Encumbrance Effects in the Real World

 I recently bought a weighted vest to enhance my strength-building from walking and basic calisthenics, and wondered what data is out there on the effects of different loads. My vest has spots for 10 six-pound weights, so is adjustable up to 60 lbs in six-pound increments. Too much? Not enough? A quick search led me to this very well-written article containing more information than I had hoped for.

https://www.cnas.org/publications/reports/the-soldiers-heavy-load-1

RPG systems often ignore encumbrance because tracking it and calculating movement speeds detracts from fun gameplay for a lot of folks. Some systems (D&D) break encumbrance down into levels along the lines of "unencumbered", "light", "moderate", and "heavy", and describe how each level affects movement. Sometimes there is a label for the amount a character can lift off the ground that prevents any movement.

Heaven forbid a TTRPG track fatigue! I have on-and-off worked on developing my own system that simulates the real world better than other systems, and I have incorporated fatigue and recovery based on effort and fitness. I have to say that I managed to make a fatigue-tracking simulator that no one would enjoy playing. As many complaints as I have about D&D's class and level mechanics, I like the creative compromise between tracking fatigue or ignoring it (fire-and-forget spells/abilities). It is practical and playable to say that some activities (sprinting, max lifting) can be done "once per scene" or "once until a short rest". 

The data I used for movements speeds all assumed being unencumbered, especially at higher speeds and distances. Elite runners wear shoes and clothing carefully designed to cut grams off of weight in order to provide a competitive edge. Competitive runners get lean. This soldier data is a treasure, showing realistic expectations for encumbered movement.

Valuable take-aways from this article: 

• Characters should consider having an "approach" load and a "combat" load.
• Encumbrance causes initiative, reaction, awareness, concentration, and other penalties.
• Caloric intake, fatigue, and recovery time all scale with encumbrance.
• Encumbered people are easier to hit.
• There is a large increase in the time it takes to start moving from a standstill to 5m. 
• 1/3 bodyweight is often used as a benchmark for the high end of a reasonable burden for a soldier.
  

 

Here are useful images from the article:

Thanks to Lauren Fish and Paul Scharre for their work.
 

Adult Deadlifting Distribution

Here is the aggregation of men's and women's lifting abilities.  Again, the graph is inaccurate for the bottom percent or so, and the estimate equation only really applies to the 5th-95th percentiles.  I assumed a 52% proportion of women, not that it significantly affects the graph.

We can see a few distinct segments of data.  The bottom third is pretty exclusively made up of women who do not lift weights.  The middle third consists of untrained men, and women who weight train.  We see a sharp upward slope around the 73rd percentile, which is due to elite women weightlifters. The 78th to 98th percentiles, roughly, are made up of men who weight train, and the spike at the end is elite weightlifting men.

Even small children and the very weakest adults can still lift at least 20 lbs.  60 lbs is a good estimate for the 5th percentile.  The average adult (in the US) can lift up to 125 lbs.  People in the 81st percentile can lift double the average amount.  People in the 95th percentile can lift about 310 lbs.  Over 400 lbs is the territory of elite men and a handful of women.  Over 700 lbs is the territory of just a handful of men.

Again, there are unrealistic steps in the graph due to how the data was originally collected, and the smoother curve is probably more representative of the population. There should be a steep slope up from a low weight in the lowest few percentiles, but data is not available. 

Here is the same graph in kilograms:

Men's Maximum Deadlifting Distribution in Pounds with Equation

I figured it would be helpful to readers to revisit the distribution for men's deadlifts using pounds instead of kilograms.  Also, as I have been working on graphs for future posts, I have been tweaking equations that generate good estimates of what a person can lift at any percentile.

 It is important to note that the line was not calculated to be a best-fit to the data, and that was intentional.  I do not like how the deadlifting data I have creates a large jump past the 50th percentile, and it is entirely an artifact of the way the data was collected, not representative of the population, which would follow a smoother curve.  The equation I settled on is 65 + 35 * 1.0225 ^ (100 * percentile) in pounds.  Some day I will learn how to make equations pretty.  What is it, LaTeX?

Also, the equation for the line should only be used to estimate deadlifting ability for the 5th-95th percentiles.  Over the 95th, we see a sharp turn upward as the elites truly separate themselves from the pack.  Below the 5th percentile, we would also see a sharp turn downward if any data had been available for unhealthy or particularly weak men.  The lowest value available is the average maximum weight lifted by men with body weights in the bottom 0.005 proportion.

