# Thread: SI-Derived KV Formula & The Relationship between KV and Conductance in BLDC Motors

1. The following is a geometric depiction of the relationship between changes in winding conductance & KV as a result of winding geometry changes in BLDC motors with a fixed copper volume. Afterwards is a new SI-derived formula I created for calculating changes in KV (which allows for changes in volume), contrasted with the "traditional" formula which is based on dimensionless quantities.

Geometric Depiction:

Suppose I have a 100kv (100 rpm per applied volt) BLDC motor with a fixed volume of copper winding and I measure the winding resistance lead to lead as 1 ohm, but I am free to change the length (# of turns), cross section area, and/or "termination" of the copper winding, while retaining the same copper volume. The geometric proof demonstrates that in this scenario, changes in KV (rpm per volt) are proportional to the square root of changes in conductance. For example suppose the original winding is 1 unit length and 1 unit cross section area. Now I divide the winding length by sqrt(3) [1.73205], new length = 0.5773 and I multiply the cross section by sqrt(3) [1.73205], new cross section area = 1.73205 to keep the same copper volume. The resistance drops to 1/3 of the original value while the conductance increases by a factor of 3. When this happens, as depicted in the geometric proof, the KV increases by a factor of sqrt(3) [1.73205], new kv value = 173.205 (square root of the conductance change factor with fixed copper volume). Another case of an increase in conductance x 3 leading to a change factor of KV of 1.73205 is keeping the same number of turns (same conductor length and volume) but changing the "termination" of the windings from Wye to Delta.

This has been previously posted elsewhere at: code to change the motor amp limit - Page 14 - vedder.se forums

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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

Changing termination wye to delta increases kv by a factor of 1x1.73205 [sqrt(3)]
Changing termination delta to wye decreases kv by a factor of 1/1.73205 [1/sqrt(3)]

^but notice "turns," "constant," and "termination" are not SI base unit derived variables. Also please note only changing winding cross section has no effect on KV -- only changes in the number of turns or conductor length (not thickness) has a resulting effect on KV.

I have written a new formula that gives identical results using only SI derived variables (no turns, constant or termination variables).

My formula for describing changes in KV is as follows -- please note unlike the above drawing, the formula allows for changes in copper volume in addition to geometric changes of fixed volume:

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)

For example, changing termination wye to delta, change factor of Resistance is 1/3 (conductance change factor 1x3) while the change factor of KV is 1.73205 (square root of 3).

Another example is shortening the winding length by a factor of 1/sqrt(3) and increasing the cross section by a factor of 1x1.73205... also leading to a change factor of Resistance is 1/3 (conductance change factor 1x3) while the change factor of KV is equal to 1.73205.

Purpose for this thread: I've been told by those knowledgeable on the matter there is no relationship between KV and conductance, but I challenge anyone to prove something other than what the drawing (with fixed copper volume) and D=sqrt(E/(V*N)) formula (with variable copper volume) predict.

2.

3. -accidental post-

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