What is the true impact speed when two cars collide head-on at 50mph?

[AJ_2010]

Its probably been done previously but a search didn't return any results for me.

But anyway,

Vehicle 'a' (Va) travels head-on into Vechicle 'b' (Vb). Both are traveling at 50mph. Both vehicles are identical in weight, tyre grip, transmission, general design, road surface etc.

Is the impact speed 50mph or 100mph?

The police and news reports always say 100mph. (Probably because higher number usually gets more attention from the viewer).
But if you look at each vehicle in turn, each one is going through a transition of 50mph down to 0mph in the space of a crumple zone. So each vehicle is surely experiencing an impact speed of 50mph. Is it?


But then, Va is 'receiving' the crash energy from Vb (and vice versa), so the energy absorption is higher than if either Va or Vb were to crash into a stationary wall for example.
So under this view could it be argued that the impact speed is indeed 100mph?

(I suppose the term 'impact speed' is open to interpretation?)

 

[tiny-tim]

Hi AJ_2010!

But if you look at each vehicle in turn, each one is going through a transition of 50mph down to 0mph in the space of a crumple zone. So each vehicle is surely experiencing an impact speed of 50mph. Is it?

I think if you analysed it, you'd find that the crumple zone is shorter, so the acceleration (and damage and injury) is greater.

But the simple answer is that if you use the frame of reference of either vehicle, the the other vehicle is approaching at 100 mph.

 

[AJ_2010]

tim - a shorter crumple zone assumes less impact speed no? Therefore acceleration (or experienced 'g-force') would be less?

Approaching at 100mph yes.
I think this is why I mentioned at the end of my post that 'impact speed' probably needs interpretation.

But the main point of my question is that I hear the police and news readers say 'impact speed' all the time. And they simply add up the speeds of the approaching vehicles.

I was just wondering if this is actually misleading at all?

 

[tiny-tim]

ok, longer instead of shorter

no, it's the opposite of misleading, it's exactly the parameter that should be given …

when you're about to be in a crash, it very much is your frame of reference that is the most relevant to finding what's about to happen to you!

 

[AJ_2010]

it very much is your frame of reference that is the most relevant to finding what's about to happen to you!

Totally agree.

But if I look at it this way:
I am in car Va traveling at 50mph and Vb hit us at 50mph.
The car I am in comes to a stop from 50mph to 0mph within a fraction of a second and within a larger* crumple zone.

*compared to hitting a stationary wall.

Is this the same as me traveling at 100mph and hitting a stationary wall? Whereby I decelerate from 100mph to 0mph within a crumple zone of whatever it is and within a time frame of whatever it is.

As kinetic energy increases on the square of velocity there is MUCH more energy involved in the impact speed of a 100mph car hitting a wall than a 50mph hitting another 50mph car..is there not? I may be wrong as I have not done the actual calcs for this.

:)

The wording of 'impact speed' is assuming the car is having to stop from quoted speed to zero. In this case my line of thinking would be that a head-on collision in this example should be an impact speed of 50mph and not 100mph.

Happy to be proved wrong of course. :)

 

[Naty1]

Is this the same as me traveling at 100mph and hitting a stationary wall? Whereby I decelerate from 100mph to 0mph within a crumple zone of whatever it is and within a time frame of whatever it is.

essentially, yes...per tinytims post #4...
but of course cars crumple differently than a wall so the nature of the deceleration would likely be different...If the wall were a perfect solid and experienced no deformation, for example, likely the single car would crumple a LOT more than if it were only 1/2 of a pair of cars crumpling...

As kinetic energy increases on the square of velocity there is MUCH more energy involved in the impact speed of a 100mph car hitting a wall than a 50mph hitting another 50mph car..is there not? I may be wrong as I have not done the actual calcs for this.

no the energy is pretty much the same but how it is disipatted would likely be quite different...damage would be very similar...look at the situation from the FT = MV perspective...
it gets to the heart of the matter...the momentum (mv) is equal to the force (F) of impact times the duration of the impact (T)...so as the duration (T) gets bigger for some momentum, the force (F) gets smaller...the resulting effects are dependent on both force and duration of the force...

