This is a section with various bits of math which are useful for calculating various parameters of helicopters.
There are three steps to calculating the headspeed:
Calculate the motor rpm
Check the motor's maximum rated RPM.
Calculate the gear ratio
In order to calculate the motor RPM, you need to know two things: the motor Kv constant, and the battery voltage.
The Kv constant is the no-load RPM/V, or basically the RPM of the motor at a given voltage with no load. If you multiply this value by the voltage, then the result is the motor speed at the voltage with no load.
As the helicopter takes off, the load on the motor will increase, so the motor RPM will drop by about 15%. So this unloaded RPM should be multiplied by about 0.85 to calculate the loaded motor RPM.
For example, a Hacker B50-18S has a Kv of 2006, so the no-load motor speed on 8 cells (9.6 volts) is: 2006 * 9.6 = 19257.6 RPM. Under load the motor RPM will drop to about 19257.6 * 0.85 = 16369 RPM.
The second step is to check the motor's maximum rated RPM. For the Hackers this is about 60,000 rpm, so 19257.6 RPM is well below the motor's maximum rated RPM.
The third step is to calculate the gear ratio. The ECO 8 has a 180 tooth main gear and if the motor pinion is 18 tooth, then the gear ratio will be 180:18 or 10:1.
The final headspeed will be the motor RPM multiplied by this gear ratio, multiplied by about 0.85 to simulate the loading effect of the main rotor blades.
So: 2006 (motor Kv) * 9.6 (battery voltage) * 0.85 = 16369 RPM motor speed
16369 * 180 (main gear teeth) / 18 (motor pinion) = 1636.9 RPM head speed