Electric Motors — part 5
Brian Muldermmmm
Motor Efficiency 101
Whether you build motors or just use them, you ought to know something on the subject of optimizing a power system.  Of course you could just adhere to the motor manufacturer’s specifications for a bought motor, but for a self-built motor, you ought to know how your motor is performing.  Doing the calculations will reveal if you have made a bad motor, or a real good motor that you would perhaps want to duplicate.  And if you take the time to measure all the motor’s parameters, you could answer a number of interesting questions without burning out a motor and learning the hard way.

What is Motor efficiency?
It is the ratio between input power and output power.  The closer we can get the output power to the input power, the better the motor system.

Doing it the Simple way
In this case, all we are interested in is finding out how well our motor is performing with a certain propeller.  If we change propellers and repeat the measurements, we can deduce which is the better setup for a particular model.

Input Power
To calculate Input power, we need Volts and Amps whilst the motor is running at full power. Measuring volts is easily done, but you need to know a few details.  For a brushed motor, you would take the measurement as close to the motor as possible.  The reason for this is to eliminate the voltage drops across the battery and motor wires.

For a brushless motor however, you cannot measure as just described.  The best place would be the speed control input wires.  This may well be where you have your Deans connector.  We are just going to have to live with the losses in the controller and wires in this case.  We will see later how these losses become apparent.

To measure current, we place a 10A (or better) multimeter in series with the negative controller wire.  This would be the input wire from the battery to controller.  To get useful results, the resistance of the sensor element in the multimeter must be low.  A meter that can only measure 5 Amps would most likely have a higher sense resistance than a 10 Amp meter.   Of course, should your motor be capable of 20 or 30 Amps, you would need a suitable meter to measure these currents.

I happened to have an old 30A panel meter lying on a shelf, but my only concern with these meters is the accuracy (or lack of) at which it can measure a pulsed current from a controller.  When compared to a digital meter, it seemed to work very well.  When taking a current reading, ideally you want a voltage reading at the exact same time.  Unless you’re using a power supply, battery voltages can drop between measurements, resulting in reduced accuracy.

Calculation of input power is simply the product of Volts and Amps.

Output power
This is where it gets interesting.  We are no longer dealing with electrical energy, but mechanical energy expressed in rotor torque and rotating speed.  The problem here is that of measuring torque.  You will need to build some kind of test fixture and then calibrate it somehow.  This is a whole project on its own and not really the route we want to go.  If you were really serious about motors though, you would probably land up making one anyway.

A pretty simple way of getting a ballpark figure of output power is to measure the RPM of a propeller attached to the motor.  The RPM value together with propeller size and pitch, will allow you to calculate an output power level and expected thrust.

Now not all propellers with a given size and pitch perform the same way.  As you may well know, propellers can look quite different from each other and produce different levels of thrust.  Therefore, to increase the accuracy of the measurement, we add a Propeller Constant (specific to the brand of propeller used) to the formula that then results in better accuracy of the output power.  A minor snag with this approach is getting good propeller constants. You could easily land up finding a few different constants for a specific propeller when surfing the net.  The only way to get any sort of real accuracy is to measure the thrust with a thrust meter and compare results against those predicted.  You can then create your own propeller constants.  The only drawback here is, you have built a thrust meter and no longer really require the use of a prediction program!

You now have output power and input power.  Efficiency is then output power over input power multiplied by 100 to give a percentage.

But wait . . . there is an even easier way!!

Sounds like an info commercial, doesn’t it?

The major problem with the above example is that of owning suitable equipment for taking measurements.

A decent multimeter can cost a fair sum of money and then you still need a tachometer.  Well, there is a nice tool available that does everything and more.  Heck, it will even do the dishes for you  . . . it is the Hyperion E-meter.

