# Crash reconstruction question

## Main Question or Discussion Point

I am trying to determine the speed of one vehicle involved in an accident. I know the speed of the other vehicle, and how far the two traveled after impact. There was no braking prior to impact. Vehicle A swerved 90 degrees to the right after impact, while vehicle B rotated 180 degrees to the left. Any suggestions would be appreciated. Thanks.

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tiny-tim
Homework Helper
Welcome to PF!

I am trying to determine the speed of one vehicle involved in an accident. I know the speed of the other vehicle, and how far the two traveled after impact. There was no braking prior to impact. Vehicle A swerved 90 degrees to the right after impact, while vehicle B rotated 180 degrees to the left. Any suggestions would be appreciated. Thanks.
Hi Sean! Welcome to PF!

You should tell us what you have tried, or considered and given up - then we'll be able to help you!

Oh, and are you told that the cars have the same mass?

Is there any other missing information?

Ah, good question - vehicle A is a van around 4200 lbs, vehicle B is a pickup around 5500 lbs. I am a total physics noob, so what I have tried is asking my friends who majored in physics in college. One told me 50-57 mph, and the other said he couldn't figure it out because vehicle A rotated so much after impact.

tiny-tim
Homework Helper
… what have you tried … ?

erm … you haven't told us what you've tried, or considered.

What equations do you think are relevant?

Is there any missing information which is bothering you?

I think there's a misunderstanding here. I'm not a physics student or expert or anything. I wouldn't have the foggiest idea how to proceed. I'm just looking for someone who is good at this sort of thing and can figure it out. Perhaps this isn't the right forum to ask for this kind of help.

tiny-tim
Homework Helper
I'm confused … your attached diagram is obviously a question from a physics textbook.

Why are you trying to solve it?

You would need to understand conservation of momentum and the equation for constant deceleration …

I designed that schematic based on an accident report. This isn't a theoretical question, it was a real accident. I am trying to solve it to see if the driver of vehicle B is liable for speeding. As you can see, my skills run more to graphic design that physics.

tiny-tim
Homework Helper
I designed that schematic based on an accident report. This isn't a theoretical question, it was a real accident. I am trying to solve it to see if the driver of vehicle B is liable for speeding. As you can see, my skills run more to graphic design that physics.
Ah … it makes sense now!

erm … midnight here, so I'm going to bed … :zzz:

I'll think about it overnight …

My immediate thoughts are that the theoretical physics of pool-table type colllisions don't work very well in vehicle collisions.

Police usually work out the speed from tyre tracks, or from knowing the coefficient of friction.

Were there any tyre marks on the road in this case?

Have the police (or anyone) measured the coefficient of friction of that actual junction in the same weather and road conditions?

Do you have a copy of the police report?

rcgldr
Homework Helper
One difficult variable is how much of the energy and momentum was lost due to permanent deformation of the vehicle bodies (the inelastic part of the collision).

Danger
Gold Member
Welcome aboard, Sean. Beautiful illustration.
Another complicating factor is how much energy was lost to the tires through lateral skidding. As Tiny-Tim mentioned, skid marks are usually investigated very thoroughly. Side-skidding, though, isn't the same as when brakes are locked up in a straight line. It sort of ties in with Jeff's concern about body deformation. Tires sliding sideways share the damage with axle and suspension components, so the marks should (I think) be shorter than they would be if the tires were rigidly mounted to the vehicle. The steering wheel deflections of both vehicles at every stage would make a difference to the marks from the front tires as well. You stated that the brakes weren't applied before impact, but what about after while the vehicles were still moving?
I take it that this is a fairly serious matter to you. If the police can't or won't investigate fully, you might have to consider hiring a free-lance professional accident reconstructionist. As with medical problems, this might be something that is just not suited to speculation on a site like this no matter how brilliant the respondents are. For one thing, our opinions would have no legal standing whatsoever if this comes to a court case.

edit: I hasten to point out that I don't include myself in the 'brilliant respondent' category. I just try to look at things from a logical standpoint.

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tiny-tim
Homework Helper
{snip} If the police can't or won't investigate fully, you might have to consider hiring a free-lance professional accident reconstructionist. {snip}
Hi Sean!

Having though about it overnight, I came to the same conclusion as Danger's above.

Assuming you intend to take this further, you simply can't go into a court and try to put your own mathematical calculations in as evidence.

The court will only accept evidence of this sort from an expert witness.

I'm afraid you need to engage an accident investigator - try yellow-pages, or googling "auto accident investigation".

I never intended to go to court with a printout of evidence from some 'guys I found on the net', I was only looking for a best guess so I would have a better idea if it's worth the money a professional reconstruction expert would charge. The speed limit was 45, the driver admitted to going 55. If that's all he was doing, then there's no point in pursuing this. If he was going 70, then there is. Obviously this calculation is way more complicated than I initially thought. Is it obvious that I got a C in Calc II?
Thanks anyway guys.

tiny-tim
Homework Helper
Hi Sean!

A speed of 55 looks about right.

Taking stopping distances from paragraph 126 of the British Highway Code, 76 feet (25 metres) corresponds to about 40 mph for braking in a straight line on a dry surface.

So car A would have an initial sideways speed of - very roughly - 40 mph, which means that car B's speed before contact would be - very roughly - in the 50 mph region.

Of course, there are other considerations. Calculations like these are very unreliable. Tyre marks are a much better indication.

Even a speed of 55 mph causes a great deal of damage and injury.

It's up to you …

Danger
Gold Member
I just thought of something that could take a lot of the calculation work out of it. Some vehicles have recording speedometers that either lock the needle in place or cause it to make a mark on the dial under high impact. Have you checked into that possibility?