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I've noticed that higher voltage batteries need lower KV motors, why is this?

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They don't necessarily, however a given amount of power will be required to rotate a motor at a certain RPM with a given propeller.

kV, the voltage constant of a motor, is the maximum RPM it can turn at per volt of power supplied. Example:

A 4S (15V to make math easy) battery will turn a 2000kV motor at 30,000RPM (with no load, inefficiencies, etc) a 6S (20V) battery will need a 1500kV motor to achieve the same RPM

In theory, the result is the same amount of power (watts) required to achieve the same RPM/power output/etc. A 4S 2000kV motor will draw say 20 amps, or 300 watts. To get the same power output, a 6S 1500kV motor will draw 15 amps (still 300 watts), and spin at the same RPM. Higher voltage but lower current generally results in less heat, because of ohm's law. Current creates energy loss over resistances (ESC components have internal (small) resistance, which is why they heat up, which is why they have a current rating in the first place).

A lot of Bardwell's videos go into the details of 4S vs 6S, but they work out to be pretty much the same. The reason larger models go with higher voltages (and lower kV to achieve the desired RPM) is because they are much higher wattage, and achieving that higher wattage strictly with higher current is unrealistic (Large scale planes would be drawing 500-600 amps at 3-4S voltages, dangerous and expensive).

To reference an earlier comment, the voltage "rating" of the motor is just the suggested voltage. The actual rating of the enamel coated wires would be much higher, but you will destroy components from drawing too much power under load if you went up to those voltages.

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The primary answer has to do with the fact that the torque constant (Kt) is proportional to the velocity constant (Kv) of the motor. That means the amount of power it costs to generate torque increase as Kv increases. A low torque constant means that less power is used to create torque, and a high torque constant means more power is used. For more information on the torque constants and how they relate, check out this article over at MathWorks.

To break this down, it means that as the Kv increases the RPMs the motor is trying to reach increases per volt of applied electricity. But that also means that the power required to reach those RPMs is proportionally greater as voltage increases assuming a constant Kv. Effectively a motor of higher Kv will burn itself out trying to reach those RPMs very quickly. If it doesn't burn it will likely put significant strain on the rest of your electrical system as the current draw increases, both the battery and the speed controllers.

That being said, if you effectively limit the maximum RPMs of the motor, there is not a major loss for running higher Kv motors, as it effectively limits the maximum current draw which is what presents the problem. You can read a further discussion of the details in this answer, and in this article on miniquadtestbench.

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It's not that high voltage batteries need to be paired up with low kV motors. There's nothing inherently wrong with this configuration, it'll just result in the motor's shaft spinning an ungodly rate.

This is because the rotation rate is (theoretically, and only when no load is applied to the motor shaft) equal to kV * voltage .

However, it usually makes sense to make this pairing because many systems, like a motor-propeller system, function most efficiently within a range of RPMs which doesn't allow for insane rotation rates.

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