# KW to HP conundrum



## Dan Hawkins (Jan 3, 2010)

This is a cry for enlightenment, and not exclusively an EV topic. I have studied the data sheets on several AC induction motors, and have not found that the numbers work out the way I would expect them to. For example, a 40 hp motor that I own is rated at 200v, 109 amps at full load. That is (roughly) 22 KW. Using the standard conversion of .746 KW for one HP, It should be called a 30 HP motor. 

Yet, when I use nameplate torque and RPM (119 lb-ft X 1764 RPM / 5252), the mechanical horsepower does indeed equal 40. There are lots of smarts in this room, so I know somebody here can help me out?

Thanks,
Dan


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## dcb (Dec 5, 2009)

can you post a clear picture of the dataplate? it might be a matter of service factor (i.e. it can do 40hp, but not continuously)

edit, doh, multiply the input current by sqrt(2) since you are just looking at the current going to one phase.

i.e. 109 * 1.414 = 154, * 200v = 30825w, which is 40hp/96% efficiency.

just guessing.


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## Sunking (Aug 10, 2009)

Simple answer is your math is wrong. 

For a Single Phase Motor

HP = E x I x Eff x PF / 746

*If this is a 3-phase motor*, and it is, you completely left that out of the formula compounded by your incorrect formula

For a 3-Phase Motor

HP =1.73 x E x I x Eff x PF /746

FWIW Efficiency and PF are a number less than 1.


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## Dan Hawkins (Jan 3, 2010)

Thanks, this would be my first try at posting an image...
(Edit) Well, I can't open the thumbnail, so I am obviously deficient in comprehending attachments as well!


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## Dan Hawkins (Jan 3, 2010)

DCB - thanks, it is indeed a 3-phase motor, and I had not realized that the published current draw is for one phase only. 

Sunking, you are right, of course that I left PF and efficiency out of the equation, but that was only because they pushed the apparent answer even further away from what I expected. 

I appreciate your responses, they really helped. 

Dan


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## dcb (Dec 5, 2009)

Sunking said:


> HP =1.73 x E x I x Eff x PF /746


Forget what I said, what he said 

I took a swag at sqrt(2) but sqrt(3)*PF makes much more sense.


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## Sunking (Aug 10, 2009)

Dan Hawkins said:


> Thanks, this would be my first try at posting an image...
> (Edit) Well, I can't open the thumbnail, so I am obviously deficient in comprehending attachments as well!


OK now you have all the numbers

V = 200
I = 113
Eff = .93
PF = .82

1.73 x 200 x 113 x .82 x .93 / 746 = 39.96 HP.

Close enough.


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## Caps18 (Jun 8, 2008)

Is there someway to compare this to gas car horsepower? Or is it a fair comparison? For some reason I think my old 110 HP Saturn would perform much better if it had a 40 HP electric motor in it. Maybe it is a top speed issue, or an ability to move a heavier vehicle with a higher HP rating. And the higher & instant torque of an electric motor at low rpm's improves the performance in typical driving.


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## piotrsko (Dec 9, 2007)

FIRST your saturn motor was making 110 Hp brand new, at probably 3500 to 5000 rpm. Think freeway speeds. Slower and the saturn makes way less, perhaps 25 hp to drive city streets. Thats why cars have multi speed transmissions.

Golf carts use 7 hp motors.

Mizlplix and ivan bennet are doing interesting stuff with 40 hp 3 phase motors, SMOKING tires, and the like. Your motor could be a brute when powered correctly.


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## Dan Hawkins (Jan 3, 2010)

To Caps18, 

My 40 HP motor is manufactured to deliver 40 hp day in and day out, possibly for years nonstop. Saturn probably did not intend similar usage at 110 HP, but their engine is a perfectly good for 40 HP continuous, and will happily push the Saturn down the freeway at 70 MPH hour after hour until out of gas. 

To soup up a 40hp 3-phase motor, you need to increase its torque and RPM beyond the name plate rating. The motor in my original post will produce more than 200% of its rated torque before torque breakdown. That by itself makes 80 HP, if RPM remains constant. Now double the RPM at double the torque, and you have a 160 HP motor. If Saturn had used that motor in their car, you can bet it would be rated at "160 HP."

This is doable by driving the 200 volt motor with a VFD designed for 480 (ac) volts, with a current capacity of at least twice the motor's current rating to get twice the torque. 

Issues will be cooling the motor at the higher current, and the need for a 700 volt battery pack to provide the DC equivalent of 480 volts AC. Not to mention that a 40 HP industrial motor is a heavy chunk. The higher RPM is probably not a big concern, as AC induction rotors are of pretty tough construction, and have no commutator. 

A fearless young experimenter with the handle of Subcooledheatpump has a number of interesting Youtube videos, including this run-up to 24,000 RPM of an off-the-shelf ac motor. 

https://www.youtube.com/watch?feature=player_detailpage&v=7rVcxZ8Xdtg

Cheers, 
Dan


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## Sunking (Aug 10, 2009)

You cannot compare ICE to Electric Motor HP. An ICE is rated at maximum peak HP. It cannot maintain that horse power continuously. One car I know about is a Honda Civic that has a 2L 158 HP @ 6500 RPM, 4200 RPM/138 ft-lb. At 70 mph cruise only uses 20 to 30 hp. All the extra HP is just for acceleration

Electric motors you have to be careful with HP rating to know if the HP rating is Continuous or Peak. In your case most likely Continuous. But here is the catch. You can force it to 2 to 6 times that of continuous by more current. 

