The Terminal Velocity of a Falling Mavic 2

[FormerMember07122019_2]

Very interesting. The three power-off events show similar initial evolution of pitch, roll and yaw, followed by varied, possibly chaotic, behavior:

View attachment 65882
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The vertical speed reflects that, with a transition to oscillatory behavior as the aircraft wobbles:

View attachment 65885

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The blue dotted lines are the model that I posted previously, with a slightly lower drag coefficient than my initial guess (0.025 rather than 0.031), and predict the motion pretty well. The terminal velocity of around 20 m/s (45 mph) is in line with previous data and reports.

I find this very fascinating. Some observations and/or questions.

It seems like the aircraft is tumbling randomly with the predominate motion of head over butt with a fair amount of yaw spin. Can I assume that the rapid changes are sign reversals or number overloads or is it actually flipping over in 100ms or less?

The negative motor speeds seem to indicate auto-rotation but why would it be constant; or is it just a data/math anomaly?

If this is too deep into the weeds let me know. My interest is purely intellectual.

 

[sar104]

I find this very fascinating. Some observations and/or questions.

It seems like the aircraft is tumbling randomly with the predominate motion of head over butt with a fair amount of yaw spin. Can I assume that the rapid changes are sign reversals or number overloads or is it actually flipping over in 100ms or less?

The negative motor speeds seem to indicate auto-rotation but why would it be constant; or is it just a data/math anomaly?

If this is too deep into the weeds let me know. My interest is purely intellectual.

Motor speed doesn't go negative - it's on the right axis. It goes to zero because the motors are off. I'm sure the props are turning in the air flow.

Here are the same data with the attitude values unwrapped (i.e. not constrained to -180 – 180):



I think it's fairly clear that the aircraft is rotating but not fully tumbling. It's rocking side to side and has some larger pitch excursions (which is on the unstable principle axis - i.e. neither the minimum not maximum moment of inertia), but it does not fully rotate - the motion is oscillatory.

 

[FormerMember07122019_2]

Motor speed doesn't go negative - it's on the right axis. It goes to zero because the motors are off. I'm sure the props are turning in the air flow.

Here are the same data with the attitude values unwrapped (i.e. not constrained to -180 – 180):

View attachment 65998

I think it's fairly clear that the aircraft is rotating but not fully tumbling. It's rocking side to side and has some larger pitch excursions (which is on the unstable principle axis - i.e. neither the minimum not maximum moment of inertia), but it does not fully rotate - the motion is oscillatory.

Thanks for the clarifications. Your right (you must get that a lot), I was looking at the wrong axis. Also, I was having trouble visualizing the overall behavior with the 180 shifts. This graph is much easier to understand. It looks a lot like one would expect, seems to be porpoising and rotating similar to a unbalanced flat object falling.

It would be interesting if someone could input this data into a drone flight simulator to visually recreate the behavior.

Thanks

 

[Kazzaaz]

Quick update -

The repair is covered under warranty! SUPER lucky considering I modified parameters and was flying in manual mode!

But now even more questions... Considering my extreme flight, what did DJI see exactly that made them determine there was absolutely a defect?
Was it this mysterious OTHER (8)? Or were simply the flight logs of the drone not recovering when switched into GPS/Sport mode enough to do it?

 

[zxcflyer]

Very interesting. The three power-off events show similar initial evolution of pitch, roll and yaw, followed by varied, possibly chaotic, behavior:

View attachment 65882
View attachment 65883

View attachment 65884

The vertical speed reflects that, with a transition to oscillatory behavior as the aircraft wobbles:

View attachment 65885

View attachment 65886

View attachment 65887

The blue dotted lines are the model that I posted previously, with a slightly lower drag coefficient than my initial guess (0.025 rather than 0.031), and predict the motion pretty well. The terminal velocity of around 20 m/s (45 mph) is in line with previous data and reports.

Yes, it all starts very similar. It must be the CSC command (both sticks inside and down) that sets it on the backward downward spiral which later develops into chaotic fall.

Here is the video of the longest fall.

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[sar104]

Yes, it all starts very similar. It must be the CSC command (both sticks inside and down) that sets it on the backward downward spiral which later develops into chaotic fall.

Here is the video of the longest fall.

Did you forget to link to the video?

 

[zxcflyer]

Added link.