If that isn't especially clear, think about the car not crashing but instead just rolling to a stop from normal friction...you'd hardly feel the small force inside but it would take a relatively long time for the car to come to a stop. And of course no energy, nor momentum, would be lost to deformation of the auto body...

The above logic is why you may see plastic barrels of sand on highways...the sand gives way gradually when impacted by a car and so extends the duration (T) of energy disippation reducing the impact (F) to passengers...if you just double the duration of impact, you cut the force in half.

 

[ElTaco]

Since you're comparing to a wall, I think you need to take two cases into consideration rather than one.

1) You are moving at 50 mph and the wall is stationary.

2) You are moving at 50 mph and the wall is also moving at 50 mph.

In which case would there be a stronger impact?

The second case, and to make sense of it, if the wall was stationary in this second case, it'd be as if you were moving at 100 mph.

 

[AJ_2010]

Since you're comparing to a wall, I think you need to take two cases into consideration rather than one.

1) You are moving at 50 mph and the wall is stationary.

2) You are moving at 50 mph and the wall is also moving at 50 mph.

In which case would there be a stronger impact?

The second case, and to make sense of it, if the wall was stationary in this second case, it'd be as if you were moving at 100 mph.

Would this be a similar analogy though?
Is the car going from 50mph to zero in both cases? Or in the moving wall situation - would the car be going from 50mph to -50mph?Or to add some 'spice' to these cases : an HGV traveling at 50mph hits head-on a car traveling at 50mph.
The car would most likely go from 50mph to -20mph (or whatever it happens to be). And the HGV would go from 50mph to 20mph (for example).

In this case is the impact speed 100mph or the change in velocity of the car? ie.70mph (assuming you are sitting in the car)I thought I had it all in place in my head but the replies here have got me thinking harder :)

 

[ElTaco]

Oh ok, after looking at Naty's post, I think that answers your question the best.

As another way to think about it (and I guess a direct answer to your question since it's from an mass x acceleration standpoint versus a momentum one), F = ma, where a = dv/dt, the change of velocity over change in time. You're correct about the change in velocity, but the length of time will be shorter for an impact where both cars are moving at 50 mph, resulting in a larger acceleration and a larger force.

 

[elemis]

Since you're comparing to a wall, I think you need to take two cases into consideration rather than one.

1) You are moving at 50 mph and the wall is stationary.

2) You are moving at 50 mph and the wall is also moving at 50 mph.

In which case would there be a stronger impact?

The second case, and to make sense of it, if the wall was stationary in this second case, it'd be as if you were moving at 100 mph.

Hang on, if two objects are spaced out and moving at constant speeds there shouldn't ever be a collision.

 

[ElTaco]

Hang on, if two objects are spaced out and moving at constant speeds there shouldn't ever be a collision.

I'm confused, isn't this the same nature as the question?

 

[cjl]

Hi AJ_2010!


I think if you analysed it, you'd find that the crumple zone is shorter, so the acceleration (and damage and injury) is greater.

But the simple answer is that if you use the frame of reference of either vehicle, the the other vehicle is approaching at 100 mph.

Yes, you will. And, if you stay in the inertial frame of your initial motion, you'll find that at the end of the collision, you are moving backwards at 50 mph.

Each vehicle undergoes a 50mph deceleration over the distance of its own crumple zone. So, as far as the vehicle is concerned, it's exactly the same as if you hit a stationary, immovable wall at 50mph.

 

[K^2]

It depends on what you want to compare it to.

Two 50mph vehicles head on are equivalent to 100mph vehicle hitting a stationary vehicle. From that perspective, collision speed is 100mph.