To get a good graphical look go to HPEV, select any motor, and look at both Peak and Continuous graphs for a given voltage and current.

Example I have an AC15 running 96 volts with a 650 amp controller on my golf cart. It is rate 15 HP continuous, and 60 HP peak. If I were to look for an ICE to replace it, I am looking for a 50 to 60 HP engine with like RPM range. While there see what happens with the same MOTOR called AC9 at lower voltages and current


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## Duncan (Dec 8, 2008)

In addition to Sunking's comment about continuous and peak you have to compare the power to how you drive

Way back in 80's I was involved with the development of the fuel system of the Ford Transit Diesel
The Diesel had 55Hp
The petrol version had 105Hp
But the petrol engine developed that power at 5000rpm
The diesel at 3500rpm
For normal driving the diesel felt much more powerful - the power was there when you wanted it
The petrol was faster - IF you drove in a lower gear and used the revs

How do you drive your car? - do you use 5000rpm?? or are you like most of us and spend most of your time at 3000rpm?


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## CKidder (Dec 12, 2009)

In addition to everyone else's comments I'd like to suggest that horsepower is a red herring and not even the most important figure to discuss. The better figure to look at is torque. This highlights the many differences and I think really shows what is going on better. An electric motor has full torque at zero RPM. An ICE has no torque at 0 RPM and in fact usually can't even sustain its own operation under something like 400RPM. So, lets compare at the same RPM. At, say, 800RPM an electric motor still has full torque (more or less). An ICE has a fraction of its full torque at 800RPM. I don't know the real figure but probably a third or half of its peak torque. HP is just torque * speed. So, it tends to obscure the important distinction here. At low speed the electric motor is outputting full torque and so it feels "powerful." The ICE has limited torque and so it needs to get up to its power band to get proper performance. This is why a 50HP electric motor can feel so much more powerful at low speed than a 200HP ICE - it really is. The 50HP motor might be capable of 120Nm of torque at low RPM while the ICE is capable of 75Nm at that same RPM. But, electric motors begin to lose torque at a certain point. Usually they're dropping off torque like crazy right at the point where an ICE engine is really hitting its stride - the 3000 to 5000RPM range. Past a certain point the electric motor quits having the same torque and tends to fall off such that HP stays constant as RPM increases. Thus, the electric motor kind of flat lines in power at a certain point and this is around the point where an ICE really starts to shine.

This complicated situation makes it tough to compare HP ratings between electric and ICE because the rating is really an apples to oranges comparison. The true comparison, and where acceleration comes from, is torque. What you want is torque and thus comparing torque between electric and ICE seems to make more sense to me. But, everyone is hung up on horsepower because that's our culture. The car culture has long centered on HP and kind of left torque as a side note. That was OK when everyone was using the same thing. But, it also highlights why a diesel can feel so nice even when the HP rating seems to be low. Diesels tend to generate better torque at low speeds and so they're more powerful sooner but they can't spin as fast and that limits HP since it inherently has RPM as one of its components.


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## dcb (Dec 5, 2009)

I think it is important to look at the whole picture. You can't just look at amps, and ignore volts, anymore than you can look at torque and ignore rpm. Specifically you have to look at wheel force(torque/arm) vs wheel rpm (vehicle speed), and compare it to weight and drag to see the effects.

With proper gear ratio selection, and without drastic changes in weight/aerodynamics, ultimately hp/kw (gas or electric) determine the top speed of the vehicle. But we usually don't care about going 150mph in a commuter vehicle, tickets, crappy range, etc. So it isn't the best point of reference, when you can trade top speed for better acceleration via gearing or other engineering compromise.

fwiw, my leaf makes ~110hp once it is up to speed, and makes more than adequate torque below that point, so it is perfectly driveable with just one speed, even at ~3500 lbs. It is designed with a top speed of 90mph, which suits me fine, but were it geared just right it could do 125mph, but it would accelerate and climb much more slowly. I would not enjoy that change in my commute, not when I've never come close to 90mph, and when I currently get pretty much every hole-shot at every light (unless there is an attentive tesla driver next to me  hasn't happened yet ).

On the other end of it, there is enough wheel torque in the leaf to spin the tires, so more torque isn't really going to help much. But the torque traction limit is a very useful point of reference. There's no reason to gear up the torque any more than the tires can handle. From there you can sort out what the top speed is and see if you can live w/it or if you need more volts or multiple gears or something.

F=M*A (don't ignore aero and rolling resistance or changes in torque/rpm).

it might also be useful comparing a nissan versa hatchback to a leaf.
They are not the same, http://www.mynissanleaf.com/viewtopic.php?f=4&t=1421&sid=9382da1c3ea161b38407a47722634f23&start=10
but they are similar enough in size and peak hp. so you will get a feel for the whole system, i.e. extra weight for batteries, 0-30/0-60 performance, etc.


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