Any clever math boffins explain this?

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i was listening to radio 2 about the German train crash and there was a boffin on that said a head on crash with both trains doing 40mph isn't the same as an 80 mph collision into a stationary object.
He sounded convincing and thought the collision would be much less energy due to some equation or other. Any one clarify that in words I might understand? :confused:
 
BruceMo said:
i was listening to radio 2 about the German train crash and there was a boffin on that said a head on crash with both trains doing 40mph isn't the same as an 80 mph collision into a stationary object.
He sounded convincing and thought the collision would be much less energy due to some equation or other. Any one clarify that in words I might understand? :confused:
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Oww! That hurt!
 
The below describe perfect conditions, it won't be precise but it's going in the right direction..

Train A hits brick wall at 100mph, it gets pancaked because the energy of the 100mph crash is absorbed entirely by train A. The wall remains unchanged.

Train A hits Train B whilst they're doing 50mph towards each other. Both trains take damage, but the energy of the combined 100mph impact is divided between the two trains. They each take half the energy of a 100mph impact, or approximately the energy of a 50mph impact into an immovable object,
 
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That's pretty much how Mythbusters explained it when they did the experiment a few series(es?!) ago.
 
Alastair said:
The below describe perfect conditions, it won't be precise but it's going in the right direction..

Train A hits brick wall at 100mph, it gets pancaked because the energy of the 100mph crash is absorbed entirely by train A. The wall remains unchanged.

Train A hits Train B whilst they're doing 50mph towards each other. Both trains take damage, but the energy of the combined 100mph impact is divided between the two trains. They each take half the energy of a 100mph impact, or approximately the energy of a 50mph impact into an immovable object,
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That's something like what he said. Must just be my old brain can't cope with maths.
I'm pretty good with mental arithmetic but maths just hurts my head haha
 
This is very crude and makes a ton of assumptions, it also ignores units as using mph rather SI units just creates a nuisance. But with all that borne in mind I think it's sound in principle.

Kinetic energy calculated as:

mass times the square of the velocity, all divided by two

So, ignoring mass (suppose it is the same in all cases) and the divide by two as that's the same in both cases, if a train is travelling at 40 of some unit, then the kinetic energy of each is 1600 of some other unit, and two trains will have a total of 3200 in kinetic energy. That energy all has to go somewhere and it will go onto deforming the structure of the object. Each train will be deformed (we'll assume they are identical) , so they'll take 1600 units of energy each in deformation.

A single train with a velocity of 80 will give a kinetic engery of 6400, so double the total of the two trains travelling at 40. A wall is not as deformable as a train, so almost all of the damage will go to the train. So a single train hitting a wall at double the velocity will absorb approximately four times the amount of energy in the collison.
 
I had to look it up for a decent explanation, but it's one of those where logic tells you the impact must have twice the energy but you forget there are two bodies to absorb it. The classic hitting a wall example generally assumes that no energy is absorbed by the wall because the train will crumple first.

Another way to look at it is to imagine a fixed wall between them at the exact point they hit each other. They both hit this wall at 50mph.
 
ignore
 
onomatopoeia said:
This is very crude and makes a ton of assumptions, it also ignores units as using mph rather SI units just creates a nuisance. But with all that borne in mind I think it's sound in principle.

Kinetic energy calculated as:

mass times the square of the velocity, all divided by two

So, ignoring mass (suppose it is the same in all cases) and the divide by two as that's the same in both cases, if a train is travelling at 40 of some unit, then the kinetic energy of each is 1600 of some other unit, and two trains will have a total of 3200 in kinetic energy. That energy all has to go somewhere and it will go onto deforming the structure of the object. Each train will be deformed (we'll assume they are identical) , so they'll take 1600 units of energy each in deformation.

A single train with a velocity of 80 will give a kinetic engery of 6400, so double the total of the two trains travelling at 40. A wall is not as deformable as a train, so almost all of the damage will go to the train. So a single train hitting a wall at double the velocity will absorb approximately four times the amount of energy in the collison.
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whoah, that takes me back to A level Physics. t is also the most sensible post I have seen here in a long while! :-)
 
Comparing the two collision types is very much a theoretical exercise. An 80 mph collision with a stationary (and presumably an immovable object) is, on the face of it, worse. When two trains collide head on they will likely deviate from their original path immediately after making contact and therefore not incur much more damage as they slide or run along the track and adjacent ground. Impact with a stationery object is more likely to see the front part of the train crumple until all the energy is expended.
Another thing to bear in mind is that it is likely that if identical circumstances were repeatedly set up and the collision re-enacted the result would probably be different every time.
 
onomatopoeia said:
This is very crude and makes a ton of assumptions, it also ignores units as using mph rather SI units just creates a nuisance. But with all that borne in mind I think it's sound in principle.

Kinetic energy calculated as:

mass times the square of the velocity, all divided by two

So, ignoring mass (suppose it is the same in all cases) and the divide by two as that's the same in both cases, if a train is travelling at 40 of some unit, then the kinetic energy of each is 1600 of some other unit, and two trains will have a total of 3200 in kinetic energy. That energy all has to go somewhere and it will go onto deforming the structure of the object. Each train will be deformed (we'll assume they are identical) , so they'll take 1600 units of energy each in deformation.

A single train with a velocity of 80 will give a kinetic engery of 6400, so double the total of the two trains travelling at 40. A wall is not as deformable as a train, so almost all of the damage will go to the train. So a single train hitting a wall at double the velocity will absorb approximately four times the amount of energy in the collison.
Click to expand...
Sounds very convincing.
Did you know that without looking it up? If so, I'm impressed.:)
 
Mythbusters theories have been debunked many times.
I don't think the families of those killed will particularly care.
 
Bobsyeruncle said:
Did you know that without looking it up? If so, I'm impressed.:)
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Yes, I didn't study physics (or maths) at university, but I rememebered the formula from my O levels (would be GCSE now, I suppose), and the rest is plugging the numbers in to get a result.
 
I agree with arc light.
In reality I don't think there would be an unmovable object that would not crumple and also absorb some of the energy. Surely that wall would fall over?
 
Nod said:
Not much movement in the wall in this video and if another F4 had hit the other side, any that there was would be negated.

View: https://www.youtube.com/watch?v=RZjhxuhTmGk
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Bebop said:
In reality I don't think there would be an unmovable object that would not crumple and also absorb some of the energy. Surely that wall would fall over?
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Mature trees don't tend to move much when cars plough into them. ;)

It irritates me when news readers/the press say `2 cars in100 mph head on accident....` if they were doing 50 mph each. It's just sensationalist journalism, but from people/researchers who should know better. :rolleyes:
 
Sort of, yes but the cars' closing speed is 100MPH if both are travelling at 50MPH.
 
I completely agree but it does show that (relatively!) immovable objects do almost exist in the real world as well as the theoretical one.

I remember seeing the clip I posted the link to on a science documentary many years ago (or, if not that specific clip, one showing the same thing) and being impressed at the destruction involved.
 
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