Women's Maximum Deadlifting Distribution

As I have done for men, I came up with a reasonable distribution of the lifting capabilities of US women.  Global data just is not available. The proportion of women who lift weights has nearly tripled over the last two decades to 21%, but this does not tell us what proportion weight-train with the goal of really getting strong.  I estimated some proportions to combine with the deadlifting table for women. 

It is interesting to note that any person can almost double what they can lift with six months of diligent training.  Also, the proportions of people rigorously training are fluid over time as weight-lifting fluctuates in popularity.  As women's sports have become more popular, and the health benefits of weight training become more obvious with increased scientific research, the curve in these graphs has become less acute, and may continue to straighten out a little in the future.  These graphs are snapshots in time, and do only apply to healthy women who have had the advantages of a first-world nation.  I've got these for you in pounds and kilograms, for your convenience. 

The strongest woman in the world has deadlifted 686 pounds (311 kg), so that is the current 0.000000001 level for women, and requires a life dedicated to building strength. 

For some clean RPG mechanic guidelines, the average woman can lift about 80 lbs (or let's say 35 kg).  A woman who is small and particularly weak should still be able to lift at least half as much.  Women at the 95th percentile can lift twice as much as an average woman.  The hard-training elite can lift four times the average.  These ratios are very similar to those for the men, except that the strongest woman in the world lifts almost nine times the average.

Next post: all adults together, which should really be the standard for developing RPG strength scales.

Women's and All Adult Weight Distributions

Continuing to use the EPA data, I plotted out a weight distribution for women.  Unlike the men's distribution, though, women's does not have a normally distributed natural log, so I filled in missing values without an equation.  The women's distribution has a more pronounced curve than men's.  I then figured overall adult weights by weighting and consolodating the men's and women's distributions with the assumption that our adult population is 52% women.

This information will be useful for players of games that take weight into consideration, such as Heavy Gear and Shadowrun.  Readers may want to keep in mind that people's weights peak in late middle age, and are lowest in early adulthood, with an average difference of about 15 lbs.  Also, there are racial differences.  Some supplementary information on racial differences (the EPA only lists Blacks and Whites) can be found here.

 

 The next step will be to find the proportion of women who weight-train, combine their weights with the deadlifting table, and plot women's deadlifting ability distribution, as well as for all adults, as I have already done for men.

Men's Maximum Deadlifting Distribution

Okay, still using the best source of strength data I could find, the distribution of men's body weights, and a scant article on a CDC study on the proportion of people who work out, I made a reasonable graph of the distribution of adult male maximum lifting ability.

Now, we know for a fact that there are dudes on this Earth who can lift over 400kg, but this graph only tracks up to the top 0.0001 of men.  About 0.00000001 of men can lift 450kg.  Also, I have no lifting data for the bottom 0.0034 of men, which should not be a big deal for RPG mechanics development.

Clearly, the average man can deadlift a max of ~80kg, or about 176 lbs.  The weakest men can still lift about half that, and men at the 95th percentile can lift about double that.  Elite lifters can handle three times as much as an average man, and the strongest men in the world can lift five times as much.  Those are some clean, easy guidelines for simulations. 

This graph is the predecessor of the top graph, and shows the same data with a different x scale:

I will eventually do this for women. Men tend to lift .42 to .64 more than women of the same body weight and same training.  Since men also tend to be heavier and lift weights more often, the women's distribution is probably about half of men's.

I will also compare the strength progressions of popular RPG systems to this real distribution, and rate them by how accurately they simulate real life, as well as by playability, of course.  I am using only deadlifts because nearly every system has rules for the maximum amount that a character can lift and not be able to move with, and most systems have no mechanics for other exercises.

Men's Body Weight Distribution

On my quest for determining how much people can lift, I developed this graph of men's body weights in pounds.  The natural log of men's weights in kilograms follows a normal distribution with a standard deviation of 0.165.  The equation I used, based on the EPA's data on the weights of American men ages 18-74, is e^(Standard_Deviations * 0.165 + 4.34) in kilograms.  The proportion of men of each weight is in percent.

Some RPG systems have rules regarding character weight.  For example, Heavy Gear and Shadowrun 4th ed. have attributes for Size or Body, respectively, based on the size of a person's body.  In real life, for the purposes of determining strength, the maximum amount of weight that a man can lift is close to 3.5 times his weight.  D&D is ridiculous for allowing halflings to have a STR of 18 at creation.

