|MadSci Network: Physics|
Headrests, Whiplash, and Related Subjects Regarding these things, I think the best place to begin is by reviewing some information which already exists here on the Mad Sci Network, so please see the first sections of these other Answers: (1) Concerning water balloons in a car http://www.madsci.org/posts/archives/nov99/943317877.Ph.r.html (2) Inside the workings of a see-saw http://www.madsci.org/posts/archives/jan2001/979658198.Ph.r.html A third reference will be introduced later. Regarding (1), the most relevant thing to the current topic is the concept of "inertia". While not explicitly named in that prior Answer, inertia is simply the tendency for any mass-possessing object to retain some steady state of motion (including zero motion). Thus when a car drives steadily down a straight road, all objects within the car eventually acquire the inertial tendency to keep moving in that same direction at that same speed. If the car makes any change in that motion, whether it be braking, turning, or accelerating, then depending on how freely the objects within the car can move, they will initially tend to inertially ignore the car's change in motion, and attempt to continue moving as before. Regarding (2), the most relevant thing to the current Answer is the description of the karate chop, which can cause a piece of wood to break when a force is applied suddenly. Carefully note that almost always, when some object is subjected to a force, the force is applied to only a portion of the surface area of the overall object. Nevertheless, the WHOLE object is subsequently affected by the applied force -- how? The answer is that a mechanical wave of force propagates through the object, at the speed of sound within the substance of the object, until every iota of the substance of the object has been affected by that wave. Since the speed of sound in most solids is usually thousands of meters per second, most ordinary objects experience the entire force in less than a thousandth of a second. DURING that small fraction of a second, the object is described as experiencing "jerk", a "rate of change of acceleration" -- just as acceleration itself is a rate of change of velocity. And, of course, the main effect of jerk is to BEGIN changing the inertial "current state of motion" of an object. However, HOW FAST does the object begin moving? Consider a billiards table and two balls. When one impacts "straight on" against another, the first always slows down to some new speed, and the second always begins moving at least at that same speed, and usually a bit faster. But if a speeding bullet strikes a billiard ball straight on, the ball simply cannot accelerate fast enough to "stay ahead" of the bullet. So, even as the ball is accelerating, the bullet is still applying force -- in the form of jerk -- to the ball! Like a karate chop against a piece of wood, any object receiving such a suddenly-applied and significant force will probably experience damage of some sort. ------------------------------------------------------------ Hopefully, the appropriate background information is now in place, to begin Answering your Question. Let us sneak up on it by starting with an ordinary fellow, Tom, who is just standing in some line or other, minding his own business. Dick is a clumsy bloke standing behind him -- he at first didn't see Tom move ahead a couple steps, but when he does, and begins to take his own steps, he stumbles. Harry is in some other line altogether, but happens to observe Dick colliding with Tom and applying a rather noticeable force to the middle of Tom's back. In this scenario Tom probably had his arms basically dangling at his side, and his head was merely resting in a comfortable balance atop his neck. Both arms and head have inertia -- so they tend to retain their quantity-zero motion while the applied force causes his torso to begin moving. Because the human body is fairly flexible at such places as shoulders and neck, the force that is causing Tom's torso to move does not immediately propagate to cause his arms and head to also move. Instead the "slack" in the connecting joints must be taken up first. Still, of the events that follow the collision, the whole sequence probably takes less than a second, before Tom's arms and head are jerked rudely. (And let us hope Harry explains to Tom that it was only an accident!) Fortunately for Tom, average human walking speed is less than five kilometers per hour, and the average human body is tough enough to experience such an accident with no more than minor and temporary pains, mostly in the neck. There will almost certainly be some pain, because of the way the force affects the neck and head in this scenario. See, although the neck will stretch slightly while the shoulders are pushed forward, there is a limit, and it is reached very quickly. The continuing forwards motion of the shoulders can only thereafter pull the neck and head along. Below are a couple crude sketches of SIDE VIEWs of Tom, before and just after impact: ( ) Standing ( ) inertia of head keeps it still | at ease / until force passes