# Horsepower confusion



## TheKid (Mar 10, 2017)

I am trying to choose a suitable motor, but am getting confused along the way. 
I require 5hp to move my vehicle at a constant 30mph, however when I look at motors power curves they always show 5hp at a really low RPM value. How do I know which motor to choose? Because the motors are always more powerful than they need to be?


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## TheKid (Mar 10, 2017)

For example, I have found an AC motor with the following specs:
Rated power: 3kW
battery voltage: 48(VDC)
rated current: 78A
Rated speed: 2590 RPM
Max speed: 6800
Rated Torque: 8.18ft-lbs

This seems like a good fit. But I am also confused about the RPM value, from my understanding the rated speed is the speed at which the rated power is achieved? 
My next task is calculating the gear ratio, but that leaves me with a ratio of 2.9.. isn't that really low for an electric vehicle? and for an AC motor in general?


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## Duncan (Dec 8, 2008)

Hi
I have moved your thread to the Technical Discussions Forum

As far as your question is concerned that motor can develop 3Kw at 2590rpm

Which sounds about right - can you show us your calculations bout the power that you need?
Remember that you will need power to accelerate to your target speed and also to go up any slope as well as to simply maintain a speed


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## TheKid (Mar 10, 2017)

Thank you for your reply.

I have attached the excel spreadsheet with my calculations on it (as a pdf). The method I am following is basically this: select the speed, select the motor for that speed, choose the rpm at which the motor delivers that hp, choose the gear ratio based on that rpm, THEN see if the motor provides the torque over the range of level and hill climbing conditions. 
I have also read that the torque required values for inclines (that have been calculated in the excel sheet) correspond rather nicely with acceleration values. I.e. incline values from 5% to 25% correspond to the acceleration values for 1mph/sec to 5 mph/sec respectively, and they can be used interchangeably. 

My selected speed is 30mph, and I have used the torque value on the worksheet (under "Total drag torque, level") to calculate the 'required' horsepower, I got a value of 4.5hp. Hence my original question about a 3kW motor because I had converted hp to kW. Underneath all the tables are some specifications that might be of interest to you. My dilemma still lies in choosing a motor to suit my application


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## major (Apr 4, 2008)

Hi TheKid,

Suggest you take a look at the DIY garage on this site or the EValbum for EVs similar to what you want. Google search maybe. Also try talking to a vendor who sells EV motors. Any EV clubs in your area (EAA)? Or perhaps a school which has a program?

major


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## Sunking (Aug 10, 2009)

TheKid said:


> For example, I have found an AC motor with the following specs:
> Rated power: 3kW
> *battery voltage: 48(VDC)
> rated current: 78A
> ...


OK this sounds like a golf cart motor and if you note the bold face above are the numbers you need to work with. 

The HP = 2590 RPM x 8.18ft-lbs / 5252 = 4.03 HP

It will use 48 volts x 78 amps = 3744 watts and that translates to 80% efficiency. 

What you have to work out is a gear ratio that gives you the desired speed at 2590 RPM with 4 hp. With electric motors if it take 1 hp for desired speed the motor peak power needs to be 3 to 4 hp. Just guessing here but the motor are looking at is just a little shy of what you want. 

However you would have to check, but if the motor can run at 60 volts might be perfect with a 200 amp controller.


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## Karter2 (Nov 17, 2011)

Why design to a precise limit.
Oversize the power capacity of the motor to allow for unforseen situations.
You dont have to use the extra power, but it is much less hassle to increase a current limit setting than to have to change out a motor to a bigger one after the build is complete.


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## TheKid (Mar 10, 2017)

Thank you all for your responses.

I have googled my heart out trying to research this! I will see if there are any EV motor vendors that I can contact for further help. I have actually contacted a couple of motor manufacturers to obtain performance curves.

Dereck, you have cleared up some of my confusion on what the values represent. As I mentioned before I am following a method for this, the bit where I am stuck at is looking at the performance curves and reading the RPM at which the motor delivers my required hp. From what you have said however, it seems that the rated speed IS the RPM at which the rated horsepower is delivered (from the HP calculation). This is very useful to me. How would you read this from a motors power curve though? I will give an example, the HPEV AC-20 is supposedly a good choice for lightweight vehicles, which mine definitely is. However, at 5hp on the curve the RPM is very low, which of course gives me a very low overall gear ratio. This is where the majority of my confusion has been..

http://www.hpevs.com/Site/power_gra...0-amp/ac-20 72 volt 300 amp peak imperial.pdf

In fact on the "peak" graph above (72 volts / 300 amps) it doesn't even measure 5hp at any point. However on the "continuous" plot for the same motor..
http://www.hpevs.com/Site/power_gra...-amp/ac-20 72 volt imperial continuous FC.pdf

I emailed HPEV and they said their ac motors "want" to run at 6000 RPM. As i said my main confusion is coming from the graphs.. 

