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# Motor Constants

Have you ever wondered if it's possible to measure the Kv of an electric motor yourself? The answer is "yes", and it is actually quite easy to do at home with relatively inexpensive equipment that you may already have. All that is required is a way to measure volts accurately (multimeter), a tacho to measure RPM and a drill press or another method to spin the motor at a constant speed.

Once you know how to measure Kv, you'd want to do it whenever you buy or rewind a motor, to confirm the Kv value.

On commercial motors, the stated Kv is usually a nominal value, because no two electric motors are completely identical.

Therefore, a manufacturer may round the Kv value to the nearest 50 or 100 according to what they measured on a test sample. In some extreme cases, manufacturers even publish inflated Kv values, hoping to take advantage of the notion that bigger is better. Some manufacturers don't even bother to give the basic specs, presumably because they don't know how to determine the motor constants.

And sometimes manufacturers make mistakes. E.g. when O.S. (who is well known and trusted for their IC engines), brought out their first electric outrunners, the specs for the OMA-3825-750 motor were horribly incorrect.

## Three Important Motor Constants

The three motor constants which are very handy to know about any electric motor are:

1. The speed constant or velocity constant (Kv)
3. And the motor winding resistance (Rm), also abbreviated Ri

Using these 3 constants, the performance of any electric motor can be predicted fairly accurately with simulation software.

Obviously, the more accurately the constants are measured, the

more accurate the simulations will be for any given motor.

This means that using nominal values or inaccurate values will yield less than desirable simulation results. It is a strong argument for measuring your own motor constants.

Some software will also predict motor temperature using a fourth value, the weight of the motor.

Examples of really great, free motor simulation software are listed at the bottom of this page.

## Kv (Velocity Constant)

It is surprisingly easy to measure the Kv of an electric motor.

The unit for Kv is RPM/volt, and in effect Kv is exactly that - the RPM that a motor will turn when one volt is applied. For brushed motors, this is straightforward: Kv = RPM / Volts.

With brushless motors however, the formula becomes slightly

more complex because power is not applied directly to the motor leads, but goes through an electronic commutator, in the form of a speed controller (ESC) first. The ESC sends power via PWM pulses to the three phases of the motor.

Below are three methods for determining the Kv of a brushless motor, not necessarily in order of preference.

1. The Drill Press Method is probably the most accurate, as well as quickest and easiest method for measuring Kv, as the motor doesn't have to be connected to the ESC and battery.

Kv = RPM / (Volts × 1.414 × 0.95)

Steps:

1. Spin the motor in a drill press at a known and constant speed.
2. Measure the AC Volts (RMS) with a multimeter. To do this, take a voltage measurement on one of the three phases of the motor (any two of the three motor leads).
3. Apply the formula to get the Kv of the motor alone - without the effects that ESC settings will introduce.

For a more accurate result (true Kv of the motor), measure all three phases and average the values.

Volts

RPM

Kv  (RPM/Volt)

I suggest measuring the speed of the drill press beforehand. Keep in mind that the accuracy of the final result depends on the accuracy of the testing equipment and readings. I usually try to get at least two decimals when taking voltage readings, because it makes a difference when the calculated Kv is going to be used in simulation software.

2.  Another method to determine Kv involves running the motor without load at full speed, and then measuring Volts, Amps & RPM, as well as specifying the motor resistance constant (Rm).

Kv = RPM / (Volts Amps × Rm)

This method provides a Kv constant that includes the effects of the ESC, which may be desirable in some cases. The result may also be called the intrinsic Kv constant of the motor and ESC.

Volts

Amps

RPM

Rm

Kv  (RPM/Volt)

3.  Hobby King sells a product called the "K1 KV/RPM Meter" which was designed to measure the Kv of brushless motors. I strongly suspect that this meter uses the "Drill Press" formula described previously. But unfortunately, in order to measure Kv, the user has to enter the number of magnet pairs into the unit (presumably to calculate the RPM). This may pose a problem if the number of poles (magnets) is not known to the user.

