# Relationship between power, RPM, voltage, and current



## Tremelune (Dec 8, 2009)

This post is informative:

https://www.diyelectriccar.com/forums/showpost.php?p=874537&postcount=3

Is there any way to calculate how much motor speed you might lose for a given drop in voltage, or is it very specific to the motor (and would thus involve getting specs from the manufacturer)? According to that thread, seems like it's pretty much half voltage = half RPM?


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## kennybobby (Aug 10, 2012)

Collin answered it for you, half the voltage will result in about half the speed due to the back emf generated in the windings by the rotation of the rotor.

In an AC induction motor torque is basically proportional to current squared. The Leaf may be an AC PM synchronous motor in which torque is proportional to current. As long as the controller has voltage headroom to overcome the back emf, it can supply current to the windings to produce torque. When the aero and friction loads match the available motor torque and rpm, then the vehicle will no longer be able to accelerate and the top speed will be thereby limited.


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## kevinjclancy (Sep 25, 2017)

if you have a gear box you can just put it in a higher gear ???


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## [email protected] (Jan 24, 2019)

kevinjclancy said:


> if you have a gear box you can just put it in a higher gear ???


Changing the gearing to increase the output speed will reduce the torque. Meaning you will hit the aero/rolling resistance barrier sooner. It's a fine balance.


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## dougingraham (Jul 26, 2011)

Tremelune said:


> I still struggle with my understanding of how these concepts affect one another.
> 
> To lean on a concrete example, I have a Nissan Leaf motor, which is designed to run up to 10k RPM at a nominal 360V. I'm wondering what happens if I only provide it with 180V.
> 
> ...


Voltage is directly proportional to RPM. If you cut the voltage in half you will cut the max RPM in half. Current is directly proportional to torque. When you step on the accelerator you are commanding current. Power is battery voltage * battery current * losses in the system. Or Power is motor voltage * motor current * losses in the motor. Lots easier to measure the battery.

If you cut the voltage in half you will be unlikely to reach redline if there is any load on the motor. You will probably have almost as much torque at zero RPM as you do with the full voltage but the torque will taper off to half the RPM. If you gear it to get the same full output speed you will be cutting your torque in half everywhere. It will poop out at 5k RPM.


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## remy_martian (Feb 4, 2019)

Tremelune said:


> I still struggle with my understanding of how these concepts affect one another.
> 
> To lean on a concrete example, I have a Nissan Leaf motor, which is designed to run up to 10k RPM at a nominal 360V. I'm wondering what happens if I only provide it with 180V.
> 
> ...


Power is volts*amps. 

746 of those gives you one horsepower. 

Energy is horsepower (or power) produced over time.

Your battery is rated for its energy (kWhr).

Horsepower comes from the fuel -- in our case, the battery.

Now, the question becomes, how can you make horsepower? Because it's horsepower that gets you your coveted "safe highway speed."

A Tesla Model S needs about 50HP to run at "safe highway speed". A Nissan Leaf, for the sake of argument, might be 32HP. So the multiplication of your voltage and current, for the hypothetical Leaf has to be 32*746...off the top of my head, 24kW.

As has been said previously here, in general terms, speed is voltage, current is torque. You HAVE to make HP to get your target speed, but halving your voltage gives you half the speed (as has been noted, because of that pesky back-EMF). 

Then you say, "F it, I'll just double the current with my controller", which doubles the NEEDED torque at a speed your motor no longer can get because you were a cheapskate and bought half the packs you needed.

So, you can either be happy with a car that will pull a trailer equal to its weight at 30MPH and have double the low speed acceleration OR, knowing you will not be happy because bragging about your 0-30MPH times over a beer would shrink your manhood, you have no other recourse but to throw in a 2:1 gearbox.

That halves your torque (which now becomes the torque you wanted at the safe speed), but doubles your lame speed to your target speed. 

Think about it...ignoring losses, a gearbox keeps speed*torque constant, which is the same as keeping voltage*current constant -- magically horsepower into a gearbox equals horsepower out and it's horsepower that gets you your highway speed...but only if you are not limited by something (back-EMF*) in achieving the drivetrain rotational speed.

TL;DR... you need a gearbox in order to return the "voltage" to the 360V you needed in the first place. Or, go plow a field with your project.

*If you really want to give yourself a headache, you can also reconfigure the motor in terms of windings and poles. But, a gearbox is a lot easier to do and, much like owning a Corvette, the EV-hoes you attract into the passenger seat won't be able to tell the difference.


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## Vendition (Aug 27, 2019)

Voltage is proportional to speed, and torque is proportional to the current. The maximum current it could take is rated current and the corresponding torque can be found out from speed torque curve (as you know the speed from the voltage (rpm=k*v)) where k is the speed constant of the motor).


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## remy_martian (Feb 4, 2019)

To add clarity: the maximum *continuous* current, if you follow manufacturer guidelines, is the rated current. 

You can go a fair bit higher than rated for short bursts.

Also, you rarely see a kV motor rating outside of the stuff you can buy at Hobby King.


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## kablammyman (Mar 16, 2017)

wow, this post is very helpful!


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## Tremelune (Dec 8, 2009)

remy_martian said:


> To add clarity: the maximum *continuous* current, if you follow manufacturer guidelines, is the rated current.
> 
> You can go a fair bit higher than rated for short bursts.


This is interesting, because it seems very beneficial for the common duty cycle of a passenger car—you stop at an intersection, you accelerate onto the road. Most of the time a passenger car is cruising along at more or less the same speed, using 20% of the motor's power...I think the average sedan needs something like 50hp to maintain 75mph.

Just need a turbo button now...

I wonder if people are building controllers that regulate power based on heat as well as some specified current max (which could thus be higher)...


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## remy_martian (Feb 4, 2019)

Tremelune said:


> Most of the time a passenger car is cruising along at more or less the same speed, using 20% of the motor's power...I think the average sedan needs something like 50hp to maintain 75mph.
> 
> Just need a turbo button now...
> 
> I wonder if people are building controllers that regulate power based on heat as well as some specified current max (which could thus be higher)...


I think you meant to say 20% of an ICE's power.

Teslas use the "turbo button".

Most good controllers/inverters will have thermal foldback and shutdown and almost all *should* current limit.

An "advanced technology" controller will dip its toe in beyond the steady state limitations of the controller/inverter/motor, recognizing that current bursts can be tolerated by devices, components and windings. What you refer to as a "turbo button."

Note: you should NOT go over the voltage ratings of a controller unless you understand the design and components used. You also can create a deadly grenade by overspeeding (overvoltage) a motor...where that point is depends on a lot of factors - don't go there unless you completely know what you are doing. You can also grenade a gearbox/drivetrain with excess torque...that gets expensive and can also result in injury, death, or worse.


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