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Tesla head on collision with a Honda

flar

Member
Apr 20, 2013
451
379
So given that the visible damage is very consistent with a combined speed of ~80mph (or possibly lower considering what a tank the Model S is, while the Honda was 20 years old and comparatively fragile), is it your contention that the Honda was parked on the roadway?

Otherwise, the impact energies are subject to the laws of physics, in which case kinetic energy is calculated E=1/2mv^2.

Just to be clear. The energy of a single car into a wall is 1/2mv^2. The energy of 2 cars into each other is 1/2*m1*v1^2 + 1/2*m2*v2^2, not 1/2(m1+m2)(v1+v2)^2 so you cannot compare "40mph into 40mph" with "80mph into parked car". The latter has twice the energy of the former because you add the squares, not square the sum.

Because the equation relies on the square of velocity, impact energies ramp up quickly with speed. Ignoring the units, 1/2*100*50^2 = 125,000 "whatevers" while increasing the velocity in the equation to 60 results in a total of 180,000 "whatevers" which is almost 50% more "whatevers" just moving the velocity from 50 to 60.

True, as long as you understand that it goes up with the square of the velocity of each individual car separately and then gets added into a sum, not the square of all of the velocities involved.

There is a reason that cars are not tested at combined impact velocities of ~140mph (which is what you would expect on a typical highway). The reason is that cars that are involved in a head on collision at that speed leave a smear of debris and gore as opposed to recognizable vehicles.

A combined impact of 140 could be one car at 140 into a brick wall which would still have a huge amount of energy, or it could be 70 into 70 which would have a bunch more energy than your 60mph car you used as an example, but not nearly as much as 140 squared compared to 60 squared.

The rest of what you said I generally agree with, but I keep seeing this "adding the velocity of the cars" mistake when people talk about collisions and wanted to make sure the math was right.

Also, if you watch Mythbusters they were rather surprised that doubling the speed didn't quadruple the damage to their car, but they chose a velocity where the car was smashed so much that the crumpling wasn't very linear when they doubled the speed. http://www.youtube.com/watch?v=r8E5dUnLmh4
 

flar

Member
Apr 20, 2013
451
379
So given that the visible damage is very consistent with a combined speed of ~80mph (or possibly lower considering what a tank the Model S is, while the Honda was 20 years old and comparatively fragile), is it your contention that the Honda was parked on the roadway?

Another bit of physics to consider - the speed of the car before the impact, alone, does not determine the energy of the impact. It is the change of velocity during the impact. If I am going 80mph and hit an object that causes me to lose 1mph of speed, there wasn't a lot of energy there compared to hitting an object, like a brick wall, that causes me to lose all of my velocity.

Given that the Tesla ended up a few hundred feet down the road having dragged a front tire or two the entire way, it did not lose all of its initial velocity in the original impact. If it was going 80 and left the impact still going 40, then it contributed "40mph worth" of energy (times a larger mass). The Honda could have been going slower than 40MPH and been driven back by the much faster and heavier car and still incurred damage that resembles a 40MPH offset collision test. Examining the damage only gives you an estimate on the change in velocity of the 2 cars, not the speeds they were going before the impact. To extrapolate that you would then have to estimate how much energy they appeared to have after the impact based on how far they bounced, skidded, or rolled and whether or not some brakes were involved.
 

Jeff Miller

Member
Jan 2, 2013
293
3
Chicago
so you cannot compare "40mph into 40mph" with "80mph into parked car". The latter has twice the energy of the former because you add the squares, not square the sum.

Think about the physics a bit. Does the damage depend on the frame of reference? Ie does some someone traveling at 40 along side the honda, who perceives the honda as stationary and the tesla as going 80 (in this example) see a different outcome than someone watching from along side the road and sees them both going 40? Another way of phrasing this is what do you think Galilean invariance means?
 

vetboy45

Member
Feb 14, 2013
62
0
Kent wa
I would like to take a moment to congratulate everyone for having the single nerdiest car club website on the net. Let the math continue....
 

ggr

Expert in Dunning-Kruger Effect!
Mar 24, 2011
6,983
27,545
San Diego, CA
Think about the physics a bit. Does the damage depend on the frame of reference? Ie does some someone traveling at 40 along side the honda, who perceives the honda as stationary and the tesla as going 80 (in this example) see a different outcome than someone watching from along side the road and sees them both going 40? Another way of phrasing this is what do you think Galilean invariance means?