 

[Cookedinlh]

SAR104 . . from your data I think the Drag Coefficient is around 0.6 . . . does that sound right if Terminal Velocity is around 17.7 m/s? . . . can you attribute any contribution to drag from the props or is the motion to Chaotic?

 

[sar104]

SAR104 . . from your data I think the Drag Coefficient is around 0.6 . . . does that sound right if Terminal Velocity is around 17.7 m/s? . . . can you attribute any contribution to drag from the props or is the motion to Chaotic?

Are you referring to a drag coefficient of this form?

If so then it's going to be dependent on what you assume for cross-sectional area, A. If you assume 0.25 m² then you get around 0.9. But since I used fitted data it makes more sense to use the fitted parameter k = A/2 to get drag force in the form kv²/m, in which case the value of c is not defined.

I did not attempt to take account of orientation and an explicit propeller contribution - that's averaged out in the fit to the data.

 

[Cookedinlh]

Thanks that helps .. I just tried to solve for drag if the real data shows terminal velocity was taken as 17.7... thinking then maybe I could figure out what the “effective cross-section” is if accounting for blades and tumbling

 

[sar104]

Thanks that helps .. I just tried to solve for drag if the real data shows terminal velocity was taken as 17.7... thinking then maybe I could figure out what the “effective cross-section” is if accounting for blades and tumbling

Hard to separate. If you assume a geometric drag factor you can solve for effective cross-sectional area, and vice versa. But I'm not sure it's worth it since you don't need them independently.

 

[Cookedinlh]

Hard to separate. If you assume a geometric drag factor you can solve for effective cross-sectional area, and vice versa. But I'm not sure it's worth it since you don't need them independently.

I'm trying to figure out the best way to determine when a drone could become lethal (~140Nm) if it's just falling and how to assess the minimum height at which one reaches terminal velocity. Here is a chart on weight and velocity I developed. I'd like to demonstrate that maximum speed is only a valid risk calculation when it's ballistic because responsible trained operators do not pose a risk. . . anymore than responsible motorcyclists are to pedestrians.

 

[sar104]

I'm trying to figure out the best way to determine when a drone could become lethal (~140Nm) if it's just falling and how to assess the minimum height at which one reaches terminal velocity. Here is a chart on weight and velocity I developed. I'd like to demonstrate that maximum speed is only a valid risk calculation when it's ballistic because responsible trained operators do not pose a risk. . . anymore than responsible motorcyclists are to pedestrians.

View attachment 69133

The graphs earlier in this thread include speed as a function of distance fallen - just by integrating velocity with respect to time. Are you looking for something more than that?

 

[Cookedinlh]

I’m trying to produce a chart that compares UAVs by model with their spec all up weight showing the height at what height they reach terminal and the height they become lethal. This to demonstrate the inherent safety of smaller lighter drones over people

 

[sar104]

I’m trying to produce a chart that compares UAVs by model with their spec all up weight showing the height at what height they reach terminal and the height they become lethal. This to demonstrate the inherent safety of smaller lighter drones over people

Okay - obviously that will require drag coefficient estimates for each model to do it properly. For those without existing data that will be a bit challenging. You could just scale drag coefficient by aircraft linear dimension squared - for most common designs that's not going to be far off.

 

[Cookedinlh]

Okay - obviously that will require drag coefficient estimates for each model to do it properly. For those without existing data that will be a bit challenging. You could just scale drag coefficient by aircraft linear dimension squared - for most common designs that's not going to be far off.

I See Los Alamos . . do you know anyone at Sandia Labs?

 

[sar104]

I See Los Alamos . . do you know anyone at Sandia Labs?

Yes - quite a few, particularly those in my field of course.

 

[Cookedinlh]

Yes - quite a few, particularly those in my field of course.

Dr Al Migliori? . .

 

[sar104]

Dr Al Migliori? . .

He's LANL, not SNL.

 

[Cookedinlh]

He's LANL, not SNL.

right . . well if you do happen to run into him, please say HI! from Dave Cooke. I've not talked to him in years, and he helped me a lot . . and also thanks so much for your ideas . . . very helpful. . . doing a presentation to Transport Canada and a Canadian MP here soon, to try to rationalize new PART IX rules coming into effect 1 June . . particularly effecting 1Kg machines.