Car Crash Physics Question

[Tsukasa Buddha]

I remember I had a teacher who was scaring us teaching us about driving, and he made an interesting claim. He said that when two cars hit head on the force is multiplies. That is, when driving ten miles per hour, it would be the same as hitting a wall at one hundred miles per hour.

It seems a bit extreme, but thinking it over I'm not sure how to go about modelling the situation. Any ideas?

[Careyp74]

That doesn't sound like a good representation of the conservation of energy. I would say that at most it would be doubled, if both cars were going 10 miles an hour.

Imagine what a game of pool would be like if this was true?

ETA: To Answer your question, I think a couple accelerometers on a couple of crash tests would prove it either way.

ETAA: Would it be safe to say that working backwards from that, hitting a non-moving wall would impart 0 force on you? 10*10=100, 10*0=0

[Macgyver1968]

Your teacher was dead wrong.

Here's an explanation of why:

http://warp.povusers.org/grrr/collisionmath.html

[ben m]

That's not right, but I can think of two different things the teacher might have garbled.

When two identical, moving cars hit head-on, the forces involved are the same as either car hitting a fixed wall. In both of these cases, you go from "full speed" to "stopped" in the length of one crush zone.

When a moving car hits an identical *parked* car, it's different---you go from full speed to half speed, and you do so over a distance greater than the size of your crush zone.

Alternatively:

The kinetic energy involved in a car crash scales as v^2. A 40mph collision is sixteen times as bad as a 10mph collision, not four times as bad, if energy is the determining factor. A 70mph collision is about twice as energetic as a 50mph collision. That's a steeper relationship than many peoples' intuition would tell them it is.

I've seen both of these physics factoids get mistranslated into "all car accidents are twice as bad as you think they are".

[alexi_drago]

2 cars, each travelling towards each other at 10mph. If the cars were mirror images of each other and the collision was absolutely perfect then each car will have the experience of hitting a static imovable indestructable object at 10mph.
Ask your teacher what the effect would be if a car travelling at 20mph collides head on with a stationery car (0mph)

[Brown]

I hope this teacher did not "teach" Physics (in addition to drivers' ed). When I went to school, a lot of driving instructors also taught shop, for some reason.

Drivers' ed instructors are notoriously bad at explaining scientific concepts pertaining to collisions, blood alcohol content, reaction time, human eyesight, judging distances, stopping time, injuries from crashes, auditory illusions (such as why it can be hard to hear an approaching train) and slippery surface motor vehicle behavior, as well as how an automobile actually functions. These things are all important for good drivers, and all have scientific underpinnings, but many drivers' ed teachers did not understand the scientific principles or explain them correctly. (I have seen virtually every one of these topics botched, if not butchered, by an "instructor.")

Drivers' ed instructors were usually better at explaining WHAT you should do rather than WHY you should do it.

Occasionally, you'd find an instructor who would get the science right. Think you don't need to wear seat belts if you're going to be running short errands at 35 mph, because a crash at that speed can't hurt? Well, a good instructor might ask you to imagine jumping from a sufficient height from a building where you'll be going 35 mph when you hit the driveway....

Or if you're wondering whether, as a general rule, you should swerve to avoid hitting a deer or not swerve and risk hitting it, a good instructor might direct you to some statistical studies. Statistical studies are also good for explaining why using seat belts is a good idea, even though in some circumstances seat belts will hurt you more than they help you.

[rjh01]

Double the speed of a car and it will need FOUR times the distance to stop. This is because energy is proportional to the square of the speed. Maybe this is what the teacher was trying to say?

[fuelair]

I remember I had a teacher who was scaring us teaching us about driving, and he made an interesting claim. He said that when two cars hit head on the force is multiplies. That is, when driving ten miles per hour, it would be the same as hitting a wall at one hundred miles per hour.

It seems a bit extreme, but thinking it over I'm not sure how to go about modelling the situation. Any ideas?

