Researching fire stunts last week got me into a ‘stunt-y’ sort of mood, and what is one of the next logical stunts to examine? Falling from height!

My initial research only brought up people who had performed incredible high fall stunts. In the *Assassin’s Creed* (2016) movie, stunt performer Damien Walters jumped from 125ft in the film’s Leap of Faith stunt. In a Twitter tweet, the *Assassin’s Creed *team touted the stunt as the highest free-fall for a film performed in 35 years. The movie that the tweet referenced was likely *Sharky’s Machine* (1981) where stunt performer Dar Robinson leapt 220 feet from Atlanta’s Hyatt Regency Hotel. In the movie, however, only the beginning of the stunt is shown.

While not involving art in any way, Luke Aikins 2016 free fall from 25,000 feet deserves an honorable mention. The daredevil jumped out of a plane without either a parachute or wingsuit and, after a two-minute free-fall, landed in a custom net.

At the end of the fall, all that truly needs to happen is to decelerate the jumper until they are moving with zero velocity (ie stopped moving). Over the years the way this deceleration has occurred has changed.

In film’s Western era, stopping falls relied quite a bit on breaking wood. Stunt teams would set up sawhorses around a crash site and delicately place a few pine boards on the sawhorses. Cardboard boxes would be placed under the boards, and some mattresses on top. When the stunt performer hit the mattresses, the boards would be put under stress and would begin to bend. After a few inches of bend (and some reduction in velocity for the performer), the boards would break, and the performer would continue their slowed fall into the cardboard boxes.

High falls performed in this way were limited to below 50 feet, as that was all the stunt performers could handle. Additionally, this way of performing the stunt was highly wasteful: the boards were broken, and the crushed cardboard boxes would not be reused for another fall.

Cardboard boxes continue to be used for lower falls today, as can be seen in this clip from an old episode of *Fear Factor*, when contestants were asked to drive a car off a building and into an (enormous) stack of boxes.

Nets, as demonstrated above, can be used for high falls, as well as for lower falls common in circus activities.

Bungee jumping has also become somewhat popular in films, as a stunt performer can be filmed from above without a need to erase their crash pad during post production.

The most accepted way of decelerating a stunt performer at the end of a high fall, however, is with an inflatable stunt air bag.

#### Inflatable Stunt Bags

The beginnings of inflatable air bags started in 1959 by John Scurlock as he attempted to create an easy-to-store, easy-to-deploy tennis court cover. As he tinkered, he noticed that his son enjoyed jumping on the inflatable mattress, and soon inflatable “moonwalks” were invented, followed eventually by the forerunners of bounce houses.

It did not take long for others to connect the child’s plaything with the fire nets firefighters were currently using to catch people trapped in burning buildings. The trick then, as is now, is how to cradle the jumper so that they don’t hit the inflatable pad and immediately bounce off it.

Inventors soon realized that the trick was to vent the air the jumper displaced.

A 1973 US patent (filed by the same John Scurlock) called for two air cushions stacked on top of each other: the top six feet in height, the bottom only three feet. As the jumper falls into the bag, the pressure build-up due to a decrease in bag volume eventually opens “breathers” on the side of the bag. With six feet of cushioned air to fall through, Scurlock calculated that a jump of 100 feet would be totally (and safely) stopped by the top cushion, but added the second, non-venting pad as a backup safety feature.

Scurlock also included equations in his patent, showing that the difficulty is in successfully balancing an energy equation.

##### The Equations

This is a reproduction of the equations filed in John Scurlock’s 1973 patent and changing technology may have rendered these equations useless. If you are trying to figure out how to safely perform a stunt, I applaud your effort, but suggest that you find someone with previous experience to work with you.

1). A_{a }= 8(1+3d- ((2d^{2})/h))

A_{a} is the affected area of depression

d is the depression

h is the height, or thickness, of the air cushion

I have no idea where this equation came from.

2). V_{loss} = 8(d+(0.9d^{2}-((0.6d^{3})/h))

V_{loss} is the volume of the air cushion lost due to depression

d and h continue to be the depression and height of the air cushion, respectively

As velocity is the mathematical integral of acceleration, this equation is (mostly) the integral of equation (1) with respect to d. It is stated that this equation was found after realizing that the depression takes the approximate shape of a cone.

3). P_{t}= 15(V_{loss}/V_{i}) + P_{g}

P_{t} is the pressure at any particular depression

V_{loss} is the volume lost

P_{g} is the initial pressure in the cushion (typically 0.5 psi in 1973)

4). Or by combining equations (1) and (2),

P_{t}= (120/(A_{i}*h))*(d+0.9d^{2} – ((0.6d^{3})/h)) + P_{g}

P_{t}, h, d, and P_{g} remain defined as above

A_{i} is the total surface area of the cushion

5). F = 1000P_{t}(1+3d-((2d^{2})/h))

F is the upward force of the air cushion on the falling body. This is essentially the same force that a chair exerts on you as you sit on it.

This equation comes from Force=Pressure*Area, with 1000 likely as a conversion factor.

6). F_{max} = 1000k(1+3d-((2d^{2})/h))

Where k is likely a modifying factor based on the height of the air cushion (?). The patent contains a table which is not well-described.

7). Work = F*D = F ʃd = 1000P_{avg}(1+3d-((2d^{2})/h))Δd

P_{avg} is the average pressure in the air cushion

Work is defined as force occurring over distance: mathematically one does the same work running a 5k as one does walking it. An integral is just mathematical shorthand for “find the (obnoxious) summation of the area under this line”

8). P_{m} = 3.3/(1+d)

P_{m} is the maximum pressure allowed in the air cushion

No idea where this formula came from, but it is likely something that a manufacturer will list.

9). V_{a} = 350(P)^{1/2}

V_{a} is the velocity of the escaping air (ft/sec)

P is air pressure (psi)

I suspect this is also something for the manufacturer to concern themselves with, and inform the client of.

Other Useful Equations

10). Potential Energy = weight*height

This is a physics formula, for the potential energy of the falling performer. This is equal to the performer’s kinetic energy:

11). Kinetic Energy = ½ mass*velocity^{2}

Essentially, any person high in the air has potential energy: if the floor suddenly disappeared, they would begin moving. As a performer has chosen to convert all of their potential energy to kinetic energy, potential energy equals kinetic energy. From this equation, one can calculate the performer’s velocity the moment before they hit the bag:

12). Velocity = (2*g*height)^{1/2}

Where g is the universal gravitational constant (32.2 ft/sec^{2}).

So there it is: as the performer falls, they will reach the inflatable air bag with some velocity depending on their weight and height they’re falling from. The moment they impact the bag, it begins to depress with affected area A_{a} and after a few moments to allow the internal air pressure to build, the air will vent out of the bag through “breathers”. At any point, the air bag is acting on the performer with a force F which is dependent on the pressure in the bag and the affected area A_{a}.

For further information (including a sample calculation and location of breathers, I would highly recommend looking at the patent).

#### Further Reading

GamesRadar’s *Assassin’s Creed* Jump

Polygon’s *Assassin’s Creed *Jump

Wikipedia’s “Dar Robinson”

USA Today’s Skydiver Stunt

Wired’s Physics Behind Skydiver Stunt

NPR’s “Hollywood ‘Stuntman’! Reveals Tricks of Trade”

Wikipedia’s “Inflatable Castle”