But if you want to compare to collision into solid wall, a 50mph collision will do the same damage as two identical 50mph vehicles head on.

Since vehicles that collide usually aren't close enough to identical, the second comparison tends to be flawed. The first holds regardless of vehicle masses. So that would probably make more sense.

 

[elemis]

I'm confused, isn't this the same nature as the question?

You stated in the case of a an object moving towards a wall (which is also moving) there would be a collision.

This can't be true as the two particles traveling at constant and equal velocities can't collide.

 

[ElTaco]

You stated in the case of a an object moving towards a wall (which is also moving) there would be a collision.

This can't be true as the two particles traveling at constant and equal velocities can't collide.

I said they had the same speed, not velocity.

In that example, the magnitudes of their velocity were the same, the signs (AKA directions) were different.

 

[cabraham]

The TV show about myths addressed this issue. Two cars identical going at 50 mph crashing head on will each receive an impact equal to a single car at 50 mph hitting an immovable wall. The crumple distance & forces on the driver were indeed measured and affirmed.

But the reaction time would be based on a relative speed of 100 mph. E.g., if you were not paying attention & suddenly realized you are headed towards a brick wall, then you hit the brakes. The relative speed is 50 mph between your car & the wall. But if another car is approaching at 50 mph, the relative speed is 100 mph, meaning you'll have less time to slow down before impact.

It's not a simple cut & dried problem, but it has been proven that the damage to the car(s) & impact force on the occupants is equivalent for 2 cars at 50 mph vs. a car & immobile wall at 50 mph. A single car hitting an immobile wall at 100 mph incurs much greater crumple of the car body, & much greater forces on the occupants. This scenario is more dangerous. Make sense?

Claude

 

[boneh3ad]

The crash is effectively at 50 mph, not 100 mph. Think of it in terms of energy. If you have one car hitting a wall at 50 mph, you have the energy from that one car (let's call it E), and it is dissipated by that one car (the wall is stationary). If you have two cars moving at 50 mph, they both have energy E, but the mass is also doubled, so you are dissipating twice the energy but with twice the mass.

You could look at it in terms of forces if you wanted as well... or momentum. No matter how you slice it, a head on crash with two cars going 50 mph is the same as hitting a wall at 50 mph assuming the cars have the same mass.

This actually was tested on the Mythbusters and they got it wrong the first time, so they revisited it after all the fans complained and got it right the second time.

Two 50mph vehicles head on are equivalent to 100mph vehicle hitting a stationary vehicle. From that perspective, collision speed is 100mph.

This isn't true either. Two vehicles moving at 50 mph will again, have 2E energy distributed between the two cars. That means that each car dissipates E amount of energy. If you have a stationary car and a 100 mph car, the total energy is 4E and the mass is 2M, so each car is dissipating 2E. That is going to be a much worse crash. To compare the head on collision to someone hitting a stationary car, the moving car would have to be moving at about 70 mph (50$\sqrt{2}$).

Apologies if the LaTeX is messed up. This site always acts so goofy when it translates it...

 

[tiny-tim]

Yes, if two cars at 50 mph simultaneously hit opposite sides of the same brick wall, then that's obviously the same as if the wall wasn't there.

Putting the wall back: if the wall doesn't move at all, the effect on one car of hitting it at 50 mph is the same as the effect (on that car) of two cars crashing head-on each at 50mph.

 

[Fredrik]

But if another car is approaching at 50 mph, the relative speed is 100 mph, meaning you'll have less time to slow down before impact.

Only if the other guy doesn't hit the brakes too.

This isn't true either. Two vehicles moving at 50 mph will again, have 2E energy distributed between the two cars. That means that each car dissipates E amount of energy. If you have a stationary car and a 100 mph car, the total energy is 4E and the mass is 2M, so each car is dissipating 2E. That is going to be a much worse crash. To compare the head on collision to someone hitting a stationary car, the moving car would have to be moving at about 70 mph (50$\sqrt{2}$).