He is wrong - and I have no idea where he got that idea -it is pure ignorance - or a scare tactic. (If both cars have the same mass) The physical effect assuming perfectly head on is like hitting a solid no-moving wall at 20mph and, even that is not perfectly correct if both cars have a good crumple zone. The formula is m1v1 = m2v2

[Montag451]

Mythbusters tested this and showed it to be untrue.

Where the mistake occurs is looking at energy. As both cars impact the energy from the movement causes deformation in the other cars. As both cars deform they deform due to the energy in the other car. If one car was undeformable then the damage to the other car would be equal to it's own energy and the energy of the other car. However this doesn't occur as car are inherently squishy, so twice the speed gives twice the deformation shared between 2 cars, or the same as 1 car hitting a wall.

[MattusMaximus]

That doesn't sound like a good representation of the conservation of energy. I would say that at most it would be doubled, if both cars were going 10 miles an hour.

It's also really a lousy representation of conservation of linear momentum and impulse. If a car hit another car head on at the same speed and they crushed together and then stopped, the same force of impact would act upon the car if it traveled into a very massive concrete wall at the same speed as before. This assumes, of course, that the time of impact in each case is the same.

ETA: Plus what Montag451 said. The more objects going into the collision, the more the energy is distributed among those objects after the collision. Just beat me to it :)

[Stomatopoda]

It's quite ridiculous if you think about it, even without understanding the physics involved. The teacher is saying that odds of surviving a head-on collision with both cars moving at 20mph would be similar to a single car hitting a wall at 400mph. Umm....

[MattusMaximus]

Occasionally, you'd find an instructor who would get the science right. Think you don't need to wear seat belts if you're going to be running short errands at 35 mph, because a crash at that speed can't hurt? Well, a good instructor might ask you to imagine jumping from a sufficient height from a building where you'll be going 35 mph when you hit the driveway....

Just as a side note, when discussing these topics with my physics classes, I always ask them how much force they think they would feel if they were in a head-on car crash with a big concrete wall when the car was moving at only 30-35 mph.

After a number of guesses, we do the math. The answer usually comes out to somewhere around 2000-3000 pounds of force, and I see jaws in class drop. Then I ask those who don't like wearing their seatbelts to join me in the weight room while I have them attempt to hold up about one ton (2000 lbs) of weight with their arms.

I never get any volunteers.

To finish the lesson, I leave them with this thought (direct quote from my lecture):
"Folks, the laws of physics do not discriminate. They don't care who you are, where you are from, how much money you have, or what you believe; they will kill you just as quickly and easily as the next poor dumb bastard. So wear your seatbelt."

[Montag451]

Just as a side note, when discussing these topics with my physics classes, I always ask them how much force they think they would feel if they were in a head-on car crash with a big concrete wall when the car was moving at only 30-35 mph.

After a number of guesses, we do the math. The answer usually comes out to somewhere around 2000-3000 pounds of force, and I see jaws in class drop. Then I ask those who don't like wearing their seatbelts to join me in the weight room while I have them attempt to hold up about one ton (2000 lbs) of weight with their arms.

I never get any volunteers.

To finish the lesson, I leave them with this thought (direct quote from my lecture):

I always end my lessons with... and what is the last thing that go through a flies mind when it hits a windscreen? It's arse

[I Ratant]

Just as a side note, when discussing these topics with my physics classes, I always ask them how much force they think they would feel if they were in a head-on car crash with a big concrete wall when the car was moving at only 30-35 mph.

After a number of guesses, we do the math. The answer usually comes out to somewhere around 2000-3000 pounds of force, and I see jaws in class drop. Then I ask those who don't like wearing their seatbelts to join me in the weight room while I have them attempt to hold up about one ton (2000 lbs) of weight with their arms.

I never get any volunteers.

To finish the lesson, I leave them with this thought (direct quote from my lecture):
.
I witnessed in my outside rear-view mirror a head-on between a Jeep and a Volvo Carryall... the Jeep had just punted a medium sized utility truck going in the same direction across the on-coming traffic, with lots of stuff flying out of the bed of the truck. The Jeep stopped in the fast lane of the on-coming traffic and was immediately struck by the Volvo. It appeared to me that the vehicles merged into each other.. with the Volvo stopping cold.
Killed one person in the Jeep, and three in the Volvo.
The perp in the Jeep which he had just stolen, a newly released parolee, was almost uninjured. His girl friend was killed.