The reason I have a precise limit is because of the method I am following, I am looking for a motor based on the required hp at my design center speed of 30mph. My next calculation is based on the RPM at which this horsepower is delivered, so that I can calculate the overall gear ratio:
overall gear ratio = RPM(motor) / RPM(wheel)

Anymore help to clear this confusion is greatly appreciated!


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## major (Apr 4, 2008)

Kid,

Don't know what you mean by center speed. Maybe you're taking a wrong approach to motor selection. Also sounds like confusion interpretating motor performance curves. Here's another suggestion. Read: https://www.amazon.com/Build-Your-Own-Electric-Vehicle/dp/0830642315. 
By Bob Brandt.
I think you can find free downloads on line. Or library. 

Regards,

major


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## TheKid (Mar 10, 2017)

Funnily enough that is the book I am following!

What I meant by "design center speed" is simply the operating point for my vehicle. It is a car designed mainly for city use, so I have chosen to base calculations around this speed (30mph)


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## TheKid (Mar 10, 2017)

If I may provide a short quote from the book, this is where the author summarises the proposed method:

"In short, you need to select a speed, select an electric motor for that speed, choose the	RPM at which the	motor delivers that horsepower, choose	the	target gear	ratio	based on that RPM, and see if the motor	provides the	torque over the range of level and	hill-climbing conditions you need."

The book even goes through the procedure for a ford pickup using 50 mph as the main operating speed. He then, as I have done, calculated the 'required horsepower' and comes to a value of 22hp and in the end chooses the FB1-4001 advanced dc motor which I am sure you are familiar with.

He then simply states that from the performance curve of the motor driven at 120 volts, and using the hp= torque x rpm /5252 formula, the motor produces roughly 22 hp at 4600 RPM at 25ft-lbs of torque and 170 amps. 

So now he is able to calculate the wheel rpm and the overall gear ratio. My problem still lies in reading the performance curves for different motors/finding the 5hp point and reading the RPM. However once I have done this and FINALLY chosen my motor, I will be able to move on with choosing the gear ratio and then onto battery selection and all that other good stuff.


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## major (Apr 4, 2008)

Hi Kid, 

Been a long time since I read it. The problem with that design logic is that with his 120V battery, it will essentially take forever to accelerate to 50mph and with any battery sag, headwind or grade, hopeless. You need to design your 50mph point for less than full voltage, say 90V, and use the controller to reduce the 120V (battery) to 90V to cruise at 50 mph (4600 RPM). That way you have torque available to accelerate and voltage headroom to produce 4600 RPM at a bit higher torque in case it's loaded more by wind or grade.

Remember that the RPM vs Torque curve is for the stated voltage only. Once you use your controller to reduce voltage to the motor, any RPM under that curve is available for a given torque value. At the lower RPM (and voltage) will be lower power and less battery current.

My opinion, 

major


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## Duncan (Dec 8, 2008)

Hi Kid

You are overthinking this - those calculations will give a "minimum" power - you need to ensure that you have at least twice that in order to be usable

You are NOT designing to a point - you are designing to clear a bar

When you drive YOU - the driver - select how much power you want at that point 
UP TO the limit of the motor/controller

Just make sure that that limit is high enough


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## TheKid (Mar 10, 2017)

I (think) I get what you're both saying. Basically choose a motor where I reach my design center speed (sorry to keep using that phrase) of 30mph but still have more in the "tank" to overcome hills etc. 

Let's just take this motor right here: http://www.cems.uvm.edu/~aero/AC24_2007.pdf
I am trying to determine the right overall gear ratio, and produce a torque available graph (wheel torque) based on the readings from the power curve.

So, I need to choose an overall gear ratio based on the motor RPM at 30mph ie, that 4.5hp value I calculated. This is why I need to use this speed value, so that I can refer to the power curve and determine the RPM of the motor at this speed (based on the torque required value/hp value I previously calculated) in order to find the overall gear ratio. Because 30mph is the speed at which the vehicle will mostly be running at, it is being designed purely for city use.
I want to do this so that I can then use these equations to generate the torque available graph for that motor:

Torque(wheel) = torque(motor) / overall gear ratio x n (transmission efficiency)

Speed(vehicle in mph) = (RPM(motor) x 60) / (overall gear ratio x revs/mile)

Quote from the book: "With all the	other motor torque and RPM values you can then calculate wheel torque and vehicle speed using the following equations." The equations are the ones I have specified above, so it is saying I need to take the torque values from the curve and their respective RPM values. This is also a major point of confusion for me. Because like what was said before, the graph is a curve of the peak voltage? How do I read these values from the curve. I am too confused about these curves but I would really like to understand this method. Just a thought but perhaps it is more suited to choosing a DC motor? I am quite intent on an AC motor.