through neck | | | | (from shoulders to head: TENSION) | | | | <--force applied to torso At this point the head is no longer balanced above the neck, and can begin to fall for that reason alone, because of gravity. However, this is much less a factor than the fact that the head is starting to be pulled by the neck's motion. As Tom's torso continues to move forward, the angle of the neck can only become more and more horizontal -- but since it cannot stretch any more, the head must move DOWNward, as well as forward (but behind the torso, still). * ( ) Here is Tom's head behind his | | torso, neck painfully bent | | Now consider the ordering of the above sketches, and note that there is another way to get from the first sketch to last. One could simply and directly apply a force to the back of Tom's neck. Indeed, the overall already-described sequence of events can be broken down into parts, one of which is exactly such an applied force (although it might be called a "psuedoforce", because it is an indirect thing). As was defined in the see-saw reference (2), to apply such force to the back of the neck is to apply a "shear" force (the most damaging kind -- hence the pain). ----------------------------------------------------------- The human neck is reasonably tough, and has a strong set of muscles surrounding it. Nervous-system impulses typically lead to muscular reaction times of a few hundredths of a second, so even as Tom's head and neck start to bend over backwards, his body's autonomic system will begin tightening his neck muscles and resisting the shear force. In such a low-speed event, hardly any significant damage will occur. As evidence of what the human neck can actually withstand, let us take time out to look at a sport called "bungee jumping". People who fear it will likely be concered about the phrase "breaking their necks", but actually this is a quite-low-probability event. Participants most certainly tie long cords to their ankles, and jump head-first off a high bridge, but after the cords become taut, the falling people do not immediately stop falling. Instead the cords stretch, and a significant but SLOWLY APPLIED force (comparatively speaking) causes the rate of decent to diminish to zero, safely. That force propagates along the legs through the pelvis to the spine, along the spine and through the neck, and finally reaches the head in quite a staight (longitudinal) manner. The whole body stretches slightly under the influence of this tensile force. Note that none of this force is applied sideways to the neck, so there is no painful shearing effect. Nevertheless, necks do have limits. One form of execution that was popular in many countries for centuries is called "hanging". A strong rope is tied around the condemned person's neck, who is then dropped from a height of a couple of meters or so. The rope starts with that much slack in it; gravity accelerates the body, and when the slack is all used up, the falling body is jerked to a sudden stop. ALL the force of that jerk is applied to the neck. Most of that force is longitudinal/tensile, but some will also be of the shearing variety. MOST of the time, the neck will break, along with the body's main internal communications trunk line, the spinal cord. With heart and lungs no longer receiving the appropriate signals from the brain, the brain's supply of oxygenated blood is cut, unconsiousness follows in perhaps half a minute, and death happens not long thereafter. On the other hand, the neck sometimes does not break when a condemned person is hanged. I've read that people who survived the jerk of being hanged were sometimes allowed to go free, the rationale being that only an act of God could have intervened. Eventually it was found that at least three ordinary physical factors, besides the obvious one (a weak rope breaks before the neck does), can be responsible: The height of the drop may be insufficient, so while the the resulting jerk may be adequate on many occations, it is not reliable, because: Some necks (including neck muscles) are just plain stronger than others; and having a light-weight body means that less total force -- less jerk -- is needed to break its fall. About the time some of the less obvious factors were identified, judges began making their death sentences more explicit: "...to hang by the neck until you are dead." At the end of a tightened rope, even if the neck doesn't break, slow strangulation is inevitably fatal (unless some external intervention occurs). Nowadays slow deaths are out of fashion, and because of the major uncertainty regarding the immediate effect of hanging, that is why other methods of execution have largely replaced it. One of the first was the guillotine, which applied a perfectly shear force to the neck, via a sharp blade.... ------------------------------------------------------------ And now it is time to introduce automobiles into the topic. Individual autos can accelerate to great speeds, especially on race tracks. There is very little jerk associated with such acceleration, and equally little jerk associated with the deceleration (or