Why do different gear ratios give different torque? Why isn’t it the faster a wheel goes the more torque it has?



Why do different gear ratios give different torque? Why isn’t it the faster a wheel goes the more torque it has?

In: Engineering

They are subject to the factors and foibles of “mechanical advantage”… Which would inevitably be a long and more than “like I’m 5” explanation to do it justice. Google will do you better.
Just remember that gear ratios are about the ratio of one circle to one or more circles. And one size of paired circles will not “act” like all the rest in the real world. Some are more “advantageous” to others… Which itself is relative to all the outside factors of what is driving each circle, and with how much physical force, and how much resistance to one or more of their spinning is there, etc. etc.

But mechanical advantage is your key factor when it comes to gear ratios.

The physical setup should be self-explanatory. If one gear has 24 teeth and another gear has 12 teeth (of the same size), the turning the 24-gear once will turn the 12-gear twice, just because of the size difference.

Now, think about the energy you use to turn the gears, or work. The work you put in, minus the losses to friction, will be equal to the work that comes out; this is the conservation of energy. Work is also equal to the integral of force over distance; more simplified, work is equal to force multiplied by the distance this force is applied.

So if you are putting work into turning the 24-gear and the 12-gear is turning twice as fast, the work has to balance out. In order for the work to balance out, the force exerted by the 12-gear must be half of the force you’re exerting on the 24-gear. F/2 x 2D = F x D. And the same is true the other way. Each turn of the 12-gear moves the 24-gear half as far, so it must exert a force twice as large in order for the work to balance. 2F x D/2 = F x D. Torque is just rotational force.

So the gear that spins faster must produce more torque, and the gear that spins slower must product more torque.

Gears are circles. Big circles take more energy to rotate. Since energy is conserved, when a big circle is connected to a small circle the energy is produced in a smaller space so the force has to be greater.

A higher RPM in an easier gear ratio can equal the power output of a lower RPM in a harder gear ratio.

This is because power output = torque x RPM.

You can test this yourself using a bicycle. Put the bike in an easy gear and spin your legs at 60rpm. Then put your bike in a hard gear and spin your legs at 60rpm. You’ll find that in the harder gear you went faster – increased power for the same RPM. You’ll also notice a much greater muscular strain. What you’re feeling there is the increased torque required to turn over the gear.