Then I can plot a graph of the torque available and the torque required against vehicle speed, I have already calculated torque required in the excel spreadsheet, which I attached in one on my first posts. This will allow me to determine if the motor will do what I want. These torque required values are for level, incline and acceleration by the way. This is the method used in the textbook, it just doesn't offer specific details about the power curve.

Sorry if I'm going in circles, I feel like I have been for the past 2 weeks now. Again I really appreciate your help and patience


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## major (Apr 4, 2008)

Hi Kid,

You need to plot your load curve on the motor speed torque curve. Choose your GR and tire size and convert that spredsheet into RPM and Nm. Similar to Brant on figure 6-9 page 158 in the edition I have. He converts the motor curve to wheel torque and mph. Same result. 

Being able to see the motor curve and load curve together will give a view of equilibrium and a available torque across the whole speed range.

Regards,

major


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## kennybobby (Aug 10, 2012)

If you are designing a vehicle, then the first thing you need to decide is the size of the wheels and which tires you plan to run. This will be a constraint to help determine the gear ratio. Here's a few questions:

1. What size wheels and tires?

2. How much does your vehicle weigh--what is your design center weight target?

3. What is the maximum design center speed that you require?

4. How much acceleration do you require--how fast do you need to reach your maximum speed? e.g. 0 to xx mph in 10, in 20, or in 30 seconds

5. How fast do you need to reach you design center speed?

Once you answer these questions then you will have some performance factors to help determine energy and power requirements.

Now consider the motor curve plotted as a torque-speed curve as shown here. [edit: didn't notice it was metric units]

Motors don't generate speed, they generate torque based upon the current. The motor will turn at a speed determined by the voltage and the current required to counteract the sum of the load torques (aerodrag, friction, rolling resistance, etc).

For example let's say you need 50 m-N of torque to make your vehicle run on the road at 30 mph. The chart shows that this motor can make 50 m-N of torque and turn, depending upon the voltage, at any speed from zero up to a maximum of ~5700 rpm at 156V.

So current and voltage will determine the torque and speed, and these are also used to determine the size of battery pack, energy and power required to meet your range and speed and performance design center targets.


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## major (Apr 4, 2008)

KB, see attachment on #4.


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## TheKid (Mar 10, 2017)

Major, I am trying to do this for the AC-24: http://www.cems.uvm.edu/~aero/AC24_2007.pdf

and for the AC-20: 
http://www.hpevs.com/Site/images/to...hs/ac-20 144 volts 500 amps imperial peak.pdf

What the book says is this: "*From these figures or curves, you can derive the RPM at which your electric motor delivers closest to its rated horsepower. *Using this	motor RPM	figure and	the wheel RPM figure, which gives you the wheel RPM from your target speed and RPM, you can determine your best gear or gear ratio from:
Overall gear ratio = RPM (motor)/RPM (wheel)
This—or the one closest to it—is the best gear for the transmission in your selected vehicle to use; if you were setting up a one-gear-only EV, you would pick this ratio.
*With all the other motor torque and RPM values* you can then calculate wheel torque and vehicle speed using the following equations for the different overall gear ratios in your drivetrain..."

kennybobby, great stuff this really helped with my understanding. Like major said, one of my previous messages containts a pdf attachment that will answer most of the questions you have posed. What I am hoping to achieve is to create a torque available graph, using values derived from the power curve of the motors. This is what the book I am following does with the FBI-4001 DC motor. I feel like I am still missing something. For example, for the AC-24 motor, I am not entirely sure which RPM value to use to calculate the best overall gear ratio. Is it the "nominal" speed value or the "maximum" speed value. 
Also, relating to the second bold sentences above in the quote, it seems that what I need to do is simply read off the RPM at 10 ft-lbs, then 15 ft-lbs etc until 74 ft-lbs. However the curve doesn't show an RPM value for 10 ft-lbs at this voltage?

many thanks


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## major (Apr 4, 2008)

TheKid said:


> ... it seems that what I need to do is simply read off the RPM at 10 ft-lbs, then 15 ft-lbs etc until 74 ft-lbs. However the curve doesn't show an RPM value for 10 ft-lbs at this voltage?


You could extrapolate and get like 12,000RPM, but it really is irrelevant because it would break something if it could go that fast. Please do as I suggested and draw the load curve on the motor speed torque graph. 

