Recently, I have been involved with the electric skateboard community because of my custom ESC. I get many questions about motor kv, gear ratio, current, voltage and efficiency. In this post, I will try to explain how things are connected and how to chose the right setup. I will try to keep things simple and not involve too many equations to provide a good intuition for the DIY community. The assumption in this post is that we are using an 50mm-60mm hobby outrunner motor.
First of all, I will try to make some things clear about the KV rating of these motors. Even if there are several versions of the same motor available with different KV, the properties of the motor are exactly the same but at different voltages/currents. The only difference the KV makes is how to choose an ESC and a battery pack, but I will explain more about that in the ESC section. For the same motor, the low KV versions have more windings with thinner wire, while the high KV versions have less windings with thicker wire. As long as they have the same mass of copper, they are exactly the same in regard to max power output, torque, efficiency, max RPM; but at different currents/voltages. If they don’t have the same mass of copper they are different, but it is always true that the more copper is squeezed into the stator, the better the motor is.
Let’s look at an example: Suppose an 8 turn motor has one ohm winding resistance. The winding resistance is proportional to the wire area times wire length. Making the same motor with 4 turns would allow twice as thick wire. Since that wire also is half as long, the resistance is four times lower: 0.25ohm. Further, since current times turns is proportional to torque, we need twice as high current with 4 turns to produce the same torque as with 8 turns. The copper losses are the voltage across the windings times the current: U*I. The voltage across them is R*I, so the losses are R*I*I. This square relation means that doubling the current will produce four times as much losses, however, since we got four times lower resistance the losses are the same for the 4t motor with double the current as for the 8t motor with half the current. Also note that the 4t motor will spin twice as fast as the 8t motor at the same voltage, so it will have double the kv. Putting this together, the 4t motor is equivalent to the 8t motor, but at half the voltage and double the current.
So, regarding KV: different KV versions of the same motor are fully equivalent. KV only affects the battery and ESC choice. Therefore, while comparing motors, lets talk about torque instead of current because torque is proportional to current / KV and, as explained above, the KV value can be changed freely with the amount of turns and copper thickness.
Now we know that copper losses are proportional to the square of the torque produced by the motor, and at low RPM and high load they are dominant. As RPM increases, other losses start to add up exponentially. In my experience, these losses start to get significant around 60k electrical RPM, which for a 14-pole motor is about 8570 mechanical rpm (most 50mm+ outrunners have 14 poles, some unusual ones have 18). Because of the square relation, it is desirable to run at as high speed and low torque as possible as long as we stay below 8.6k RPM. To express the square relation in some numbers, having double the RPM and half the torque at a certain power output will cause four times less losses. The lesson from this is that: make sure the top speed you design the skateboard for is at around 8.6k rpm on the motor if you are using an 50mm-60mm outrunner.
For my longboard with 84mm wheels, where I would like to design for a top speed of about 35km/h with a sing motor, I would need a gear ratio of about: (35 / (0.084 * pi * (8600 / 60) * 3.6) = 0.257 which is 1:(1/0.257) = 1:3.9. Note that this gear ratio is independent of battery voltage and motor kv. Keep in mind that 8.6k rpm is not an exact number, but a guideline that seems to apply quite well to all 50mm-60mm hobby outrunners I have tested so far.
As noted previously, we are designing for 8.6k rpm since we are using 14 pole motors and 60k electrical rpm seems to be a good value according to my experiments.
The resistive losses in the MOSFETs in an ESC are proportional to the square of the current, because the voltage across the MOSFETs is Ron*I and the power, which is U*I, in this case is Ron*I*I where Ron is the ON-resistance of the FETs. This means that for a given FET, doubling the current will produce four times the losses. Remember that current is directly proportional to motor torque. From the ESC perspective, we should run on as high voltage and low current as possible. Now, one interesting fact about MOSFETs is that the lower voltage they are designed for, the lower resistance they tend to have. So if I make an ESC for a lower voltage, the FETs will also have lower resistance. However, the PCB traces always have the same resistance and MOSFET resistance does not seem to decrease as fast as their voltage decreases, meaning that an ESC designed for higher voltage tends to be more efficient in general. When the voltage gets too high, handling it while switching fast starts to become problematic. I have discovered that a good trade-off is at around 60V (quite safe for 10s or 12s lipos), where the efficiency is good and the voltage is not too problematic to handle.
Going back to my longboard example with 84mm wheels and a top speed of 35 km/h at 8.6k RPM with a 1:3.9 gear reduction, let’s look at a good motor KV. At 12s, which seems good from the ESC perspective, and a moderate charge level, we have 3.8 * 12 = 45.6 volts. Since we want to run the motor at 8.6k RPM, we need a KV of 8600 / 45.6 = 188. Now, that is quite low. Since there are none or few 50mm outrunners with that KV available, we can do two things:
1. Run at 10s. Then we need a KV of 8600 / (10 * 3.8) = 226. Luckily, there happen to be 225 KV motors available on hobbyking
2. Change the KV of the motor. Yes, this can be done quite easily without rewinding the motor. Almost all outrunners are connected using a delta-connection. By removing the heatshrink of the motor wires, they can be split up and reconnected in a star-connection. This reduces the KV by a factor of sqrt(3) = 1.73. For this modification, we can use a motor with a KV of 188 * sqrt(3) = 325. There are several hobby motors available close to that KV, so that is no problem. I have tested this modification on several motors and it works really well.