Cover of paper

I want to thank Patrick Egan at sUAS News who presented this article with the brief though very tantalizing comment, “A paper well worth reading.”
Which indeed it turned out to be. Written by Andrew V. Shelley, “This article is derived from material to form a Masters Degree in the School of Economics and Finance, Victoria University of Wellington, New Zealand.” It is shared through free and open access by ERAU Scholarly Commons and may be downloaded here.
If you want the Cliff Note, the paper seeks to quantify the harm resulting from someone being hit on the head by a falling UAV. The assumption is that the props are not spinning. It does not consider airspeed beyond the speed of gravity which will accelerate any object at a rate of 32 feet per second per second or a horizontal strike or strikes to other parts of the body. Just a drone falling out of the sky.
In his calculations, the author considers a variety of factors including the weight of the UAV, the height, the density of the people over which the UAV is operating and the social cost of various levels of injury. End of Cliff Note.

If you are like me and wondered just how good the science was that led to the half-pounder rule and the proposed Micro UAS ARC overflight regulation, your worst fears will be confirmed.

This is a well-reasoned, meticulously researched scholarly piece of work. There is no way to paraphrase it, nor any reason to, but I would like to share a few things that caught my attention.

…There is little published analysis that supports the various existing and proposed rules. The limited quantity…makes it difficult to judge whether the various rules overstate or understate the risks posed by sUAS. This paper is a contribution to expanding that body of analysis.

He sets the paper up to explore his premise, then articulates what concerns me and many other observers:

The optimal level of safety occurs at the least-cost point where cost is comprised of the cost of harm, the cost of precaution, and the opportunity cost of foregone benefits from any reduction in the activity in question. In theory, this optimal level could be achieved by allowing sUAS operators to choose their level of activity and level of precaution, given the knowledge that they will be subject to liability under tort for any harm that does occur.

[BUT] The person on the ground has no way of knowing the relative level of danger posed by different unmanned aircraft, the skill level of the pilot, whether a particular unmanned aircraft has been properly maintained, or whether it is being operated safely (for example, whether the UAS is being operated with sufficient battery power remaining). These factors all mean that the person on the ground has no way of knowing the appropriate level of precaution to take if an unmanned aircraft flies overhead.

In such cases, the appropriate standard of liability is that of strict liability (Shavell, 1980; Davis, 2011), and aviation regulation does indeed impose strict liability for harm caused by anything falling from the sky.

Indeed, nothing in the proposed or current regulations that has been shared with the public, addresses any of these variables beyond the weight of the drone and its height above ground level (AGL). What also goes unstated is that manufacturers who are proposing to self-certify their flying machines are not proposing to indemnify the owner operator. Who would with this number of variables at play?

Figure 1. Schematic Diagram of UAS-Induced Human Harm Model

The model (Figure 1 above) presents all of the variables used in the analysis. The paper explores each in turn, providing studies and references that support the assumptions that Shelley used to develop his model.
Pay particular attention to the detail from Figure 1 (below) which shows the relationship of Energy to Injury Given Impact. Notice that at 99J such an injury is likely to be life-threatening. What does that mean? It means enough to ruin someone’s day and possibly the rest of their life. The best that can be said for it is that it means not dead.



Next is Figure 2 which shows the six (6) weights Shelley modeled at various altitudes. I have added a thin red line at 100J. In fact, I would think a Major Skull Fracture at 50J is probably where I should have put the line. Either way I think that you will be unpleasantly surprised.

graph showing impact energy

But impact is only part of the equation. The FAA models are based on a density that is equivalent to four people standing on a football field. This is probably reasonable in a precision ag situation, but how about over a riot or a rock concert? Glad you asked, here’s how it plays out.

Graph showing maximum allowable height based on weight

The maximum height at which the safety goal of 6×10-7 fatality-equivalents per flight hour was met.

So based on the weight of the craft, the height is a function of the density of the crowd it is flying over. (ie how many people are under it. 1 person per sq m is very low.) What all this suggests is that even a half pounder falling from 35′ (not the promised 500′) can inflict grievous harm.

The results in Figure 6 suggest a considerably different outcome than that derived by the UAS Task Force. The difference between the UAS Task Force and the current analysis arises from two sources: first, the safety goal adopted by the UAS Task Force is based on a ground fatality rate approximately 100 times higher than the actual ground fatality rate; second, the UAS Task Force assumes a very low rate of people exposed to the falling aircraft.

Consider the Conclusion.

With a safety goal based on the ground fatality rate for existing manned aircraft, the analysis indicates that there should be significant restrictions on flying over people, including maximum heights that are quite restrictive compared to the maximum of 400ft AGL currently allowed. Flying over people is also only safe at low population densities.

Unmanned aircraft in excess of 1.5kg should not be flown over a crowd of people at any density.

The model also indicates that the recommendation of the Micro UAS ARC to allow unmanned aircraft of 250g or less to fly over people without restrictions is unsafe.

As the publisher of a website and owner of a marketing agency devoted to all things drone, I certainly have no interest in slowing the wheels of progress. Which is why I promote a long-term view of the industry. I have repeatedly objected to the rushed and ill-considered way that the FAA has assembled what can only charitably be described as special interest committees to set policies and do science in a month.
I do not know the literature, there may be other studies that refute, change or challenge the calculations that could or should be used. I do know that there are those who will want to argue with the list of drone and RC deaths he lists, four in
2013 alone.
But I for one am willing to take the author at face value. The work is certainly much more rigorous than anything I have seen to date. It is written in the cool, dispassionate voice of a scholar, not someone with an ax to grind or a dog in the fight. Being published under the imprimatur of Embry-Riddle only adds to
its credibility.
If you choose to take objection to the conclusions, and there will be those who do, I think that this paper provides a rational framework for a discussion based on both science and social cost, as opposed to one based strictly on the perceived opportunity for economic gain and the growth of an industry.
People accept risk in exchange for benefit. It is a time-honored exchange in every culture and at every level of society. That is why we tolerate deaths on our highways, and less frequently deaths on our rails and in our skies. I would rather take a little more time to let the genie out of the bottle, instead of trying to reinsert him which as we know all too well, is all but impossible.

Allowing a 13-year-old to fly his drone across a crowd of people, because the manufacturer certifies that it is safe to do so, will not pass the test of social benefit.

For some visceral, visual context take a look at this report from CNN on early research at Wichita State at the FAA ASSURE Center.
Andrew Shelley, is an Accredited Safety Auditor and Member of the New Zealand Safety Council with Aviation Safety Management Systems Ltd in New Zealand. 


  1. Hi Dan – Thanks for bringing that up. I have the video of the Quebec strike posted here and it’s pretty clear that it rocked her world. No word on the extent or severity of her injuries – I hope that she has recovered without any lasting damage.

    The tables in the article are based on statistical research and projections. No one incident validates or invalidates this kind of data. I value and shared the article because it makes clear that there needs to be a more transparent discussion of how the committee’s recommendation were developed and what variables were considered.

  2. An interesting thing to consider is the drone that recently struck the woman in Quebec. That was a free-fall from ~10 meters and the woman remained standing (although was injured).

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