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I'm designing a quadcopter weighing around 250 grams, while maintaining a thrust-to-weight ratio of 2:1

Optimize: Maximize the thrust-per-watt for the motor+propeller pair

Constraints:

  • weight of each motor + propeller pair: ≤ 30 grams
  • thrust of each motor: ≥ 125 grams

Everything else (frame size, drone shape, battery, motor, propeller, number of blades in propeller) is flexible and can be changed as needed.

In order to maximize the flight time, I will require a motor + propeller combination that is efficient in terms of thrust/power.

How does one go about optimizing the motor+propeller design?

Current Approach:

Look at datasheets provided by manufacturers and check if the given motor matches my constraints.

For example, the EMAX MT2204 motor weighs 25 grams and provides a thrust of 240 g using 51.2 W power using a 6x3 propeller. That puts its thrust/power at 4.7 g/W

Issues:

  • The propeller chosen by the manufacturer might be suboptimal (since they often try to choose a propeller that maximizes thrust rather than the one that maximizes thrust/watt)
  • The manufacturer might not report performance data at around 125 grams of thrust
  • Manufacturers usually reports the spec sheets for FPV racing communities, and maximizing the flight time isn't a major concern for them

Is there a way to mathematically model or simulate the design of motor+propeller in order to maximize the efficiency?

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The most efficient propeller is infinitely large. However, that would give you a zero top speed, like this human powered helicopter:

To fully optimise this, you need a target top speed, and to know how much drag you'll need to overcome at that speed.

I don't have a complete equation for you, but here are the facts you need.

You can calculate the pitch speed of a prop from its pitch and rpm. You can approximate the air flow as a cylinder of air being accelerated from a standstill to the pitch speed.

Thrust is a change in momentum, so it's the mass of air flowing through the prop disk per second, times the pitch speed.

Power used is the 1/2 the mass-per-second times the speed squared.

As the drone speed increases, the air is no longer starting from stationary, so it's not accelerated as much, and you get less thrust. If you fly at pitch speed, you get zero thrust.

A drone will fly at an angle, with the vertical component of its thrust balancing it's weight and the horizontal component balancing its drag.

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  • $\begingroup$ Thank you. The thrust = change in momemtum makes sense. However, the power calculated via this method is the output power of the motor+propeller combo. How do I convert it into the "input" power that the motor will consume in terms of watts? Any motor will have a max thrust/rpm that it can generate. That is what will determine the motor+propeller combination in the end. How does one model that? $\endgroup$
    – Pragy Agarwal
    Nov 8, 2022 at 22:19
  • $\begingroup$ I've seen similar calculation about the propeller pitch, rpm and output power across a lot of forums. Sadly, none of them take into account the motor part of the equation. That is where I'm completely stuck. $\endgroup$
    – Pragy Agarwal
    Nov 8, 2022 at 22:20
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    $\begingroup$ A brushless motor is something like 85 to 90% efficient when it's not bogged down. To get an exact figure you'd have to bench test a particular motor with a range of props and voltages. There's a good article here: tytorobotics.com/blogs/articles/… Prop performance is similarly complex, but there are a number of sites (like e-calc) that have measured how much thrust you get at a range of RPM $\endgroup$
    – Robin Bennett
    Nov 9, 2022 at 8:37

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