K1 KV/RPM Meter

Io is the no-load current of a motor and in my opinion is best measured at intended operating speed. Usually, a reading is taken at 10 Volts, however I prefer to measure Io at the RPM at which the motor will most likely be going to work. There are other methods, i.e. the 'four constant model' which is outside the scope of this article.

With outrunners, it's quite easy to measure RPM when two marks or lines are placed on opposite sides of the outside of the rotor. Then a tachometer set to 2-blade setting can be used to measure RPM.

It's best to use a variable power supply and varying the RPM by adjusting the voltage until the desired operating RPM is reached with the ESC at max. speed, and not by varying the speed with the ESC.

If a variable power supply is not available, try battery packs of different voltages till you find one that gives the closest speed to what is required.

Record the current and if possible, the RPM of the motor shaft.

With no load on the motor shaft:

Io = Amps

More accurate modeling of Io is possible by employing advanced curve fitting equations, but then multiple readings at various voltages and speeds will be required.

## Rm (Winding Resistance)

Rm (or Ri) is the resistance of one phase of a motor (after termination). In other words, if one measures the resistance between any two motor leads of a brushless motor, that value would be the Rm. Unfortunately, this measurement is a little more tricky to perform than meets the eye, because a multimeter is just not sensitive enough for this purpose.

But fear not. There is a method to measure Rm which is within the capabilities of the average DIY person, yet it's very accurate and only requires a few pieces of inexpensive equipment.

It's a variation of the Kelvin (4-wire) method and has served me well for many years.

Equipment needed: Ammeter, voltmeter, 10-20 Ohm (10 Watt) resistor and a high capacity battery of about 12volt. The exact values are not important, because the accuracy gets taken care of by the calculation. A 2000mAh 3S or 4S LiPo battery is ideal.

The ammeter and DVM (digital volt meter) can be cheap multimeters, as long as the one used for amps can measure current to at least 5A.

Being an electric model flyer, I already had an accurate ammeter in the form of a Hyperion e-Meter. Although the standard 100A shunt will work, I chose to use the 20A shunt because then Amps is displayed with an extra decimal.

The formula:

Rm = Volts / Amps
4-Wire method for
measuring Rm
Typical setup using
Hyperion e-Meter

## Calculating Efficiency

Now that we know how to measure the three important motor constants, Kv, Io and Rm, lets see how we can apply this knowledge.

One possibility is that the efficiency of the motor, as well as the efficiency of the complete system (motor, ESC and battery) can be calculated. More importantly, it's possible to establish what exactly robs a system of efficiency.

Efficiency changes as the load on the motor varies. In other words, with a certain size or pitch propeller, a motor will have a certain efficiency at WOT. If a different size or pitch propeller is used, the efficiency will change. If the voltage goes up (by adding a cell or two), the efficiency will also change. If the motor is run at part-throttle, the efficiency will also change.

Some manufacturers give a 'Maximum Efficiency' rating, but don't be fooled. That number is calculated and is far from what the efficiency is when the motor has to work hard, like when powering a model airplane, multicopter, or helicopter.

In order to calculate efficiency, we have to run the motor with a load (propeller) attached while taking Volt and Amp measurements using a reliable Watt meter.

This calculator is based on these formulas:

Copper Loss = Amps² × Rm
Iron Loss = Volts × Io
Motor Losses = Copper loss + Iron Loss
Power In = Volts × Amps
Power Out = Power In All Losses
Efficiency = Power Out / Power In
Kt = 1/Kv (SI units: with RPM in rad/sec)
Torque = Kt × Amps
Km = Kt /

Hopefully, with the help of this efficiency calculator, you'll be able to make informed decisions about choice of motors, ESC's and batteries.

## Motor Simulation Software

No respectable electric flier should be without a decent motor simulation tool. The two applications listed below are at the top of my list. Both are very realistic and powerful stand-alone applications that are free to download and use.