This tiny little gadget measures Volts, Amps and RPM.   It even allows you to enter propeller constants into the unit so that it can display output power, efficiency and expected thrust. To add to its usefulness, it also has a battery monitoring function and shows the accumulated current going in and out of a battery.   So by using a cheap power supply, you can have the features of a more expensive battery charger.   Oh yes . . . it also has a serial port output that allows it to stream data to a computer!  You then have access to neat looking graphs, which you will be seeing shortly.   Let me say it again . . . a very neat tool for under R1000!!

I was about to order one of these E-meters from abroad, when Hobby Warehouse had a special that made it attractive enough to purchase locally.    Although, the unit comes with a 100 Amp probe which is great for those Amp- hungry setups, for measuring under 20 Amps for our small CD rom motors and battery charge features, an optional 20 Amp probe is required for better accuracy.  Unfortunately, I could not find a 20 Amp probe locally and had to bring it in from overseas.  I would recommend that the local hobby shops look into the 20 Amp probe, as it really is a necessity.

So how does it work?  Simply connect your Deans battery plug into one end of the power sensor and your motor into the opposite end. Power up the motor and whilst moving your throttle stick, you can monitor the RPM via an optical sensor on the E-meter and simply read the data displayed.  It’s that easy.

The motor data displayed here is what I stored in the E-meter’s memory and recalled later.  It shows a Warp 4 motor’s no load test data.
The Battery mode would show Volts at the top followed by charge or discharge rate.   Right at the bottom is a timer function to monitor progress.


For measuring thrust, we enter suitable propeller constants (very easy to do) and read the thrust directly from the E-meter.


Motor theory — Wading In deeper
I had always wanted to experiment with the mathematics side of motor theory and having to write this article finally gave me the push I needed.  I had downloaded an article or two some time back that explained everything I needed to know, so I dived in, expecting to find everything reasonably straightforward.

Unfortunately, this has turned out not to be the case and has resulted in more questions than answers.

Lets have a look and see what the issues are.

To measure efficiency, an alternative method to measuring output power is to rather measure certain parameters and calculate the losses in the motor instead.  Output Power is then the difference between Input power and Losses.

Before we can calculate any figures, we need some data to work with.  It happens that there are just three bits of information that are required,  those being . . .

    Io current
    RPM/Volt (KV)
    Motor resistance.

These three variables are the critical ingredients for all motor prediction calculations.

Io Current —
     is the current required to overcome frictional, iron and other related losses in a motor.  If a motor is drawing a current of 1 Amp at 20 000 RPM without a load attached to its shaft, then this is the current that will not be contributing towards driving a load.  It is regarded as wasted.  If a load is attached to this motor that results in 4 Amps being drawn, then only 3 Amps will be doing useful work.  Your 1 Amp of Io current in this case would represent 25% wastage.  So before even calculating other losses in the system, you are already down 25%.

What is interesting about Io current though, is that it is not voltage dependant.  If you draw 1 Amp at say 6 Volts and then increase the voltage to 8 Volts, the RPM will rise, but the Io current will remain the same.  Well, this is what motor theory says . . .

I tested the theory with a new speed 400 motor and found that the Io did stay reasonably constant.  It fluctuated a little, but more or less followed the theory.

The same test applied to a fairly used 400 motor however revealed a different story.  The Io value simply rose all the way with RPM.    The motor did sound a bit rough, so I deduced that the rising current was a result of an unwanted load — worn brushes and bronze bushes.

The next test was related to brushless motors since these are the motors we want to build and test.  I used a power supply to vary the input voltage to the controller and left the speed controller throttle setting at maximum power.

Current vs Voltagemmmmmmmmmmm
From the graph, you can clearly see that the current is rising reasonably linearly with voltage.  The current gain is not that much though, and considering an outrunner has a lot of external area that is rotating, it ought to be expected.

The Io is an important value for our calculations, and an inflated value will result in prediction calculations not being as accurate as they could be.

