Monster Tires

The mass of a fully-loaded strip-mine hauler is 330,000 kgs (~360 tons : hauler plus load). To carry such a great load, we might expect the air pressure in each of its six large tires to be great. While it is not possible to calculate the precise pressure, by knowing the hub dimensions (given below), an approximate calculation is possible.

Estimate the least possible air pressure required within each tire to support the truck and its load.

Solution: For this approximate calculation we envisiage a special, silly-looking physical scenario consisting of a single tire configured to support one-sixth of the load or 60,000 lbm [(360ton x 1,000lbm/ton)/6]lbm. The scenario resembles a giant unicycle.

Next, to apply Newton's 2nd Law, we must "extract a system" from our scenario. It is "with the system" that forces and pressure-forces apply. For air pressure in the tire to support the truck, that air pressure (acting over an area to be a force) must be a boundary force of the system. To make that boundary force relevant to the system, we pass the system boundary through the tire and the air it contains. Of course the tire walls will help support the load. Since we cannot calculate that support we must assume it is negligibly small.

Our system sketch is shown to the right. Notice how we "cut it around" the tire hub. While drawing the system boundary be sure to include atmospheric pressure which acts over its top.

Calculations with attention to units yield:

Were a tire gage applied to our approximated tire, the gage would read 20.8 psi, meaning the pressure within the tire is:

14.7 psi + 20.8 psi = 35.5 psi.

We've calculated an approximate, "very least pressure." Actual inflation pressures are much greater of course. Tire wear happens as the tires flex. Higher pressures minimize flexing and prolong tire life.

Monster Tires

The load carried by the six large tires of a fully-loaded strip-mine hauler is 360 tons. Carrying such a great load, we expect that the air pressure in the tires to be great. It is not possible to calculate the pressure of the air in the tires of a given truck. However knowing the hub dimensions (given below), a calculation is possible.

Estimate the least possible air pressure required within each tire to support the truck and its load.