Recently, Toyota showed the world the drawbar pull capabilities of one of its full-sized pickup trucks, the Toyota Tundra CrewMax. The television commercial begins with the truck on a roadway near the edge of a 180-foot cliff at the Sierra Rock Quarry in Placerville, Calif. A metal cable is attached to the truck's towing hitch, and the other end of the cable is attached to a 6,400-pound shipping container. The container is dangling in mid air more than halfway down the quarry wall, and for the moment, the weight is supported by a nearby crane. All at once, the full weight of the container is released, causing the truck to be pulled even closer to the edge. Just in time, the truck's wheels grab the road surface, the rear end squats down a bit, and somehow the Tundra CrewMax pulls the enormous shipping container -- all 6,400 pounds of it -- up and out of the deep quarry.
Visually, the display an impressive demonstration of the pulling power of the truck; however, there are more common examples of drawbar pull all around us every day. Granted, these examples may not be as visually dramatic as the rock quarry stunt, but they're equally impressive in their own way.
Probably the most universally familiar example of drawbar pull is displayed on rails. A locomotive pulling a long train of freight cars is demonstrating drawbar pull. The next time you're at an airport, take a moment to walk over to a window and watch the activity on the ground. The low and wide tractors that push and pull enormous jet airplanes exhibit drawbar pull as well. Another place you may see drawbar pull in action is on a farm. The tractor that pulls you and your friends or family along on that fun-filled hayride is drawbar pulling, too.
These examples give us an idea of what drawbar pull looks like, but what exactly is drawbar pull, anyway? Basically, drawbar pull is the pulling force, or pulling ability, of a vehicle. The definition of drawbar pull is the towing force of a truck or other industrial vehicle, exerted at its coupler (or equivalent) in the direction of motion of the coupling point. Drawbar pull is typically expressed in pounds or Newtons [source: A&G Mercury].
That's fundamentally what drawbar pull is all about; but now that you know the drawbar pull definition, perhaps you'd like to find out how to calculate the drawbar pull of a specific vehicle? Maybe even your own tow vehicle? For more drawbar information and the equation you'll need to calculate the drawbar pull of your own vehicle, read the next page.
Calculating Drawbar Pull
Calculating the drawbar pull of a vehicle doesn't have to be complicated. In fact, once you know the equation and how to find each of the factors involved, it's rather simple.
To find the drawbar pull (DP) of a vehicle in pounds, you'll need to multiply the torque of the vehicle's motor (T) in inch pounds by the gear reduction (R) (including the axle and transmission) and divide that number by the radius of the drive tire (r) in inches. The resulting number represents the tractive effort of the vehicle. In other words, it's the gross pulling force the vehicle is capable of.
But that's not all of the information you'll need. To determine the actual (or net) drawbar pull, you'll need to know how to figure out the rolling resistance (RR) of the vehicle. Drawbar pull is the tractive effort minus the rolling resistance. The equation looks like this:
DP = T x R ÷ r - RR
DP = T x R ÷ r - RR
To determine the rolling resistance (RR) -- the force necessary to move a vehicle over a surface -- multiply the gross vehicle weight (GVW) in pounds by the rolling resistance of the surface (R). The rolling resistance of the surface is measured in pounds per thousand pounds of vehicle weight, divided by 1,000 (100 if you're using metric measurements). The rolling resistance of several different surfaces can be found in tables like this one that you can easily locate online. So, for example, to determine the rolling resistance of an 8,000-pound vehicle on good concrete, you would multiply 8,000 (GVW) times 15 (pounds per thousand pounds of rolling resistance on good concrete) and divide that number by 1,000 (a constant). If you're using metric figures, you'll use 100 as your constant. After you do the calculations, you'll find that the rolling resistance of our example vehicle is 120 pounds. The equation looks like this:
RR = GVW x R ÷ 1000
RR = GVW x R ÷ 1000
Now that we know the rolling resistance, we can get back to the drawbar pull equation. Let's say that the torque of our example vehicle's motor is 4,800 inch-pounds (400 pound-feet) and it has an overall gear reduction of 10:1 along with a tire radius of 18 inches. Again, complete the calculations, and you'll discover that the tractive effort -- or gross pulling force -- of the vehicle is 2,667 pounds. To find the net drawbar pull, subtract the rolling resistance from the tractive effort. In this case, the drawbar pull of our example vehicle is 2,547 pounds.
Now that you know the equation and how to find all of the factors involved, it shouldn't be difficult to calculate the drawbar pull of your own vehicle. If you'd like to read more about towing, weight and other related topics, follow the links on the next page.
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More Great Links
- A&G Mercury. "A&G Mercury Tow Tractors: Information Guide." April 20, 2005. (Oct. 9, 2008) http://www.agmercury.com/Tow%20Tractor%20PDFs/ Tow%20Tractor%20Sales%20Information.pdf
- Mraz, Stephen J. "Engineering an ad." Machine Design. Jan. 10, 2008. (Oct. 9, 2008) http://machinedesign.com/ContentItem/71927/Engineeringanad.aspx
- The Raymond Corporation. "Glossary." (Oct. 9, 2008) http://www.raymondcorp.com/solutions/glossary.cfm?selector=D
- Webtec Products Ltd. "Draw Bar Pull." (Oct. 9, 2008) http://www.webtec.co.uk/techinfo/equation/eqnfr/eqn03.htm
- Webtec Products Ltd. "Road Rolling resistance." (Oct. 9, 2008) http://www.webtec.co.uk/techinfo/equation/eqnfr/eqn14.htm