Current vs RPMmmmmmmmmmmmmm
The accepted method here is to use an Io value that is reflective of the intended RPM we would expect to see when the motor is loaded.  For example, should you expect to swing a propeller at 10 000 RPM, then looking at the current vs RPM graph, we would like to use the Io current that represents the losses that occurs at this RPM level, which in this case would be around 0,7 Amp.

So, if you purchase a brushless motor and read the Io current specified in the data sheet, it may well be a useless value.  You would need to run some tests to establish the correct Io for the intended RPM.  As a guide, if you intend using a 3-cell Lipoly pack, do the Io test on a 2-cell pack.  This will give you a reasonable value to work with.

RPM per Volt (KV)
You may remember for an earlier article, I mentioned that this figure could be calculated by taking the no load RPM and dividing it by the voltage used to power the motor.  This method gives you a pretty good idea as to what the KV figure is, but for better accuracy, we must measure it . . . or calculate the figure from certain test results.

Measuring KV Directly
This is supposedly the most accurate procedure for determining the KV specification.

The most popular method is to spin the motor to some known RPM, in a drill press or hand-held drill, and measure the voltage produced at the motor terminals.

I happened to purchase a rotary impact drill some years ago that had the RPM listed.  It stated 0 – 1000 RPM, but just to make sure, I attached a marked disc to the drill and measured the RPM with the E-meter.  The meter read 1050 RPM, with a resolution of 15 RPM.  After playing around a bit, I felt I needed better accuracy than the 15 RPM and used my digital scope to get a more reliable RPM figure.  It worked out to be 1040 RPM.

The first motor tested was an old brushed Speed-400 motor, which produced a voltage of 0,33 Volt DC at 1040 RPM.  Doing the math, we work out the KV to be around 3120 RPM/volt.

If you power the motor without a load and measure the RPM achieved, you could also calculate the KV this way, as already stated.  To do this, you need to attach some sort of disk to the motor that has two black and two white quadrants as required for the tachometer to sense.  After trying this and comparing the results to the above described method, I found I could not get close (about 75%) to that of the drill test.   John L explained that this was due to air resistance. A flat disk may not pose a real load to a motor, but the viscosity of air and disc area does result in the motor seeing enough of a load to drop its RPM.  Fair enough, makes good sense.

For a brushless motor, we can do the same drill test, but this time we measure an AC voltage across any one phase.   The actual measurement though is not as straightforward as you might think.  Multimeters, when set to read AC voltage, will display an RMS AC voltage (RMS = root mean square, and is 70,7% of the peak-to-peak value), which is not the correct value to use.  We want half the peak-to-peak voltage, which represents the actual peak voltage produced by the motor.

To make this statement a little clearer, I attached the motor terminals to my digital scope and recorded the waveform at 1040 RPM.

As you can see, the voltage peak-to-peak is around 1,47 V for a single sine wave.  This voltage is swinging symmetrically above and below a zero volt potential.  As we only want the positive value, we divide the peak-to-peak value by 2 and arrive at 0,735 Volts.  This is the generated voltage the motor is producing.  A multimeter goes one step further and multiplies the 0,735V by 0,707 and arrives at the 0,52 Volts.   If you do not have a scope, you can in fact work backwards with the multimeter by multiplying the value by 1,414.  This then gives you your Peak voltage you require.

Right ...
1040 RPM divided by 0,735 V
          = 1414 RPM/Volt

Voltage vs RPMmmmmmmmmmmmmm
Lets now see how the powered test compares. The Io test data, as already shown, contained all the data required already.  Using the E-meter pc software, we select the data we would like to view and created this nice graph.

The graph represents what we would expect to see, a linear rise of RPM with voltage.  To calculate the KV/Volt, we could take the RPM reading at 9,0 V (13230 RPM) and divide it by the 9 Volts.

But wait ...
   Is the motor really seeing the 9 Volts?

No it is not!  A motor has resistance due to its windings.  Current flowing through this resistance creates a voltage.  This voltage is referred to as “lost volts” and needs to be subtracted from the 9 Volts.  We then arrive at the real voltage the motor actually responds to.

