Mythbusters on Head-on Collisions

Posted by Greg Laden on October 1, 2012
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I’m sure you all have cable and/or satellite setups and thus see the Mythbusters, which is clearly one of the best things on TV, as they produce them. But I am always a couple of years behind because I watch them on Netflix. Two more seasons were released on Netflix very recently, so I’ve been watching them, and I thought one of the Myths addressed was worth bringing up.

Here’s the Myth: If a car is going 50 miles an hour and hits an immovable concrete wall, it suffers a certain amount of damage. If, however, the car hits head on another similar car moving in the opposite direction, then that is like hitting the wall at 100 miles per hour. This belief is widespread, and it makes sense at first. Yet, it is wrong. Having said that, it is actually correct, and when the Mythbusters busted the Myth they may have not noticed that they just busted a perfectly good Myth, and they actually confirmed it while they busted it. In a way.

The myth was tested first by using a scale model. The scale model involved pistons cleverly rigged up with cylinders of mush-able clay. Here was the experimental protocol and results:

1) A pendulum of a fixed weight rigged with mush-able clay is dropped from height A against an immovable object. The clay gets mushed to P% of it’s original thickness.

2) The same pendulum rigged the same way is dropped from height B where (B=2A). The clay gets mushed to 2P% of its original thickness. This simulates the effects of a 50 mile per hour and a 100 mile per hour collision with a fixed concrete wall, respectively.

3) The same pendulum is matched up to an identical opposing pendulum. They are dropped simultaneously from height A. The clay cylinders are found to mush down to P%, not 3P%. Myth busted in scale model.

Then, of course, they do it with cars.

1) A car is driven at 50 mph against a solid wall. It gets mushed.

2) A second car is driven at 100 mph against the wall. It gets much more mushed.

Here are the two cars, the red one was driven at 50 mph, the yellow one at 100 mph:

Screenshot of an episode of Mythbusters.

3) Two cars are then driven at each other at 50 mph, head-on. They are both mushed the same as the red car shown above. Neither car seems to experience a “100 mph” collision.

So, the myth is busted in full scale with the actual objects that the myth is about (cars).

But hold on a second, not so fast. The following two things are also true:

1) With the clay, when two pistons were used, there was sufficient energy to mush two lumps of clay down to the A-height amount, not just one.

2) With the cars, two cars each suffered the effects of a 50 mph collision.

Once you either run this all through in your head, or watch the episode, if you previously thought that a pair of cars hitting each other head on at 50 mph would cause one of them to experience a 100 mph collision, then you will absolutely change your mind. But, if you now think that two cars running into each other at 50 mph each is the same as one car running into a concrete wall at 50 mph, then you’ve got that wrong. Because, when in the end, you’ve got two recked cars not one, and the energy used to wreck each of those cars as per a 50 mph collision is twice the energy it would have taken to wreck one of them.

So it is like a 100 mph collision, shared evenly by two cars (so each gets 50 mph worth!)

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The show in question is Netflix Season 8 Episode 2, “Mythssion Control” subtitle Hyneman vs. Newton. The numbering, arrangement, and possibly editing of Mythbusters shows on Netflix seems to be different from that aired on TV.

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  1. #1 makeinu
    October 1, 2012

    Which is why Mythbusters, great enjoyable TV that it is (and how often can you say that with a straight face) is actually pretty terrible science.

  2. #2 Matty
    October 2, 2012

    Hi Greg,

    This was my same comment on the show when it first aired. They busted one myth and created a new one. Doing my graduate work in particle physics, I ran into this problem all of the time.

    I have been watching to see if they bring this up again, since the conclusions they made were confusing.

  3. #3 Tom Pelletier
    Long Island
    October 2, 2012

    Although I love the show, my complaint from a scientific standpoint is that they are often testing things that have at least the possibility of a random component, but they base their “myth busted” or “myth confirmed” conclusions on a single trial. I realize the economics of blowing something up 15 times are prohibitive, but in those cases, they should say something.

  4. #4 daedalus2u
    http://daedalus2u.blogspot.com/
    October 2, 2012

    Except energy goes as velocity squared. The energy at 100 mph is 4 times that at 50 mph.

    If you look at the deformation of the two cars, the 100 mph care has (to my eye) ~4x the deformation of the 50 mph car, which is what you would expect. Energy equals force times displacement the force needed to deform steel or clay in the plastic region is approximately independent of deformation, so it takes a 4 times longer deformation to stop a mass with 4 times more energy.

