This is probably among the most bizarre and controversial observations I've yet made regarding BLDC electric motors... & the purpose of this conversation is that some very knowledgeable folks have previously denied the truth of this tale...

I have observed that there is a direct linear relationship between changes in themaximum rotor velocity at no load rpm-- ie maximum rotor speed when there is no mechanical load applied to the rotor -- and changes in theelectron drift velocity at stallin the winding of a BLDC electric motor -- ie when the rotor is mechanically held stationary.

In other words:

A=B

A = Change Factor of Electron Drift Velocity at Rotor Stall

B = Change Factor of Maximum Rotor Velocity with No Mechanical Load

For example:

Suppose I have a100kv BLDC electric motorthat has100 "turns" copper winding per "stator tooth"and a10 volt battery. When I apply the 10v to the 100kv motor with no mechanical load in a vacuum, themaximum rotor velocitywill be1000rpm= 10v*100kv.

Now Idouble the battery voltage (20v). At stall, theelectron drift velocity is doubled. At maximum rotor velocity, therotor rotation rate is doubled - 2000rpm= 20v*100kv.

Now using the original (10v) battery, Ihalve the length of the stator/armature copper winding-- ie half the number of "turns" -- now the motor only has50 "turns"of the same cross section copper winding and according the the KV formula, thisdoubles the KVor rpm per volt of the motor to200kv. At stall, theelectron drift velocity is doubled. At maximum rotor velocity, therotor rotation rate is doubled - 2000rpm= 10v*200kv.

In both cases -- doubling the battery voltage or halving the number of turns -- the outcome is the same: a doubling of the electron drift velocity at stall and a doubling of the maximum rotor velocity with no mechanical load.

Image Caption: The stator/armature on the right has half as many "turns" as the stator/armature on the left (and half the "conductor length"), but both wires have the same thickness or "cross section." The stator/armature on the right has double the "KV" or rpm per volt, double the "maximum rotor speed" at the same applied voltage, and double the electron drift velocity at stall at the same applied voltage.

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KV Formulas:

The "traditional" formula for describing changes in KV is as follows (no change in termination):

KN=C

K=C/N

K = kv = new kv (max rpm per volt) no load

N = turns = new # of wire turns per tooth

C = constant = original kv x original # turns

or:

D=sqrt(E/(V*N))

E=N*V*D^2

V=E/(N*D^2)

N=E/(V*D^2)

D = Change Factor of KV (rpm/v)

E = Change Factor of Conductor Resistivity (ohm-meters)

V = Change Factor of Conductor Volume (meters^3)

N = Change Factor of Conductor Resistance (ohm)

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Source: https://en.wikipedia.org/wiki/Drift_velocity

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^We can seehalving the conductor length doubles the electron drift velocity... &doubling the voltage doubles the electron drift velocity... & and doubling thewire cross section has no effect on electron drift velocity... behaviorsalso describing changes to the maximum rotor velocitywith no mechanical load (halving conductor length doubles no load rpm, anddoubling voltage doubles no load rpm, andchanging the thickness of the conductor has no effect on maximum rotor velocity).

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Simply when the electrons go twice as fast at stall, the rotor goes twice as fast with no mechanical load.