N.B. I could be completely misunderstanding this, and I could be completely wrong. I was drinking, after all.
Mythbusters has frustrated me again. A few months ago I pointed out an inaccuracy in a previous episode. If my post was not sufficiently clear, my point was that a single car going 100 mph has double the total energy of 2 cars going at 50 mph, and not the same, as Jamie Hyneman had asserted.
In an episode which I watched a few days ago, “Mythssion Control“, I was delighted and rather pleased with myself when the program mentioned that ‘the fans’ had objected to the same statement that I did. Sadly, the feeling lasted perhaps only 2 seconds.
As I saw it, the original Compact Compact myth was seeing whether a head-on collision between two lorries would crush and fuse a small car at the point of impact. Clearly, when Jamie came out with his statement1, he was talking about how much damage would be done to the car in the centre: after all, seeing how much damage was done to the car2 was the aim of the myth. When Jamie took his statement as justification to test the myth with the easier double-speed single lorry3, this shows he considered them equal in terms of how much damage they will cause the impacted car.
- Therefore, it makes sense to assume that he was saying: ‘2 lorries would cause the same damage to the compact car (when placed between them) at 50 mph as would 1 lorry smashing into that car (when placed against a wall) at 100 mph‘.
Right? Is that what you thought he meant?
Yet, when the Mythbusters came to verify Jamie’s statement, they approached the myth in a way that, in my opinion, seems completely removed from the original scenario. They completely changed the perspective of the myth to something like: “Two cars colliding head-on at 50 mph will each receive the same damage as if each car were independently crashing into a wall at 50 mph, rather than at 100 mph as Jamie said”.
OK, so the inclusion of a correction complicates things a bit more, so a simplified version would suit my desires: “Two cars colliding head-on at 50 mph will receive less damage than if each car were independently crashing into a wall at 100 mph”.
Do you see what’s changed? The original myth and Jamie’s statement was about how much damage was caused to a car which was being crushed by lorries on both sides, but in this revisitation, the situation is now in terms of how much damage is caused to the lorries themselves.
- The physics involved is the same4, and I’m not arguing with the accuracy of the Mythbusters’ results. My problem is that the new investigation bears no pratical resemblance to the original myth, and no explanation of why the physics is the same in both cases, justifying the change in perspective. The object of the damage has been completely changed!
The way I thought about the situation was this: damage in a collision is caused by energy being transformed from kinetic energy into energy used to deform a material5. The more energy, the more damage: simple. As I showed in my previous post, the single vehicle travelling at 100 mph has twice the total energy as two vehicles travelling at 50 mph. Therefore, there is twice as much energy available to cause damage with the single vehicle, so damage will be much greater6.
So what does that mean? Firstly, the way I see the original myth, there is 2 times as much energy to cause damage with a single lorry at 100 mph crashing into a car as two cars at 50 mph crashing into it: that is, they can not be considered equivalent. Furthermore, I calculated that the single car would need to be going 71 mph to have the same amount of energy as the two cars at 50 mph7.
However, the way that the Mythbusters changed the perspective, it is now about damage to the lorries (now cars) themselves. But the energy involved is still the same: at 100 mph, the single car has twice as much energy to damage itself as the 2 cars at 50 mph have in total. Therefore, the 50 mph cars will sustain much less damage: Jamie was indeed wrong. How much less? Well, the 2 cars at 50 mph have the energy of 1 car at 50 mph plus the energy of the other car at 50 mph. This is shared equally between the two cars at the collision, meaning that each car receives half of this, or the energy of 1 car at 50 mph. That is: each of the 2 cars at 50 mph crashing head-on will have the same energy available to damage it as would a single car crashing into a brick wall at 50 mph. The fans were indeed right.
The Mythbusters did not present the case like this. Whilst I prefer working through the equations, they instead couched it in generalities in terms of Newton’s third law of motion: every action has an equal an opposite reaction.
Well. I thought about this and it did eventually make sense, but that was a while ago and I can’t think of a way to explain it now. Think of it like this: as car A hits car B, you could imagine that all of car A’s energy is transferred to car B, causing it a single-car-going-at-50-mph’s worth of damage. However, due to Newton’s third law of motion, all of this force is resisted by car B, which transfers all of its energy to car A in return, similarly causing it a single-car-going-at-50-mph’s worth of damage. There is no energy left now: that is, both cars are at rest, though each car has only been damaged as much as it would have if it had crashed into a brick wall.
Or think of it this way: it is equivalent to crashing into a brick wall, as the point of collision stays in the same place. When the bumpers meet, they crush equally, until, at the same point, the bonnets touch, crush, then the windscreens, roof etc. It’s like pushing two marshmallows together: the point where the meet stays in the same place even as you push, just like with a brick wall. The cars wouldn’t know the difference. (Yes, that’s not at all scientific, but it lets you visualise what’s going on).
But I like the numbers. The maths is simpler:
The total energy is 2 x 1/2mv2. However, this is distributed over 2 cars worth of mass, meaning each car is only damaged by the amount of energy equivalent to that which it possesses as kinetic energy: exactly what happens in a wall-crash at the same speed. This is the physics that the show displayed into the closing seconds to explain what had happened. It makes sense to me.
- Mythbusters is not a technical show; that is, they’re not going to sit down and just work something to test a myth, even if that would be by far the easiest method8. I actually don’t have a problem with that: the hands-on approach is generally much more amusing, if less accurate. But if they feel they do have to bring physics equations into it, as they did in this episode (explaining in 10 seconds mathematically what they had spent 20 minutes showing by crashing cars together), they should do it properly: do the theory first, and then spend your time confirming it through experimentation. An explanation of the physics largely composed of hand waving is worse than nothing, in my opinion.
In conclusion, although the Mythbusters were accurate, I believe they were approaching the issue the wrong way. These should have tested: “does a single lorry crashing into a car at 100 mph cause as much damage to the car as 2 lorries each going at 50 mph crashing into that car head on?”. The answer to that, as I spelled out in my previous post, is no – the single car would only need to go about 71 mph – although it would have been much more difficult to gauge the damage in that case9. Sadly, the Mythbusters presented Jamie’s error in a confusing way that, without an explanation of why they changed perspective, made the argument harder to follow.
P.S. I don’t know why I just wrote this.
- Admittedly, it was a rather casual, off-hand thing. ↩
- ie. Did it fuse? ↩
- Crashing a lorry into a wall is easier than co-ordinating a head-on collision between two of them. ↩
- Or at least it’s very similar. ↩
- And then heat… ↩
- I can’t say that damage will be double, as how do you measure something as ill-defined as ‘damage’? ↩
- Now, with the original myth, that energy will be shared between the impacting car and the impacted car, which complicates things in terms of measuring damage, if you think about it, but it doesn’t really matter. Ignore this. ↩
- This episode was a perfect example of that. ↩
- The damaged caused to the car would look different with two points of impact as opposed to just one, making visual comparisons of damage difficult if not impossible. ↩