What value resistor to add, so my motor provides the correct amount of power?

Question

Motor Specs & Circuit Diagram

I'm an Aero student with virtually no electronics knowledge. I'm trying to figure out what value resistor to add to this circuit, so my motor provides the correct amount of power.

The motor is usually part of a small quadcopter drone. The battery used is 3.7 V, 650 mAh. When this battery was powering the whole drone (lights, 4 motors etc) the meter readings from a single motor at full power were 3.203 V and 1.88 A.

I have now separated one motor in order to build the simple circuit (pictured) just to measure RPM. (This is a very small part of my project. I am aware of more sophisticated methods to vary motor output, but I am using a variable resistor as the results only need to be rough). This circuit will use the same battery as before.

I would like to add a resistor to this circuit, so that when the variable resistor is turned to zero, the motor cannot output any more power than it was before. Then, when the variable resistor is increased, it eventually stops the motor.

My question is: What values of resistance do this normal and variable resistor have to be?

Answer 1

The motor controller in your drone doesn't use resistance to control motor RPM. Instead, it uses a PWM chop to vary the duty cycle and thus the delivered power. Duty cycle has roughly a linear relationship to power delivered to the load, which will have some not-linear relationship to RPM.

An inexpensive bench supply with variable voltage and current is a way to model delivered power. In this way you can directly characterize motor input power vs. RPM, a somewhat useful figure.

You have two ways to do this.

• Vary the voltage, observe the current and RPM
• Vary the current, observe the voltage and RPM

Either one will give you W vs. RPM.

Answer 2

Rough calculation of resistor:

Equivalent impedance of the motor at full power from your test = 3.2V/1.88A = 1.7 ohms.

Guessing that you will need 10X this to stop the motor. 1.7 * 10 = 17 ohms. Next standard value is 25 ohms.

Next calculate the worst case power dissipated in the variable resistor. This will occur when the voltage drop across the motor and resistor are equal.

3.2V / 2 = 1.6 V.

Power = V^2/R = 1.6^2 / 1.7 = 1.5 W

Since the power won't be distributed evenly, I would add considerable margin, use a 5W.

It is unlikely that you will have something appropriate on-hand. But, if you happen to have something close to a 25 ohm, 5W variable resistor, give it a try.

A variable power supply is the right way to perform this test. When neither the voltage or the current to the motor are constant, taking measurements will be a pain.