Drone Exemptions 1

[BUGGAR]

I’m working on an FAA Exemption for a client to fly commercial drones. A typical FAA requirement is to fly no faster than 100 mph and no higher than 400 feet above ground level. Also, your operational boundary has to be 500 feet away from someone you don’t want to hit. Before I do the math, does anyone know drone aerodynamics to determine if a 55 lb drone going 100 mph at 400 feet altitude will fall within the 500 feet safety zone if power and control quit immediately? This would be a quadcopter type drone, not a glider.

Of interest: a 55 lb drone at 400 feet has 22,000 ft lb of energy, same as a 4 ft x 8 ft x 1inch steel road plate falling from 17 feet. A drone freefalling from 400 feet with no air drag will hit the ground at 110 mph.

Thank you everbody.

 

[GregLocock]

Worst case scenario is that the entire drivetrain locks, the rotors break off and you have the quadcopter's body hurtling through the air. Cd is say 0.5 to 1 cross sectional area might be anywhere from front view to plan view (I guess it'll tumble which is a good thing in context).




Cheers

Greg Locock


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[BUGGAR]

But will it travel laterally more than 500 feet before it hits earth?

 

[IRstuff]

Student posting is not allowed ;-)

It depends on too many specific factors, but the QC would take 5 seconds to fall the ground with no air resistance. 5 seconds * 100 mph = 733 ft. Air resistance downward would be higher than air resistance laterally, so a more realistic calculation would probably still allow the copter to reach 500 ft.

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[GregLocock]

Oh, I thought "Before I do the math" meant that you were going to the math, not me!

The equation for ballistic trajectory in the presence of drag is not analytically solvable, the easy way is a numerical sim. I'll see if I get time today.

Cheers

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[desertfox]

Hi Buggar

I'm with IRstuff on this one, I calculate 4.99 seconds to fall to earth and it would have covered a distance of 739 Ft horizontally before hitting the ground but without considering any air resistance.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[BUGGAR]

Not meant to be a student post. I was wondering if there were established "drone rates of fall". We are writing a subconsultant agreement for drone use and are finding loose legal ends within FAA Exemptions.

 

[IRstuff]

I know you've been around the block a couple of times. The bottom line is there is no closed form solution, not even for a normal aircraft. See:

http://andrew.gibiansky.com/blog/physics/quadcopter-dynamics/

http://andrew.gibiansky.com/downloads/pdf/Quadcopter Dynamics, Simulation, and Control.pdf

http://www.ijstr.org/final-print/aug2014/Quadcopter-Flight-Dynamics.pdf

http://sal.aalto.fi/publications/pdf-files/eluu11_public.pdf

http://www.europment.org/library/2014/santorini/bypaper/SYSTEMS/SYSTEMS1-07.pdf

TTFN
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[BUGGAR]

O.K., the kid down the street is into drones and he's interested. He has a couple quadcopters and we're going to tie a string to one of them and tie it to a pole hanging out the side of my car, speed down the road, and see how much drag we're getting. We'll have to tie the string as close to the center of gravity as possible and see how it tumbles. Then by measuring the angle of the string, we can compute the drag coefficient at different speeds. That brings up the question, is there an "average" drag coefficient for a tumbling drone? We'll find out.

I tried to talk him into trying a 100 mph free fall from 500 feet up with one of his drones and he came up with the drone on a string out of the car idea instead. This sounds more fun than doing it on a computer. But I'd rather test crash one.

 

[KENAT]

Any weapons range type folks should be familiar with how to estimate this as they have to do it for things they are deliberately dropping from air craft moving at speed. Used to refer to it as 6 DOF "6 degrees of Freedom" models.

I'd probably use a CD value for a sphere of approximately equivalent cross section in the 'lowest drag' orientation.

Don't forget to add a good margin of error.

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[IRstuff]

He doesn't necessarily need to do a complete freefall, since he's probably got gyros and accels on board for the nav system, and you can use that data to see what it's actually doing. I'd actually be more worried about a tethered test, as I've had lots of time with errant kites, which is what this will look like, and it's very likely that the drone will bounce off the road surface a few times and that'll be that.

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[KENAT]

Short string, long pole;-)

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[IRstuff]

Still, it'll be like a flag fluttering in the wind. I doubt that it would representative.

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[tbuelna]

Calculate the trajectory of a 55lb mass with an initial horizontal velocity of 100mph and a vertical height of 400ft. And then draw a 500ft radius around every possible impact point. If there are no people, structures, vehicles, livestock, etc within the area that might be injured by your drone, you'll probably be OK.

However, you probably still need to provide some liability insurance coverage for your activities. And I imagine it would be very difficult (and expensive) to obtain this type of coverage.

 

[GregLocock]

In order to limit the maximum range of an unpowered projectile with an initial velocity of 100 mph horizontally at an altitude 400 feet, to 500 feet, a 55 lb drone needs a minimum Cd*area of 2.5 sq ft, according to my whiz bang sim.





Cheers

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[BUGGAR]

Greg,

That looks like a good number. Drone Kid and I went to a drone shop to see what was available. The ratio of weight to projected area (and Cd) of all the drones we saw varied so much that we would have to prequalify a specific drone for a specific use. We looked at some 55 pound drones that are allowed by FAA. These things are monsters and you do not want one falling on you from 400 feet.

Your Cd area of 2.5 square feet breaks down approximately to a 1.6 ft. x 1.6 ft. size drone (solid area). We didn't measure the 55 pounders but I estimate that their area is less than that, and they would have to descend in the "projected area" position which isn't likely. Therefore, in all probability, their kill zone is beyond the FAA horizontal limit. There are lawyers that specialize in applying for FAA exemptions. Don't they read these things?

Can you tell me what simulator you used for the drag coefficient?

Thanks.

 

[tbuelna]

Is the 500ft requirement considered part of the operational envelope, or is it measured from any potential point of impact, similar to a margin of safety?

 

[GregLocock]

I wrote the sim myself.

http://www.mediafire.com/download/ox6sj50sc0lyjdr/drone1.png

Cheers

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[BUGGAR]

The 500 feet is the operational limits at 400 feet above ground level and at 100 mph. These are typical FAA mandated limits of operations. My findings are that this is not sufficient to contain a drone suffering loss of power/control as we have determined.

During my research, I found out that drones are being operated by a local utility to inspect their powerlines and facilities. They are operating drones at a nearby substation with 38 houses and an open space park in the "kill zone" of their drones (laterally within 730 feet from drone operations).
I have sent a letter to the FAA and the Utility. This is a politically powerful utility here and if you don't hear from me, I'm probably in a buried electrical vault somewhere.

These Exemptions are public information and are internet-searchable under FAA Section 333 Exemptions. The one for the subject utility is Exemption No. 11238. Most of these Exemptions seem to rely on the blanket 500 ft lateral/400 vertical/100 mph rule. I argue that they should be site-specific. Can't drones be preprogrammed for these variables?

Greg, special thanks for the chart. Your Cd looks like it may fit some of the drones we looked at but when we compared some that had similar weights, their configuration (and Cd) were radically different from each other.

 

[BUGGAR]

Since this is all in the public information realm, here are the coordinates of the substation using the drones. Note the nearby houses. Substa Coord: 32 47 15 N, 117 08 20 W, in Degrees, Minutes, Seconds.