I understand how that works width wise, but length-wise I’m still having a hard time visualizing it 
The measured kv factors the magnets, geometry, windings, everything but the resistance is just the resistance. essentially a bigger motor has more room for beefier windings so generally you can get lower resistance for the same kv.
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Gotcha. So when just increasing the length, it’s more complicated to keep the same kv, so a lot of factors change to in the end get the same kv, lower resistance. Fair enough, thank you!
So confused now. If someone can walk me through how long it will take to go from 0mph to 1mph when you full throttle with these settings, I can code it.
All I’ll say is from 0 to 1 you’ll be hitting the motor current limit and not the battery current limit but at a higher speed you’ll be hitting the battery current limit and not the motor current limit.
I know this. I have factored this in already. There is three potential motor currents:
- using the formula sqrt(Max power / winding resistance)
- the motor current setting in your Vesc
- actual motor current available depending on your duty cycle and battery current.
We have to pick the lowest of these three at every increment of 1mph. Am I correct?
Can someone help me work out the latter two?
Yes you need the actual motor current based on the battery current limit, speed and duty cycle.
Thats what I am asking help with. lol. How do I get this?
just use algebra with the equations I posted. you have everything you need right there.
before I go into this, does a duty cycle of 50% always mean that the motor is at half the voltage of the battery? No if or Buts?
at 50% duty, the vesc is applying half the battery voltage to the motor.
Ok SO battery at 50v, duty cycle at 50%, motor is 200kv
Does that mean that the motor is at 5,000 RPM or that IT IS TRYING to get to 5,000 RPM?
Reason I ask is, you said this earlier
This seems a long winded way compared to multiplying battery voltage by duty cycle and multiply by motor kv to get motor RPM. Why can’t I do this instead?
It’s trying to get to 5000rpm but not necessarily going 5000rpm. The reason it can’t get to 5000rpm is when you do the calculation you’ll see that the motor current and battery current drops to 0 right when it reaches that speed under those conditions.
I’ll save you from pulling your hair out…
You can use:
((d * ((e+sqrt(e^2+(4 * h * f)))/(2 * d)))-e)/f=g
where d is battery voltage, e is bemf, h is electrical wattage, f is winding resistance, and g is the motor current
then you can find the duty cycle by dividing the battery current by the motor current.
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Very interesting discussion. Im also a proponent of more voltage. Makes battery building easier. Thinner cables and nickel, Smaller connectors and ports.
Also another thing I didn’t hear yet is hubs. Hubs usually go like 50-60 km/h at 12s and you cant change anything. You need higher voltage to make them faster.
If you have Infinity customizable parts then voltage shouldn’t really matter but with what’s available its easy to get more speed and power out of existing stuff when you just increase the voltage.
I know its a “dumb” no formula reason but everything gets higher voltage when it gets higher power. E bikes and EUCs all run on 20s+ and i think there has to be a real reason its better.
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Thanks for all the help dude. I just can’t seem to get my head around it. I might come back to it a few weeks from now but I gotta focus on some work. 
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if you run that formula for a given battery voltage, back EMF, electrical wattage and resistance, and then you decrease the resistance, you will see the motor current increase, and that’s why you can feel more torque with a bigger, lower resistance, same kv motor.
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I got stuck on this for a bit because I was thinking how can motor_current be independent of battery amps (2nd equation) …
but I think i got it …
- the battery amps are in the wattage_electrical (3rd equation)
- I had been thinking a fixed voltage. voltage is not fixed it will sag.
- either that or vesc will hit battery current limits and reduce duty_cycle.
Lets say you know the electrical wattage (battery amps * battery volts), motor rpm, kv, bemf_v, and winding resistance, it will be hard using those equations to deduce the motor current and duty cycle that makes all of them valid (except by trial and error or rearranging them)…
that’s where this one comes in handy:
(ps winding resistance is ohms not mOhms)
The motor amps are separate from the battery amps because they are at a significantly different (lower) voltage than the battery voltage, and the duty cycle determines how much lower. If you apply the full battery voltage to the motor at low speeds (100% duty) you would get way, way, way too many amps and too much power.
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