MadSci Network: Physics

Re: what physics terms or areas do the use of an automobile head restraint use

Date: Sun Dec 16 02:59:09 2001
Posted By: Vernon Nemitz, , NONE, NONE
Area of science: Physics
ID: 1006990700.Ph

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
(2) Inside the workings of a see-saw
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

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:
" 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
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

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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