Efficiency is often overlooked as a factor in math. We use math as a tool for our daily lives, but rarely does a mathematical equation work perfectly when applied in real life. There are so many variables that can play a factor in any application of mathematics that affect the outcome. Efficiency is one of the most common variables that affect math in applications. It is especially common when math is applied to a mechanical system.
The core purpose of a mechanical system is to transfer, convert or apply power in a useful way. The laws of energy state that energy is never created or destroyed. Energy is merely transferred. Unfortunately, every time you transfer, convert, or apply energy, there will be efficiency issues.
In mechanical systems friction and the resulting heat are a major issue that causes efficiency issues. Can you think of a motor, whether in your car, or in an appliance, that does not get warm as it runs? Every surface within a system that comes in contact and moves against another surface will have friction. This friction converts some of the input energy of motion into heat energy. Think about the heat that is created when you rub your hands together. Every metal surface that makes contact with another metal surface creates heat from friction in a similar way.
So, efficiency is a factor in many systems. If you take a car, you can see where energy is transferred from one system, to the next, and where the efficiency losses affect the system. Start with the fuel, the potential energy in the fuel is converted to mechanical motion in the cylinder. But, this process isn’t perfect, some of the fuel will end up not burnt and exit through the exhaust. Even the piston that moves down creates friction with the cylinder wall and the crankshaft. As power is transferred to the transmission, all of the gears and bearings rub and wear against each other, creating more friction and heat. As power moves out of the transmission and into the final gear drive to the wheels, energy is lost to more friction to the gear sets in the final drive. Even the tires will create heat from the friction between the tire and road.
There are many ways that we fight this friction by properly maintaining the systems of our vehicles. Fresh oil, proper tire inflation, and regular tune-ups help each system transfer power more efficiently.
So, when applying math to real world applications, it is always important to be aware of the energy losses and efficiency issues that could be a factor.
For more information on some of the calculations used in gear drive systems and other mechanical calculators, follow the links below.