A car is driving 50mph and hits a wall.
Two exactly the same cars are driving 50mph and hit each other heads on.
Is there any difference for passangers, if wall can't absorb any energy?

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Request for Question Clarification by omnivorous-ga on 30 Jan 2003 06:32 PST

Two cars driving 50 mph have a relative impact speed of 100 mph -- or
twice as much energy to dissipate as the car hitting the wall.  Is
this the comparison that you wish to make?

Best regards,

Omnivorous-GA

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Clarification of Question by ap12-ga on 30 Jan 2003 07:06 PST

I want to establish if there is a difference in impact on driver, if
he hits the wall compare to head-on collision with another car, which
is exactly the same, the same weight, same type and driving the same
speed.

ap12-ga,

I looked at the question clarification by you and at the comment by
michael2-ga and have a critical component to add.

You can't look at closing speed and put 100 mph into the energy
equation:

Kinetic Energy = 1/2 mass times (velocity squared)

You have two cars, each with their own mass and reference frame. Don't
think about "inertial reference frames" because we're talking about a
crash, not simply relative velocities.

The total collision has twice the energy that the independent
collision into a wall has. Why?

Kinetic Energy = (2 Cars) times 1/2 mass times (velocity squared)

However, you have two cars to dissipate the energy.  So divide the
total energy by two.

So yes, the total energy of hitting a wall head on is exactly the
total energy of hitting a oncoming car traveling at the same speed. 
Except now you have _two_ people and cars in need of repair.

Having said all that, your still dealing with a total of twice the
energy compared to a simple wall-crash.  If the energy is not
distributed equally between the two cars (very likely), the poor
driver in the car that gets the bigger chunk of the energy will have a
rougher time than the other guy.

NOTE: This answer _definitely_ uses your assumption that the wall
can't absorb any energy.

Let me know if you need a clarification of this answer.

Best to you,

krobert-ga

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Request for Answer Clarification by ap12-ga on 30 Jan 2003 11:51 PST

Really good, thanks a lot. Can we categorically say, that impact will
not be twice as bad, or alternatively, will not be the same as one car
hitting the wall with the speed 100mph?

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Clarification of Answer by krobert-ga on 30 Jan 2003 12:47 PST

For the impact to be twice as bad, all the energy from both cars would
have to be transferred to one of them. Just thinking about this, it's
pretty impossible for that to happen. One car would have to come out
just as good as it came in. So, in the real world... yes, we could
categorically state that the impact will not be twice as bad.

Of course this doesn't take into account a tumble down a hill or
impact with any other vehicles after careening from the first impact.

As the old saying goes, your mileage may vary.

-
krobert-ga

The energy dissipation is four times as much at a relative closing
speed of 100mph as it is at 50mph (as energy is proportional to the
square of the velocity).  So the head-on collision will be far, far
worse.

I agree with krobert-ga that the head-on collision of the two cars has
twice the energy.

In your original question, you asked "Is there any difference for
passengers?"  To further explore this aspect of the question, I
suggest that you look at some articles on the kinematics of trauma. 
The following excerpt from the book "The Basic EMT" will serve to
introduce you to this field:

"In motor vehicle collisions three separate impacts (collisions)
occur:  (1) the vehicle crashes into an object, (2) the unrestrained
occupant collides with the inside of the vehicle [edited:  or
unrestrained parts of the occupant collide with the vehicle], and (3)
the occupant's internal organs collide with one another or with the
wall of the cavity . . . In frontal collisions, the sum of both
vehicles' speeds become the velocity at which damage is produced."

This gets to the physics of the impact.  However, the actual injuries
suffered by a passenger in such a crash depend critically on whether
or not they are restrained, how they are restrained (there is a big
difference between seatbelts and a seatbelt/airbag combination), and
(if they are unrestrained) whether they end up going "up and over" or
"down and under."

You can order The Basic EMT from Amazon for $51.95    
http://www.amazon.com/exec/obidos/tg/detail/-/0323022561/qid=1043951691/sr=1-7/ref=sr_1_7/002-1180689-0840034?v=glance&s=books
or 
 
The slide presentation "Things That Go Bump in the Night - Kinematics
of Trauma"
does a nice job of summarizing factors that affect the different
degrees of trauma that passengers will experience in a crash such as
the one you describe.
 
file:///C:/WINDOWS/Temporary%20Internet%20Files/Content.IE5/CHOX2BKX/256,1,Things
That Go Bump in the Night Kinematics of Trauma

For a discussion of "up and over" vs. "down and under" injuries, see
the article "Trauma Mechanisms."
http://www.nordictraumarad.com/Syllabus/Traumamechanisms.pdf

search term="kinematics of trauma"

The answer to the question is that both cases are exactly the same. 

It's true that in the real world, any wall will budge at least a
little bit, and one of the cars might have hit a slight bump before
the collision and so be a little higher than the other, or the
left/right asymmetry of the cars might mean that they crumple
differently than they would if hitting a wall, but I don't think these
issues are in the spirit of the question.