[Brown]

Just as a side note, when discussing these topics with my physics classes, I always ask them how much force they think they would feel if they were in a head-on car crash with a big concrete wall when the car was moving at only 30-35 mph.

After a number of guesses, we do the math. The answer usually comes out to somewhere around 2000-3000 pounds of force, and I see jaws in class drop. Then I ask those who don't like wearing their seatbelts to join me in the weight room while I have them attempt to hold up about one ton (2000 lbs) of weight with their arms.

I never get any volunteers.It's been a while since I did the math, but if memory serves, a supposedly "low-speed" collision is comparable to jumping from the roof of a two-story house and landing on the driveway, face first. Naaaah, that won't hurt a bit.

Can you secure in your arms a fifteen-pound infant during a 35 mph crash? It's only fifteen pounds, right? Easy to hold, right? Do the math and find out!

One of the more surprising physics problems related to driving pertained to accidents that happen quite some distance away from you, yet affect you. A classic is one in which someone passes you on the left, and can't quite get back into the proper lane before side-swiping an oncoming car. The accident SEEMS quite far away, but the side-swiping can cause the oncoming car to pivot, and be aimed right at you; and suddenly you find yourself to be quite "involved."

[Turgor]

It's been a while since I did the math, but if memory serves, a supposedly "low-speed" collision is comparable to jumping from the roof of a two-story house and landing on the driveway, face first. Naaaah, that won't hurt a bit.

Maybe a 3 story house? 35mph is about 15m/s, that takes about 1,5 seconds to reach, or falling from a height of about 11m.

[Careyp74]

Maybe a 3 story house? 35mph is about 15m/s, that takes about 1,5 seconds to reach, or falling from a height of about 11m.

Thanks, I was about to do the math myself, which would at this point be a headache since I don't use physics as much as I used to.

Eh, did it again anyways, with the help of Google. I got 12.49 meters when using more exact figures.

[Brown]

Maybe a 3 story house? 35mph is about 15m/s, that takes about 1,5 seconds to reach, or falling from a height of about 11m.Yeah, sounds about right. Again, I haven't done the math. There's also some psychological aspect to the thing: jumping off a two-story roof sounds worse than jumping out a three-story window (for example), and one can also say that the impact from a two-story drop is LESS than the impact from a 35 mph crash.

Importantly, a drop is not necessarily equivalent to an actual collision, as was illustrated in an episode of "Mythbusters." The Mythbusters used a dead drop to simulate an airplane crash and the effectiveness of "brace" positions. The drop, however, caused brief free-fall (near-zero-g) conditions, which affected the participants' abilities to maintain their "brace" positions; their arms and legs tended to swing out of position at the moment of drop, and they were not able to reposition them prior to impact on the ground.

[Earthborn]

It seems a bit extreme, but thinking it over I'm not sure how to go about modelling the situation. Any ideas?Here's an idea to model the situation:

q_vCuE4KaUU

[ben m]

The crash-test-dummy experiment I'd like to see: Sit a dummy in a stationary car seat. Not a car, just a seat, facing forwards into empty space. Then you mount a *dashboard* (steering column, windshield, etc.) on the front of a test vehicle, speed it up to 35mph, and drive *that* straight into the dummy like a battering ram. That's what an un-seat-belted car accident is like.

If you could do this really precisely, maybe you could have a seat belt rig suspended in front of the dashboard, such that, at the moment the rig makes contact, the driver is effectively "seat belted in" from the dashboard point of view. Then you could add airbags.

[MattusMaximus]

Since we're on the topic, I highly recommend that everyone in the thread watch this short video. It does a beautiful job of explaining the necessity of various safety features in modern vehicles:

fPF4fBGNK0U

Some of the comments are... interesting, mostly for the fact that they are denying basic physics.