So looking at the Voltage vs Current graph, we see that the Io is 0,8 A at 9 V.  If the motor resistance (plus controller losses, we’ll get to this later) happens to be 0,25 Ohms, then the lost voltage will be 0,8 x 0,25 = 0,2 Volt.

Thus the motor only sees 9 – 0,2 = 8,8 Volts

KV = 13230 divided by 8,8 = 1503 RPM / Volt.

But hang on ... that is quite a bit higher than the drill test.  What do I believe now?  If anything, I expected the 1503 value to be a bit lower than the drill test, taking winding resistance and controller variables into account.  This result puzzled me more than a little, and had me put my thinking cap back on.

After various discussions, somebody mentioned the speed controller might be artificially increasing the RPM due to timing advance.  The Castle Creations controller had been set to automatic timing and did not really allow me to set a low timing advance.  The various programming options only allow you to set maximum timing settings.

So, as an experiment, I repeated the test with a Hyperion 30 Amp and a E-flite 20 Amp controller.  They gave me slightly lower RPM/volt values to those using the Castle Creations controller, from which I deduced that the CC-35 Controller was using a slightly harder timing.

Another issue to consider is that of the square wave drive sequence a controller uses.  The drill test produces sine wave that will have a lower RMS value than that of the 3 phase square wave sequence used to power the motor.

A fellow user group member supported this theory, and informed me that the value for the conversion is 0,955.  He had been using this “constant” for some time already to increase his measurement accuracy.

So if I apply 0,995 to 0,735 volts above, we arrive at an RPM of 1481.

I still think that our “powered” test ought to have revealed a lower value than the drill test due to air resistance, but I’m now convinced that the discrepancy is a result of motor timing as well.

Late addition —
I have just received a new motor I purchased from Japan.  It is an RCer Warp 4 motor.  It came with all the motor constants printed on a nice glossy sheet.  Must say, it is a very nicely produced motor.

I tested the motor with a drill and got a peak-peak value of 808 mV.  Without using the RMS 3 phase value, I arrived at 2574 RPM/volt — a mere 6 RPM off the specification.  This did not do my theory much good at all!

The powered test however with CC-35 controller worked out to 2779 RPM/Volt and the Hyperion controller gave me 2688 RPM/Volt.  These values were also over-inflated.

It has since been confirmed by a “motor expert” (MRK Group member) that a factor of  0,95 must be used to convert the “peak voltage” to a more accurate voltage figure for use in the KV formula.  Whether or not motor manufacturers know about this is another story!

Motor Resistance
Well, it sure sounds simple enough.  Measure motor resistance with a milli-ohmmeter or pass 1 Amp (or more) through motor terminals and measure the resulting voltage.  Resistance is the Voltage divided by Current.  For a brushed motor, you would need to prevent the shaft from turning if you are measuring resistance with the latter method.

Physically measuring motor resistance is the accepted method and is used by all motor manufacturers.  If you purchase any decent motor, you will find the motor resistance specified in the motor data.  MotoCalc seems to prefer this value for its predictions too.

As I do not own a milli-ohmmeter, I measured my motor’s resistance by passing 1 Amp through a winding (phase) and measuring the voltage, from which I then calculated the resistance to be 0,2 Ohms.

Now an alternative method to measuring resistance is to calculate the value based on real world results.  My understanding was that the value ought to be very close to the measured value.  But based on what I have discovered thus far, you just never know.

What we need to do is run two tests with similar propellers and record the results.  For the data to be of any use, the propeller loads should be suitably matched for the motor.   It could be two propellers you have in mind for use with the motor, but not sure which one is the best choice.    This is what an Ezone article explains.  It also says that after calculating the resistance, you must calculate the maximum current the motor can handle and then compare the current readings obtained with the two selected props and check that one falls within 30 to 60% of maximum current and the other prop falls within 80 to 100% of maximum power.  If they do not, then the reading will not be as accurate as they should be.

