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I am designing a quadrocopter style aircraft that uses a 20 inch propeller 1.625 inches in width and has a pitch of 8 inches. How do I calculate static lift / thrust and the dynamic thrust / lift forces when it would be moving in a direction (not diagonal in an upward or downward).

Thank you.

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  • $\begingroup$ Here's a pretty good version of the theory as taught to aeronautical engineering students: aerodynamics4students.com/propulsion/… $\endgroup$
    – Robin Bennett
    May 1, 2020 at 10:45
  • $\begingroup$ Reminds me of "how to count all the cows" : just count the legs and divide by four :-) . $\endgroup$
    – Carl Witthoft
    May 1, 2020 at 12:30

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The usual way to calculate exact thrust is actually experimentally, through testing on a thrust stand. There are countless factors that may influence the performance of your particular motor and propeller combination, some of which are hard to measure and quantify, so the exact number has to be found out just by testing it.

That said, if you only need a rough ballpark, testing your particular combination is not required; you can look up test results for other motors and props of the size you want. 20 inches is very uncommon, so the data may be scarce, though; if you don't find any, doing it yourself is the best bet.

As for dynamic thrust, it is even harder to predict, especially as it depends on the quadcopter's configuration in addition to its attitude and speed; if you want precise enough numbers, you'd probably have to employ either a wind tunnel or a numerical simulation (which is not that unreasonable of a cost for the size of drone you're planning). That said, I'm not entirely sure you actually need it, it's usually sufficient to ensure that the drone's static thrust to weight ratio is high enough (2.5+ is a good number for slow flyers such as camera drones; 4 is good for sporty flying, 8 is good for competitive flying).

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Many common motors will come with a data sheet for a range of voltages and propellers, such as the data sheet at the bottoms of the description for these motors: https://www.quadcopters.co.uk/iflight-xing-e-2207-motor-2-6s

This is the easiest way to check.

Alternatively, you can build or buy yourself a motor test stand (like this: https://banggood.app.link/KZc4Dzop75) and get real-world data about the performance of your motors with whatever propellers you choose.

Once you know the maximum thrust of the motor, you can use trigonometry to resolve the thrust vector into its vertical and horizontal components for any given tilt angle of the drone using this method http://www.mathcentre.ac.uk/resources/uploaded/mc-web-mech1-7-2009.pdf

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  • $\begingroup$ "Most motors will come with a data sheet for a range of voltages and propellers" — In my experience, most BLDC drone motors don't provde these, unfortunately. $\endgroup$
    – ifconfig ♦
    Apr 30, 2020 at 23:33
  • $\begingroup$ Also, I'd recommend describing the trigonometry in your answer. $\endgroup$
    – ifconfig ♦
    Apr 30, 2020 at 23:34
  • $\begingroup$ @ifconfig just updated now, thanks $\endgroup$
    – Drones and Whatnot
    Apr 30, 2020 at 23:34
  • $\begingroup$ @ifconfig that’s a shame, I generally use readily available motors, most of which have come with spec sheets. However, I realise that I mainly use IFlight motors so my experience is biased $\endgroup$
    – Drones and Whatnot
    Apr 30, 2020 at 23:37
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    $\begingroup$ I’m afraid I don’t know any reliable methods - as @ifconfig said it is dependent on different prop geometry. There is also the factor that props tend to flatten out under high RPM so the maths may not be accurate for higher rotational velocities. $\endgroup$
    – Drones and Whatnot
    Apr 30, 2020 at 23:43

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