As long as we're neglecting friction between the cars and the ground, it's pretty obvious that velocities 50 and -50 (relative to the ground) are equivalent to 0 and 100. In both cases, the velocities are 50 and -50 in the center-of-mass frame, where the cars will eventually come to rest.

Apologies if the LaTeX is messed up. This site always acts so goofy when it translates it...

You need to refresh and resend after each preview. It's not supposed to be that way, but no one knows what's causing it or how to solve it.

 

[K^2]

This isn't true either. Two vehicles moving at 50 mph will again, have 2E energy distributed between the two cars. That means that each car dissipates E amount of energy. If you have a stationary car and a 100 mph car, the total energy is 4E and the mass is 2M, so each car is dissipating 2E. That is going to be a much worse crash. To compare the head on collision to someone hitting a stationary car, the moving car would have to be moving at about 70 mph (50$\sqrt{2}$).

Apologies if the LaTeX is messed up. This site always acts so goofy when it translates it...

Wrong. Final velocity of a 100mph car in a collision with stationary one is 50mph, not 0mph. Both the energy dissipation and momentum transfer are identical to 50mph head-on collision.

Not to mention the fact that this is a simple coordinate system transformation.

 

[Drakkith]

The TOTAL energy that must be dissapated from two cars hitting head on at 50 MPH each will be equal to a crash of 100 MPH vs a stationary object. However, since both cars are designed to crumple and such, each equally absorbs half the energy of the collision, which is equal to a 50 MPH crash against a totally solid object which absorbs 0 energy. Rarely do two identical cars hit each other head on, so in the real world its a bit more complicated. (Such as semi's vs Mini Coopers)

This is why they put those barrels of water or whatnot on many exits, so that the barrels absorb and dissipate energy over a greater distance than, say, a guard rail post, thus making the accident much less severe.

Decelerating over a greater distance makes the accident much less traumatic for the passengers.

 

[boneh3ad]

Not to mention the fact that this is a simple coordinate system transformation.

That isn't what makes what I said wrong.

Wrong. Final velocity of a 100mph car in a collision with stationary one is 50mph, not 0mph. Both the energy dissipation and momentum transfer are identical to 50mph head-on collision.

That is.

The TOTAL energy that must be dissapated from two cars hitting head on at 50 MPH each will be equal to a crash of 100 MPH vs a stationary object.

Only if that object is not permanently stationary. In the case of the wall, where no matter what you do the wall won't move, this claim is no longer valid.

 

[K^2]

Invariance under coordinate system transformation already tells me the statement has to be wrong. Damage can't depend on such a transformation. Analysis of final kinetic energy simply tells me exactly what is wrong with the statement.

 

[boneh3ad]

Invariance under coordinate system transformation already tells me the statement has to be wrong. Damage can't depend on such a transformation. Analysis of final kinetic energy simply tells me exactly what is wrong with the statement.

It was a big red flag, sure, but it wasn't what was actually wrong with my statement. The problem was I overlooked the fact that the hulking mess that is left over after such a crash would not be stationary.

But now I am just arguing semantics so I will just stop, because that is silly.

 

[AJ_2010]

I had a strong suspicion I was on the right line of thinking (even though my description of such may not have been the best ;) ).

So to summarise (on a basic level):
Sitting in a car traveling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.

 

[tiny-tim]

welcome to pf!

hi angela25! welcome to pf!

best thing to do (now you're here ) is to show us some problems that you've tried …

go to the appropriate homework forum, click on the "NEW TOPIC" button, show us your full calculations, and then we'll see what went wrong, and we'll know how to help!

 

[K^2]

So to summarise (on a basic level):
Sitting in a car traveling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.

Correct. Though, you probably wouldn't survive either.

 

[AJ_2010]

True :)

Although part of my line of work is to do with road accident data, (just the database side of things).
But it would surprise you the number of high speed accidents with modern cars that people walk away from without as much as a scratch.

