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So I got myself questioning what could be worse for the driver... a collision of two identical cars at equal speed (frontal crash) or the same car with the same speed crashing through a wall? The first case I see it would double the impact, but also it will absorb the energy into the other car structure, otherwise, in a solid and rigid wall, all the energy would come back to the vehicle.

Which situation is worse for the passengers?

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  • $\begingroup$ Related on Physics: Injuries and numbers $\endgroup$
    – Mast
    Jun 9, 2015 at 4:21
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    $\begingroup$ "Same car with the same speed..." are we talking absolute speed or speed relative to collision object? Two cars each traveling 50km/h hitting head on VS one car travelling at 50 or 100 km/h hitting an ideal wall? $\endgroup$
    – Myles
    Jun 9, 2015 at 14:26
  • $\begingroup$ @Myles: I am pretty sure he Alessandro meant absolute speed, with all cars travelling at 50 km/h. $\endgroup$
    – Nicolas Raoul
    Jun 11, 2015 at 3:52
  • $\begingroup$ The wall has no driver nor passengers, two cars is worse. $\endgroup$
    – Hernán Eche
    Feb 12, 2016 at 11:44
  • $\begingroup$ The question says "crashing through a wall" yet it also says "a solid and rigid wall". I suspect you meant "into" rather than "through", but it would be good to know for sure which you really wanted. $\endgroup$
    – Ray Butterworth
    Jun 16, 2019 at 0:16

4 Answers 4

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From the point of view of the driver of a car, impacting another car is about as bad as crashing against an ideal wall (a wall with zero deformation whatsoever).

If there were a plane reflection between the two cars, then vs. Car would be exactly equal to vs. Wall (the contact points between both cars would all be on the same plane, due to reflection, so each car could be considered a wall for the other). But this plane reflection does not exist:

Cars crash from above

What we have instead is a 2-fold rotational reflection.

Let's say the left part of the car is heavier than the right part. The left and right parts will get crushed differently, with the left part of each car going further than if there had been an immovable wall. Heavy parts of each car will slide beside each other, with a lot of the energy absorbed by steel deformation, and a longer distance between point of impact and final point, thus lesser deceleration. In this scenario, if you happen to sit on the heavy side you are lucky, but if you happen to sit on the light side it might be worse than a wall.

Also, rather than all forces having the same direction, some of the energy will be converted into rotation, which can be either a good or bad thing depending on where you sit.

Finally, cars have a few hard structural beams (or parts that can be considered as beams) and most of the rest is softer. If hitting a wall, deceleration is immense as soon as a beam touches the wall. If hitting another car, the beams will probably enter the other car's soft parts. Here again, distance between point of impact and final position will be longer, thus a less violent deceleration. This is especially true at very high speed, with beams of each car piercing through most of the opposite car.

All in all, crashing into an ideal wall is probably a bit worse than crashing into another car, but better drive safely and avoid crashes :-)

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    $\begingroup$ I don't agree that plane reflection would make it exactly equal. In the car vs. car case both cars will have crumple zones designed to turn the kinetic energy of the impact into deformation of the car rather than allowing it to transmit to the passengers and increase the time over which deceleration occurs. Car vs. car therefore will double the benefit of these crumple zones. $\endgroup$
    – Jack Aidley
    Jun 10, 2015 at 9:38
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    $\begingroup$ @JackAidley Let's say you have complete knowledge of exactly one car involved in a collision. You know that it collided either with a perfect mirror image of itself or an infinitely strong wall. How would you distinguish, based solely on your omniscient observation of the one car, whether it hit another car or a wall? The second car contributes another crumple zone but it also contributes a whole lot of energy that the wall does not. I don't think you could distinguish between them. $\endgroup$
    – Air
    Jun 10, 2015 at 16:13
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    $\begingroup$ @JackAidley You have exactly double the absorption, but exactly double the energy to absorb. The other car is moving with the same velocity so it would contribute just as much energy. $\endgroup$
    – Rick
    Mar 2, 2016 at 15:34
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In the limit of the cars being identical and the wall being immutable, I would argue that the two situations are the same based on symmetry.

Consider the collision of the two cars with no wall. Conservation of momentum implies that the end result is both cars at a stand-still. If they hit each other perfectly head on, the vehicles will buckle and absorb energy identically.

Now imagine placing a completely inflexible wall between the two cars as they collide. Nothing about the situation changes; the cars still end up at a stand-still and absorb energy in the same way.

If you instead consider a wall which collapses when hit by the car, then hitting the wall is safer. Neglecting the added danger of flying bricks and a building on top of your car, that is.

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    $\begingroup$ This is wrong. The two cars colliding against each other will not react identically because they are not mirrored, the driver's seat is on the same side in each car. This results in a different outcome when the cars collide because the distribution of mass is not identical. Unless you are driving into an exact mirror copy of your car, the cars are going to skid off slightly away from the center of the collision, resulting in a different outcome. For example, the passenger seat might be crushed more than the driver's. $\endgroup$
    – vero
    Jun 9, 2015 at 6:11
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    $\begingroup$ It's not just the driver seat too, the engine is asymmetrical, the fuel input is only present on one side, etc etc. $\endgroup$
    – vero
    Jun 9, 2015 at 6:12
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    $\begingroup$ Mythbusters tested this in 2010. mythbustersresults.com/mythssion-control $\endgroup$
    – Taemyr
    Jun 9, 2015 at 7:33
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    $\begingroup$ @Rodolvertice You correctly point out that cars don't exhibit perfect mirror symmetry. However, since the center of mass of a vehicle is kept near the center of the vehicle, the effect is rather small. In the rigid-body limit it just results in some of the motion being conserved in the form of angular momentum. Real collisions are of course much messier, and experiment is the best way to determine the reality. As Taemyr pointed out, mythbusters did the experiment and 'confirmed' the result of my symmetry argument. $\endgroup$
    – Chris Mueller
    Jun 9, 2015 at 12:01
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    $\begingroup$ @ChrisMueller We're not doing rigid-body mechanics so the centre of mass being close to the centre of volume doesn't really tell you a lot. Car crashes deform the vehicles significantly, and a huge amount of engineering is put into managing that deformation. $\endgroup$
    – David Richerby
    Jun 10, 2015 at 11:01
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I'm guessing you haven't seen the Mythbusters episode on this. Then, see this writeup that explains why they are correct, since Mythbuster's explanation leaves something to be desired.

In short, it's exactly the same. In the 2 car example, each car has the same amount of energy (as each other, and as the car in the 1 car example) since they are all going the same speed (and have the same mass). In the two car crash, the total energy in the crash is doubled, however, the energy is distributed equally between the two cars. Therefore, the energy for each car is identical to a single car hitting a ridged wall. The tests in Mythbusters illustrates this.

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The answer will depend on the wall, and on the other car.

Consider the comparison to an ideal, immovable wall. In the case of a hypothetical collision between a Humvee (2500 KG) and a VW Beetle (850 KG), for the Humvee "vs. car" is better, whereas for the Beetle "vs. wall" is better.

Now consider the comparison to a paper thin, soft wall. For both the Humvee and Beetle "vs. wall" is better.

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  • $\begingroup$ I wonder how this Beetle would fare! $\endgroup$
    – dotancohen
    Jun 9, 2015 at 10:06
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    $\begingroup$ The question says "same car" though ;-) $\endgroup$
    – Nicolas Raoul
    Jun 10, 2015 at 3:08

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