[jojonete]

That is, when driving ten miles per hour, it would be the same as hitting a wall at one hundred miles per hour.

It seems a bit extreme, but thinking it over I'm not sure how to go about modelling the situation. Any ideas?
I'm used to measuring car speeds in km/h (kilometers per hour), and probably that's why the first reaction I got to this is "units don't match!".

"If a car at 10Mph hits another car at 10Mph, it's like hitting a wall at 10*10=100 Mph".
Then:
"If a car at 16 km/h hits another car at 16 km/h, it's like hitting a wal at 16*16=256 km/h".

This does not add up as 16 km/h is 10Mph, but 256 km/h is 160Mph, not 100Mph.

[Careyp74]

I'm used to measuring car speeds in km/h (kilometers per hour), and probably that's why the first reaction I got to this is "units don't match!".

"If a car at 10Mph hits another car at 10Mph, it's like hitting a wall at 10*10=100 Mph".
Then:
"If a car at 16 km/h hits another car at 16 km/h, it's like hitting a wal at 16*16=256 km/h".

This does not add up as 16 km/h is 10Mph, but 256 km/h is 160Mph, not 100Mph.

Well there is one simple way to argue against it. Bravo.

Although, to be sure, I am going to drive a little bit slower when overseas. :)

[Brown]

Although, to be sure, I am going to drive a little bit slower when overseas.Go driving on the Autobahn. The Germans will LOVE you.

[grmcdorman]

Not even necessary to use different measurement systems; the basic unit check one is taught to do in elementary physics applies. Multiplying speeds doesn't result in a speed. What's mi2 / hr2 or km2 / hr2?

Mind you, I always assumed the speeds add. As others have pointed out, it isn't even that. Presumably the reason people think head-on two vehicle crashes are more horrific than single-vehicle into stationary obstacles is that full-speed head on crashes into stationary obstacles are less common (or less reported?).

[jasonpatterson]

There is a product called a DriveCam that takes video and speed/acceleration data of commercial drivers (some parents buy them for their kids as well.) The intent is both to make sure that the drivers aren't being unsafe as well as to help prevent commercial drivers from being unfairly blamed in crashes (according to the manufacturers this is common.) You can find lots of DriveCam video of crashes on Youtube, and some of the best include both interior and exterior video of the car/truck involved.

I like to work through some of these with my students, both for the "Wear your seatbelt." thing and to be able to see the physics of a collision.

This guy falls asleep at the wheel wearing no seatbelt. He winds up hurt but alive at the end, lying on the roof of the car with his head in the back passenger window. The accelerometer readings at 15 seconds are particularly interesting. According to the instruments he's trying to hold himself still in a car that is experiencing a force of almost 10g. The blur flying across the screen at that point shows how well his attempt to do so went.
CqQy4xT2AVQ

[fuelair]

.
I witnessed in my outside rear-view mirror a head-on between a Jeep and a Volvo Carryall... the Jeep had just punted a medium sized utility truck going in the same direction across the on-coming traffic, with lots of stuff flying out of the bed of the truck. The Jeep stopped in the fast lane of the on-coming traffic and was immediately struck by the Volvo. It appeared to me that the vehicles merged into each other.. with the Volvo stopping cold.
Killed one person in the Jeep, and three in the Volvo.
The perp in the Jeep which he had just stolen, a newly released parolee, was almost uninjured. His girl friend was killed.

I do hope the perp was handled properly for the murders of 4 real people. But, somehow I doubt it.

[Howie Felterbush]

Ask your teacher what the effect would be if a car travelling at 20mph collides head on with a stationery car (0mph)

You end up with paper all over the road.

[I Ratant]

I do hope the perp was handled properly for the murders of 4 real people. But, somehow I doubt it.
.
He got some kind of jail sentence.. but there was a civil suit also.
I was contacted by the city of Palmdale immediately after the event.. I'd stopped by the CHP office and told them what I'd seen.
The city person took a deposition.
Then some months later I was contacted by a lawyer who wanted to discuss the deposition.
I told him I would not/could not change a thing, knowing how memory can be modified.
Was subpoenaed to testify at a court hearing, but nothing came of that.

