This is somewhat of a question -- calculations about my car accident

[squilliam]

Now, I had a collision approximately two weeks or so ago, however, I was the one blamed for the collision due to a "witness" but I need some help with the correct calculation I need.

You see, her car weighed 2602 pounds, where as my car weighed 3359 pounds, but she hit me hard enough on the back right wheel to end up not only denting my car a fair bit(several things bent in fact), but she ended up spinning me approximately 300°, while her car slid about 50 ft after she hit me.

The only thing I can figure out is that she must have been going way to fast, I mean I could be wrong, but I would very much like to know.

 

[Simon Bridge]

Welcome to PF;
Your calculations are unlikely to be acceptable as proof of anything, neither will mine or anyone's you meet here - you need to find a specialist in investigating accidents.

To work out this sort of thing, even back of envelope, I'd need more detail on the location of the impact and the nature of the surface the cars were sitting on. But spinning someone right around is not unusual in even quite slow collisions.

 

[jedishrfu]

Welcome to PF!

You could start to solve this by making a drawing that shows before and after the collision.

So were you going through an intersection and she hit you in the back passenger tire?

Were you running a RED light? or was it a four way stop?

Its hard to say without knowing more about the accident.

 

[squilliam]

Simon

It's not that I even really want to prove to my insurance company, I just want it for me really, like I doubt walking in their with an equation will turn the claim around like that. But I find it annoying that the person who hit my car even told me that she thought, and I quote " I hope I don't hit him" , she even said to me that she "closed her eyes".

The place of the collision was a two way intersection through a stretch of road, all normal asphalt, she collided with the back 2 ft or so of my car with the front end of her dodge neon. It just seems to me though, that in order fer her car to slide an extra 50 or so feet she would have had to been going more than the speed limit at 35 mph.

 

[squilliam]

Here are some pictures that I took

 

[jedishrfu]

These pictures don't really help with an analysis of the collision and as Simon said there's nothing that we can say that would support your case. If you
hire a lawyer then yhey may be able to have an accident reconstruction specialist do the numbers and be an expert witness for you.

The sad part about accidents is that people will say one thing to you and another to the police. Similarly for witnesses, they hear the bang and usually see the accident after it happened, drawing conclusions from that to report to the police. The end result though is that you have a car you must get fixed, papers to file, possible increased insurance rates and sometimes medical bills to pay.

So get it processed and get your car fixed and do something nice for yourself.

 

[squilliam]

Well see, that's just it my car is now drive-able, it just doesn't look pretty as the fact I only have liability would only give money to the other person anyways, I'm just trying to figure out what equation I should try to figure out if she was in fact going the speed limit or not, therefore, only proving really to myself if she was at fault.

I mean they already gave her money for a new car and everything, so it's settled as far as claims go, I just want it for some piece of mind, you know?

 

[jedishrfu]

A simpler thought is to do an experiment. Get two toy cars and make one twice the weight of the other and crash them in the same way and look at the outcome. Its not accurate but it may give you a better understanding of what happened. My feeling is your intuition is correct but of course she would never admit that she was speeding.

I had a similar accident on a rainy day coming up to an intersection. I had to stop because I saw a police car with lights and siren on about to come through. I stopped and a few moments and I mean a few moments later an SUV driver crashes into my truck. The officer stopped to document the accident instead of going to where he was going. My feeling was the driver was on a cell pone and didn't pay attention to me stopping because in general no one stops at that intersection (a Texas highway access road) if they have the right of way.

It was blamed on the rainy conditions...

 

[jack action]

Crude approximation, but here we go:

I assume the car is sliding and the tire friction coefficient for sliding can be assumed to be 0.75. So if you see 50 ft of skid marks (using $v = \sqrt{2\mu gd}$), that means that she was going 33.5 mph when she started to skid. Thus, using $E = \frac{1}{2}mv^2$, the car had 132.34 kJ of kinetic energy.

For the energy required to spin your car, let's assume you have a wheelbase $L$ of 105" and your rear tires (and half the weight of your car sitting on them) slide with the same CoF of 0.75 for 0.833 turn (= 300°/360°). That requires 78.27 kJ of energy (using $E = \mu mgd$ and $d = 0.833\times 2 \pi L$).

Adding both (210.61 kJ) and using $v = \sqrt{\frac{2E}{m}}$ means that the car was going at least 42.3 mph before hitting your car.

Values in every equation must be in SI units (I did all the conversion).

Again, crude approximation. It could be lower or higher, but I doubt it would be less than 35 mph.

ref.:
https://en.wikipedia.org/wiki/Braking_distance
http://hpwizard.com/tire-friction-coefficient.html

 

[jedishrfu]

Good analysis, I would conclude she was going at 42 because she was clearly thinking about the meaning of life while she closed her eyes as the display of 42 flashed across them and then boom. Douglas Adams would be so proud.

 

[Simon Bridge]

regular tyres on dry asphalt: sliding friction 0.9, rolling resistance 0.011
http://hpwizard.com/tire-friction-coefficient.html (and elsewhere)

s=15m sliding from the collision to rest, suggests

$\mu mgs$ went into the ground while sliding.
That puts the speed after the collision at: $v=\sqrt{2\mu gs} = 11.5m/s$
... so she was, easily, going faster than 26mph before the collision.

Energy that went into your car is trickier - the collision is inelastic, so kinetic energy is not conserved.

he car was going at least 42.3 mph before hitting your car.

... that's about 70kmph.
A somewhat messier back-of-envelope that accounts for the engine being at the front of the car, so center of mass is more forward making it easier to rotate by pushing on the back, and some notes about accident studies, I get about 60kmph for the ballpark speed before the collision.

60-70kmph sounds like about the right range ... this is a common type of accident.
There are quite a few examples of collisions at this speed-range online.
Many people think that 35-40mph is slow ... and then get surprised by the damage.

 

[Danger]

Squilliam, go back to Dave's first comment. You pretty much have to hire a professional accident reconstructionist to have any traction (pardon the expression) in court. An investigating police officer would be a good witness, and you wouldn't have to pay him, but that would be supplemental to the expert who can say under oath that things happened in a particular manner. It is also essential that you obtain copies of the investigation photos to show where everything ended up. Also, get copies of the first responders' notes (cops, EMT's, etc.).