If two identical and left/right symmetrical cars collide head on, with
no offset, the plane of impact remains motionless as both cars squash
toward it.  This must be the case because the situation is exactly the
same from both sides.  Since the impact point is motionless, there
could just as well be a solid wall there from the point of view of
either driver.

Dear ap12-ga,

As our Comments are coming to different conclusions on the physics of
the accident (total energy dissipation), I thought it might be useful
to you if I identified experts in the field.

Searching on the term "physics of motor vehicle accidents," I found
the following useful sites:

1.  THE PHYSICS CLASSROOM

This site is the headquarters for a high school physics tutorial.  It
works through the physics of several very specific accident scenarios.
 These are animated scenarios with physics explanations (and
calculations!) including a car and truck in a  head-on collision (an
"elastic" collision) at
http://www.physicsclassroom.com/mmedia/momentum/cthoi.html
and a moving diesel engine crashing into a stationary flatcar (an
"inelastic" collision) at
http://www.physicsclassroom.com/mmedia/momentum/dft.html

What are elastic and inelastic collisions?  The instructor says
"Certain collisions are referred to as elastic collisions. Elastic
collisions are collisions in which both momentum and kinetic energy
are conserved. The total system kinetic energy before the collision
equals the total system kinetic energy after the collision. If total
kinetic energy is not conserved, then the collision is referred to as
an inelastic collision."  (NB:  In an inelastic collision, total
energy is not lost.  But, kinetic energy is changed into other types
of energy such as sound energy and thermal energy, so the kinetic
energy goes down.  This gets to your assumption that the wall can't
absorb energy.)

I am not a physicist, and I have not attempted to calculate the forces
in your accident.  It appears to me that this site's examples give you
the tools to do so, and that - no matter what - your head-on collision
is going to have more impact on the driver than the crash into the
wall.  However, I was too quick to say (in my earlier comment) that it
would have twice as much energy.

2.  ACCIDENT RECONSTRUCTION TECHNIQUES AND ACCURACY
http://www.mchenrysoftware.com/genintro.html
Brian McHenry, who has developed software to analyze accidents,
discusses Newton's Laws of Motion as they affect motor vehicle
accidents.  You may contact him at McHenry@mchenrysoftware.com.

3.  ADDITIONAL RESOURCES

The Glenbrook South (High School?) Project Information Sheet on Auto
Collisions and Auto Safety includes additional links that you may find
useful.
http://www.glenbrook.k12.il.us/gbssci/phys/projects/yep/autos/austupa.html

Lots of people seem to be getting interested in your question!

One cannot vote on truth,
 of course. But perhaps one more comment will help
 ap12 to make his mind. The reasoning of the answer
 allowed for the incorect conclusion, actually made by michael2. 
 One does not divide total energy by number of particles to get
 the peak acceleration. Deceleration of the car is
 what casuses the injury, as it propels the passenger against
 the windshield, as corectly explained by pocopolo.

 So question can be modelled by two billiard balls colliding,
 or one such ball hitting heavy stationary wall.

  Is the the deceleration profile different in such two cases? 

In his second comment pocopolo confused things:  The wall may
be elastic or plastic and that has nothing to do with it being stationary 
or not. So we assume that wall and balls (and cars) have same
elastic properties. Let's consider elastic collisions only.

In that case ball rebounds the same way:
It just changes the direction of velocity
(in the same time interval) and threfore the effect
(measured e.g. by peak deceleration) is same in both cases.

So, racecars is essentially right 
(I hope it is not based on experience :-)
 but there are some implicit assumptions . 

If you would consider balls made of different
 materials and mass, 
a wall which has less then infinite mass (a net),
 it would be slightly more complicated.

  I hope this clarifies things

hedgie

Hello, all!  

This morning, I sent an email to Brian McHenry, an engineer who
specializes in accident analysis (see his resume here: 
http://www.mchenrysoftware.com/bgm.htm).  I referred to his company,
McHenry Software (http://www.mchenrysoftware.com/genintro.htm) in my
second comment above.  His company produces software for accident
reconstruction and analysis.

I copied Mr. McHenry on our entire discussion and asked him if he
could comment.  He emailed back (within an hour!) as follows:

QUESTION: A car is driving 50mph and hits a wall.  Two exactly the
same cars are driving 50mph and hit each other heads on.  Is there any
difference for passengers, if wall can't absorb any energy?

ANSWER: The main question is 'Is there any difference for
passengers'?The Answer is NO.

DISCUSSION: The passengers in each vehicle experience a 50 MPH change
in speed, impact speed change or DeltaV.  Of course in scenario 1
(car-to-barrier), the occupants of veh 2 are stationary, watching
those in Car 1 crash, and therefore they do not see any speed change,
so, if you want to get technical, the speed change WOULD be different
for the veh2 occupants in test 1.

One other point: A minor difference between car-to-car and car-to-wall
is that in the car-to-car scenario, since the other car is not a
wall/barrier, there may be some minor differences due to the fact that
to line up the impact exactly in the theoretical sense is impossible
so the offset, etc would make the car-to-car slightly different than
the car-to-barrier.

Yes, this is clearly correct, and if I had thought about it for more
that 5 seconds I should have realised my earlier comment was quite
wrong.  Sorry.

Michael2