Relationship between Kt and Km constants in a motor?

[TheAnalogKid]

I know how to measure Km, but I already know Kt from the datasheet and according to some motor calculation guide's I've found online, they say you can know one from the other by using the relationship:

Kt (oz.-in) = 1.345 * Km (V/1000 rpm)

I checked this on other motor's datasheets that give both Km and Kt, and the relationship is fairly accurate. So I'm wondering why? Where does this relationship come from?

Where does this 1.345 value come from? I'm trying to workout what the units of this factor would need to be to give me some kind of clue, but does anyone have an explanation?

 

[TheAnalogKid]

Ok, I just realized that V*I = Watts = T*RPM . . and then take the motor efficiency to make up the discrepancy so the relationship value of 1.345 is between electrical power and mechanical power and that number arises from the units

 

[m.s.j]

The motor constant or Km defines the ability of the motor to transform electrical power to mechanical power and is a valuable tool for the application engineer particularly for recommending a “best fit” replacement for a competitor’s motor.
Motor Constant is calculated by the following equation (in English units):

Km = Kt/√Rt - where Kt is the torque sensitivity (oz.-in./amp) and Rt is the terminal resistance (ohms)
Units for Km are oz.-in./_watts (in English units)

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