THERMO Spoken Here! ~ J. Pohl ©  ( B3350~2/15)( B3700 -  Volume of a Sculpture)

Monster Tire Pressure

The load carried by the six large tires of a fully-loaded strip-mine-hauler is 180,000kg. We might expect the air pressure in the tires to be great. While it is not possible to calculate the porecise tire air pressures, by knowing the tire/hub dimensions (of the FBD) an approx­imate calculation is possible.
Estimate the least air pressure within each tire to support the truck and its load.

♦  Under normal conditions we would expect each tire to support one-sixth of the load - 30,000kg. As our scenario, we sketch an approx­imation of a single tire with "its load" above it. The scenario, right, resembles some manner of giant unicycle.

The scenario, a "volume of interest," is not a system sketch. Newton's 2nd Law does not address a "scenario" but rather a "system" extracted from the scenario. Forces are shown in the system sketch. Our interest here, is the pressure-force of fluid contact (inflation air pressure) acting over its contact area.

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 our system (we are yet to define). To make our system boundary relevant to the system-supporting-force, we pass the system boundary through the tire walls, then through the contained air. Tire walls will help support the load but since we cannot calculate that, we assume it is negligibly small.

Our system sketch is shown to the right. While drawing the system boundary it was realized that atmospheric pressure over the top of the system needed to be included.

(4)

Calculations with attention to units yields:
sol

Were a tire gage applied to our approximated tire, the gage would read 16,500kPa, meaning the pressure within the tire is:

101.3kPa + 16,500.0kPa = 16601.3kPa

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.