### Tricopter physics help

Hello!

I have been studying how exactly a tricopter works and I came across a problem that is not quite clear to me...

I understand that the tail rotor has to be slightly tilted for a specific angle alpha in order for the horizontal component Fx to counteract the unbalanced torques of the 3 propellers. However this Fx component of force F now causes that the sum of all forces is not zero - therefore the tricopter will constantly try to drift in the direction of Fx when trying to hoover!?
(see the attached sketch)

Am I missing something here or is my conclusion correct?
How is this problem handled? Do you constantly have to correct for this drift by rolling or is this effect negligible?

Thank you for any input! =)

#### Replies

• unfortunately I can't help

• oh i see. Well that definitely seems like an uphill task. Could you provide me whatever links that you used in order to get any sort of insight into this? I would be very glad if i could get some sort of starting point to go about my research!
Primoz K said:

Vidur said:

Hi. I was hoping you still check this site or whatever but you would greatly help me if you could tell me about the sources of your knowledge and where you got to know such detailed info along with the diagrams and stuff? i desperately need them and wherever i look, its wayyy to complex for my understanding. Its imperative that i manage to find the completer working of the tricopter-equations,torque balancing and all. Thanks! :D

Hi Vidur! I was notified per email of your reply, however, I am afraid I don't have any specific sources I could recommend because I derived the equations above myself.

I started by researching the tricopters frame geometry and kinematics, then I found a suitable (simplified) relationship between propellers angular velocity and its thrust & torque. After that you just need to set the balance of forces and torques in all three directions (x,y & z) and use algebra to get to the solution you seek.

Note that my deriavation is far from complete since it is limited to a steady-state solution (tricopter hovering still). I only used it to clear up some confusion I had about the hovering state of a tricopter. If you wanted to derive a complete dynamic model for a tricopter you would also need to include acceleration terms, as well take air drag into account. Note that at higher velocities, incoming airflow could also significantly affect the thrust on the rotor, which you would somehow have to take into account and when flying at low altitutudes ground effect might also play a role.

As you probably see, there are many physical phenomenon that affect tricopter's flight, which is probably the reason most derivations of dynamics equations become so complex. You first need to consider what is actually the goal you are trying to achieve with your model (equations) and then evaluate which physical effects you will have to include and which you could neglect.

Tricopter physics help
Hello!I have been studying how exactly a tricopter works and I came across a problem that is not quite clear to me...I understand that the tail rotor…
• Vidur said:

Hi. I was hoping you still check this site or whatever but you would greatly help me if you could tell me about the sources of your knowledge and where you got to know such detailed info along with the diagrams and stuff? i desperately need them and wherever i look, its wayyy to complex for my understanding. Its imperative that i manage to find the completer working of the tricopter-equations,torque balancing and all. Thanks! :D

Hi Vidur! I was notified per email of your reply, however, I am afraid I don't have any specific sources I could recommend because I derived the equations above myself.

I started by researching the tricopters frame geometry and kinematics, then I found a suitable (simplified) relationship between propellers angular velocity and its thrust & torque. After that you just need to set the balance of forces and torques in all three directions (x,y & z) and use algebra to get to the solution you seek.

Note that my deriavation is far from complete since it is limited to a steady-state solution (tricopter hovering still). I only used it to clear up some confusion I had about the hovering state of a tricopter. If you wanted to derive a complete dynamic model for a tricopter you would also need to include acceleration terms, as well take air drag into account. Note that at higher velocities, incoming airflow could also significantly affect the thrust on the rotor, which you would somehow have to take into account and when flying at low altitutudes ground effect might also play a role.

As you probably see, there are many physical phenomenon that affect tricopter's flight, which is probably the reason most derivations of dynamics equations become so complex. You first need to consider what is actually the goal you are trying to achieve with your model (equations) and then evaluate which physical effects you will have to include and which you could neglect.

Tricopter physics help
Hello!I have been studying how exactly a tricopter works and I came across a problem that is not quite clear to me...I understand that the tail rotor…
• Hi. I was hoping you still check this site or whatever but you would greatly help me if you could tell me about the sources of your knowledge and where you got to know such detailed info along with the diagrams and stuff? i desperately need them and wherever i look, its wayyy to complex for my understanding. Its imperative that i manage to find the completer working of the tricopter-equations,torque balancing and all. Thanks! :D

• Thank you for all the responses! =)

@Johnatan Hair

Somehow I forgot that the helicopter has a very similar situation going on with the tail rotor! Thank you for reminding me on that! =)

@WuStangDan
I would be very grateful if you could do that and explain the problem from your perspective. I draw a figure by hand as you asked - I hope it is clear enough. I chose the tricopter where the front two rotors rotate in opposite directions, so that the unbalanced torque and therefore angle alpha can be smaller.

In addition I added two pages of my calculations. On first page there are the three conditions for balancing torques and on the second page I wrote the sums of forces. Clearly the force Fx remains in the end.

Thank you!

• Okay perfect.

So yes your calculations are correct. If a tricopter was flying exactly like you have drawn, where the servo motor is at the exact angle $\alpha$ to balance out the the moment in the z axis, the triopter would have a single force in the x axis.

The reason why I wanted you to do the full calculations is make sure that you understood that you haven't actually missed something in your calculations. Becuase the real answer to your question is somewhat of a let down, I didn't want you to go back to your calculations because you didn't believe me.

So tricopters don't "drift" in the x direction when flying in real life. So that means there is something missing from your drawing. You have propellers, motors that can rotate the propellers, and most of the standard parts of a multirotor. But you don't have a negative feedback controller that all multirotors have. Now the IMU in a multirotor cannot detect when it is "drifting" at a constant velocity. So if you had your multirotor sitting in the trunk of your car while you drove down the highway, the gyros would report the same values as if they were flat on the ground. But a constant force on a body does not move it at a constant velocity. Newtons second law states that the tricopter would begin accelerating in the x direction, not just slowly "drift" like I'm assuming you thought it would based on the wording you used in your question. IMU's can detect acceleration so therefore the negative feed back controller would detect it, and change the speed between the two front motors to balance that acceleration.

This will make the tricopter no longer perfectly flat, but rather at a slight angle, making it so that F1 and F2 now both have x components.

• The OP was close, and it's great you made sure he found the answer himself. If my teacher explained everything as professionally as you did, I could become an engineer. Now I'm interested in writing at https://sunnypapers.com/paper-samples/professionalism/ where I publish my research papers on various topics. So I have the opportunity to help students with their homework and answer the work that has become a chore.
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• First of all thank you very much for the detailed answer!

Reading your explanation confirmed my own thinking when I was doing the calculations above:
"Tricopter cannot hoover still when oriented horizontally. It has to be slightly tilted around y axis to counteract the F3x force"

Maybe "drifting" was a poorly chosen word - I understand that the tricopter would accelerate in direction of F3x until in equillibrium with air drag.

Thanks - now I really understand how a tricopter works. =)

• Conventional helicopters have this same problem too as a result of the tail rotor, and often hover at a very slight roll angle.

I had not considered the tri copter in this same way before, but at first glance, I believe you are right.

• I can help you out. But first I want you to draw a full tricopter diagram so that way I can better explain it to you by referencing your own figure.

So draw a tricopter from a top down. Include all the the prop rotations, the resulting moments, and resulting forces like you have above. Label each motor to make things easier. If you do that I can do my best to explain what is going on.