## Jun 4, 2011

### Death by Falling: Real World Information to Guide Mechanics Development

So I don't turn away too many readers with the length of this post, here is the executive summary:

For an average person in the real world:

• The shortest fall distance that can result in death: 0m (or I guess ~1m if we focus on center mass)
• The average distance that will result in death: ~15m
• The maximum distance a person can fall and survive: technically any with a lot of luck and medical attention, but practically closer to 30m (still with luck and medical attention)
[Edit: For a graph of chances of death by distance fallen, see the next post.]

My Process:

To help game designers (and for myself) with developing simulation mechanics for falling fatalities, I tried to get some real world data on fatalities and injuries from falls. My first stops, of course, were the Center for Disease Control and Prevention (CDC, because it tracks all causes of death), the National Institute of Health, and the Occupational Safety and Health Administration (OSHA, part of the Dept. of Labor). Amazingly, none of these sources made available the proportions of falls that result in fatalities or injuries by distances fallen. There was just a lot of information on the numbers of people who died from falls each year by profession, age, job, and fall context (ladder, roof, scaffold, etc...) In fact, I could only find one document via the CDC reporting a proportion of falls resulting in injuries, and it was only for Americans over the age of 65 in 2006.

I turned to regular Google searches and found a few research articles from over the last four decades with some data on fall fatalities. I also explored some information on pedestrians and unbelted drivers in front-on car collisions in case I would have to use it as a not-ideal proxy for a person hitting the ground (like the Marvel system's use of charging attack mechanics). Interestingly, the fatal car collision speeds are very close to the fatal fall speeds that I found, despite significant situational differences such as body position and impact angles. People tend to survive slightly higher speed impacts in front-on car collisions than falling.

In this graph, falling speed is estimated based on distance fallen, which was also estimated because Ramos & Delany (1986) only reported distance fallen in floors (like the Marvel system).  The rest of the data points are generated by the regression equations from the Richards (2010) document, which is why the curves are so smooth.

[I later revised this graph using different assumptions about floor heights.]

Terminal Velocity:

I learned a lot about terminal velocity, and made a calculator in Excel that works for dry air. Humidity and water vapor decrease air density, but I do not know how much. For an average spread man, terminal velocity is about 56 m/s near sea level.
m = mass of object in kg
g = gravity (9.81 m/s at sea level)
p = air density, which equals 1.225*0.9883^(altitude_in_meters_over_sea_level/80)
a = object surface area facing down, generally .5-.6 square meters for a spread skydiver
d = drag coefficient, which is probably .6 for a person (McIlveen, 2002)

I derived the equation for air density based on other information I found, so it may not be precise.  Terminal velocity is largely irrelevant because 99% fatality rates occur at about .6 of terminal velocity at sea level. Using v=at works well enough up to the nearly assured fatality point that I do not feel pressured to accurately model how drag affects falling acceleration. Wikipedia says that half of terminal V is reached in about 3 seconds, which matches v=at, but that .99 of terminal V takes 15 seconds instead of <6s. This equation relatively closely approximates velocity in m/s as a function of time (s) for a 70kg person falling near sea level: y = 0.0375 x^3 + -1.28 x^2 + 14.9x + -4.02.  [Edit: I do not like how the line starts at a positive value and tilts up anti-asymptotically at the end, so I would probably replace x in the equation with (x-0.35), and say that terminal velocity is fully reached at 12 seconds.]

Facts:

Falls are one of the leading causes of injury and death, especially for kids and the elderly. Kids take less damage, and the elderly take a lot more. Falls are the 2nd leading cause of death for Americans age 60-72. About a quarter of elderly falls (from standing, steps, or furniture) result in injuries, and 1% of those result in death.  20-30% of elderly falls result in permanent debilitation.

Fatalities in the data here occur up to months after the falls.  I do not have real data on instant deaths.

The average survived work-related fall results in 100 days of missed work.  These falls are generally among contractors and roofers, from ladders, scaffolding, and roofs.

20-30% of fatal falls at work are not from a height!  Tripping can be fatal if the head is struck against something in a bad way.

The record speed of falling is 614 mph, achieved over 40 years ago by a guy who jumped from a balloon at 30,000 meters where the air is only 0.015 as dense as it is at sea level.

Jumps from the Golden Gate Bridge, about 70m, have a 2% survival rate, but even many who survive the fall drown quickly. 80% break bones, mostly ribs, and 75% suffer lung injuries. More than half rupture their livers, and a quarter fracture their skulls. The record high dive is from about 52m (you can find videos on YouTube). It is vital to hit the water feet first, minimizing surface area and protecting the torso and head.

The Richards document for the London DfT has a great graph on injury severities by velocity.

Sources:

Center for Disease Control and Prevention. (2008). Self-Reported Falls and Fall-Related Injuries Among Persons Aged >65 Years --- United States, 2006. MMWR, 57(09), March 7, p. 225-229.

McIlveen, J. (2002). The everyday effects of wind drag on people. Weather, 57, p. 410-413.

Occupational Safety and Health Administration, Department of Labor. (2010). 29 CFR Part 1910. Federal Register 75 (99), May 24.

Ramos, S. and Delany, H. (1986). Free falls from heights: a persistent urban problem. Journal of the National Medical Association, 78 (2), p. 111-115.

Richards, D. (2010). Road Safety Web Publication No.16: Relationship between Speed and Risk of Fatal Injury: Pedestrians and Car Occupants. Department for Transport: London.

Snyder, R. and Snow, C. (1967). Fatal injuries resulting from extreme water impact. Aerospace Medicine. 38 (8).

#### 1 comment:

1. Thank you for collecting this information, I've used in in my own little homebrew. It is frustrating that there's so little data available! Ditto for gunshot wounds, let alone more exotic injuries like swords.