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The instantaneous power, or energy rate, of a truck varies considerably during its motion through the gears, speeds and such. Suppose in normal operation a truck loaded to 80,000 pounds moved horizontally from stop to a speed of 40 miles per hour (27 feet per second) in a distance of about 1/4 mile (1320 feet). Use the definition that “truck horsepower” is the time-average change of kinetic and potential energy of the truck in its event.
What average horsepower is required to accomplish this event?
♦ Calculations regarding automotive performance are complicated because the system is difficult to specify. As a simplification for this discussion will take the truck, motor off and in neutral gear, as system. We imaging the power of the event to be supplied to the truck by some outside source such as a tow truck. Also we will only be able to calculate the average power of the event.
The event is an increment type. The energy equation is:
The initial and final potential energies of the truck are zero. Next consider the summation works. The tow truck will supply power to the truck through the displacement-rate of its towing-force. Some of this power will pass through the truck to the surroundings, and some of it will come to reside within the truck components (as increased internal energy). Some will be energy as work by the work of the tow, and work of friction. Potential energies are negligible and the work of the event can be expressed as an integral:
The mean value theorem of calculus is used to reduce the integral.
Next, numbers are applied and we see the time of the event must be determined.
If acceleration is constant then velocity increases linearly from zero to 27 feet per second. Therefore the average velocity would be one half the final velocity and the distance traveled would equal the average velocity times the time.
With the time, we return to the energy equation.
The engine of the truck is rated somewhere near 400 horsepower. However we see much less power is required to bring the mass up to speed. There are substantial losses.