Death by Falling: Revisions and Simulation

One thing I realized while looking over my last post was that I only showed chance of death by impact velocity, not by distance.  Of course, you could calculate distances yourself, but I want to be more helpful than that (see second graph below).  Also, I've been bothered by my assumption of how many meters tall a "floor" is.  I had originally used the average height of the Empire State Building (12' per floor), but later used 3.5m.  This morning I checked out a resource for average floor heights by building type, and used those numbers instead, assuming that Ramos's and Delany's data was mostly from residential buildings.  Here is the revised graph of probabilities of death by impact velocity:

Here is the graph that I have put together from my estimates for chance of death for an average person by distance fallen, as well as two possible dice systems for simulation:

So, for a 3d6 system, you would try to roll higher than or equal to (meters_fallen - 9).  For a 3d10 system, just roll higher than or equal to the number of meters fallen.  For elderly characters, maybe add 2 to the number of meters fallen, or multiply by 1.5.  For children or acrobats, maybe subtract 1 from meters fallen, or multiply meters by .8.  Remember that even survivors are typically severely injured, even from falls of as little as 3m, and can require extensive medical treatment.   

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.

Terminal Velocity = SQRT(2mg/pad)

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).

Death by Falling

 [Edit: If you're looking for real information on deaths by falls, see my next two posts here and here.]

This is the first of several posts I have planned about simulating the results of falls from elevations.  Here I simply determined the minimum distance necessary to fall for an average human to die, the distance at which an average person would die on average, and the maximum distance that an average person could fall without dying for ten different systems.

As you can see, there are wide differences among systems.  The grades I give are subjectively based on how each mechanic models reality and contributes to game balance.

• Aberrant: For any fall under 30 meters, even the most feeble person has a 99.6% chance of only sustaining minor injuries that will heal in a day (bashing damage).  At 30 meters, damage becomes lethal and maxes out at 10 dice (an average of 4 levels of damage), with only a 1.3% chance of dying even when falling miles.  F
• Chaosium: Average health is actually 12hp, not 11, but the distances are correct.  1d6 damage for each 3 meters gives us a nice distribution of injuries and chances of death up to the assured death point at 36 meters. B
• D&D 3.5 (OGL): The average human in this system has 1d4 hp, which I round up to 3, but does not die until reaching -10 hp.  Most falls that are not immediately fatal will still result in wounds that may result in a person's eventual death if not stabilized, but I did not calculate that.  B
• D&D 4th ed.: The most appropriate stats I found for a non-heroic person in this game were for "Human Rabble", who have 1 hp.  At 1d10 damage for each 10' fallen, everybody dies from any fall of at least 10'. D
• GURPS 3rd ed.: Damage involves rolling 1d6 and subtracting a constant for each yard fallen.  Since it is possible to roll the constant or less on each 1d6, it is possible to take no damage at all when falling from any height.  Instant death requires 6xHealth damage in the GURPS systems. D
• GURPS 4th ed.: Now there is an equation for determining how many d6 to roll based on velocity.  GURPS in one of the few systems that takes acceleration into account instead of just distance.  A-
• Heavy Gear: Roll 1d6 for each meter up to 10 meters, and multiply the result by meters fallen up to 30.  Remember that the Silhouette system is funky, so "result" means the highest number rolled among the dice, and additional 6s each add 1 to the first 6.  It is possible (ridiculously unlikely) to roll all 1s and survive any fall.  It is also possible (ridiculously unlikely) to roll all 6s and die falling 5 meters.  An average person has a 40% chance of death falling 8 meters, and an 81% chance of death falling 9 meters. B-
• Marvel Super Heroes 2nd ed.: The rules as written were clearly not proofread or edited.  They make absolutely no sense in the English language.  On page 21 the rules say to take 1 point of damage for each floor fallen (a person would have to fall 24 floors), but also say to treat falling as a charge attack.  Charge attack rules on page 27 gave me the numbers I use for this post.  Using the Empire State Building for reference, I decided that a "floor" is 12 feet. F
• Rifts: People take 1 point of damage for each 10' fallen.  Instant death is at -(PE+1) hp.  A healthy average person will survive any fall under 390'.  F
• Shadowrun 4th ed.: I did not find stats for an average human.  Humans have 1-6 body points, bought up from 1 at character creation.  Looking at sample characters, I figured that an average human has a body of 2. Damage from falls over 6m is about (distance+4)/2, and characters roll (Body)d6 to resist some damage.  For someone with a Body of 3, the distances are 22m, 24m, 28m.  C
• 7th Sea: This is a game focused on dramatic swashbuckling stories, and seems to not have rules for falls.  

And here is a graph: