How to calculate quadrotor propeller torque due to aerodynamic drag

In summary, the propeller pitch is constant, but the propeller diameter and RPM vary based on the maneuver being performed. The thrust and torque generated is based off of the propeller's angular velocity.
  • #1
marcin123
2
0
I'd like to know the right formula to calculate torque of a quadrotor propeller (propeller pitch is constant) due to aerodynamic drag in terms of angular velocity ω. For the sake of my simulation I'm assuming `APC 10x4,7` propellers. I'd like to refer to http://www.ae.illinois.edu/m-selig/props/propDB.html#APC, so please assume only the set of data given there is available while answering. I know really little of aerodynamics, I'm planning to design a control system in Simulink later on, but would like to derive a non-linear mathematical model first.

Please note I need to use data from http://www.ae.illinois.edu/m-selig/props/propDB.html#APC for APC 10x4,7, which means the propeller below. I'm guessing all is there to derive a formula τ(ω), I just don't understand how to do it.

http://img19.imageshack.us/img19/7838/apcsf10x47side.jpg
http://img853.imageshack.us/img853/7319/apcsf10x47front.jpg
http://img850.imageshack.us/img850/8931/apcsf10x47geom.png

Static data from UIUC:
RPM CT CP
2377 0.1039 0.0431
2676 0.1058 0.0437
2947 0.1059 0.0437
3234 0.1083 0.0444
3494 0.1096 0.0450
3762 0.1121 0.0460
4029 0.1136 0.0466
4319 0.1155 0.0474
4590 0.1177 0.0484
4880 0.1199 0.0494
5147 0.1213 0.0500
5417 0.1228 0.0508
5715 0.1239 0.0513
5960 0.1253 0.0520
6226 0.1261 0.0524
6528 0.1274 0.0531
 
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  • #2
marcin123 said:
I'd like to know the right formula to calculate torque of a quadrotor propeller (propeller pitch is constant) due to aerodynamic drag in terms of angular velocity ω. For the sake of my simulation I'm assuming `APC 10x4,7` propellers. I'd like to refer to http://www.ae.illinois.edu/m-selig/props/propDB.html#APC, so please assume only the set of data given there is available while answering. I know really little of aerodynamics, I'm planning to design a control system in Simulink later on, but would like to derive a non-linear mathematical model first.

Let me clarify a few things.

  • You are simulating a quadrotor.
    You want to develop a non-linear Thrust model. Torque isn't particularly useful in your simulation unless you need to know if your motor can spin the prop without overheating.
    Your thrust model consists of a prop - motor combination. A prop alone cannot help you.
    The three variables you should be concerned with are Thrust-RPM-Throttle (or current)

If you want to take a stab at this model you find a motor that will operate at some range of RPMs given on the table and use the formula

[itex]C_T = \frac{T}{\rho n^2 D^4}[/itex]

Where T is thrust, D is the blade diameter, n is RPS (convert to RPM)

Then you can multiply by some efficiency factor [itex]\eta[/itex] ~0.95 or so to account for heat losses etc...

You will probably end up with a lookup table and not a formula
 
  • #3
Thank you visciousflow. I had some problems with Imperial units, but were able to overcome those and am able to model both thrust and torque in terms of angular velocity now (inserted below, thrust in [g] on the left, torque in [Nm] on the right axis, angular vel. in RPM) with the UIUC data.

http://img594.imageshack.us/img594/1466/apcsf10x47characteristi.png

My goal is to simulate all:
  • dynamic response of a motor together with prop
  • thrust
  • torque

I'll ask a follow-up question when I get there, if I encounter problems. For now the case is solved - thanks all who read and gave a short thought.
 
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  • #4
Quad rotors are usually designed so that the props are counter-rotating and thus, the reaction torques are self compensated (for most maneuvers). For maneuvers that they are not self-compensated, they are negligible. I just completed my thesis and worked with the APC 12x9 prop. Trust me, it would not be worth adding to the simulation. Although, the model would look more complete if you do add them.
 
  • #5
Can you link me to your thesis razorhash? I would love to read it. It's an interesting topic, I'm also researching something similar.
 
  • #6
I hope this isn't dragging up an old topic, but I'm currently looking for the governing equations for propellers and the relevant thrust/torque generated. I'm having a nightmare of a time trying to work out the relationship between RPM, pitch, diameter and generated torque/thrust. Could someone help point me in the right direction, please? I've tried asking on various RC plane forums, but their general answer is "50-75W per pound of craft is the minimum". While that's a helpful answer for a hobbyist, I'm working on a MEng project for uni so would really like something more substantial to justify my decisions.
 

1. How do I calculate the aerodynamic drag force on a quadrotor propeller?

To calculate the aerodynamic drag force on a quadrotor propeller, you will need to know the propeller's surface area, air density, and the velocity of the air flowing over the propeller. The formula for calculating drag force is F = 1/2 * p * v^2 * A * Cd, where p is the air density, v is the velocity, A is the surface area, and Cd is the drag coefficient. Simply plug in these values and you will have your answer.

2. What is the drag coefficient for a quadrotor propeller?

The drag coefficient for a quadrotor propeller is dependent on its design and shape. It can range from 0.05 to 0.15, with lower values indicating a more aerodynamic design. However, the exact drag coefficient can vary depending on the operating conditions and angle of attack of the propeller.

3. How does the angle of attack affect the propeller's drag force?

The angle of attack, or the angle at which the air flows over the propeller, can significantly affect the drag force. A larger angle of attack will result in higher drag force due to increased air resistance on the propeller's surface. However, a smaller angle of attack can also cause poor aerodynamic efficiency and lead to higher drag forces.

4. Can I reduce the aerodynamic drag force on my quadrotor propeller?

Yes, there are several ways to reduce the aerodynamic drag force on a quadrotor propeller. One way is to design the propeller with a more streamlined shape and lower drag coefficient. Another way is to adjust the angle of attack to minimize the drag force. Additionally, reducing the propeller's rotational speed can also decrease the drag force.

5. How does the aerodynamic drag force on a quadrotor propeller affect its overall performance?

The aerodynamic drag force on a quadrotor propeller can significantly affect its performance. A higher drag force will require more power to overcome, leading to shorter flight times and reduced maneuverability. It can also impact the quadrotor's stability and control, making it more difficult to fly. Therefore, it is crucial to consider and minimize the drag force when designing a quadrotor propeller for optimal performance.

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