Launch worksheet

Launch solution 

The Scenario

You’ve just graduated from stunt school and are starting your first year on the Hollywood blockbuster movie circuit as a stuntperson. During training you’ve been warned that doing stunts is a risky career and that you should prepare for the possibility of regular, sometimes career ending accidents. You’re going to have to manage your level of risk and set yourself up to have other options at the end of your career.

Math Scenario 1: Workload

Being a stuntperson is brutal on your body. For one movie, you may be required to shoot the same stunt dozens of times in a row, until you get “just the right shot” for the director.

Needless to say, falling from a height, being lit on fire or fighting is not easy on the body and it takes a toll. Just like an elite athlete must not do too many events in one year, you must also restrict your workload to a safe amount.

Let’s say your risk of severe injury obeys the following equation:

R = x^1.5

where x is the number of movies you do in a year and R is the risk of severe injury occurring that year as a percentage

You are happy with a 35% chance of a serious injury each year, given the nature of the job. How many jobs should you aim to do?

The first thing we can do is graph the relationship between number of movies and injury risk:

Eyeballing the graph, it looks like the acceptable number of movies is going to be about 10 or 11 movies. However, we can use logarithms to calculate it more accurately:

R = x^1.5

35 = x^1.5

We can take the log of both sides:

35 = x^1.5

log(35) = log(x^1.5)

log(35) = 1.5 * log(x)

log(x) = log(35) / 1.5

log(x) = 1.029

x = 10^1.029

x = 10.69

So you can do up to 10 movies in a year and still meet your acceptable level of injury risk.

Math Scenario 2: Person on Fire

For your latest film, you’re the stunt double for one of the main villains. The scene involves racing through a warehouse on a motorbike while entirely on fire!

Safety always comes first. The stunt organizer wants to set up crew along the route so that if you crash, someone with a fire extinguisher will reach you within 3 seconds and put the flames out.

You’ll be riding down a 15 metre wide track, and will be riding wildly all over the entire area.

If the crew can sprint at an average of 7 m/s with the extinguisher, and they’re only allowed to stand off on one side of the main track area, what’s the minimum spacing between them so that they can reach you within 3 seconds?

We can use the right angled triangle formed in the diagram above to work out the answer.

w^2 + (0.5s)^2 = r^2

w^2 + 0.25s^2 = r^2

s^2 = 4(r^2 – w^2)

s = sqrt[4(r^2 – w^2) ]

r is the distance the fire extinguisher backup can run in 3 seconds:

r = speed * time

r = 7 * 3

r = 21 m

Substituting back in:

s = sqrt[4(r^2 – w^2) ]

s = sqrt[4(21^2 – 15^2) ]

s = 29.39

So the fire extinguisher backups should be spaced out at 29.39 metre intervals.

Math Scenario 3: Body Doubles

A large number of stunt scenes are based around fighting. Film directors don’t actually want to risk their superstars getting bloodied faces, so much of the fist fighting and kung fu is often done by stunt doubles.

The challenge with close up fight scenes is that the body double has to be convincing. Although effects and CGI can help, it’s often easier if the double does actually look like the actor.

For your next film, you’re responsible for auditioning body doubles for the main actor.

You know there’s a 2% chance that any person you audition will look close enough to the actor.

How many do you need to audition before you can be 90% certain of getting a match?

Chance of match = 1 – (chance of no match)^#people

(chance of no match)^#people = 1 – Chance of match

Take log of both sides:

(chance of no match)^#people = 1 – Chance of match

log[ (chance of no match)^#people ] = log [1 – Chance of match]

#people * log[ (chance of no match) ] = log [1 – Chance of match]

#people = log [1 – Chance of match] / log[ (chance of no match) ]

#people = log [1 – 0.9] / log[ (0.98) ]

#people = 113.97

You’ll need to audition 114 people to be 90% sure of getting a match.

Real Life Example – The Stunt Industry

1946 car stunt scene. Image public domain from Wikipedia:

The stunt industry has a long history dating back to the start of the 20th century. Safety at the start was non-existent, and performers were injured and sometimes killed on a regular basis – being safe for any period of time was more the exception rather than the norm.

Because stunt work is complex and dangerous, computer generated imagery offered a promising alternative, especially in performing ridiculous stunts that no stunt person would be safe doing – for example the end of the crane chase scene in Terminator 3:

However CGI is still often more expensive then doing it “for real” and there has also been some backlash from audiences, some of whom prefer the stunts to be genuine rather than computer wizardry.

Many stunt careers are cut short by injury, but there are famous examples such as the legendary Jackie Chan, who despite many injuries is still doing stunts in his 60s.