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Could it be possible to implement wattage control for desired electrical wattage at all physically possible RPMs via duty cycle control?

edited: the following formula is not valid, i've posted the corrected formula in a later post....

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A = 500W = Full Throttle Desired Electrical Wattage at all physically possible rpms

B = 500rpm = Present RPM

C = 0.1ohm = Winding Resistance

D = 50V = Battery Voltage

E = 100kv = Motor KV or RPM Per Volt

F = XX.XX% = Duty Cycle <—— What Duty Cycle Supplies 500w @ 500rpm

G = XX.XXV = Volts BEMF Per RPM

H = XX.XXV = Volts BEMF at Present RPM

I = XX.XXV = Volts Above BEMF Required For A - Desired Electrical Wattage

J = XX.XXV = Effective Voltage Required For A - Desired Electrical Wattage

% Throttle is % Motor Amps as defined by A

—————————

1/E=G

1/100kv=0.01V BEMF Per RPM <——100kv is 0.01V BEMF Per RPM

Therefore:

G = 0.01V = Volts BEMF Per RPM

BG=H

(500rpm)(0.01V) = 5V BEMF at Present RPM <——5v BEMF @ 500rpm @ 0.01V per RPM

Therefore:

H = 5V = Volts BEMF at Present RPM

&

Watts=Volts^2/Resistance

Therefore:

V = sqrt(R)*sqrt(W)

Therefore:

XX.XXV = sqrt(C)*sqrt(A)

XX.XXV = sqrt(0.1)*sqrt(500)

7.07107V = sqrt(0.1)*sqrt(500) <——7.07107V Effective Volts above BEMF needed for 500W

Therefore:

I = 7.07107V = Volts Above BEMF Required For A - Desired Electrical Wattage

I+H=J

(7.07107V)+(5V)=12.07107V <—— 12.07107V J - Effective Volts Needed For A - Desired 500W

Therefore:

J = 12.07107V = Effective Voltage Required For A - Desired Electrical Wattage

&

(J/D)*100=F

((12.07107V)/(50V))*100 = 24.14214% Duty Cycle <— 24.14% Duty is 12.07V Effective V w/ 50V Pack

Therefore:

F = 24.14214% = Duty Cycle

Therefore:

A = 500W = Desired Electrical Wattage at all physically possible rpms

B = 500rpm = Present RPM

C = 0.1ohm = Winding Resistance

D = 50V = Battery Voltage

E = 100kv = Motor KV or RPM Per Volt

F = 24.14214% = Duty Cycle <—— 24.14214% Duty Cycle For 500w @ 500rpm

G = 0.01V = Volts BEMF Per RPM

H = 5V = Volts BEMF at Present RPM

I = 7.07107V = Volts Above BEMF Required For A - Desired Electrical Wattage

J = 12.07107V = Effective Voltage Required For A - Desired Electrical Wattage

——————

Simply, in theory 24.14214% duty cycle is required for exactly 500w desired electrical at present RPM 500rpm with 0.1ohm winding resistance, 50V Present Pack V, and 100kv detected motor kv.

*haven't had time to double check this so could be riddled with errors

^this formula is not valid, correct formula below: