# Torque needed to keep a wheel spinning at high RPM

I have a treaded wheel which is 16'' diameter and 4'' across (trailer wheel).

If I want it to spin constantly at 2750 RPM, what amount of torque do I need to apply to combat friction and air resistance?

I need to find this out for one of my projects and I am only knowledgeable of ideal world physics. Is there an equation for measuring non-conservative forces on a spinning wheel (like F= b*v^2)?

Any advice would be appreciated. Thank you.

Edit: Thanks for all the insights. I wanted to get an estimate because I have to choose the proper motor to use in this situation. Much cheaper to know which motor/wheel to go for now than to realize the motor/wheel combination is too weak. In case I have been misunderstood, I purely want the force to keep the wheel spinning. The wheel isn't moving an object body. So, would any drag (v^2) still apply?

• Depends mostly on the shape of the wheel and the bearings it is running on. Nov 13 '17 at 10:01
• you are probably right aero drag will scale with v^2. proabably easier to measure than to figure out an accurate calculation. Nov 13 '17 at 12:40
• @Sol: The air drag scales with the square of the speed. It is the power that therefore scales with the cube of the speed. Nov 13 '17 at 13:00
• Wheel air drag is the least of vehicle loads. You want max acceleration vs vehicle drag brake power then choose RPM/V motor for no load Nov 14 '17 at 4:15
• It will be conductive losses from reactive current which may be about 10% of rated current and eddy current losses, which generate heat. Tires are pretty smooth unlike fans so they don't make much noise or drag. The motor power is only to reduce the acceleration time to reach full speed where torque declines due to back EMF and is greatest at start by 5x to 8x in most AC motors depending on starter mechanism. It will be much like a big grinder with a small motor unless you want it to start quick. Start by computing rotational energy then power and time to reach that. Nov 15 '17 at 9:52