The physics of Bungee Jumping 1

[GregLocock]

Never seen the attraction myself, but this paper investigates why a bungee jumper accelerates at more than 1g

https://www.fc.up.pt/pessoas/psimeao/desafios/Bungee_Jumper_maior_que_g.pdf

Good stuff.

 

[waross]

I was always taught that you can't push with a rope.
On construction sites, I have seen many times a suspended load with two taglines.
When the load has to be aligned by pulling on one of the taglines, that man on the other tagline tries to help by pushing on his rope.
This has never been successful.
Now you tell me that it is possible to push with a rope?
I'm too old for this. grin
ps; Joking aside, I may spend a lot of time trying to get my head around this.
Possibly a related effect, and possibly a way to aid in visualizing.
First investigate the physics of a vertical post, pivoted at the bottom end. Calculate the forces and acceleration as the post falls 180 degrees around the pivot.
Now take a series of fairly long members joined by pivots and let them fall similar to the chain, fastened at one end..
As each section completes its 180 degree arc its downward motion abruptly stops.
The next section of the chain of members has falling at the same speed when one end is abruptly halted.
The next section already has a lot of downward velocity and if one end is abruptly halted the inertia of the mass will act at the center of the section and the free end may be accelerated rapidly.
This will be in addition to acceleration due to gravity, The acceleration will be restrained by the free end still above, but as the free end becomes shorter, the effect and the velocity will increase.
If a link chain is used, the links will tend to bunch up and the action will not be the same.
The action of a roller chain may be closer to the action of a rope.

 

[MintJulep]

Did it once years ago, thought it was a blast.

TLDR:
Bungie cords stretch under their own weight.

 

[waross]

Bungie cords stretch under their own weight.

Another factor.
Thanks Mint.
Would that add to the acceleration?

(I will have to put old boring reruns on TV tonight and bore myself to sleep.
Else I will be awake all night trying to figure this out.

Nite all.

 

[MintJulep]

Would that add to the acceleration?

Sure,

As a near-analogy:
Consider a horizontal Bungie anchored to a mass at one end and you at the other.
Walk away from the mass to stretch the Bungie.
Take one more step - onto a skateboard.
As soon as you stop being able to resist the force in the Bungie, the Bungie accelerates you.

Taking that to the actual Bungie jumping case, stepping onto the skateboard = stepping off the platform.

 

[XR250]

Very interesting. Thanks for sharing.

 

[LittleInch]

ot sure if they actually covered it, but I guess as the jumper starts to descend, the bungee inflexion point is also moving faster than a rigid chain or rope as the suspended mass of the cors increases and hence the elongation of that section of the cord increase. Though is this not taken account of by the fact that the bit attached to the jumper is shortening??? hmmmm.

SO it looks like the extra mass of the bungee, plus some effects of the cord stretching under its own weight increase force on the jumper.

Interesting.

Never done one myself - too close to the ground for this ex skydiver....

 

[GregLocock]

The energy argument is rather neat, if an over estimate. L=length of bungee S is the distance the suicidal body has fallen, B is the mass of the bungee, M is the mass of the man . So initially the CG of the bungee is 1/4L below the platform.PE_S=0=g*(0*M-B*L/4) KE=0

When the bungee is just taut, and hence stationary

PE_S=L=g*(-L*M-B*L/2) KE=1/2*M*v^2=g*(-L*M-B*L/2)-g*(-B*L/4)=g*(-L*M-B*L/4)

which if we ignore the sign convention I've used to confuse myself is obviously bigger than just g*L*M if you forgot to clip onto the bungee (it has happened).

I love energy arguments, they cut through all the pesky details.

 

[prex]

The energy argument is used incorrectly IMO.
Take an inextensible chain suspended at one end, as in the bungee, falling under its own weight. When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.
This should mean that the cord does not add any actual energy to the mass of the jumper, so the acceleration can't be higher than g (which is BTW evident per se).
I would like to analyze this scenario with Lagrangian mechanics, but of course g is the maximum acceleration for a freely falling mass on earth's surface.

 

[GregLocock]

Looking forward to your explanation of MEASURED acceleration>1g

 

[prex]

Greg, read their conclusions, and you'll see that they are (were) not positive on the demonstration of the calculated accelerations by the tests.

 

[XR250]

When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.

The energy argument is used incorrectly IMO.
Take an inextensible chain suspended at one end, as in the bungee, falling under its own weight. When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.
This should mean that the cord does not add any actual energy to the mass of the jumper, so the acceleration can't be higher than g (which is BTW evident per se).
I would like to analyze this scenario with Lagrangian mechanics, but of course g is the maximum acceleration for a freely falling mass on earth's surface.

The chain will bounce up and down and burn up energy with air resistance and friction. A bit of a different situation.