19 Principles of Recreation

These are Nineteen Principles of recreation from Howard Braucher, Secretary of the National Recreation Association in the mid-1930s.  I took these from Charles Smith's book, which I posted about here and here.  They are quite applicable to the children and adults of today, though there are new forms of recreation available today.  As you read, pretend that "man" means "adult".  Emphasis is mine: 

1) Every child needs to be exposed to the growth-giving activities that have brought satisfaction through the ages -- to climbing, chasing, tumbling; to tramping, swimming, dancing, skating, ball games; to singing, playing musical instruments, dramatizing; to making things with his hands, to working with sticks and stones and sand and water, to building and modeling; to caring for pets; to gardening, to nature; to trying simple scientific experiments; to learning team play, group activity and adventure, comradeship in doing things with others.

2) Every child needs to discover which activities give him personal satisfaction. In these activities he should be helped to develop the essential skills. Several of these activities should be of such a nature that he can keep them up in adult life.

3) Every man should have certain forms of recreation which require little space and which can be fitted into small fragments of time.

4) Every man needs to know well a certain limited number of indoor and outdoor games which he himself likes so that there will never be an occasion when he cannot think of anything to do.

5) Every man should be helped to form the habit of finding pleasure in reading.

6) Most men should know at least a few songs with good music so that they may sing when they feel like it.

7) Every man should be helped to learn how to make something of beauty in line, form, color, sound, or graceful use of his own body. At least he should find pleasre in what others do in painting, woodworking, sculpture, photography, if he cannot himself use these forms of expression.

8) Every man should be helped to form habits of being active, of breathing deeply in the sunlit outdoor air. Man thrives best in the sunlight. Since living, not business, is the end of life, our cities should be planned for living as well as for business and industry. Sunlight, air, open spaces, parks, playgrounds, in abundant measure are essentials to any living that is to give permanent satisfaction.

9) Every man should be encouraged to find one or more hobbies.

10) It is of the greatest importance that every person be exposed to rhythm bcause without rhythm man is incomplete.

11) About one year in every ten of a man's life is spent in eating. It is of fundamental importance that this one-tenth of a man's life shall be so lit up by play of mind upon mind that eating shall not be a hurried chore but an oppourunity for comradeship and for growth for the whole man. Eating should be a social occasion, in the home something of a ceremony.

12) Rest, repose, reflection, contemplation are in themselves a form of recreation and ought never to be crowded out by more active play.

13) Those recreation activities are most important which most completely command the individual so that he loses himself in them and gives all that he has and is to them.

14) Ultimate satisfaction in recreation comes only through one's own achievement of some kind.

15) The form of one's recreation as an adult, often, though not always, should be such as to use in part powers unused in the rest of one's life.

16) A man is successful in his recreation life in so far as the forms of activity he chooses create a play spirit, a humor, which to some extent pervades all his working hours, helping him to find enjoyment constantly in the little events of life.

17) The happy play of childhood is essential to normal growth. Normal men are most likely to grow from the children who have played well and happily. Normal men more easily continue normally as they keep up childhood habits of play.

18) Participation as a citizen in the cooperative building of a better way of life in which all may share is one of the most permanently satisfying forms of recreation.

19) That children and men and women may be more likely to live this kind of life, experience shows there is need for community action:

• Every community needs a person, and an unpaid committee or board charged with thinking, planning, and working to provide opportunity for the best possible use of the leisure hours of men, women, and children.
•  Community recreaion programs should continue throughout the year
•  Support of community recreation proams should be through tax funds under some dpartment of the local government.
•  Every community needs playgounds, parks, and recreation centers just as every city and town needs streets and sewers.
•  Every community should provide opportunity for the children when they leave school to continue the musical and dramatic and other specialized recreation activities which they have enjoyed during school days.
•  Community recreation progams should allow for a broad range of tastes and interests and varying degrees of mental and physical energy.
• Every community needs persons trained to lead in recreation just as much as it needs persons trained in education.
• Satisfying recreation, whether for the individual or for the community, involves careful planning.

The message I get from these principles in regards to role-playing games as they exist today are that RPGs are a great form of recreation for children and adults, but clearly should not be the sole form of a person's recreation.  Engage in live-action role-play.  There is joy in creation, storytelling, and community. 

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).