[I Ratant]

There's some "interesting" videos and images of texting accidents.... Not for the squeamish.

[Cuddles]

Just as a side note, when discussing these topics with my physics classes, I always ask them how much force they think they would feel if they were in a head-on car crash with a big concrete wall when the car was moving at only 30-35 mph.

After a number of guesses, we do the math. The answer usually comes out to somewhere around 2000-3000 pounds of force, and I see jaws in class drop.

By coincidence, a recent article on Cracked (http://www.cracked.com/blog/4-insane-things-nobody-tells-you-about-riding-motorcycle/) made an interesting point about just how bad our intuition is when it comes to cars. Basically, when you're in a car you're almost completely insulated from the outside world. 30mph doesn't feel fast at all, because you feel like you're just sitting still and you're just not close enough to things, especially the ground, to notice how fast it's zipping by. Get on a motorbike or boat, or even better go some downhill biking or skiing, and suddenly you really get a feel for just how stupidly fast even relatively slow speeds actually are. Humans are not designed to faceplant into solid objects at 30mph.

[Hellbound]

Not even necessary to use different measurement systems; the basic unit check one is taught to do in elementary physics applies. Multiplying speeds doesn't result in a speed. What's mi2 / hr2 or km2 / hr2?

Not specific to you, but just using your observation as a starting point :)

I think a lot of this comes from the confusion between momentum, kinetic energy, and the actual damage incurred.

If you look at the math, you get the following formulas:
momentum = mass * velocity
kinetic energy = 1/2 mass * velocity squared
actual damage = variable depending on imact angles, crumple zones, etc, etc, etc.

People look at mometum and think "oh, so two head on, each at 25mph, is like a wall at 50mph". Or they look at energy and conclude "well, the raltive speed between scenarios is the same, so the energy is the same". Both of which are roughly true statements.

For momentum, there is twice the momentum involved, but it's in opposite directions. Still, the magnitude of the change in momentum is comparable (hitting a wall the momtum goes form 100% to 0%, a change of 100. Head on collision goes from 50% and -50% to 0% and 0%, also a change of 100%).

For kinetic energy, the impact speed (one vehicle realtive to whatever it hits) is also twice as high, so it makes sense that the total KE involved is identical.

However, the damage caused is not identical, and that's the jump people make that isn't supported. The main reason being that both cars in the head on collision include crumple zones and other safety features that absorb some of the energy. So while the energy involved may be the same, in the head on scenario that energy is partially absorbed by two vehicles. In the double-speed-into-a-wall scenario, the total energy is applied to a single vehicle (brick walls being notoriously inelastic ;)), casuing a higher degree of damage.


Mind you, I always assumed the speeds add. As others have pointed out, it isn't even that. Presumably the reason people think head-on two vehicle crashes are more horrific than single-vehicle into stationary obstacles is that full-speed head on crashes into stationary obstacles are less common (or less reported?).

I think you're on to something. In head-on collisions generally both vehicles are moving, and often this results when one vehicle swerves into the oncoming traffic lane. I can easily see how this would result in very little time to react and slow down, meaning speeds remain high. Add that this would often be on highways and interstates, and that just increases the speeds further. Hitting a stationary object most often happens on roads where such objects are close at hand. We tend to clear away objects near highways and interstates, but you may have walls.buildings/whatever directly off the road surface in city streets, curving mountain roads, and similar. In other words, there are more stationary objects close to the road in areas where speeds are generally much slower. Least, that's my thoughts :)

[TubbaBlubba]

Yeah - from a stationary observer, car one goes from 50 km/h to 0 km/h, regardless of whether it hits a wall or another car. The momentary force applied is as such dp/dt. Integrate to get the impulse, and you'll find that the integral is just as large regardless of what the car is. You don't even have to consider whatever the car hits.