Bernoulli's principle and the Coanda effect in drone rotors

[mxchapz]

Hi there, I am building a drone for a school project and I am looking at physics behind how it flies. I stumbled upon Bernoulli's principle and the Coanda effect but I am struggling to find out how it can apply to the rotors of a drone. I understand the primary aspect of as the fluid's speed increases, it's pressure decreases but I am struggling to find an exact description for rotors. Any help is appreciated, thanks!

 

[berkeman]

This Insights article by @boneh3ad should get you started. It's about wings in general, but applies to propellers as well.

https://www.physicsforums.com/insights/airplane-wing-work-primer-lift/

 

[cjl]

You need to be a bit careful with your reference frames when talking propellers/rotors, since Bernoulli assumes no energy addition (which is obviously not the case in the frame where the prop is spinning). If you don't care about the details of the flow around the blades themselves, the easiest treatment is to just treat the rotor as a disk that accelerates air by creating a step pressure gradient across the disk. Thrust is then created by the acceleration of the mass through Newton's third law. A decent summary of the math involved can be found here: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html

 

[russ_watters]

Hi there, I am building a drone for a school project and I am looking at physics behind how it flies. I stumbled upon Bernoulli's principle and the Coanda effect but I am struggling to find out how it can apply to the rotors of a drone. I understand the primary aspect of as the fluid's speed increases, it's pressure decreases but I am struggling to find an exact description for rotors. Any help is appreciated, thanks!

You'll need to tell us what information you have about the rotors and what exactly you are trying to calculate. Bernoulli's equation may or may not be needed here.

 

[mxchapz]

You'll need to tell us what information you have about the rotors and what exactly you are trying to calculate. Bernoulli's equation may or may not be needed here.

I apologize if this isn't what it's typically used for but I don't really know anything about it yet. I'm not really looking to use calculations, I'm just researching into how lift is generated by the propellers of a drone.

 

[russ_watters]

I apologize if this isn't what it's typically used for but I don't really know anything about it yet. I'm not really looking to use calculations, I'm just researching into how lift is generated by the propellers of a drone.

If you are just looking for a general understanding of lift, then yes, it can be applied.

 

[russ_watters]

You need to be a bit careful with your reference frames when talking propellers/rotors, since Bernoulli assumes no energy addition (which is obviously not the case in the frame where the prop is spinning).

I don't understand what you are getting at there. For a hovering helicopter, for example, no work is done on the helicopter. The lift force is perpendicular to the rotation plane (though the drag force is not).

If you don't care about the details of the flow around the blades themselves, the easiest treatment is to just treat the rotor as a disk that accelerates air by creating a step pressure gradient across the disk. Thrust is then created by the acceleration of the mass through Newton's third law. A decent summary of the math involved can be found here: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html

I definitely agree that that is a common and useful model for helicopters (and hovercraft). But since it describes what happens to the mass of air because of the interaction with the wing and not the interaction itself, it may not satisfy the OP.

 

[cjl]

I don't understand what you are getting at there. For a hovering helicopter, for example, no work is done on the helicopter. The lift force is perpendicular to the rotation plane (though the drag force is not).

No work is done on the helicopter, but work is done on the air. As a result, even though the downwash is at a higher velocity than the air above the rotor plane, it does not have a lower pressure (even though a naive application of Bernoulli would lead you to believe the opposite).