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So, Bora tagged me today with the Eight Random Facts meme. And since it's Bora, I will respond. Here are the rules:
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What is your blogiste doing instead of writing posts and working on her new book these days? She is frantically trying to make her home a suitable place for the workshop she's running in it in a few days. That means moving furniture that might get moved and discovering things horrible beyond…

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Fellow scienceblogger Coturnix is assembling some posts about science for an anthology. He's been asking for people to contribute suggestions. I've been meaning to thumb through my old posts in order to send one over, but it's been more of a challenge than I thought. Part of the problem is that…

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.

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.

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.

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.

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.

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.

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.

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...

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.

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.

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.

Can someone just compare formulae for me please?

Go back 8 comments for the formulae.

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.

You want formulae? Rhett Allain did this one a couple of years ago.

http://scienceblogs.com/dotphysics/2010/05/06/mythbusters-and-double-th…

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

Ok thanks velocity squared. That makes sense.

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.

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.

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.

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.

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.

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.

? 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?

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)

The myth is based on work done (W=F*D). The work to stop a car of a given weight going a given speed is the same weather that car hits a wall or hits another car going the same speed. Therefore, the damage to the test car will be the same either way. However, the total work done on the system is NOT the same. The difference is that if both cars are moving towards each other, then the work is done twice (Total work = F*D + F*D) but is also spread across two objects, and therefore the SAME amount of work is done to an individual car.

Those tested cars have deformation (crumple) zones, the front end is easily crushed, is is engineered so to dissipate the energy by deformation. On the other hand the cabin is reinforced, dissipates energy on a higher scale by deformation, so deforms in length to a lesser degree.

Not to mention, that the "real" moving mass is dropping up to zero when the vehicle is in stand still (in the middle of the collision only the rear section of the car is moving, those having kinetic energy to be dissipated)..

Its true that 2 identical cars in a head on collision at 50mph each suffer equivalent damage to hitting a wall at 50mph. This might lull you into a false sense of security about head on collisions. How about a truck and a car in the same scenario ? I think in this case the car would suffer damage closer to a 100mph impact and the truck a lot less. Due to the different masses the car is likely to end up going backwards after the smash so the change in velocity will be closer to 100mph (+50mph to -50mph). So I think it depends on what you hit and some head on collisions for the smaller vehicle can be very dangerous !

Cars being equal, each car absorbs it's own energy. Duh. Neither physics models or math are needed to understand this basic idea.

I'll never grasp why some misguided people think that two same cars hitting each other head on, each going 50, is just like two same cars hitting each other head on each going 100. Um...no.

All I know is that as a passenger in a car going 60 mph being hit head on by another vehicle going 60 mph in the opposite direction, it hurts! I am confused after all your comments. Is this scenario equivalent to driving 120mph into a wall (give or take based on the wall having no give)?

For LoriE: no, it is not the same. As Rob Booth said in comment #28,

"Its true that 2 identical cars in a head on collision at 50mph each suffer equivalent damage to hitting a wall at 50mph."

and OrionE on #29 "Cars being equal, each car absorbs it’s own energy."

The idea is that the concrete (or better granite) wall does not deformate, and has a much bigger mass than the vehicle that will collide with the wall. So the vehicle will nee to dissipate all the kinetic energy that has at that moment.

When two IDENTICAL car will collide head on, each having the same speed OR NOT, does not matter, that one is stand still, and the other coming with 120 mph, or both having60 mph, the total energy that need to be dissipated is that what counts, and as being identical, both contribute to the kinetic energy absorbtion, they absorb 50:50 of that energy.

But the concrete wall does not absorb any energy (only a fraction, has almost zero deformation and a much bigger mass).

When the car is hitting a concrete wall is like the fat bug hittig the windscreen at 120 mph, the windscreen has a much higher mass than that bug, and does not deformate, so the bug will make itself a greasy patch, so you need to use the windscreen washer.

So in conclusion, just a question of life or death:

You are driving your Bentley Continental GT with all your family or loved ones at 80 mph on a one way road that will enter into a concrete reinforced tunnel, only one car can pass.

Then suddenly you see another identical car with the same "mass" of people coming from the tunnel at...let's say 70 mph, so a little less than your speed. I have not choosed 120/110 mph, so you have some chances for survival, so keep your speed down.

What will you do to maximalize the survival of your genes, not caring that if you choose B then you can hurt other people (although they are coming on a one way road at the wrong direction, so theoretically they would "deserve" it).

Also you have no time to press the brake pedals (or there is a brake failure) you can only choose the direction of travel:

Answer A: You corner into the concrete wall next to the tunnel entrance, colliding at 80 mph

Answer B: You continue your way of travel, colliding with the identical car at 150 mph.

???

Any explanation that tries to equate the two cars' hitting each other at 50 mph with one hitting a wall at 100 mph is wrong. kinetic energy = one half of emm vee squared. One car at 100 mph has four times the ke of a car at 50 mph. Two cars each at 50 mph only have, collectively, half of the kinetic energy of the single car moving at 100 mph. The car in the second case therefore has to dissipate (by being deformed) twice as much energy as each car in the first case. And that was completely confirmed by the Mythbusters' results. Any other interpretation is clever, but misleading, wordsmithing.

