertical point passes a line perpendicular to the ground, gravity pull it the rest of the way and the vehicle rolls over. The vehicle's tendency to roll over changes with wheel position, which changes with suspension compression. Calculating a vehicle's rollover angle to the millimeter requires a huge amount of data, and a degree in calculus wouldn't hurt. However, you can get a good estimate using a couple of fairly simple measurements and a couple of your biggest friends for ballast.
Step 1
Pop the hood and look at your engine. Standing outside the car, mark a dot on the fender at just about the height of center of the engine's cylinder heads. You can stick a tape measure down through your engine bay and measure the distance between the heads and ground, or you can "eyeball" it from the outside if you can't get a tape measure into the engine bay. Alternately, you could place a 2-by-4 across the top of your fenders, measure down from the board to the heads and subtract the distance from the 2-by-4's distance from the ground.
Step 2
Go around to the back of the vehicle and make a mark on the back of the trunk lid or tailgate that corresponds to the cylinder head's distance from the ground. The mark should fall about 1-1/2 inches to the left of the trunk's centerline to account for driver weight. Except in the case of an SUV or station wagon, the engine's cylinder heads generally tend to fall fairly close to the car's vertical CG plus or minus a couple of inches. This is a huge shortcut, and it'll save you an hour of migraine-inducing measurement and calculus.
Step 3
Place one end of your string on the ground and place a block on top of it that falls even with the wheel rim on the passenger side. This will serve as a pivot for your string. Have one of your assistants push down or sit on the vehicle's rear fender to compress the suspension as far as you can. This will simulate suspension compression during rollover conditions.
Step 4
Lift the string up and tape the other end to your trunk or tailgate at the engine head-height reference mark. Now, measure the angle between the ground and the string where it meet the block. This is your vehicle's rollover angle.
References
- "Auto Fundamentals"; Martin T. Stockel, Chris Johanson; 2000
- "Race Car Engineering & Mechanics"; Paul Van Valkenburgh; 2004
- United Nations Economic Commission for Europe: Determination of Vehicle's CG Position
- Ford-Trucks: 2000 Ford F-150 Technical Information
- Ford-Trucks: 2000 Ford Expedition Technical Information
Tips
- SUVS are generally based on pickup trucks, but all that extra roof and seating adds a significant amount of weight; about 25 percent of the vehicle's total weight in the case of a 4WD Ford Expedition. Worse, a big portion of that is above the base-truck's vertical CG, raising it even higher. To account for the heavy SUV top, measure the distance between your head-height reference mark and the top of the SUV's roof. Now, divide that measurement by half and add it to your previous head-height reference mark. Make a new mark on the rear window at this height, measure the angle as previously described and sit back in wonder that the thing hasn't fallen over yet.
Things You'll Need
- Tape measure
- String
- Grease pencil
- One or two assistants
- Speed square or protractor
Writer Bio
Richard Rowe has been writing professionally since 2007, specializing in automotive topics. He has worked as a tractor-trailer driver and mechanic, a rigger at a fire engine factory and as a race-car driver and builder. Rowe studied engineering, philosophy and American literature at Central Florida Community College.
