Propulsion

Propulsion

Motor Dimensions & Sizing

Thrust & Performance

Electric Motor Performance

A motor (DC or phased) has a specific ratio which relates the Revolutions Per Minute (RPM), when it is under no load, to the voltage applied to the motors itself. This ratio is practically a linear relationship, meaning that the more voltage is applied, assuming that the motor can handle it, the faster it spins. When a motor is designed, a factory measurement is taken to record the motors performance, and is typically expressed as a velocity constant, Kv (not to be confused with kV, as in kilo-Volts).

With this value, the no-load RPM of a motor can be determined:

RPM = Kv x V

When a load is attached (the propeller), we assume that the power supply is capable of providing the current that is required to drive the load, and that the motor can provide enough torque to turn the load. For the purposes of selecting a motor for fixed-wing or multirotor applications, a recommended propeller that will give the best performance is usually specified.

Thrust Calculations

The aerodynamics of a propeller can be quite complicated, but a few assumptions can be made to allow us to take a ballpark estimate.

Firstly, it must be understood that the thrust generated from a spinning propeller is inversely proportional to the relative speed of the airflow. As an example, the faster a plane is flying through the air, the difference in airspeed between the front and the back of the propeller begins to lower, and less thrust is generated. This creates a practical limit to how fast a propeller aircraft can actually fly. For slower, less than 20m/s, applications of mid-sized aircraft, this can mostly be ignored. For small-sized multirotors, this limit can become an issue in dramatic flight, however for stable hovering, we can usually ignore it.

Secondly, things like following can cause major issues: crosswind, which changes the direction of the airflow around the propeller, ground effect, which causes an extra cushion of air and "increases" thrust, and turbulence, which causes the thrust generated to vary and can even cause the motor to stop generating thrust completely in rare cases.

With all this established; for a relatively slow flight in clean air with no objects too close to the exhaust, the thrust output of a propeller is nearly directly proportional to the RPM of the propeller.

While testing should be conducted to get real-world values, as a propellers shape and design can have widely varying effects on the thrust profile, a fair amount of resources are available online to aid us in calculating a thrust estimate. If you know the type of propeller you are using, and the RPM your motor is capable of, you may be able to use a tool like the FlyBrushless Thrust Calculator to get a good estimate.

Another tool that may be useful for performing thrust and power calculations is eCalc.

Maximum Take-Off Weight (MTOW)

Fixed-Wing Aircraft

Multirotor Aircraft

A good rule-of-thumb to get the most out of the system when designing a multirotor aircraft is to specify your maximum load, then perform your motor design such that at 50% throttle (1/2 your maximum RPM), the system will output just enough thrust to hover. This design choice provides you with a good amount of fidelity for manoeuvring, while not putting too much load on your motors and ESCs during normal operation.

To get the specifications for the motors required, first decide on the mass. Next, you must decide on two things simultaneously: the frame design (+4, X4, X6, X8, etc, refer to the QUTAS airframe page), to get the number of motors you will use, and the actual motors you could use to generate enough lift to match the required lift value (m2). The Kv rating of the motors, with their recommended propeller, should be a good starting point for the lift estimate, as you can fine tune your performance later by using different propellers.

From here, you must then perform some form of comparison or trade-off to pick out your motor. Remember, you are aiming to achieve hover at 50% throttle. Take the following example:

Battery: 3S LiPo (~11.7V average over flight from discharge profile) 

Airframe: X4 (quadcopter)
Weight: 1.5kg

Motor/Propeller:
  Kv: 960
  Max RPM: 11232
  Prop: GWS RS 8x4.5 (typical multirotor propeller) 
  Thrust: ~750g (from FlyBrushless Thrust Calculator)

Max Thrust: 2.6kg (for 4 motors)
50% Thrust: 1.3kg
Hover Throttle: ~57% (Weight / Max Thrust)

This shows us that we could expect this combination to hover at ~57%, which is probably still quite acceptable. We didn't quite hit the 50% throttle mark, but at least we know that it won't be too far off. If we were really unhappy with these results, we might go for slightly larger motors, or if we would like to improve efficiency, we could look at using larger props to get a bit more thrust out (but manoeuvrability and performance would start slightly).