Kinetic energy of Spark

[Dronason]

In another "Pilot Check In" thread (Hi from new pilot from Croatia), an out of topic discussion started about the Kinetic energy of the Spark. In Croatia, it seems to be an active criteria for drone regulation. In some other countries like in Switzerland, it is discussed as a parameter for drone classification regarding potential risk of drone use.

At first, the question is what is the start hypothesis?

1. Free fall to ground due to a drone fault.
2. Hit at full speed due to a pilot error?

Case 1), free fall:
The first idea is a worst case scenario of a Spark hovering at a given altitude, falling down after a total loss of power. The Spark will reach ground at its terminal velocity. The potential energy at start is given by altitude and mass. This energy will be converted to kinetic energy by the gravity but a part of this energy will be loss due to air resistance. So in theory it is simple. The main question is the air resistance of the Spark.

Unfortunately the DJI assistant 2 simulator cannot be used to try to get such parameter as there is no way (CSC) to kill the motor and set it to free fall on request. The flight record during a simulation can be retrieved but it is not possible in the simulator to simulate a fatal power loss in the simulator.

Input parameters:

• Altitude: h = 100 m (should be highest legal altitude)
• Mass: m = 0.305 kg
• Air friction: f = 0.24
• Gravity: g = 9.81 m/s2

Calculations:

• Potential energy: = m * g * h
• Velocity: = f (air friction), see Free fall - Wikipedia (a case on its own)
• Kinetic energy: = 1/2 * m * v^2

Case 2), hitting at fully speed, a more easy case.

• Here it is simple, Energy = 1/2 x mass x velocity ^2

I made a google sheet available HERE. Let me know for correction to it.
It is based on official specifications from DJI.

The worst case is expected to be the free fall case and the height should be take as the highest legal height. This is typically > 100 J for Spark, so no a negligible case but currently there is no proven model case about the air friction of Spark falling down. So there is no current really know kinetic energy for the Spark for free falling case. The collision worst case is 29 J but the free fall worst case is currently higher.

It is really just a thought on this subect, comments and corrections are really welcome.

 

[noooris]

Your last row should be 150+ instead of 500m. That’s because if the Spark falls from 180m, 500m, 10,000m, or the edge of the stratosphere, the max energy is achieved at terminal velocity which happens roughly in the first 8-10seconds. Many people will not understand the concept of terminal velocity. A fall from 200m will have the exact same impact as a fall from 500m.

 

[Dronason]

Your last row should be 150+ instead of 500m. That’s because if the Spark falls from 180m, 500m, 10,000m, or the edge of the stratosphere, the max energy is achieved at terminal velocity which happens roughly in the first 8-10seconds. Many people will not understand the concept of terminal velocity. A fall from 200m will have the exact same impact as a fall from 500m.

I understand your point, but 500m is the max setting possible allowed by DJI, so from a regulator point of view, it is the worst case, whatever user set. I don't even speak of idiot hack that could be done.
Yes, these aspect are not simple one, in any case the concept of kinetic energy will hard to get for newbie pilot.

 

[Blue Baron]

I've done that calculation months ago and I don't remember the details. But AFAICR I obtained an impact energy of ~50J for the Spark. I used the terminal velocity, as obtained from the body surface and mass. Terminal velocity was a bit larger than max. travel speed. That's the lower end of rubber pellets shot by the Irish police into crowds (up to 200 J, 17 deaths ...). 10 J are considered non life-threatening. 50 J still is a serious health danger.

I try to redo the calculation now:

Drag coefficient = 2 (brick)
Surface = 143 x 50 mm (assuming it doesn't fall nose first)
Weight = 300g
Air density = 1.2 kg/m^3
Terminal velocity = 18.52 m/s = 66.66 km/h = 17.5 m vacuum free fall
Energy = 51 J

The Spark core body with its rounded edges certainly has a drag coefficient closer to 1, if not smaller (i.e., better than a brick). However, with the arms and rotors extending beyond the core body, I guess this still is a reasonable assumption for the drag coefficient.

If Spark must be classified by impact energy, I would go with the "50J" figure.

 

[Buddy411]

Not to derail the thread, but they do make emergency parachutes for certain larger quad models. That could be part of a risk mitigation plan if need be.