# Gear Ratios and Constant Power/Torque: find max velocity?

I'm trying to determine how exactly gear ratio limits velocity. I know that a high torque configuration is generally regarded as low speed, but my calculations do not seem to support that.

Basically, I've written a small problem where we have an input gear with constant torque and an output gear with a load on it. If I apply a gear ratio of 1, I get a lower angular acceleration than if I do a gear ratio of 10 (output has 10 times the teeth) -- this makes sense.

When calculating maximum angular velocity though (assuming about 0.3*<omega> on the output gear), I get a maximum velocity that is much larger than with a lower gear ratio. The torque is the same, the power required is very large (orders of magnitude difference). I am assuming 100% transmission efficiency.

So, if we have a motor which can produce constant torque regardless of RPM (possibly in excess of 22000) while being able to provide the necessary power, is it reasonable to say that the output gear would be driven at a faster speed than if the gear ratio was 1? Attached is a quick sketch of my problem.

#### Attachments

• Geerz.png
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Baluncore
Rate of energy flow = Power = Torque * RPM.

JBA