Why it must be T²/P and NOT T/√P or T/P: Argumentation for motor constant Km = T²/P

This motor constant shall be expressed by the SI Units N²m²/W, since resistive power loss "P" is not dependent on current (or torque) linearly, but quadratically.

P = I²R (resistive loss)

Torque "T" and armature current "I" are proportional to each other. This is expressed by the Torque constant Kt. Back EMF Force (or Voltage) constant "Ke" in [Vs/rad] or Torque constant "Kt" in [Nm/A], as it is both the same.

T= Kt * I

Some manufactures specify the motor torque constant as Nm/√W. But this is wrong, too as i can show you by a little example. Imagine a machine that has a Ke = Kt of 1 Nm/A and a terminal resistance "R" of 1 Ω. At 1Nm it pulls an armature current of 1A. It’s resistave power loss is I²R=(1A)² x 1 Ω = 1W. At 10Nm it is 100W as it pulls 100A armature current respectively.

A motor that is double the armature stack oft the above one, would have a Kt of 2, as Back EMF would be doubled and resistance would be doubled, too, as conductor length was doubled. So the resistance of this machine is 2 Ω. Everything is double the motor oft he first one. So we should expect a Km figure that is double the Km figure of he first machine. By definition Km =T²/P=Kt²/R = 2²/2= 2 this is the case. With the other definitions if have seen, this is not the case. For example Kt/R = 2/2 which equals one. Makes absolutely no sense. Or Kt/√R = 2/√2 which equals 1.41. Better, but still not near a figure of 2.

Low quality

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Hi, I'm no expert but this article seems to have a lot of original research and is generally poorly written. I even think some of the information is outright wrong (like the kv-kt calculations). Would appreciate input from veteran Wikipedians Leav (talk) 10:22, 21 June 2017 (UTC)Reply

Yes, it's awful and should be deleted. This was an unwanted split by one user, who neither seems to understand the topic nor how to behave (INDEF sock blocked) on WP.
Kv is a "motor constant" widely used to describe an attribute of brushless motors in particular. The rest is a mix of unsourced OR and downright invention, WP:NEOLOGISMs at best. Andy Dingley (talk) 10:29, 21 June 2017 (UTC)Reply
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The unit conversion table lacks vertical labels

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The unit conversion table claims to provide conversions from one to another common SI units, but the converted to references don't exist. It frankly makes no sense either, it references Km from these sources and Km cannot be derived from most or all of them alone. Seancf (talk) 16:53, 11 October 2023 (UTC)Reply