For a "normal" speed or whatever you call it, just pick 3000 RPM and 30 mph, figure the GR, draw the curve, and then adjust from there. 

major


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## TheKid (Mar 10, 2017)

I have come up with a torque required or available vs speed graph. Major were you suggesting that I did it in reverse to what Brant does? 

Here is the graph I made (attached), few details to explain first:
Wheel RPM at 30mph = 443
Gear Ratio 1 = 6000/443 = 13.54
Gear Ratio 2 = 4500/443 = 10.16
Gear Ratio 3 = 3000/443 = 6.77


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## dcb (Dec 5, 2009)

very nice graph! fyi it looks like peak though(~56hp at the turn), limit it to 30nm for continuous? (less at low rpm/less cooling)


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## kennybobby (Aug 10, 2012)

Which motor did you use?

The AC24 would show 368 ft-lbs max available at 30 mph with GR3. The AC24 curve is metric and you will need to convert--looks like you forgot to do that or something else is not right about the GR3 calculation. There should be a data point at 30mph for GR3.

i think gear ratio 3 for the AC24 should be something like the fat green line that i've drawn on your chart. The line forms a performance envelope for which this motor could meet any torque requirement within the "box", i.e. underneath the line.


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## dcb (Dec 5, 2009)

I concur w/kenny that the 6.77 ratio line should be "level" at ~368 ft/lb, something is wonky. (also still a peak value probably)


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## TheKid (Mar 10, 2017)

Unbelievable, you're right I didn't convert the torque Nm to ft-lbs. I'll fix that shortly and post the graph again.


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## major (Apr 4, 2008)

TheKid said:


> I have come up with a torque required or available vs speed graph. Major were you suggesting that I did it in reverse to what Brant does?
> 
> Here is the graph I made (attached), few details to explain first:
> Wheel RPM at 30mph = 443
> ...


It really is just preference. I like to look at the system on motor parameters. Wheel RPM and torque is just scaled by GR.

I like KB's green line box. That is what I was talking about. You can operate at any point inside that box. GR3 (6.77) doesn't look too bad.


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## TheKid (Mar 10, 2017)

As promised:


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## TheKid (Mar 10, 2017)

I agree major, the 6.77 gear ratio looks best, although perhaps it is overkill for the requirements of my vehicle?

From the gear ratio data values I uploaded in the previous post, I hope you can all see why the graph looks the way it does, and doesn't follow the green line kennybobby and dcb proposed. Also, in "Build your own vehicle" it follows a line similar to the ones on my graph, they don't ever touch the y-axis. If it was a motor torque against RPM curve you would of course expect it to, however the graph I have created is a Wheel torque vs vehicle speed curve. The usable area still follows the green line (ie to the left and underneath, bounded by the "0%, level" line), only it is not visually represented here.

The way in which I collected the data was simply reading off the AC24 curve at different torque values up to the maximum (ft-lbs this time NOT Nm). I wasn't sure how to get any more information from the motor curve once I reached the maximum torque.


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## TheKid (Mar 10, 2017)

I confess I don't even know where to start with the HPEVS AC-20 curve:
http://www.hpevs.com/Site/images/to...hs/ac-20 144 volts 500 amps imperial peak.pdf

It has all that torque over a huge RPM range! I can't read off RPM values from 10, 15,20 etc ft-lbs.. Any clues on how I might achieve this? I would like to create a similar graph to the AC24 one.


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## dcb (Dec 5, 2009)

for 144v/500a
http://hpevs.com/Site/images/torque-curves/ac-20/144 volt/ac-20 144 volts 500 amps.xlsx

or for 96v/650a
http://hpevs.com/Site/images/torque-curves/ac-20/96 volt/ac20 96 volt 650 amp.xlsx

those have continuous for different cooling (TE,open,etc) and peak tabs.

reduce the current means reduced torque porportionally


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## major (Apr 4, 2008)

TheKid said:


> I confess I don't even know where to start with the HPEVS AC-20 curve:
> http://www.hpevs.com/Site/images/to...hs/ac-20 144 volts 500 amps imperial peak.pdf
> 
> It has all that torque over a huge RPM range! I can't read off RPM values from 10, 15,20 etc ft-lbs.. Any clues on how I might achieve this? I would like to create a similar graph to the AC24 one.












See the horizontal green line which KB drew down to zero mph? Do the same thing. At the maximum motor torque, draw the line horizontally to zero mph or zero RPM. That's the torque limit. Motor/controller will not produce any higher torque. And typically the motors used for EVs deliver full torque from stall (0 RPM) up through base speed (usually max power point).


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## TheKid (Mar 10, 2017)

Okay I have got a graph for the AC-20 now:
Edit: X - axis is vehicle speed in mph
Y - axis is Wheel torque required or available


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