# Electric motor theory, refining kv, kt, continuous power understanding

#### perpetualthoughts

##### 1 µW
The kv of a motor doesn't change the continuous power rating of a motor. Regardless of if it is a slower or faster wound, the output power will be the same.

When a manufacturer states the maximum continuous power of a motor, they are indicating the maximum power a motor can output at given rpm.

If however, you run this motor slower than the indicated max rpm, you will be able to attain or even surpass the maximum power output, but you will not be able to do so continuously without overheating the motor.

For example, when I calculated the power needed to propell a 120kg object up a 20% slope at 20km/h. P=grade*speed*weight*(gravity constant)
I found out that I needed a minimum of 1300watts of output power just to maintain that speed. With an estimated motor efficienty of 75%, a minimum of 1625 watts is needed. I pedal 100watts (i don't know). So the motor has to provide at least 1500watts just to maintain that speed, not counting acceleration nor friction losses.

Knowing this I bought a cheap 1000watt chinese motor, thinking that I could get to 1500watts with oil cooling and fins.

Now, what really happened was, I found the motor overheating at grades of only 7% and 110kg. Where 418 watts were theoretically needed to maintain such speeds. So, well below specs. Yet, it still over heated (coil temp 70C and rising fast). Max speed without load is 50km/h. 530rpm @ 48v in 20" wheel ~ 50km/h top speed. So I think it surpassed its current limitations and ran huge i²R losses.

The only way I see is to reduce the diameter of the wheel even further. Maybe mount a 12" tire directly on the 232mm hub motor ? Reducing the max speed to 30km/h, essentially reducing the amps required to go up the same grade, therefore reducing i²R losses and thermal runaway. I don't hope for 20kmh 20% anymore because the motor isn't powerful enough, but 10-12% continuous would be nice.

What do you guys think ? Is my way of thinking correct ? Or would a different kv motor rating change anything, how about rewiring ?

#### DogDipstick

##### 100 kW
Do you know about apparent power, true power, reactive power, and how the motors are turned with the brushless commutations? There are very clear ways of deciphering how a electric motor will react ot ay given current and voltage for any ( rpm range desired to sustain) certain traction event ( tractive effort curves).. and prime mover, or motor under voltage ...

It gets quite complex, but.. Here it is in a nutshell: Motors take power to increase RPm... But take less power to keep spinning.. Takes power to speed up, takes power to slow down, does not take power to hold RPM.. Motors and engines alike... without regard to load.

Then there is loping, loading up, or bogging. This is bad, and this is what you may be feeling with the wrong kV combo or up this hill.. that even though you calculated X amouunt to go up, you are really demanding (X + more) the motor to bog and load up.. Bad. Poor battery will increase this lope, heat generation of lost efficiency...

My 1000w motor does not get hot on 4kW contin and 8kw peaks because I do not lope or bog. Mine is correctly kV in the right rim diameter and yours is not. I rip up all hills in my way, throwing rocks and not bogging down at all. In fact, the front wheel is usually coming up.. Unintended wheelies.. cause I geared my kV / wheel dia. voltage rang/ power range correctly.

Your motor is wound for too high a kV at the voltage and power you run. Run more power, . Hill is done for. Or go slower with a smaller rim like you said.

#### john61ct

##### 1 TW
The whole concept of a motor's "maximum power output" is just as nebulous as that of a battery pack, pretty useless to try to nail that down in isolation.

https://ebikes.ca/learn/power-ratings.html

#### perpetualthoughts

##### 1 µW
From ebike.ca, thank you John ! :
- "An important point to realize here is that it's not the output power but the output torque of the motor which causes it to heat up and eventually fail."

So, i've just checked the motor specifications and it is rated for 24nm max which I discounted back then...

Why did it overheat ?

Some calculations :
- torque required at 7% grade, 110kg with 20" wheel (circumference 1.515m) (I'm using unnecessarily long formulas. I'm not confident with my algebra knowledge... )
P [watts] = Grade [%] * Speed [m/s] * Weight [kg] * Gravity constant
P = .07 * 5.55 * 110 * 9.8 = ~418.8 watts

T [n*m-1] = (P * 60) / (2 * π * RPM)
T = 418.8 * 60 / 2 / π / 220 = 18.2 newtonmeters

Still, overheated below spec, but perhaps I was accelerating or grade calculations were slightly off. But these chinese specs probably can't be counted on. The culprit is probably the torque constant which leads to uncontrollable copper losses at a higher than 7% grades with a 20" wheel.

Thank you DogDipstick for your long reply. Maybe I need to read more threads about high power systems and how they manage to get more out of their motor. I basically think that is just a question of how fast the motor spins without exceeding torque ratings. I don't think I can salvage this motor in this wheel setup without rewiring. Atm it is probably bogging, yet I don't feel it because throttle doesn't control torque. The controller compensates. 3kw overspec is very impressive. No, I am not familiar with those power terms yet, but i'm learning.

#### ZeroEm

##### 1 MW
Most want to go fast, but ride slow and over heat the motor. Check the speed your spend most of your time at. bet it is much lower than you think. It should be in the upper range of your motor.

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