Bungee jumping: eye-popping stuff
By Lewis Dartnell (a) and Mike Clifford (b)
(a) Centre for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX), University College London and (b) School of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham.
Adventure sports such as abseiling and skydiving attract enough scare stories and bungee jumping is no exception. Everyone’s probably heard about the lady killed whilst jumping from a 60m high bridge in Australia because she’d accidentally been tied to a rope 80m long. Or the newly-weds that tried a tandem jump on their honeymoon, but didn’t hold on tightly enough on the way down and cracked face-first back together at the end of the rope. Fortunately most of these are urban myths and survive only due to their pub-gossip potential rather than their accuracy.
Bungee jumping is, however, undeniably responsible for a range of serious medical complaints, including musculoskeletal pain in the neck and back, headaches, dizziness and blurred vision1. Thankfully, most of these symptoms have no lasting effects, yet there are tales of much rarer and more severe afflictions. In this paper we review some of the occurrences of bungee-induced injuries and report on some bungee jumping physics - it’s even possible, under the right conditions, for bun-gee jumpers to cheat gravity itself. We’ll then try to answer that burning question; can it make your eyeballs pop out?
Medical Mishaps
Some of the first medical research into bungee jumping found, perhaps unsurprisingly, that heart rate, blood pressure, and cortisol levels - all indicators of psychological stress - increase markedly in novice jumpers prior to a bungee2. These all then decline rapidly again after the jump and are replaced with a temporary increase in beta-endorphin - the hormone associated with feelings of euphoria. In other words, it’s petrifying beforehand but after the event it’s all smiles and back-slapping. More shocking is the great range of horrific injuries reported in the medical literature. Below is our non-fatal top 3 of when bungee jumps go bad.
3 Judging the bungee jump so that your head just dips into the water below may be exhilarating, but it’s also an insanely good way of causing yourself some serious mess. If the height or your weight is even slightly miscalculated, then hitting water at speed is not much different from tarmac. Another consequence of head-dipping is the sudden pressure change as you plunge underwater. In one patient, who rather unfortunately had their head angled back at the time, this trapped a pocket of air in their nose. The shockwave of compressed gas pulsed through his sinuses and forced its way into the eye socket. 3
2 ‘Reverse bungees’, where the victim is catapulted upwards for a bit first, have been increasing in popularity over the last few years. With this has come a change in the variety of bungee injuries, as the acceleration on an unprepared jumper can approach that of a fighter pilot. In one case, this initial crushing force has been blamed for the sudden change in chest pressure that resulted in a collapsed lung. 4
1 The all-time nastiest non-fatal bungee jumping incident resulted from a ‘normal’ jump. The sudden whip-like straining of the bungee cord cracked the man's spine and caused a ‘unilateral locked facet’ - painful in any language. This dislocation of the vertebra damaged the spinal cord leaving the man paralysed from the neck down. 5
The Physics of Bungee
The vast majority of jumping injuries arise from the immense accelerations generated by reverse bungees, the pressure changes during head-dipping or the sudden body-whip as the bungee cord first tightens. This third effect is the most common because bungee jumpers often fall in a characteristic horizontal body position with arms swung back to the sides and rope trailing up from the
attachment point by the feet. When the rope first pulls straight it starts to stretch, which tugs back on the ankles. The body’s centre of mass (somewhere near the stomach) is forced round and the head, the furthest point from the rope’s attachment, is viciously whipped around; this can put an enormous strain on the bones and muscles of the back and neck. As with most things, computer models can be used to simulate the physics of a bungee jump to reveal a range of possible behaviours. The MADYMO software is one such simulation code, plug in the values, press ‘enter’ and you’re away - almost as easy as jumping off a bridge yourself (see figure 1). The physics of a bungee jump, which is just like a weight on a string, is very similar to other systems such as buildings swaying during earthquakes, ships rolling in stormy seas or even a ruler held over the edge of a desk and twanged.
The implication of some of this physics for bungee jumping is that the up-and-down bouncing of the jumper can be converted into a side-to-side swinging movement (figure 2). For simplicity, the jumper is shown as a point on the end of the rope but it shows quite a scary series of movements. Some might argue that this additional sideways freedom would only add to the thrill and enjoyment of a bungee jump experience. The authors, however, are rather alarmed by the popularity of jumping with long ropes from bridges spanning narrow canyons; the effects of a system where vertical bouncing is converted into wide lateral swings could be somewhat unfortunate in a confined space! A problem of bungee jumping that the computer does not take into account is that the rope is not mass-less, but is bloody heavy; in fact, for the higher drops the weight of the rope can be equal or greater than that of the jumper. This situation results in a very interesting phenomenon - the bungee jumper accelerates faster than gravity. It sounds like something out of a Star Trek movie, but it’s a real effect because as the heavy rope falls and snakes around your body, it transfers its own momentum to you and you actually fall faster than you should according to free-fall physics and, more alarmingly, faster than a skydiver.
But what about those eyeballs?
The only points in a jump where you are being thrown one way then pulled rapidly the other is at the point when the rope gets to its longest. We know this causes whiplash, but is it possible that this can dislodge your eyeballs and leave them dangling around on stalks, Jim-Carrey-in-The-Mask-style?
Your eyeballs are held in place by six muscles, the lateral, inferior and superior rectus, the inferior and superior oblique, and the levator palpebrae superioris - more than enough to hold your eye in place even during strenuous forces. In 1954, Captain John Stapp, an American medical doctor endured 25Gs for 1.1 seconds during speed testing in Los Angeles6, the equivalent of someone hitting a wall in a car at over 120mph, but for nine times as long. Although he did burst nearly every capillary in both his eyes they didn’t pop out - and these are way beyond the kind of forces that would be reached in a bungee jump.
So, the answer? Bungee jumping, although a sport safely enjoyed by many, can cause some horrific injuries. Our MADYMO computer model has raised a few interesting new ideas for bodily damage, but this work’s unlikely to be much consolation as you rebound crazily between the walls of a narrow canyon on a long bungee rope. One thing seems ok though; it’s unlikely that your eyeballs will pop out while you twang back and forth on the end of the rope. Thank heavens for small mercies.
References
1. The Physician and Sportsmedicine 26, 1998.
2. Neuropsychobiology 29, 28-32, 1994.
3. Medicine & Science in Sports & Exercise. 29, 850-852, 1997.
4. Ugeskr Laeger 161, 5547-8, 1999.
5. Ann. Emerg. Med 22, 1060-3, 1993 .
6. see www.ejectionsite.com/stapp.htm for the full story.
| The Null Hypothesis Guide to keeping your eyeballs where they belong. In order to minimise the dangerous acceleration of the head; the point of attachment should ideally be as close to the rope as possible. Therefore bungee jumping with the rope tied around the neck could counteract this problem (although the authors have not yet fully investigated other problems that may occur with this method of attachment). Alternatively, jump head-first like you would off a swimming pool diving board, rather than the more heroic-looking swallow dive. This means that by the time you have fallen the length of the rope and it begins slowing you down, your head is already directly beneath the point of rotation and your body is pointing straight downwards. The resultant force is now almost completely towards the earth, pushing your guts into your lungs and your brain into the top of your skull, but happily minimising the sideways whipping-action. Hurrah. Finally, why not just stay at home with a cup of tea instead? |
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