If the two vehicles fuse into a single lump, this is a good way to think about it. If both the Tesla and the Honda were doing 40 mph before the collision, the TesHonlada lump would be doing, say, 10mph in the same direction as the Tesla because the Tesla is heavier. Only for an instant, of course, since the lump wouldn't roll very well. Taking that as the frame of reference, the Honda might as well have been doing 50 mph in terms of the damage it took, while the Tesla would feel like it was only doing 30.

... but having written that, I'm not sure it's correct. It works for momentum but not necessarily energy. Have to think some more.
 

ModelS1079

Member
Jun 23, 2012
871
139
Suburban Boston
Tell that to the wives and children of the two men who died. I think they'd kinda like to know if there was a culpable homicide there, alternatively the Tesla owner might like to be publicly exonerated if it wasn't his fault.

BTW, "ain't cool in no kinda way" is a double negative so either you mean it is cool or this was just provocative?

+1
Kinda summarizes how I feel about the whole, terrible accident.
 

RDoc

S85D
Aug 24, 2012
2,736
1,588
Boston North Shore
Think about the physics a bit. Does the damage depend on the frame of reference? Ie does some someone traveling at 40 along side the honda, who perceives the honda as stationary and the tesla as going 80 (in this example) see a different outcome than someone watching from along side the road and sees them both going 40? Another way of phrasing this is what do you think Galilean invariance means?
As was pointed out before, the issue is the change in velocity. Someone in the Honda frame of reference sees the Honda as stopped and the Tesla approaching at 80 mph. Then the collision occurs and the cars don't stop in that reference frame, rather they both move in the negative direction at 40 mph (assuming equal masses). So the energy of the Honda when from zero to 1/2 M * 40^2 and the energy of the Tesla went from 1/2 M * 80^2 (2 M * 40^2) to 1/2 M 40^2 and the net change in energy was M * 40^2.

Crashing into a parked car at 80 mph is very similar to two cars hitting each other head on going 40 mph. However, that's not the same as hitting a brick wall at 80 mph even though the energy is the same. The difference is there's no crumple zone in a brick wall so the average deceleration of the car during the crash into the brick wall is significantly higher.
 
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vfx

Well-Known Member
Aug 18, 2006
14,790
40
CA CA
I would like to take a moment to congratulate everyone for having the single nerdiest car club website on the net. Let the math continue....


I'm sure the DIY EV group tops this bunch. And the Leaf group has a plethora of pocket protector types too. Tech cars, tech owners.

(proud I used the word plethora)
 

dflye

S Sig Perf 414, VIN 814
Oct 7, 2011
565
4
Raleigh, NC
I'm sure the DIY EV group tops this bunch. And the Leaf group has a plethora of pocket protector types too. Tech cars, tech owners.

(proud I used the word plethora)
Apparently the usage was apropos; still shocked that some folks haven't heard of that particular word; guess having used it as a unix command line tool for decades it has become second nature for me.
 

jeff_adams

Member
Mar 18, 2013
618
2
Monterey
I Googled for any info on the investigation a couple of days ago and read two interesting things.

A lawyer's blog referenced a KTLA news report that said the Benz had collided with the Tesla. I have my doubts about that because it hasn't been mentioned elsewhere.

The second interesting thing was a local saying she saw a tow truck carrying a white c230 Benz with body damage (black paint like the Tesla) going towards Laguna Beach. This was 3-4 days after the accident. I haven't seen any mention of the model of the Benz involved, but if it turns out to be a c230, that could be the car. If so, and the driver didn't stop at the accident scene, they have big problems with hit and run.
 

flar

Member
Apr 20, 2013
451
379
As was pointed out before, the issue is the change in velocity. Someone in the Honda frame of reference sees the Honda as stopped and the Tesla approaching at 80 mph. Then the collision occurs and the cars don't stop in that reference frame, rather they both move in the negative direction at 40 mph (assuming equal masses). So the energy of the Honda when from zero to 1/2 M * 40^2 and the energy of the Tesla went from 1/2 M * 80^2 (2 M * 40^2) to 1/2 M 40^2 and the net change in energy was M * 40^2.

