Bl conversion factor

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The quick answer is that the conversion is 1:1, they are identical.
The longer answer is to consider fundemental units, a very valuable technique. It goes like this:-
magnetic flux desnity is measured in Tesla, whose fundemental units are Wb/m^2.
Bl is therefore Wb/m^2 times m = Wb/m
Now units for flux (Wb) is V x s (volt seconds)
Therefore Bl is = V.s/m
But, Volts are W/A (watts/amps)
And watts are Joules per second (J/s)
therefore V=W/A=J/sA
But Joules are Newtons times metres =N.m
Therefore V=N.m/s.A
Almost there... V=W/A=J/s.A=N.m/s.A
Finally Bl = V.s/m = (N.m/s.A) . (s) / m = N/A !!!!!!

The other quick route is that Force equal Bl times current ie F=Bl.A
Since force is in newtons, then Bl must equal Force/current ie N/A

Hope this hasn't confused you too much!!!
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What does Re really mean as a practical consideration? I take it as higher numbers are bad because it will create more heat.

Minimize Re and you put more power through the coil w/o changing the alignment as much. True?

Bl^2/Re? Is this what someone came up with as a more linear comparison of motor structure? How much does this number need to change to be a significant change? 10%, 100%?
This is why Bl^2/Re is not such a usefull measure of motor efficiency. You cannot simply talk about the effect of changing Re independantly. Re is not a independant parameter. To change Re, you have to change the diameter of the wire or the length of the winding. Changing diameter changes the overall length of the coil and hence how much of the gap flux it intersects, changes to volume occupancy of the magnet gap, changes the mass of the coil and hence the moving mass of the driver ......and so on.
If you consider Bl^2.Vc where Vc is the volume of the copper, then things become much clearer. After all, to a first order drive unit efficiency is independant of the actual resistance chosen. This is different from driver sensitivity, which is very much governed by actual resistance value.
But where do you get Vc without dismantling the driver? Anyway, Bl would seem to already be an indicator of the volume of copper winding.

Back to my question. And yes, like any spec, Bl^2/Re would only be an indicator. I would think, that since Re doesn't change much (it does increase with heating, agree?) it would be useful. I just am curious why it is divided into the (square) of the horsepower.

I am a newby. If any of this is not making sense, tell me.
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