Motor Constants for Micro Motors - RC Groups
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Feb 19, 2002, 04:02 PM
in persuit of low wing loading
Gordon Johnson's Avatar

Prop & Micro Motors Constants

I'd like to suggest that we start generating some data on motor constants for various motors we use in micro planes. This could then be used with ElectriCalc or MotoCalc. A good place to start would be on the low and high voltage versions of the N20 and M20 motors. If more than one of us did the measurements we could average the numbers, or simply report both of them. I think this is why ElectriCalc lists some motors with slightly different constants and the contributor's initials for each. If we do this, I'll put a table of constants on my site which would help them not get lost.

Jochen, elsewhere you posted a request that I measure the constants for an M20 motor. Could you post the steps and equipment required again here?

BTW, would we next need prop constants for various props? How does one go about measuring prop constants?

I think if we collectively start creating this set of data it would be a resource to all of us involved in the micro area. It would make it easier to spec out a particular rubber power conversion to electric, or just an original scratch built design.
Last edited by Gordon Johnson; Feb 19, 2002 at 08:22 PM.
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Feb 19, 2002, 04:38 PM
Registered User
jberg's Avatar

motor constants can be calculated like this (just copied my old posting):

The basic theory of DC motors:

output momentum: M = c_m x (I - I_0)
ideal rotor voltage: U_r = c_m x 2 x pi x n
terminal voltage: U = U_r + Ri x I
rev per second: n = ( U - I x Ri ) / ( 2 x pi x c_m )

1) measure Ri with your multimeter. Ri will not be constant as alternator switches from winding to winding. Take some measurements at different rotor positions and calc the average value. Take also I_0 (idle current)

2) take two measurements at the same voltage, but with different loads, for instance with the biggest and the smallest prop that seems to be suitable. Take amps, volts (directly at the motor terminals!) and rpm.

3) calc:

U_r1 = U1 - Ri x I1
U_r2 = U2 - Ri x I2

c_m = (U_r1 - U_r2) / ( 2 x pi x ( n1 - n2))

Now you have Ri, I_0 and c_m. You can calc

M as above
n as above
input power: P_in = U x I
output power: P_out = M x n x 2 x pi
- or -
output power: P_out = ( I - I_0 ) x ( U - I x Ri )
efficiency : eta = P_out / P_in

So you can predict rpm, output power and efficiency at every combination of volts and amps at the motor terminals. Besides that you can predict the prop rpm at this output power level (reduce motor power by 10% for gearbox efficiency ) by using the prop formulas from my older posting (ok, only for the GŁnther prop yet) and so select a proper gear ratio, and you can predict static thrust.

There is also a clever way to calc Ri from the two measurements but I don't have it at hand at the moment.
Feb 19, 2002, 04:46 PM
Registered User
jberg's Avatar
If it would not cut down building time then I should really write that down into a nice HTML document ... but next indoor date is coming and the model is not ready yet (nice kind of problems that I have :-)

A whole bunch of information including my N-20 measurements is buried in Gordon's old gearbox construction thread. This and some other data (constants for GWS props for instance) would really make up an interesting information base.

We need:
- motor constants c_m, Ri, I_0
- prop constants c_thrust, c_power
- airfoil constants c_l_max, c_d

Of course you can use programs like motocalc but if you do the calculations by hand you get some very interesting insights. I call that fun!
Last edited by jberg; Feb 19, 2002 at 04:51 PM.
Feb 19, 2002, 05:05 PM
in persuit of low wing loading
Gordon Johnson's Avatar
I too have an indoor fly coming up on Friday and a Micro IFO to finish and some changes to make to my Punkin bipe. So, doubtful I'll do any measuring constants between now and then. Here's your N20 post re-posted here from the Gearbox thread


I've made some measurements and done some calculations. The N-20 motor I've examinated has the following characteristics:

c_n ~ 7000 rpm/V
c_M ~ 1.36 mNm/A
Ri ~ 2.5 Ohm
I_0 ~ 0.17A (with gearbox, without prop)

