# Why is the mechanical power of a DC brushed motor at a maximum at around 50% of the stall torque?

I don't currently fully understand how a DC brushed motor reaches maximum mechanical power at around 50% of their stall torque. I know that a decrease in the speed of the rotor will decrease back-EMF and in turn, increase current, thus the increase in power.

However, I don't exactly understand why the maximum power stops at around 50% of the stall torque. What determines the stop at 50%?

• See lancet.mit.edu/motors/motors3.html for useful graphs and details Mar 9, 2021 at 7:33
• It's just another instance of the Maximum Power Transfer theorem at work. en.wikipedia.org/wiki/…. Mar 9, 2021 at 12:36
• Note that this is only true at constant voltage, and the rated voltage is a somewhat artificial limit. If you really want to get the maximum amount of power out of a motor safely, and you pay close attention to the real limits, then you can get closer to the stall torque at a higher speed. Assuming a constant voltage is what creates the linear torque-speed curve and that puts the max power at 50% Mar 9, 2021 at 13:58