Originally Posted by KreAture
I did not say that for two given motors, k would remain constant.
It would change if pole parameters, airgap and such were to change. What I wanted to get clear was that if you can increase the diameter by a tiny bit, you would get it back squared compared linear when increasing the length of the stack.
The formula itself comes from Dr Duane Hanselman.
It can be used to estimate the benefit.
For me, it has a big significance as I am working on a in-wheel motor. By reducing the rubber around the motor and increasing the motor diameter I can gain significant torque. Also, the formula to get Kt from Kv is quite usefull as it is much more versatile.
I know the torque I need maintaining a speed on the scooter so I can use the Kt to see if I have the amperage in the right magnitude for my batterys. Since I will be using 12 LiIon's in series I have a lot of voltage, but the cells do not like high discharge.
You are ofcource right in that there are many more factors changing with D than with L. Also, it is important to realize that although the motors maximum power will be the same regardless of the number of winds for instance due to the rpm being related to torque and power it is also reliant on increasing the voltage to the motor or it will simply fail to draw enough power.
In a first approximation, if you increase the diameter D a little bit
1) Keeping L
2) Keeping the same magnets, turns, teeth ..
You get only a linear increase of Kt = kD not squared (lever/arm influence)
But of course if you change D the geometrical dimensions of slots/teeth vary a little so there could be some little influence regarding the magnetic flux reluctance.
That secondary influence is not necessary linearly related to D, nor constant.