Calculating Bungee for Theatre, Dance and Circus: A Textbook Guide

[Steven Santos]

So, I am writing a textbook on working with bungee in the theatrical, dance and circus industries. This book is focused mostly on the "these are the knots you use and how to tie them; this is how to splice bungee; this is how to make a bungee pack; this is how to put on a bungee harness; this is how you keep this part safe, ect". In the real world of human life and bungee we typically use a load/elongation curve and a rebound curve to calculate out how much and what length of bungee to use for what effect. In large part we do this because these curves easily adapt to the changes in production run of the rubber, heat, humidity and other real-world factors that are a lot harder to deal with in a simple formula. To be clear, the focus in this book will be on making and using elongation and rebound curves to determine what to use, so little to no fear of people getting killed using this.

BUT this is a textbook. The publisher wants me to find and in a page or two explain a SIMPLE physics formula for calculating bungee that can be fairly easily explained to students without a physics background (why? To piss off physics and non physics students I am sure...).

The three parts of the equation are obviously

Freefall (mass * acceleration of gravity over the unstretched length of the cord)
Deceleration (energy of the fall taken up by the spring constant of the bungee until it stops the mass)
Rebound (built up energy in the spring overcomes the force of gravity and rebounds them upwards)

So, does anyone got any resources that might help? Anything that is aimed at middle school age is probably most applicable.

Thanks everyone.

 

[jedishrfu]

Welcome to PF!

There was some discussion on bungees and whether they follow Hooke's law:

https://www.physicsforums.com/threads/hookes-law-f-kx.329417/

 

[Steven Santos]

Interesting. A LOT of incorrect or not-quite-correct info in that thread

All rubber used in tubes or as bungee (both natural and synthetic) is vulcanized, typically in a Banbury mixer.

That rubber is then put through a milling process, where it is rolled between two or more steel rollers. This makes the rubber more consistent and brings it to the desired softness. Additional dry chemicals are often added at this point, depending on the desired properties of the rubber.

The rolls of rubber produced from the milling process are then fed into extruders, which produce the tubes or strands. It can also be fed into sheeting machines that make sheet rubber.

For bungee cords, parallel strands are brought together in a machine known as a bungee braider that produces the cotton or nylon sheath.

Milspec bungee has an ultimate elongation of 200% (3 times the original length) before failure.

New Zealand bungee has an ultimate elongation of 700% (8 times the original length) before failure.

French bungee has an ultimate elongation of 1100% (12 times the original length) before failure.

Most bungee is only used to a fraction of its ultimate elongation. French bungee is typically used to 300% elongation (4x its original length). Milspec is usually used to about 50% elongation (1-1/2 times its original length). Going past that will result in rapidly decaying bungee.

Surgical tubing is a crap shoot in terms of what it will do. Its not designed to be stretched, though bungee tubing is designed for that.

Still looking for a simple formula :)

 

[Steven Santos]

And having made thousands of load/elongation curves, no, they are not strictly linear. Hookes law more or less works in part of the range however, and this makes it useful.

 

[A.T.]

And having made thousands of load/elongation curves, no, they are not strictly linear. Hookes law more or less works in part of the range however, and this makes it useful.

If you have so much data, just fit some non-linear function to it, and there you have your simple formula.

 

[Steven Santos]

I never took physics. One of my major faults is that I don't know what the functions are. Hense why I am asking for help.

 

[jedishrfu]

One thing you should consider for your book is the potential liability with publishing something that could be wrong such as a bungee stretching formula.

I would suggest getting a qualified mechanical engineer to review it before publication as a possible protection against a liability claim. I am not a lawyer but that may be someone to review it too.

 

[Steven Santos]

As to the legal liability, that is easily solved. Beyond the scope of this forum other than to day that's why we have lawyers and peer review.

And the stark reality is that at the end of the day, you just don't know what the spring constant is without testing the particular piece of bungee. Same manufacturer, same specifications, as much as a 20% difference in stretch between todays run and yesterdays. Change the relative humidity and you can get a 50% change in the bungees elongation. This is why load/elongation curves are the standard - NO ONE in their right mind would use a simple static formula based on a spring constant for calculating bungee used for a human life, or if they did, they would sure as hell test it with a sack load (dummy load, usually sand in a sack).

I need such a formula because they want one more 'testable on paper' thing. Now I am stuck finding it. The formula doesn't have to be perfect. A perfect formula would be incomprehensible to 99% of the target audience of the book anyways. I need a few formulas for bungee that could be followed by middle schoolers with some hand holding.

Anyone have any leads for me on where to find this?

 

[jedishrfu]

Then use Hooke's Law and pose it as an experiment where they can determine the k value for some bungee cord that they may have.

http://en.wikipedia.org/wiki/Hooke's_law

 

[Steven Santos]

Now that's something I had not thought of. Thats a GREAT idea!