Is it possible for an engine with higher horse power and lower torque to outperform an engine with lower horsepower and higher torque.

Question

Given that you are allowed to use any combination of gears for both engines, is it possible that the peak potential torque of an engine that at the shaft makes higher horse power and lower torque, could be greater than the peak potential torque of an engine with less horsepower and more torque.

Engine modification is not allowed, and this is in disregard to real world limitations.

Both engines are geared for the highest amount of torque possible.

Answer 1

Hi Jackson! Since this is a purely hypothetical problem, we can discount both the efficiency and the friction of the gears and engines which makes our job a lot easier. If you are looking to go from a lower torque to a higher torque, the gear ratio will always be a bigger gear connected to the engine shaft and a smaller gear connected to the output shaft. Since both engines are geared to the highest possible torque, it would mean that they have the same gear ratios. This gear ratio can be thought about as as infinitely big gear attached to the engine shaft and an infinitely small gear attached to the output shaft. If you have learned about the concept of different "sizes" of infinity, then you can think about it like that. You have

Big_Engine_Output_Torque = (Engine_Big_Input_Torque * Infinite_Gear_Ratio)

as the torque of the initially higher torqued engine, and you have

Small_Engine_Output_Torque = (Engine_Small_Torque * Infinite_Gear_Ratio)

as the torque of the initially lower torqued engine. If the original ratio of the bigger input torque over the smaller input torque was >1, then the new ratio of the bigger output torque over the smaller output torque will be the same (>1) because you can cancel the gear ratio term out of the top and the bottom. You can see that no matter how much you crank the gear ratio up, the engine with the higher initial torque will always produce a higher output torque.