An important thing to keep in mind is that the frame of reference cannot be affected by the collision or you must apply more math to adjust for the change of the frame of reference. You used a frame of reference that was similar to the Honda's before the collision, but then continued unaffected by the collision. That's a reasonable way to do the math as you don't have to adjust for changes in the frame of reference as the collision occurs. I'm not sure I'd call that "in the Honda's frame of reference" because it parted from the Honda at the point of impact - it's more "in a frame of reference that matched the state of the Honda before the collision". Either way, the analysis you gave was consistent with that "similar, but not identical to the Honda" frame of reference and that frame of reference remained unchanged by the collision so the math is good.

Most people try to apply the frame of reference of a passenger that sees an approaching object at double the speed and then continue mentally anchoring the frame to that person through the collision to the aftermath and that leads them to think of a 40+40 head on collision as involving an 80mph change of velocity, but they cannot hold on to the frame of reference like that as they suffer the collision and get correct numbers.

Crashing into a parked car at 80 mph is very similar to two cars hitting each other head on going 40 mph.

Not really. All they have in common is some numbers that add up to 80, crumpling someone else's property, and the look of fear in the passengers eyes as they watch the "approaching" other object. But, their energy is quite different. In particular...

However, that's not the same as hitting a brick wall at 80 mph even though the energy is the same.

Hitting a brick wall at 80 is similar in terms of energy to hitting a parked car at 80, true, but neither has the same energy as two cars hitting head on at 40+40. For "80 into brick wall" and "80 into parked car (assuming the car is anchored well enough not to move)" have 1/2m80^2 or 3200m energy. The head on 40+40 cars have 2 * 1/2m40^2 or 2 * 800m or 1600m or half the energy of the single car 80 example.

The difference is there's no crumple zone in a brick wall so the average deceleration of the car during the crash into the brick wall is significantly higher.

Hitting a parked car does add more crumple zone than hitting a brick wall and that helps, but two cars hitting each other at half the single-car speed not only have the extra crumple zone, but they also have half the energy to deal with.

The other consideration is that hitting a parked car at 80 will probably result in a deceleration of <80 because you are going to carry the parked car along unless it had a bat tether wrapped around a very large utility pole.

So, hitting brick wall at high speed gives you 1 crumple zone and high energy.
And hitting parked car at high speed gives you 2 crumple zones and high energy (and probably residual velocity that lowered the total energy of the collision itself).
But, hitting another car with each of you at half that speed gives you 2 crumple zones and half the energy of either of those two.

And that is assuming that the two cars are of similar mass and end up stopped at the point of impact.
 

jkirkebo

Model S P85+ VIN 14420 EU
Jun 13, 2010
961
12
Fredrikstad, Norway
Hitting a brick wall at 80 is similar in terms of energy to hitting a parked car at 80, true, but neither has the same energy as two cars hitting head on at 40+40. For "80 into brick wall" and "80 into parked car (assuming the car is anchored well enough not to move)" have 1/2m80^2 or 3200m energy. The head on 40+40 cars have 2 * 1/2m40^2 or 2 * 800m or 1600m or half the energy of the single car 80 example.

I find it helpful to consider the example of two identical cars, travelling at the same speed (say 40mph), hitting each other exactly head on. Both cars will stop dead, and the result will be the same as hitting a brick wall at the same 40mhp speed.
 

deonb

Active Member
Mar 4, 2013
4,057
4,209
Redmond, WA
I find it helpful to consider the example of two identical cars, travelling at the same speed (say 40mph), hitting each other exactly head on. Both cars will stop dead, and the result will be the same as hitting a brick wall at the same 40mhp speed.

No, it's not. Remember a cars' speed (in this case 40mph) is not an absolute number, but a number relative to the earth. The cars didn't crash into the earth, so why take speed relative to the earth into account at all? If at the same time a Boeing was flying overhead at 500mph ground speed, then relative to the Boeing, one car would have been travelling at 460mph and the other one at 540mph. Saying one car imparted damage as if it was travelling at 460mph is equally as invalid as saying it was travelling at 40mph.

What matters is that the speed of one car relative to the other car at the point of impact is 80mph. Whatever the car's speed is relative to some other arbitrary point in space is irrelevant. So relative to the earth, whether one car was 0 and one at 80, or one at 40 and the other at 40, or one at 100 and the other reversing at 20 - it's all the same thing. (If it helps, take the earth out of the equation and imagine the collision happens in space).
 

brianman

Burrito Founder
Nov 10, 2011
17,533
2,997
This talk about running cars into brick walls and collisions in space are going to give me nightmares that will wake me up in the middle of the night to check my garage.
 

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