negative acceleration) of applying the brakes, so nobody suffers neck problems as a result. Seats in vehicles were generally made to be both reasonably comfortable and inexpensive to manufacture. Headrests were not introduced for decades after the automobile went into mass production. Headrests were eventually introduced because it was discovered (the hard way) that automobile accidents can cause tremendous amounts of jerk to happen. Even one-car accidents can have fatal results. For example, consider a race car that encounters an oily patch during a curve of the track. For general background details about this event, now is the time to refer to other information already existing here on the Mad Sci Network: (3) Concerning motorcycles and high-speed cornering http://www.madsci.org/posts/archives/apr2000/955980971.Ph.r.html If enough wheels of an auto lose friction/traction with the road (by whatever means, not just an oily patch), then the auto may end up moving in a sideways manner, because it will have acquired some rotational inertia ("angular momentum") while starting to follow the curve in the road. If traction vanishes, that rotation will continue, thanks to inertia, and so the car can, at certain moments during its rotation, literally be sliding sideways. ALSO, however, the car still possesses all the inertia of a very large overall straight- line velocity ("linear momentum"), and therefore will simultaneously continue to move in a straight direction, as previously described. Obviously if the auto is travelling straight, it is NOT following the curve in the road, and so it will very probably move directly off the edge of the curve of the road -- unless there is a wall in the way, as is often true at race tracks. So, as has actually happened on occasion, a race car may hit a wall sideways, at a speed of perhaps 300 kilometers per hour. VERY sudden negative accelation then occurs! The driver's torso is strapped tightly to the seat, so when the auto is so drastically jerked to a stop, the jerk propagates nicely into the torso, and very little damage occurs there. However, the driver's head still has all the inertia that you can imagine is associated with the former velocity of 300 kph...and drivers have indeed died of broken necks, as a consequence of such "whiplash". In many accidents an air-bag deploys from the steering wheel, or a seat has a head-rest, so that the inertial motion of the driver's head can be stopped safely. But neither are effective in the above scenario, because the car hits the wall sideways. To add some sort of side-rest for the head is quite impractical, because the driver needs to be able to see out the side of the auto. Probably the best solution will be a clever air-bag design. Already some cars have air-bags on both interior sides, but something is needed in the middle, at least for race cars. ------------------------------------------------------------ Finally we reach the specific case of the rear-ended auto. This event can always be described as involving two vehicles that move at different speeds, the faster one being located behind the slower one. The magnitude of the impact will always depend on the difference between the two speeds. If that difference happens to be five kph, then very little damage will occur to the driver in front, just like the prior description of what happened to Tom after Dick stumbled. Larger differences in speed can have more serious results. As the rear of the auto is pushed forward by the impact, forces propagate thoughout the body of the car, including the seats. The seats propagate the impact/force to the occupants, and depending on the shape of a seat, and how (and by whom) it is being occupied, the effect upon the occupant can differ widely, in different scenarios. A low head-rest might be totally ineffective if the seat is occupied by a tall person, for example. There is a similarity of EFFECT, in describing a speeding auto that slams into a wall, and a stationary car that is slammed by another vehicle. In the latter, the slammed auto is jerked into motion while the head's inertia holds it still; in the former, the car jerks to a stop while the head's inertia keeps it moving. As far as the neck is concerned, the potential for whiplash is the same both ways (as long as the amount the slam is the same, both ways). The major effect of a properly-fitting head-rest, in any rear-ender scenario, is simply this: It allows the force of a jerk, which is being applied to the torso by the seat, to also be applied to the head, at practically the same time. Thus very little stress is placed upon the neck, so there is practically no whiplash effect, even when a rear-end impact causes major damage to the vehicle. In closing, it should now be obvious that auto-seat head- rests have saved many necks. Because one never knows when a rear-ender accident might occur, and which seat one might be occupying at such a moment, it would probably be a Good Thing if EVERY automobile seat had a head-rest. Anything less means you could be literally risking your neck.
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