Calculating head speed

The first question I asked myself is why calculate the head speed when I can simply measure it with a tachometer?

There are few answers, 1) if you are going to buy a new one you’d know what the head speed is with the various Motor and pinions out on the market today. 2) Upgrading an existing heli, I am always calculating head speed when trying to upgrade my Trex 600E to a 8 or 12s setup.

Calculating the head speed will not give you exact head speed but it can get you in the ball park to answer questions like what motor based on KV and amps. What ESC, what Pinion?

Also you are going to find a bunch of head speed “Calculators” online. I use them mostly when I am in a hurry, but I try to use this formula to keep my Algebra skills.

HS = ((motor KV x Battery Voltage)/(Main gear teeth/pinion teeth)) x Efficiency
coefficient

KV of the motor is the RPM it turns per volt. For example a Scorpion HK-4035-560 has a KV of 560 and if you plan to run that on a 10s system (~38volts) the RPM will be 21290 unloaded. However sense electric motors are not 100% efficient we have to take the RPM and multiply it by the Efficiency coefficient. Brushless Motor have an EF of anywhere between 85%-90%.

So if or motor has an EF of 90% we would have a RPM of 19152 unloaded. (unloaded means the motor is not under any load like spinning your main gear).

The battery voltage is the nominal voltage of the pack. Even though a 6s will be around 22.2v when fully charged, it runs at around 37v under load so that’s the number you’ll use for head speed calculations, not the fully charged / discharged voltage.

The teeth on your main gear and pinion is simply the number of teeth on the gears. Most manufacturers publish that info, but if in doubt, count it out.

Here’s an example for my Trex 600E on 6S setup:

Align Stock 600XL with a KV of 1650.
Main Gear teeth 170
Pinion Teeth 10
Motor Efficiency I would say is 89%
Volts from a 6s battery I’ll set to 22.8v

Here's the calculation:

Head Speed = ((1650kv x 22.v)/(170/10) x .89
Head speed = (37620/17) x .89
Head speed = ~1960 RPM

My tachometer reads 2050. But I take the measurement with freshly charged batteries so the voltage will be higher and in turn increase the head speed. My eLogger says I float anywhere from 1962-2100 during a hover. So the formula gives me a good idea of what I need to get to increase or decrease your head speed.

Keep your bird in the air.