Defining Speed – using mathematics
If we know the
Power (P) and the Tire Size (given C, r, or d), theoretically we can calculate
Speed (Linear Velocity, mph, kph).
- Mechanical Power (P) (kW) = (τ (Nm) * 2π * rpm)/60000
ω = 2π * Revolutions per second (rps)
τ = Force (F) * 2r
Electrical Power (P) = Current (I) * Voltage (V)
The motor constant (K) is determined by Torque (τ) divided by Angular velocity (ω).
K = τ/ω
Kv = RPM (rads/s)/Volt (V)
Kt = Torque (t)/Amps (I)
Therefore Kv is relative to Tire Size. If we keep Power the same, Kv and Kt will change proportionally to the Tire Size.
In the ideal world, Kv and Kt are at inverse of each other: High Kv motors will have low Kt, and vice versa.
The highest efficiency the motor will display is during no-load at the highest possible battery voltage and current provided by the system, regardless of tire size –
so long as it doesn’t overheat. It goes downhill from there.
- High Kv motors benefit from smaller tire sizes to improve their Kt.
- Conversely, high Kt motors will benefit from larger tire sizes to boost Kv.
Therefore,
if desiring speed, higher-wind motors work best with larger tire sizes, and lower-wind motors work best with smaller tire sizes…
Unless you have 2WD, where you can definitely use lower-wind motors on larger tires and still have an excellent torque experience at higher speed.
I just love it when it snows and I have winter tires front and back!
Good hunting,
KF