Why so much analyzing? Both vehicles met @zero. Mathematically 1-1 is zero. Both vehicles are the same. If they would of have put a different vehicle or a heavier vehicle the smaller vehicle would had sustain more damage than the heavier vehicle. 2-1 equals to 1. This has been explained before just in numbers there is no need to proof theory wrong.

Jamie hanrahan, you are almost correct. However the whole exp riment is tainted. Evryone on these posts are discussing kinetic energy. However the outcome is being measured byndamage to a car. Damage is not done by energy but by decceleration. Running a 100mph car into a perfectly rigid and infinite mass wall will do more damage than running a 100 mph into a stationary car due to the plastic deformation. Therefore you cannot measure the impact based on appearance since the car vs wall and car vs car are not identical scenarios. Unlike what PaulG said this is not a perfeclty elastic collission so a 100mph car and stationary car wont move in opposite directions. They will create a heap of metal. Anyways, there will be a greater impact of two cars hitting at 50mph head in than a sungle csr hitting a stationary car at 50 mph due to the split of energy between the two masses.

good post

"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%."

Did you mean to to type here, "P%, not 2P%" instead of 3P% ???

david --

To answer your question, since your car is going a bit slower than the other, and since we don't care about hurting anybody else -- all we care about is ourselves -- and I assume that the tunnel wall is 100% rigid and immovable ... it would be slightly better to hit them head on than to hit the tunnel wall.

And if the two speeds were equal, it wouldn't matter which one you did -- both would result in approximately equal damage to your car and yourself.

I get it for hitting a wall that is that force is mainly distributed to crush the car while wall provided it doesnt move and is really solid doesnt absorb much.

But...

If we would replace the wall with not moving car then that comparision (2*stat = 1*head on) will be true right?

Question, don't miss the assumptions in your #42 that the wall is "solid and immutable", and therefore absorbs some of the energy of impact without any substantial damage...

Whereas your "not moving car" differs considerably: It is SIGNIFICANTLY lower in mass than the wall (which is presumed to be so massive that it can be treated as having essentially infinite mass for the purposes of calculating the collision effects), and it is "plastic", in that the energy of collision will very significantly --and easily-- deform the second car.

The deformation will absorb some of the energy of collision, while having a mass comparable to the moving car will result in it acquiring a velocity post-impact.

In short, you have a very different physics problem if you replace the wall with a stationary car...

hi guys, In my project of accident detection i m using accelerometer to detect impact and i m placing it at footweel(driver foot place) in car so which g value sensor do i need for appropriate detection.

i m confuse about 40 to 50 or 100g sensor. i think the main concern here is the place where we can place our sensor(accelerometer).

Hello.

I was thinking about the test with the 2 cars crashing with 50 mp/h. But what if car 1 was at 0 mp/h and car 2 at 100 mp/h.

Same result?

This is all fun theory but bottomline:

Head-on collisions are VERY DANGEROUS!

Better to nudge or side swipe car going in same direction or hit a small stationary object.

P.s. who would drive head on into a solid wall?

they didn't actually test the myth - a third test of one car going 100 mph hitting a stationary one was the missing point. Assuming the two masses are the same and ignoring road friction and other minor annoyances, the math is pretty straightforward . if a moving mass hits a stationary mass and neither deforms (think of a newtons cradle with only two balls) the moving mass stops and the second accelerates away and is soon moving at the same speed and direction that the first had. If the masses connect and lock together but do not deform, the new blob of twice the mass will move in the same direction as the initially moving mass, but (in this case) at around 70.7 mph. If both masses deform (momentum, kinetic energy converting into deformation and heat) both masses travel in the same direction as the initial mass at some speed less than 70.7 mph - and because they are still moving, (and still have some energy) the deformation to each is likely to look like 50mph for vehicles with moderate deformability IMHO. Look at it one more way, if a moving car hit a stationary car backed up to touch the wall, at 50mph, some energy would deform the moving car, and both ends of the stationary one. At 100 mph, the deformation would be 4X the energy spread out where the two vehicles touch each other and where one touches the wall The myth IS busted no matter what.

TL;DR one car, 50mph, strong wall - energy converted to smush =X, car stops. Two cars, each 50mph, hit each other - energy converted to smush =2X, each gets half, both stop. Two cars, one 100mph and the other zero, energy AVAILABLE to convert to smush =4X ... identical smush would be related to the final speed of the still moving combined mass..

super TL;DR: one car moving at 50, hits wall and stops, energy is X, car absorbs it. Two cars moving at 50 hit each other, energy is 2X spread over 2 cars, therefore same outcome as hitting the wall - all STOP. if one moving 2 times speed and other zero, energy is 4X the lower speed, both cars will smush, and the combined mass is STILL moving after the collision (with the possibility for more smushing - where is that wall exactly?).

Myth busted with math.

Here's what you knuckleheads aren't understanding... it's actually not about what the cars experience, but what the PEOPLE driving the car experience. They are not only feeling half of the impact, they are feeling 100% of the force of the impact.