Motor Selection for Multi-Copters

Essential to overcoming gravity is the ability to generate thrust. Hovering requires the copter to generate slightly more than its own weight in thrust. For example, a 1000 gram copter must generate at least 1000 grams of thrust, preferably more in order to apply directional movement while hovering. Maneuvering swiftly and with good control will require more thrust, but not too much; a copter with too much thrust will be difficult to keep in a hover, which should be around 50% throttle (1/2 max thrust).

I’ve found the following formula useful for calculating the total amount of thrust needed for a quadcopter of a given weight:

Thrust Required = (Total Copter Weight) x 2.2

A copter weighing 1000 grams (2.2 US pounds) should generate around 2200 grams (4.85 US pounds) of thrust in order to perform well. The process of figuring the system weight is a bit circuitous: the weight of the motors factor into the overall weight, and motors determine how much thrust is produced. Motors capable of producing lots of thrust are relatively heavy.

Here are the calculations I made for a quadcopter that I built recently. I used the Turnigy Multistar 2213–980Kv 14Pole Multi-Rotor Outrunner motor. The motors weigh 58 grams each, for a total motor weight of 232 grams. I’ll allow 750 grams (1.6 US pounds) for the remaining components, including battery, RC receiver, flight controller, FPV camera and transmitter, ESCs, and the airframe.

How much thrust do these motors generate, and will it be enough?

The motors have a KV (RPM/Volt) value of 980. When using 3s batteries that operate around 11.1 volts I’ll get a maximum RPM value of 10,878 (980 x 11.1). This number matters because it determines how fast we can spin the propellers.

Aside from motors, another important component of generating thrust is the propeller. Longer propellers generate more thrust per rotation, but require more power per rotation than would be true for a smaller propeller. Smaller propellers must complete more revolutions to generate an equivalent amount of thrust produced by a larger propeller. Select a propeller that won’t exceed the power limits of the motor, yet still generates enough thrust to support your flight configuration. The following table illustrates the estimated thrust produced with a single motor with varying propeller sizes (calculated using http://personal.osi.hu/fuzesisz/strc_eng/):

The motor I selected has a maximum power of 165 watts, meaning that the largest propeller I can use with this motor is an 8-inch prop (118 watts required < 165 watts max). Using a larger propeller (e.g. 9-inch, 10-inch props) would likely overwhelm the motor and cause it to overheat (i.e. break) if forced to operate at full throttle for an extended period. An 8-inch propeller will yield 2,360 grams of total thrust, which is slightly more than the desired 2,200 grams of thrust needed to operate a 1000 gram copter. I think we’re set!

I measured the total weight of the copter with a 2200 mAH battery and it was extremely close to the estimate: 990 grams!

Perhaps most importantly, the copter flies beautifully. It is very easy to maneuver and has good flight times (~12 minutes on a 2200 mAH battery).

So, TL;DR version of the steps is:
1) Estimate the total weight of the copter and any payload (cameras, etc)
2) Calculate the thrust needed by multiplying the total weight by 2.2
3) Determine which battery you’ll be using to figure the motor voltage (e.g. 3s operates at 11.1 V)
4) Try different motor KV values (e.g. 980) with the motor voltage to figure the max RPM
5) Enter the max RPM with various propeller lengths (8,9, 10) and pitch (4.5) into a thrust calculator to determine the thrust generated.
6) Choose the motor & propeller configuration that generates the thrust value closest to the amount needed