<p>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. </p>

<p>That said, if you only need a rough ballpark, testing <em>your particular combination</em> 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.</p>

<p>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). </p>

CC BY-SA 4.0
2020-04-30T23:41:24.460Z
2020-04-30T23:41:24.460Z
FlashCactus
<p>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: <a href="https://www.quadcopters.co.uk/iflight-xing-e-2207-motor-2-6s" rel="nofollow noreferrer">https://www.quadcopters.co.uk/iflight-xing-e-2207-motor-2-6s</a></p>

<p>This is the easiest way to check.</p>

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

<p>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 <a href="http://www.mathcentre.ac.uk/resources/uploaded/mc-web-mech1-7-2009.pdf" rel="nofollow noreferrer">http://www.mathcentre.ac.uk/resources/uploaded/mc-web-mech1-7-2009.pdf</a></p>

CC BY-SA 4.0
2020-04-30T23:33:07.033Z
*"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.
ifconfig
CC BY-SA 4.0
2020-04-30T23:34:41.003Z
Also, I'd recommend describing the trigonometry in your answer.
ifconfig
CC BY-SA 4.0
2020-04-30T23:34:58.400Z
@ifconfig just updated now, thanks
Drones and Whatnot
CC BY-SA 4.0
2020-04-30T23:37:13.387Z
@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
Drones and Whatnot
CC BY-SA 4.0
2020-04-30T23:38:14.313Z
Yeah, name brand stuff is different. :) Chinense sellers usually don't give a...
ifconfig
CC BY-SA 4.0
2020-04-30T23:39:06.740Z
Hi, is there any reliable mathematics to calculate the thrust just from calculations?
Gabriel Kusiak
CC BY-SA 4.0
2020-04-30T23:41:00.547Z
It's usually awfully complicated due to the interesting geometries of the propeller. Motor physics isn't too terribly difficult.
ifconfig
CC BY-SA 4.0
2020-04-30T23:43:54.780Z
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.
Drones and Whatnot
CC BY-SA 4.0
2020-04-30T23:31:22.350Z
2020-04-30T23:44:22.183Z
2020-04-30T23:44:22.183Z
Drones and Whatnot
<p>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).</p>

<p>Thank you.</p>

CC BY-SA 4.0
2020-05-01T10:45:08.203Z
Here's a pretty good version of the theory as taught to aeronautical engineering students: http://www.aerodynamics4students.com/propulsion/blade-element-rotor-theory.php
Robin Bennett
CC BY-SA 4.0
2020-05-01T12:30:26.407Z
Reminds me of "how to count all the cows" :  just count the legs and divide by four :-) .
Carl Witthoft
<multirotor><aerodynamics><thrust>
How do I calculate thrust for a quadrocopter?
Gabriel Kusiak
# How do I calculate thrust for a quadrocopter?

(Asked by: username_0 on 2020-04-30)

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.

**Tags:** multirotor, aerodynamics, thrust
> **Comments:**
> **username_1**: Here's a pretty good version of the theory as taught to aeronautical engineering students: http://www.aerodynamics4students.com/propulsion/blade-element-rotor-theory.php  
> **username_2**: Reminds me of "how to count all the cows" :  just count the legs and divide by four :-) .  

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## 2 answers

### Answer by username_3 on 2020-04-30. Score: 4 | Accepted answer

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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### Answer by username_4 on 2020-04-30. Score: 2

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>

> **Comments:**
> **username_5**: *"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.  
> **username_5**: Also, I'd recommend describing the trigonometry in your answer.  
> **username_4**: @ifconfig just updated now, thanks  
> **username_4**: @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  
> **username_5**: Yeah, name brand stuff is different. :) Chinense sellers usually don't give a...  
> **username_0**: Hi, is there any reliable mathematics to calculate the thrust just from calculations?  
> **username_5**: It's usually awfully complicated due to the interesting geometries of the propeller. Motor physics isn't too terribly difficult.  
> **username_4**: 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.  

---

