Practical Quad Dynamics Sim - RC Groups
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Jan 01, 2018, 01:43 PM
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Data

Practical Quad Dynamics Sim


I'm working on a project to simplify the process of modeling quadcopter dynamics for the average pilot so one could in theory estimate how components and/or frames influence flight. My objective is to make the model as accurate and user friendly as possible while using common product spec data that's freely available for parts users might actually purchase for their racing/freestyle quads. The intent of this project is not to build a tool for in-depth scientific research, rather for practical cause & effect analysis that may or may not save folks money or wasted effort before building their next quadcopter. I make no promises about the accuracy of this tool and welcome any suggestions folks may have for its improvement.

The basis for this project came from Quad Star Drones and Mini Quad Test Bench, along with test data from EngineerX, and many other websites & white papers throughout the internet. I will attach formulas & conceptual sources as they become available.

In it's current state the kinematics of velocity, acceleration, distance traveled, impulse, jerk & yank are being calculated by a simple MS Access database utilizing a straightforward gui for users to enter their frames, LiPo info, motors, props, and other miscellaneous data pertinent to linearly approximating the applicable forces involved one recursion at a time. The primary fudge-factor in the tool is the drag force Cd, which should be calibrated for unique frame styles using known speed data. Information can filled in within a couple minutes and the calculations take a couple of seconds to 10 seconds max to execute. The tool can be connected to GnuPlot, Tableau, or MATLab for plotting or a text/CSV file can be sent and analyzed in Excel with a push of a button. For simplicity there are 8 built-in plots for the basic dynamics described above and 13 plots for throttle efficiency, dynamic response, and power curves (pictured below) that can be selected from a drop-down and generated immediately.

Check-back often for updates. :-)

Updated: 01/14/2018

Below is version v1.8 of the PQD

PQD.v1.8

Free MS Access Runtime
Last edited by AILERON8; Jan 14, 2018 at 09:38 PM.
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Jan 01, 2018, 09:36 PM
Test Pilot
teracis's Avatar
Great work AILERON8!

I'm subscribing to this thread and plan to actively participate, this is already a very valuable resource and you've already provided great insights into the data.
Jan 01, 2018, 09:40 PM
the people squad
schrodingers cat's Avatar
Subbed, thanks for this valuable work
Jan 01, 2018, 09:55 PM
Forward ever, backward never!
Brainstorm's Avatar
Good stuff, Aileron8! I've subscribed as well.

I'll be following along with interest, even though my understanding of the math and physics involved is below basic.
Jan 01, 2018, 10:12 PM
Registered User
Thanks guys, I wouldn't be able to do it without you. This tool will be as good as the data that goes into confirming & streamlining the output, calibrating the Cd coefficients, and improving the gui and calculations moving forward. So I'll be leaning into folks in here and elsewhere for data and output confirmations.

Over the next few weeks I'll be installing a bunch of motors and frames along with the tutorial. Thanks again!

One of the primary goals of this project is making something most people can use while still getting some enlightening results the average joe could interpret. It's not there yet, but that's the goal at least.
Last edited by AILERON8; Jan 01, 2018 at 10:18 PM.
Jan 02, 2018, 04:42 PM
Registered User
I updated the Jerk & Yank Forces to read in G's per second & Kg*G's per second, respectively. This should make the values more intuitive. Originally I had derived the Jerk force to include the angle of attack by integrating acceleration using the velocity and thrust equations, which included vector. The values were accurate with respect to change, but not magnitude, so were confusing. v1.5 sets the Jerk force as simply the differential of acceleration and the Yank force as mass multiplied by the Jerk force. The latter equations assume thrust is aligned with the direction of flight. Oh well, it makes more sense to use, because the magnitude is accurate regardless of delta t which is set to 0.02 seconds per recursion by default, but is user configurable.

To add: Differentiating this twice to get the Jerk force doesn't give what's needed. I updated the picture so folks don't get the wrong impression. The last segment of the equation is true though.
Last edited by AILERON8; Jan 02, 2018 at 05:55 PM.
Jan 02, 2018, 05:09 PM
Registered User
Great Stuff, much appreciated
Jan 02, 2018, 05:14 PM
Registered User
Quote:
Originally Posted by SirDomsen
Great Stuff, much appreciated
Thanks, I'll update the dB itself to v1.5 this evening. The photos are up to date though. I'll also be adding 12 brother hobby motors and a few others to the dB this eve.

