# Auto Accident

1. Aug 2, 2009

### chlight02

My wife was in a car accident her ford expedition was totaled by a motorcycle. Everyone is ok, the motorcycle guy jumped off the bike with out breaking and slid on his leather about 200 feet. (he walked away with out a scratch)

The question I have is how fast was the motor cycle going?

The motorcycle weighed 566 pounds and the expedition weighed 5,345 pounds.

The motorcycle hit the rear passenger wheel. He broke the rear axle, bent the frame and pushed the entire truck 12 feet on asphalt.

My wife was moving 5 mph crossing the lane that the motorcycle was in.

We know it was fast, but canâ€™t figure it out.

2. Aug 2, 2009

### Danger

Welcome to PF, Chlight.
This subject has come up several times in the past, and the only advice that we can offer is that you hire a professional accident reconstructionist. It is impossible, and not legally admissible in court, for anyone here to answer you.

3. Aug 2, 2009

### chlight02

Yes, I seen that after my post. It's not something that I would bring up in court. The lawers will handle that stuff. My friends and I are interested in how fast would 566 lbs be going to move 5,345 lbs 12 feet and what was amount of force to do it?

4. Aug 3, 2009

### Danger

Oh, okay then. I'm afraid that I am totally incapable of answering that. (Grade 9 math education, most of which I don't remember.) Someone else will have to take over.

5. Aug 3, 2009

### uart

Well it depends on the friction of the road surface, but for dry asphalt (coefficient of friction > 0.5) then I calculate that the bike would have to have been doing about 200 km/hr to push the truck 12 feet (3.66m) sideways.

The required speed reduces a little on wet asphalt (coefficient of friction > 0.25) in which case the required speed is about 145 km/hr.

The above calculations assume that the bike transferred 100% of it's momentum to the truck. If the bike recoiled (as in bounced off the truck) then it actually could have transferred more than 100% of it's momentum. For example in a perfectly elastic collision the bike could have transferred almost 200% of it's moment to the truck (surprising as that may seem). In this case the required speed would only be about 70% of the figures given above, but such an elastic collision is very unlikely for this type of accident so I'd say the original assumption (100% momentum transfer) would give the most likely "ball park" figures for the bikes initial velocity.

Bare in mind that these are only rough calculations and the real situation could be different. For example the calculations assume that the trucks tyres stay in contact with the road surface throughout the slide. If however the truck is bouncing up and down significantly during the slide and the wheels are losing contact then the required initial bike speed is also less.

Last edited: Aug 3, 2009
6. Aug 3, 2009

### chlight02

And the guy got up and walked away.

Thanks, I couldn't figure it out

7. Aug 3, 2009

### sganesh88

I get an incredible value. 142 mph! (about 228 kmph)
Assuming a perfectly inelastic collision. And the sliding friction coefficient to be 0.5.

8. Aug 3, 2009

### uart

Yeah it's pretty amazing.

BTW I assumed the tyres were sliding for the full 12 feet (as in the bike pushing the truck sideways). If the truck spun around and rolled part of the way then obviously the figures would be different and the bike speed might not have been as high. Really there are so many unknowns in a problem like this that any calculations should be considered as "just for fun" if you know what I mean.

9. Aug 3, 2009

### uart

Yeah I got a little over 200 km/hr but rounded it down given all the uncertainties about the exact nature of the collision.

10. Aug 3, 2009

### Cyrus

11. Aug 3, 2009

### chlight02

this is for fun so to speak, It amazed me to see it. The rear wheel that was hit broke the axel bent the frame and pushed spun the rear around 12 feet, dragging a whole in the rear tire.

is there a way to post the photo?

12. Aug 3, 2009

### rcgldr

Accident reconstruction is more art than science. The rear tires probably hopped during the impact, the relatively light rear end of the SUV would allow it to swing around, ..., so there's no way to tell what the average coefficient of friction was.

13. Aug 3, 2009

### Lok

Use imageshack.com and post the link. I'm very curious.

My calculations give a modest 70 km/h or 43 mph...

There is another method if you have the coefficent of friction between the motocycle driver and road.

Assuming a 0.3 coefficent ( leather road?!? ) the speed is 71 km same as above.

14. Aug 3, 2009

### sganesh88

Ya. "Just for fun" is right. Curious to see what real time values you would get by applying the Conservation of momentum and energy--roughly atleast-. Waiting to see some x kmph pop out of equations.

You mean the arc length with the frontal tire contact patch as the radius was 12 feet? I have a trouble understanding your english.

15. Sep 10, 2009

### accident-law

As long as you and motorcycle driver are safe, dont bother about anything else

16. Sep 10, 2009

### Andy Resnick

I got a much more reasonable answer- (warning, poor use of units ahead)

A 6000 lb car sliding 4 meters on a surface with a coefficient of friction 0.3 dissipates 3265 joules of energy. If this is supplied by a 550 lb motorcycle, the cycle's velocity comes to a modest 12 mph.

17. Sep 10, 2009

### uart

Hi Andy, I think you forgot to multiply by "g" (9.8). I get approx 32 kJ when I repeat your calculations.

BTW. If you correct for this you'll still get a more modest answer (similar to Lok above though he used a slightly higher coefficient of friction). The reason for the lower value of Loks calculation is that he, like yourself, used conservation of energy instead of conservation of momentum. There are many sources of energy loss in a collision so conservation of momentum is much more appropriate.

Last edited: Sep 10, 2009
18. Sep 11, 2009

### Andy Resnick

Thanks for finding that error.. I guess converting pounds to kilograms causes trouble for everyone at some point.. :)

I think it's wrong to try and calculate a highly accurate result for this situation at all- as you point out (as well as others), there's lot's of effects: vehicle spinning, energy absorbed by breaking the axle, energy used to damage the bike, etc. etc. At best, we can estimate a lower and upper bound.