How to Calculate the Turning Radius of a Truck With a Trailerby Richard Rowe
Tractor-trailers are complex beasts; every aspect of the unit's performance depends on dozens of factors within not only the truck but the trailer also. A truck's purpose is to tow a trailer, which is why the trailer makes up most of the unit's size and mass. So, you don't need to ask what the tractor's turning radius is, since the unit's overall turning radius and diameter usually depends more upon the trailer than the tractor. Either way, all you need is to apply a bit of simple trigonometry to calculate the truck's steering and Ackerman angle.
Measure your truck's wheelbase in inches from the center of the rear axle hub to the center of the front axle hub. If you have tandem drive axles, as most tractor trailers do, then measure from the center of the empty space between the tires on the two rear axles. For the example Freightliner Classic XL and 53-foot trailer combo, say the tractor's wheelbase comes out to 250 inches.
Check your manufacturer's info for the maximum steer angle of the inside turning tire, the left tire turning left and right tire turning right. If you can't find this info you can measure it pretty easily with a store-bought protractor. For the Freightliner, the inside tire's steer angle comes out to exactly 55 degrees at full lock.
Break out your trig calculator, enter the degrees of steer angle and hit the "sin" key. In the example, we wind up with 0.819. Now, divide the wheelbase of the truck by your sin figure; for the example, the result is a turning radius of 305.25 inches, or about 25.43 feet. Multiply that by two to get the truck's total turning diameter, or turning circle, which is 50.87 feet for our example. If you're measuring that in traffic lanes, that's five 10-foot-wide country roads or a little more than four 12-foot-wide state roads to do a U-turn.
Perform this same calculation with the trailer, but this time measure from the center of the tandem trailer tires to the center of the drive axles and use the angle of the truck relative to the trailer as your steering angle. With the 53-footer's tandems set all the way forward, the wheelbase measures 400 inches. With a 10-degree angle of truck to trailer the turning radius is 2,312 inches, or 192 feet. Increase the turning angle to 45 degrees, and turn radius decreases to 565 inches or 47 feet. Jackknife the truck at 90 degrees or more and the trailer rotates on its tandems with a turn radius of 400 inches or less.
- Measuring from the center of the drives or tandems isn't a perfect approach, mathematically speaking, but it's the best way to get an estimate since you have no way of knowing which set of tires are slipping and which are grabbing to act as a fulcrum. Taking the average this way will get you very close to the actual turn radius, which may vary depending upon load distribution, tire pressure, tire grip and road surface.
- If you don't have a trig calculator, just go to your favorite web browser and type "sin of __ degrees" into the search window. Most browsers will offer up this kind of general information without directing you to a separate page.
Things You'll Need
- Calculator with trigonometry functions
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.