The following table lists the results I obtained.  All measurements are taken with the E-meter.

    Table 1a

data 1
9 x 4,7
7 x 4

Initially I did not use the 7x4 propeller and found that when I calculated the resistance and maximum power numbers, the currents obtained for the lighter load did not fall within the 30 – 60% range.   Luckily, I had a 7x4 propeller lying around which gave me the results I needed.

To calculate Ri, we use —

    Table 1b

data 1
data 2
9 x 4,7
7 x 4
calculated resistance
max current
maximum motor efficiency
69 %

Using the data above, I calculate Ri to be 0,3616 Ohms

The calculated Ri is significantly higher than the measured resistance!  Unlike a brushed motor, where you can measure voltage right at the motor terminals, we now have to measure voltage before the controller.  This Ri value now takes wiring losses and controller variables into account as well.   So at the end of the day, we are not just looking at figures relating to a motor, but a whole power system instead.

To calculate the maximum current the motor can handle we use —

Because the voltage is almost the same for both sets of data, and I have chosen an Io value of 0,55 Amp for all my measurements, the two figures would be very similar.

In this case the maximum current the motor should ever handle is 9,8 Amps.

Now this figure is interesting.  Should you exceed this current, you will not be creating any more power — just more heat and less power!

What you should keep in mind though, depending on wire used in a motor (and other cooling factors), you may not actually be able to sustain this level of current in normal use. My own motor was already starting to fry itself at about 80% of this value!

As you can see from the data, motor data 1 current falls within 80-100% maximum current and motor data 2 falls within 30-60%.

And finally, to measure motor efficiency —

So looking at the Motor Data 1

And if we do the maths for motor Data 2, we get a much healthier 65%

But hang on . . . if we use the ideal load for the motor, what maximum efficiency could we attain and what would be the current draw?

To find this out we use . . .
This formula calculates the maximum efficiency for our motor, which is this case, works out to be 69%.
The current requirement at this efficiency would work out to be 3,23 Amps based on formula ...

At this point, I decided it would be interesting if I could have a look at how this motor performs with different battery packs and find the “sweet spot”.

I ran some tests and compiled the data contained in Table 2 below.

Table 2

8 x 4,3
9 x 4,7
8 x 3,8
7 x 4
max motor
2 cell
1500 mAh
 69,0 %
6 cell
1300 mAh
68,5 %
2 cell
850 mAh
68,4 %

Now it is quite interesting to note how the different pack voltages affect the calculated resistance.  The Nicad pack is a 15+ year old 6-cell 1300 mAh pack that was able to hold a steady voltage better than an equivalent sized Lipoly.   The Lipoly would come into its own though, once warmed up.

The Nicad higher voltage results in more current being consumed and results in a higher Ri value being calculated.  One would think that the Ri value ought to be constant due to fixed cable and controller FET resistances.

You have got to remember here that as current increases, heating effects cause the resistance of copper to rise as well as the FET resistances.  It is worth noting that as current levels drop and calculated Ri falls slightly, the max efficiency calculations might reveal better results.  But this would also depend on how the Io current rises as a result of a lighter load and higher RPM figure.  You would need to experiment if you want more accurate results in this case.

The 800 mAh pack is the one I have been using in my Shock Flyer, and it is barely able to hold the minimum allowed 6 Volts for a 2-cell pack when cold.  The lower current drawn though, results in a slightly lower Ri and better efficiency.   The only snag here is that the 7x4 propeller offers the best efficiency as a result of the lower current level (it is approaching the 3,23 Amps we calculated) but can’t be used because it develops too little static thrust.

*  *  *

Well finally I am done for now.  This article has been a bit of a nightmare to research and write. I made a few observations along the way that enlightened people on RC groups found surprising.  It’s only when you start to question certain issues that you open up a can of worms.

For further reading, find E-zone’s Inside Story — Feb 2003, and look for feature article “Motor Constants — How to find them and use them” — by Joachim Bergmeyer.

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