# How to find coefficient of friction that will maximize torque?

When using DC motors with a drive wheel (aka "direct drive") to propel a vehicle (e.g. an RC car), force and torque play a role in how efficiently that motor's power is transferred into motion via the drive wheel in contact with the surface of travel. Here's one resource on force and torque when it comes to motors.

However, the coefficient of friction between the two surfaces will also affect how efficiently that power is translated into motion. My specific question is: what are the equations that govern optimizing drive wheel coefficient of friction to the surface of travel's coefficient of friction in order to realize a given motor's maximum RPM while in motion traveling that surface? In other words, how does one calculate the optimal coefficient of friction to achieve the maximum (rpm/motion) out of the motor?

To use some hyperbole, a given motor with drive wheel on an icy surface will be lossy, as will the same combination on a sticky or overly gritty surface. So somewhere in-between will be optimal for maximum power transfer (and therefore, maximum speed) between the drive wheel and the surface of travel. So how does one calculate that optimal coefficient of friction?

• You appear to be asking a few different but inconsistent questions. Your question of what equations govern "this" is not clear what "this" is. How do you define "optimal"? In your first case "maximum (rpm/motion) out of the motor" would imply zero friction to let the wheels spin as fast as possible but the vehicle wouldn't move to maximize rpm. Later if you want "maximum power transfer" you're going to want maximum friction. Can you please reword your question to provide a more context and a full description of your system and goals? This is too open ended to be answerable at the moment.
– Tully
Nov 22, 2022 at 17:46
• @Tully, appreciate the critique. I updated the specific question in the text. Nov 23, 2022 at 19:01
• Maximum power transfer will be when there's no slipping, so add long as your coefficient of friction is high enough today it won't slip then you're at the maximum power transfer
– Tully
Nov 24, 2022 at 9:09