How to calculate quadrotor propeller torque due to aerodynamic drag

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Discussion Overview

The discussion revolves around calculating the torque of a quadrotor propeller due to aerodynamic drag, specifically using the APC 10x4.7 propellers. Participants are interested in deriving a non-linear mathematical model for simulations, with a focus on thrust and torque relationships in the context of quadrotor dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks the correct formula for calculating torque due to aerodynamic drag in terms of angular velocity, referencing specific data from a propeller database.
  • Another participant suggests focusing on thrust rather than torque for the simulation, proposing a formula involving thrust, RPM, and diameter, and mentioning the importance of motor characteristics.
  • A third participant reports success in modeling both thrust and torque using the provided data, indicating a progression in their simulation efforts.
  • Discussion includes the design of quadrotors with counter-rotating props, which self-compensate for reaction torques, suggesting that torque may not be critical for all maneuvers.
  • One participant expresses interest in accessing a thesis related to propeller dynamics for further insights.
  • A later post raises a request for governing equations for propellers, highlighting challenges in understanding the relationships between RPM, pitch, diameter, and generated torque/thrust.

Areas of Agreement / Disagreement

Participants express differing views on the importance of torque in simulations, with some suggesting it may not be necessary while others indicate it could enhance the model's completeness. The discussion remains unresolved regarding the best approach to modeling these dynamics.

Contextual Notes

Participants note challenges with unit conversions and the complexity of deriving relationships between thrust and torque. There is mention of efficiency factors and the potential need for lookup tables rather than simple formulas.

Who May Find This Useful

This discussion may be useful for individuals involved in quadrotor design, aerodynamics, or control systems, particularly those seeking to understand the dynamics of propeller performance and simulation modeling.

marcin123
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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
 
Last edited by a moderator:
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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
 
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.
 
Last edited by a moderator:
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.
 
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.
 
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.