I am trying to figure out the required voltage to send to a motor to stall it at a certain current. Seems simple enough, but I have conflicting data.

My mathematics reasoning is below:

Note: VEX Robotics motor curves were made at 12 V. The four key characteristics (free speed / current, stall torque / current) approximately scale proportionally with system voltage. If Motor A was running at 6 V, its stall current would drop from 130 A to 65 A, and its stall torque would drop from 0.7 N Âˇ m to 0.35 N Âˇ m.

This implies that if I scale specs proportionally with voltage, I should get a âclose enoughâ approximation for how the motor will perform at said voltage.

These are the specs I pulled from the Falcon 500 page of motors.vex.com. I determined internal resistance by taking 12V / Stall Current (257 amps). kV is determined by Free Speed (6380 rpm) / 12V. kT is determined by Stall Torque (4.69 N-m) / (Stall Current (257 amps) - Free Current (1.5 amps)).

So if I wanted to figure out the motor specs at 4V, for example, I could take the 4 main specs (free speed, stall torque, stall current, and free current) at 12V and divide them by 3 (12/4 = 3) and get the right specifications.

For the Falcon 500, this gives me the following specs:

- Free Speed: 2126.67 rpm
- Stall Torque: 1.56 N-m
- Stall Current: 85.67 Amps
- Free Current: 0.5 Amps

Now this is fine and dandy, except motors.vex.com shows that their dyno testing provides the following specs for a Falcon 500 at 4V:

- Free Speed: 2110 rpm (very close to the 2126.67 rpm estimate)
- Stall Torque: 2.15 N-m (Almost 38% higher than the 1.56 N-m estimate)
- Stall Current: 39 Amps (Only ~45% of the 85.67 Amp estimate)
- Free Current: 0.6 Amps (Very close to the 0.5 Amps estimate)

Free Speed and Free Current seem pretty much correct, but the difference in Stall Torque and Stall Current are enough to give me a bit of confusion. I asked around to some good friends and was told to use the motor torque constant kT, as that would be a better reflection of how the motor will perform at a given voltage.

I determined kT for the Falcon 500 at 12V by taking the Stall Torque and dividing it by the quantity of Stall Current minus Free Current , which gave me a kT value of ~0.01836. Based on my understanding, for a motor at stall at a given voltage, the output torque of the motor is equal to Voltage * kT / R, where R is the internal resistance of the motor. If I plug in 4V for the voltage and use my kT of 0.01836 and my internal resistance of ~0.047 Ohm, I get and output torque of ~1.56 N-m, which is the same as the estimate from dividing by 3.

My findings lead me to wonder why the VEX test had the stall torque so much higher and the stall current so much lower than the mathematical estimates. I trust VEXâs test results are correct, but they also donât cover the full range of values that I need, so I need to find a way to formulaically represent the motor specs at given voltages (and vice versa). Normally I would use the mathematical estimates, but these donât seem to be matching up with VEXâs test results, so I look at one of two options:

- I create a best fit line using the test results for each motor spec at 4V, 6V, 8V, 10V, and 12V and determine my approximate performance from a given voltage based on what follows the trend.
- I use the mathematical models and assume that they are a safer representation of performance at data points that were not tested by VEX.

Which should I use?