Voltage vs Current vs Heat

[El_Steak]

Lets say I have 2 motors. One is high rpm / Volt, the other is low rpm / Volt

The high RPM motor allows me to roll at 30mph at 50V, using 30 amps (1500 watts)

The low RPM motor allows me to roll at 30mph at 100V, using 15 amps (1500 watts)

To simplify the question, lets also assume that both motors have identical efficiencies at 30mph at their respective voltages.

Will the high RPM motor using half the voltage but double the current generate significantly more heat than the low RPM motor?

 

[jag]

Most likely both motors generate the same amount of heat.
Heat generated in the motor is I^2*R, so at a quick glance it would appear that the high rpm/volt motor would generate more heat.
However, the high rpm motor will likely have half the number of turns of twice as thick magnet wire, so while the I^2 term quadrupled, the inner resistance of the high rpm motor is only 1/4 of the low rpm motor and thus exactly compensating for the increased I^2 term.

 

[jag]

While from the motor point of view, 50V at 30A is just as good as 100V at 15A, what matters more is that for all the wiring on the bike, the higher current should have twice a s thick wire. not a big deal at 30A, but if you made the comparison between 25V at 60A and 50V at 30 A, the wiring for 60A would be noticeable clumsier on the bike. You would also need a 60A controller which is typically about 2x the price of a 30A.

 

[John in CR]

The key is that you said identical efficiencies at 30mph, so the heat loss (the inefficiency) is identical. The high voltage motor will have greater torque, so I believe it will be more efficient accelerating to 30. Something I'm finding with the high speed wind hub motors I use is that it's stressful for the controller, resulting in more heat loss in the controller than others report with the same controllers, which means overall lower efficiency. In addition, under the high loads of hills and big head winds the current will go way up with the higher speed wind motors, creating more heat and lower efficiency.