# POWER, TORQUE & RPM

### FOUNDATION

Firstly, let's set some things in stone to clear any confusion;

• Work is the amount of applied force over a distance or time, measured in joules or J.
• Torque is the potential capacity to complete work, measured in Newton-meters or Nm.
• Power is how rapidly work is completed, measured in kilowatts or kW.
• RPM is the revolutions per minute of an object.

The relationship between these is equated to a simple mathematical formula, where power is equal to torque multiplied by RPM, or where power is equal to amperes (A) multiplied by voltage (V). These are interchangeable, since torque is a product of amperes and RPM is a product of voltage in electric motors. This means that to increase the overall power output a motor needs to produce more torque, spin at a higher RPM or both. As such, the relationship between power, torque and RPM under normal conditions can be seen here: As illustrated, it is only at full RPM where all of the power is produced, whereas torque remains a constant. For motors, this is Kt.

### MOTOR POWER

The first common mistake, is seeing a rated power output for motors and assuming that's the end of the story. It is rampant throughout the electric skateboard world, where motor ratings are all that are mentioned. What's most important, is the system. This means that from the battery > ESC > motors, power ratings are the same. The foundation for power output is going to be the battery, using the simple equation of amperes multiplied by volts. An ESC is then able to manage input power from the battery, and distribute to the motor/s. In this fashion, an ESC can provide more current to the motors than received from the battery, but it will never increase the total power. This method only allows for greater torque until an RPM threshold is reached and the current (A) can no longer be supplied by the battery in combination with the required voltage (V).

What's all this nonsense mean? Basically, the capacity to do work decreases as RPM increases, so the power never increases past the threshold of difference. As an example, if a battery can produce 1kW and a motor can produce 2kW, the torque will begin to decrease at 50% of maximum RPM: As you can see here, system balancing is important and the motor power means nothing without battery power. The only gain of this example is that startup torque will be greater than a 1kW motor.

### RPM

The next common mistake is the understanding of motor RPM (Kv). A relationship exists between RPM, torque and efficiency for brushless DC motors known as Kv (velocity constant), Kt (torque constant) and Km (motor constant). The former you may already know, the latter is a version of motor efficiency which relates to heat production.

Kv is essentially the RPM/volt, and is figured by the back EMF generated by a motor when it spins. A 1000Kv motor spun at 1000RPM will generate 1V. This is determined by the number and thickness of copper turns around a stator tooth.

Kt is the torque/amp, which is also relative to the copper windings around a stator tooth.

Km is simply the sum of applicable torque efficiency, the potential torque minus the losses.

The difference between low Kv and high Kv motors is important to recognise, and it specifically applies to the efficiency and power of our boards. A low Kv motor has thinner copper windings in a greater quantity, while a high Kv motor has thicker copper windings in a lesser quantity. If we compare identical motors, the practical torque of both motors is actually the same: Things in Motion 2019

Technically, the lower Kv will have more theoretical  torque/amp, but resistive losses are higher and so the torque will remain equal between both motors. In a nutshell, the lower Kv runs at lower amps, and higher voltage. This is how ﻿Km﻿ applies.

So why all the fuss?

Well, it comes down to RPM and the final power output. If both motors are placed on the same voltage, naturally the higher Kv motor will spin to a higher RPM and handle more amps, in turn producing more power than the lower Kv twin. Remember, power is the rate at which work can be completed. More power at equal torque means getting the job done quicker, or in our case the ability to maintain higher speed and potentially accelerate quicker.

For instance, a high Kv motor on a higher reduction will produce more power, which translates to much more wheel torque after the gear reduction than a low Kv motor geared for the same speed. This means the wheel will see more torque when both conditions have the same wheel RPM, an easy way to increase acceleration ability. This is, for the most part, why reduction drives are used at all.

Changing voltages across motor Kv is an entirely different topic which we will discuss at a later date, but the principles are mostly universal. Voltage differences are mainly aimed at system efficiency, with little regard to motor performance itself.

### RECOMMENDATION

Most quality outrunners will support up to 10,000 RPM, for this our recommendation at common voltages is as follows:

• 12s 190Kv @ 9,576 RPM
• 16s 150kv @ 10,080 RPM
• 18s 130Kv @ 9,828 RPM

Inrunners support higher RPM due to design, and as such produce much more power in a similar size factor but gearing remains an issue.

### KEY TAKEAWAYS:

• An unbalanced system will not produce the power of the motor rating.

• High RPM and greater reduction is the key the most powerful motor output.

• Low Kv offers no advantage unless voltage is equated.
Disclaimer: this is subjective, simplified information and is open to error.﻿