The following formulas give the basic data at every operation point:

U: voltage [Volt]
I: current [Ampere]
n: rpm

n = c_n * (U - Ri x I) [rpm]
M = c_M x (I - I_0) [Nm]
P_el = U x I [W]
P_mech = (U - Ri x I) x (I - I_0) [W]
eta = P_mech / P_el x 100% [%]

These formulas show that the N-20 will have about 50% of efficiency at about 5.2V and 0.7A. That is quite good for a motor of this size, the N-20 is not an amp-hog, but a good performer *with proper gearing*. Always let him turn, don't overprop him!

This combined with prop data gives some interesting insight. The GŁnther prop (125mm dia, 110mm pitch) has the following characteristics:

static thrust produced: F ~ n_prop^2 / 0.84e6 [g]
mechanical power consumed: P ~ n_prop^3 / 49e9 [W]

So assumed that a single stage gearbox has an efficiency of about 90% including all bearings (don't be too optimistic here) you can expect >21g of thrust at 5.2V and 0.7A and a gearfactor of about 1:5.5. Now you know why I would never treat this motor with high current and low voltage. This motor is hot-wound, let him turn! And you know why I built a DC booster to get 5.2V out of one single Lithium cell.
It is quite interesting and instructive to type these formulas into an Excel sheet and to play around with them. Always take into account that the data differ from motor to motor, even of the same type.

and another post
you need two multimeters to measure amps and volts simultaneously, a tacho to measure rpm and (if you want to investigate props) a scale to measure prop thrust. Everything else can be done by calculations. I don't have a dynamometer. In fact with a bit of clever calculation you can use the motor that you investigate as dynamometer at the same time.

The GŁnther prop will press-fit on 2-2.3mm shafts. I use a 2mm carbon shaft in my gearboxes.


my N-20 is from I think that is the low-voltage version. Resistance is about 2.5 Ohm.

Regarding the flywheel: a bit of numerical math a la Runge-Kutta, and we will even deal with this. No black magic is involved (though the efforts would be a bit bigger). But I don't think that we need this. Or do you want to perform a short takeoff by revving up a variable pitch prop to the maximum and then giving more pitch suddenly to create a thrust burst? And besides that, the N-20 does not have a second shaft end at the back side which would be needed to put the flywheel to the proper high-rpm place.

and another
just to make it clear: the load does not need to be constant with the method I use. You *need* to have two different loads if you don't change voltage. The easiest way is to use two different props at the same voltage (if the props differ too less then the calculated values could be inaccurate).

and one from Gene Bond
I see what you are doing now. Makes sense. Didn't realize we were on the same page, where you change one variable, and calculate the constants!
Feb 19, 2002, 06:28 PM
Registered User
jberg's Avatar

GWS prop data

Just measured these data for a GWS 5x3 prop:

static thrust produced: F ~ n_prop^2 / 1.63e6 [g]
mechanical power consumed: P ~ n_prop^3 / 92e9 [W]

and the data for the GŁnther 5x4.3 was:

static thrust produced: F ~ n_prop^2 / 0.84e6 [g]
mechanical power consumed: P ~ n_prop^3 / 49e9 [W]

I don't consider this off-topic here although these are no motor data .
Feb 19, 2002, 08:22 PM
in persuit of low wing loading
Gordon Johnson's Avatar
Thanks Jochen,
I'll have to digest this later. I'm off to my workshop. I don't think it's off topic. Maybe I should have titled the thread motor & prop constants.
Feb 21, 2002, 10:00 AM
in persuit of low wing loading
Gordon Johnson's Avatar
Crossup showed me that I was wrong and some of the Mabuchi motors are in the MotoCalc database, but under the gearbox manufacturers, not the Mabuchi section. I'll check Ecalc later. Here they Are. It's a start.

Constant 8880
Current 0.160
Resistance 1.6000
Weight 0.24

KR-1 (HV, LV ??)
Constant 7700
Current 0.100
Resistance 2.0000
Weight 0.20