Update: I'm working on getting the tool to a state where it functions as a stand alone application, the
Practical Quad Dynamics Sim = PQD.exe for short, which should be by this weekend. I'll upload all the motor/frame/prop data at that time. Thanks again
Last edited by AILERON8; Jan 02, 2018 at 11:23 PM.
Jan 03, 2018, 05:22 AM
Brisbane, Australia
Excellent work Aileron8, watching with great interest!
Jan 03, 2018, 09:40 AM
Registered User
For the benefit of those who ... well like me, may not understand the practical or "hands on" feel of your metrics jerk and yank - could you elaborate what these look/feel like in flight and what values or ratios you look for to optimize a setup?
Jan 03, 2018, 10:32 AM
Registered User
Quote:
Originally Posted by NotFastEnuf
For the benefit of those who ... well like me, may not understand the practical or "hands on" feel of your metrics jerk and yank - could you elaborate what these look/feel like in flight and what values or ratios you look for to optimize a setup?
Certainly.. and when the PQD.exe is created I promise there will be a description for each of the terms used.

The Jerk is what causes your quad to accelerate. Think of the Yank Force like a hammer that slams into the bottom of your quad, Jerking it upward into the air. Initially the acceleration will shoot-up in proportion to the Jerk, but as soon as the Jerk (oscillation) damps to zero the acceleration is on its own and will decay as the Kinetic energy from the Yank is transformed into Potential energy left over to transform into Velocity and Momentum as Power continues to feed the motors. If a mouse was sitting in the enclosed cockpit of your quad it would experience G forces equal to the max Jerk and Acceleration, then the Acceleration alone as Jerk quickly decays to zero, but the motors are still being fed Power so Acceleration approaches a constant, decaying to zero. Therefore the mouse experiences nothing at all as the Velocity approaches its maximum(other than vibration). If the mouse opened a little window it would see the ground moving at max speed below while experiencing Forces only as the quad changed direction or orientation in the air.
Last edited by AILERON8; Jan 03, 2018 at 10:47 AM.
Jan 03, 2018, 04:31 PM
Test Pilot
teracis's Avatar
Quote:
Originally Posted by AILERON8
Certainly.. and when the PQD.exe is created I promise there will be a description for each of the terms used.

The Jerk is what causes your quad to accelerate. Think of the Yank Force like a hammer that slams into the bottom of your quad, Jerking it upward into the air. Initially the acceleration will shoot-up in proportion to the Jerk, but as soon as the Jerk (oscillation) damps to zero the acceleration is on its own and will decay as the Kinetic energy from the Yank is transformed into Potential energy left over to transform into Velocity and Momentum as Power continues to feed the motors. If a mouse was sitting in the enclosed cockpit of your quad it would experience G forces equal to the max Jerk and Acceleration, then the Acceleration alone as Jerk quickly decays to zero, but the motors are still being fed Power so Acceleration approaches a constant, decaying to zero. Therefore the mouse experiences nothing at all as the Velocity approaches its maximum(other than vibration). If the mouse opened a little window it would see the ground moving at max speed below while experiencing Forces only as the quad changed direction or orientation in the air.
Isn't jerk defined as the rate of change of acceleration? Which you've described quite well just here I might add.
Jan 03, 2018, 05:52 PM
Registered User
Quote:
Originally Posted by teracis
Isn't jerk defined as the rate of change of acceleration? Which you've described quite well just here I might add.
Indeed it is, thank you. With Yank just being mass times Jerk. These are the types of descriptions I’ll include in the tutorial.
Jan 03, 2018, 07:10 PM
Registered User
As far as optimal values or ratios go though, I think it depends. The term Yank implies pulling, and stated like the definition of Jerk, Yank is the rate of change of Force. That's how it's measured, but as to what Yank is I'll leave it to an imaginary scenario:

The props are pulling the quad into the air, but given two quads with the same Jerk(rate of change of acc) if one quad weighed double the other that means it takes double the Force to Yank the heavier quad with the same Jerk. Doubling the Force means doubling the Thrust. Doubling the Thrust means, well, you get the idea... Heavier quads are harder to Yank and require more Power to Accelerate to the same Velocity. That said, it's not quite as simple as that, because as your quad travels faster than 70kmh or so drag Forces complicate matters. Then to add another wrench, Power isn't exactly linear as you jam on the throttle. The PQD.exe assumes constant voltage sag as measured by the static motor test. While I believe this is still a relatively accurate way to measure max acceleration and velocity, most static motor thrust tests are using decent quality packs or other constant voltage sources.
Jan 03, 2018, 08:25 PM
Registered User
Crystal clear now. Reading back I can see where you already explained it - but my head just stalled on it for whatever reason. Thanks for reiterating. Jerk = derivative of acceleration. Yank = mass * jerk. I'm on board now. Truth be told ... line of sight still intimidates me and although I do practice - I keep it to brushed micros for now. But I believe these metrics also apply quite well to fpv in both racing and acro. I'm excited to use the tool to plan future builds. I'm following with great interest and admiration of your work here. Thank you for sharing with us!


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