  5. #5 Greg Laden
    October 2, 2012

    daedalus 2U: The measurement was the lenght of the car after the crash, and the second car was shortened, it happens, twice as much as the first car. But, squishing in the front of the car is not at all the same as squishing in the next few feet. Also, the second first car got squished. The second car (in the 100 mph hit against the wall) also got flipped. So, right, overall the measurements needed to evaluate all this were not adequate. You really want to crash object that have more uniformity. Big giant force meters.

    They did also measure g forces, which I do not report here. But, these are g-forces in the trunk of a crumpling car that may or may not also be flipping and spinning.

  6. #6 Eric Lund
    October 2, 2012

    The myth probably originates from people misidentifying the relevant frame of reference. A solid wall isn’t going anywhere, so the appropriate frame of reference is that where the wall is at rest. But if you are talking about two cars of similar mass, then the relevant frame is not that of the other car, but the frame at which the two cars are approaching at equal speeds from opposite directions (the “center of mass” frame). In this example, each car goes from 50 mph abruptly to zero, so each car suffers the effects of a 50 mph collision. The damage is still greater than the scenario where one car at 50 mph hits a stationary car. And if one of the vehicles involved in the head-on collision were a loaded semitrailer, the effect on the car probably would be close to that of a 100 mph collision with a wall.

  7. #7 Dave X
    October 2, 2012

    Last sentence:

    It is like two 50 mile an hour collisions, shared evenly by two cars.

    What one car experiences in the two car collision is exactly the same as what one car experiences in the head-on with the immovable object.

    In the clay experiment, you might think of two parallel pendulums side by side, each hitting the immovable object and getting smushed P%.

    This might also help in thinking of the difference in cars and pendulums of different sizes. If you had a VW beetle vs a Mack truck collision, it might analogize to clay pendulum vs a 10 times clay pendulum. Head-to head, differently-massed clay pendulums won’t come to a dead stop, like same-massed pendulums, or like clay pendulums against an immovable object.

    Also, 2X the speed means 4X the energy, so you’d need to raise the pistons to 4X the height to get to the same energy as double the speed. Doubling the height would get you to 1.414142 times the speed, or only 70.7107 mph.

    And the clay/car-mush-length-percentage-reduction measurement seems odd as well. For example, if you had some lightweight super-long tailfins or spoilers adding to the length, the percentage would go down with the larger divisor while the damage to the front was unchanged.

  8. #8 Greg Laden
    October 2, 2012

    Right. … people should not make the mistake of thinking that if they run their Ford Pinto at 50 mph into the front of a fully loaded semi head on going at 50 mph that the two vehicles will share that energy evenly. Right? The proper test for Mythbusters would have been to have a car going 50 mph in one direction, and a large steel-clad concrete wall going 50 mph in the other direction…

  9. #9 Greg Laden
    October 2, 2012

    I think it might be necessary for the Mythbusters to get some more cars and trucks and stuff and have another go at this. I also object to not having the gas tanks full at the time of the collisions.

  10. #10 sailor
    October 2, 2012

    There some level at which I think you are all nuts. Two cars hitting each other at 50 miles an hour is like one car hitting a stationary car at 100 miles an hour. Using a brick wall as a comparison is is like oranges and apples, cars give, brick wall do not. If you can show me that a car hitting a stationary car at 50 miles an hour is the same as two cars hitting head on when both are going 50 miles an hour, I will have to do some serious rethinking. Until then if you are going to crash I suggest you choose another car to hit rather than a brick wall.

  11. #11 Greg Laden
    October 2, 2012

    I would like to see that experiment done: A car going 50mph into an identical car head on instead of into a stationary wall. That, and the “stationary” wall moving at 50 mph. Until these experiments are done, we will not really have a handle on this.

    That, and instead of cars we should be using spherical cows.

  12. #12 Phil
    October 2, 2012

    Can someone just compare formulae for me please?

  13. #13 Greg Laden
    October 2, 2012

    Go back 8 comments for the formulae.

  14. #14 lepton
    Holland
    October 2, 2012

    Ek = 0.5 x m x v^2.

    So 100 mph results in 0.5 x 2^2 = 2 times the energy, not 4 times.

  15. #15 CherryBombSim
    October 2, 2012

    You want formulae? Rhett Allain did this one a couple of years ago.
    http://scienceblogs.com/dotphysics/2010/05/06/mythbusters-and-double-the-spe/

  16. #16 Greg Laden
    October 2, 2012

    He addresses a different aspect of this issue in that post. It is interesting, though.

  17. #17 Phil
    October 2, 2012

    Ok thanks velocity squared. That makes sense.