 

[K^2]

If 50mph collision isn't quite head on, you have a descent chance. But surviving a perfect head-on would be near miraculous. Still, if the car crumples just perfectly, we are talking about 10g-15g, and that is technically survivable. There are just way too many things to go wrong.

 

[elemis]

The TV show about myths addressed this issue.

Mythbusters ? Adam Savage is so cool :P

 

[Fredrik]

So to summarise (on a basic level):
Sitting in a car traveling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.

If the situation is perfectly symmetrical (one car being the mirror image of the other and the collision being exactly head-on), there can't be any difference at all. In the real world, the situation is never perfectly symmetrical. If the collision isn't exactly head on, the driver won't accelerate as much, and is less likely to get crushed between the front and rear of his own car. Even the fact that the driver of the other car isn't sitting directly in front of him improves his situation somewhat.

 

[AJ_2010]

If the situation is perfectly symmetrical (one car being the mirror image of the other and the collision being exactly head-on), there can't be any difference at all. In the real world, the situation is never perfectly symmetrical. If the collision isn't exactly head on, the driver won't accelerate as much, and is less likely to get crushed between the front and rear of his own car. Even the fact that the driver of the other car isn't sitting directly in front of him improves his situation somewhat.

But we've already established that there is a difference.
A person in a car decelerating from 50mph to 0 is very much different than a person in a car decelerating from 100mph to 0 (in a crash situation).
The energy from hitting a stationary wall at 100mph is totally taken up by the car. Therefore, yes the crumple zone is larger, but a crumple zone is not linear in terms of force/deformation. And therefore deceleration increases dramatically in comparison to lower speed crashes.

With a head on, both traveling at 50mph, the crumple zone of BOTH cars absorb each speed of 50mph. Resulting in reduced acceleration at this lower speed. (Crumple zone smaller than at 100mph yes, but also less force required/involved which in turn equals less deceleration).

As the driver is connected to the car's deceleration in terms of seat-belt (and anything in front of him/her that makes contact ie.dashboard etc, the forces on the driver can be looked at as being relative to those that are on the car.

 

[Fredrik]

But we've already established that there is a difference.

I see now that you were comparing driving into a wall at 100 mph with a head-on collision between two cars both doing 50 mph. When I wrote the answer, I was somehow thinking of the car hitting the wall going 50 (the same speed as the two cars hitting each other). I guess I didn't think about what I was actually reading. Now that I am, I don't see why anyone would want to compare 100 mph into a wall with 50 mph head on. The relevant comparison is between 50 mph into a wall and 50 mph head on. My answer is correct for that comparison, but obviously incorrect if you double the speed of the car going into the wall.

 

[AJ_2010]

I don't see why anyone would want to compare 100 mph into a wall with 50 mph head on.

The police and the media seem to do it all the time.
This was one of the reasons I asked this question. Just to put my mind straight on the reasoning side of things.

Road safety is a big issue in the UK (and rightly so), but there is a constant pushing of big numbers relating to speed.
In my line of work I often use facts/figures/information from the accident database and speed is not ranked very high at all in terms of cause factor for injury accidents.

But most of our public tax money is aimed at reducing speeds on the road. And as such the media/police/politicians etc. always seem to push big numbers when referring to speed to cause 'shock' for use of a better word. (Well, this is my interpretation of events anyway).

Targeting speed is, as we all know, also a form of 'revenue' and generally the cheapest so called 'solution' to a 'black spot'.

Whether people agree with the above or not I'd just like to point out that its just personal opinion formed from work experience.

:)

 

[torquil]

Targeting speed is, as we all know, also a form of 'revenue' and generally the cheapest so called 'solution' to a 'black spot'.

According to the sources I've seen: for a given road, a lower speed limit leads to fewer deaths and less emissions.

Why? Less kinetic energy involved and less energy dissipation per unit distance.