  18. #18 Greg Laden
    October 2, 2012

    Oh, wait… we also want to see vehicle A going at 50 mph hitting vehicle B standing still (but head on) and vehicle A going 100 mph and hitting Vehicle B (standing still head on) where vehicles A and B are identical other than the paint job.

  19. #19 Greg Nelson
    USA
    October 2, 2012

    Thankfully I only drive one car, so practically only care what happens to one car. It’s good to know if I’m driving 50 and another car hits me I only receive the damage that I myself would inflict upon myself for driving the same speed and running into an immobile object. Of course a bigger worry for me is the drunk teenager in Bigfoot’s younger brother outweighing me 3 to 1 and traveling at 75 miles an hour. I guess that’ will be addressed in a future program.

  20. #20 Eric Lund
    October 3, 2012

    Greg @1712: In the case of the cars, we know what’s going to happen. The fundamental principle of relativity (and this concept predates Einstein; what he was trying to do was to preserve this concept for bodies moving at a noticeable fraction of the speed of light) is that the laws of physics are identical in two frames which differ only in that one is moving at a constant velocity with respect to the other. The actual speed of the two identical cars is irrelevant; only their relative speed matters, and the damage will be as if each car were traveling at half that relative speed. (I’m neglecting what happens after the collision; there will probably be knock-on effects if the center of mass frame has a significant speed.)

    Having a moving wall is truly a different experiment from having a stationary wall. The difference is that the stationary wall is anchored to the Earth, but a moving wall can recoil. Relative mass of car and wall becomes important.

  21. #21 PaulG
    October 3, 2012

    In both cases, a car goes from 50mph to 0 via pressure on the hood, over a few seconds. You’re simply examining two ways of doing the same thing. Somebody mentioned dring a car at 50 mph into a stationary car. That won’t have the same result, it’s going to end up with one car going 25 mph forwards, the other 25 mph backwards. Another case would be a car going 50mph head-on into a truck going 50mph. Result, since the truck weighs about 5x the car, probably a truck going 30-40 mp forward with the car going 50-100 mph backwards, with damage consistent to a 100-150 mph collision. Depends.

  22. #22 daedalus2u
    http://daedalus2u.blogspot.com/
    October 3, 2012

    Energy = mgh, dropping something from twice the height does give it twice the energy, not twice the velocity.

    As I look at the red and yellow cars, the yellow car is smooshed to about half the total length of the red car, that is after smooshing the red car is 2x the yellow car. I don’t have a before crash image, but the red car doesn’t seem to have that much of its length smooshed. Call it 1/10 for a 0.9 length after crash. If the yellow car is 0.45 after crash, then the crash compressed 1/10 of the red car and 0.55 of the yellow car.

    This is a front-wheel drive car, so most of the mass is in the front, in the engine and drive train. The stopping of those masses is not mediated through the smooshing of sheet metal (which results in a force ~ independent of deformation and deformation rate), so I see nothing inconsistent with the amount of deformation of the two cars.

  23. #23 MadScientist
    October 3, 2012

    I fail to see how their pendulum experiment is meant to simulate a crash; it’s a bit like the creationist model of the spontaneous generation of animals vs. the scientific model of evolution. In short, the model only makes sense if you know nothing of crashes.

  24. #24 Watching
    October 4, 2012

    ? In the case of 2 equal vehicles moving opposite at equal speeds.
    “So it is like a 100 mph collision, shared evenly by two cars”

    So what’s the issue? With two identical vehicles, they hit a virtual wall located on the spot where they hit. Each stops dead at that spot, etc.

    What else could one reasonably expect?

  25. #25 Greg Laden
    October 4, 2012

    daedalus2u: As I recall, the lost length of Car 1 is half the lost length of Car 2. But, as you say, the physical layout of mass in the car makes this very difficult to compare.

    (That’s why the clay is a good check)

    Eric: I like the relativity (not special or general, just relativity) framework for describing this.

    MadScientist: I thought it was a good model!

    Watching: I think the myth starts with the idea that if you are driving your car along at 50 mph and hit a bridge abutment, that’s bad, but if you hit another car head on, it is wroth. The busting of the myth is to recognize what you said, but I’m adding two elements:

    1) It is actually twice as bad in the big picture to hit a similar car travelling at a similar speed because that car gets wrecked as well (this is trivial but I’m not at all convinced it is understood by all onlookers) and

    2) If the other car is a semi that weights 30 times the size of your car, that will not be the same as going 50 mph into a bridge abutment. It will, in fact, be worse (for you)