Calculating Force (Rear-End Auto Collision)

An automobile collision has both plastic and elastic characteristics determined primarily by crushing of the sheet metal and body components. The acceleration of the struck vehicle and deceleration of the striking vehicle occurring during the time of contact is a dynamic variable and not easily calculable with any accuracy. If you know masses of both vehicles and the initial and final velocity of the striking vehicle you can calculate the theoretical final velocity of the struck vehicle through momentum transfer under the law of momentum conservation. This doesn't account for real world friction losses due to braking. That's the main reason automobile manufacturers do crash testing to validate/prove the crashworthiness of their designs.

Why??

As a retired traffic crash investigator, with over 20 years experience I can tell you one thing. 1. It's highly doubtful the vehicle was traveling 50 mph. That would be at over 70 Feet Per Second. 2. I imagine from the single photo it was closer to 30.

I'm not sure of the "exact" speed of the caddy. All I know is I just stopped at the light (about 4-6 feet from the car in front), and then impact! No screeching tires, no horn, no warning. The pic wasn't taken immediately after it happened. The back bumper of the honda in front was all the way at my windshield before being stabilized so they could cut the top off. (both cars were complete losses)

Did you have your foot on the brake pedal? That way the car moves less when hit (helps to prevent whiplash) and the brakelights warn following drivers.

I instructed both my wife and two Daughters many years ago, to always "sit" on the pedal when stopped. It has proved to be good advice without exception up to now at least!!

It really sounds as if you didn't have your foot on the pedal, maybe only the handbrake or nothing at all......by the way, even quite low speed accidents sound/look like the other car was doing 100MPH Hopefully he was braking as he hit you.....that helps a lot.....

I'm sure my foot was on the brake. Impact happened within 3 seconds of stopping. I was in process of turning my head left to look in my side mirror. My front bumper dipped below the bumper of the car in front. (indicating my foot was on the brake. Air bags in my car did'nt deploy. I did not have bumper to bumper contact with the honda. My front bumper is pretty clean.

I believe my foot was on the brake as impact occurred. The crash happened so fast! (within 2 seconds after completely stopping, maybe sooner)

You have already got all the answers you needed.

I will only thank god, and you should too, that you are able to talk to us...

Wangito

My father said I was "lucky". "Your'e lucky it wasn't a DUMPTRUCK"!! (that hit me)

In almost 50 years of driving, I always leave a good space in front of me when stopped in traffic, I also stand on the foot brakes so that:-

a) the brake lights are always on and

b) also due to the fact that if the handbrake only works on the rears, that is largely ineffective due to the car behind usually "diving" under the car in front, (as yours did) lifting the rear wheels off the ground....

I also keep a good lookout for morons behind me and press myself back into the headrest when one is on his way!!!

I have been run into a total of 11 times (or so!), every one from behind, not all were at lights or stop signs, sometimes I was at the end of a traffic holdup.

In all those "hits", the front of my car has never been damaged by hitting the car in front.

I almost always have had a tow-bar, which usually "guts" the car behind and leaves my car in every case:-

a) drivable

b) repairable too....

(It also stops people hitting the rear end when parking!!! Though I may hit them sometimes.........)

No I don't know how fast they were all going, most looked damn fast, at least the ones I noticed first.....especially the big truck!!!........never thought to ask any of them......

Hi Greg I saw your question, and since I have worked with rear end collisions I'll share how to analyze a problem. In this case where all cars are in connection you should use the equations as for a plastic collision. From the physics we knew that all momentum is preserved and that the final velocity for involved cars are the same. If you think that the car in the middle first was hit and jumped forward before it hit the car in front, be aware of that the maximum difference in velocity between the two rear cars could maximum be 2 miles/hr more likely 1 miles/hr if they separate after the first collision. Looking at the pictures i would judge that the very rear car could have had a velocity within the range from 30 to 42 miles/hr when it hit the car in the middle. If the car in the middle used the brake this would have a minor effect on the velocity change for the car in the middle, but would reduce the velocity before it hit the first car in the lane. Typical collision time with damages is 0.15 to 0.12 s. =>F =m*dv/dt dv= 36 miles/hr and dt=0.15 s Then you have the force when you know the mass of your car. Your braking might be the reason for your car to slide underneath the honda in front. Hope this could be helpful for you

f Dt = m d v

Great responses. Where were you guys when I was up late doing reports? One thing to remember is at the point of collision, your foot most likely came off of the brake pedal allowing it to roll. (and it could be checked on the vehicles black box. I believe 96 was the first year for all Saturn vehicles to be so equipped). This lack of braking has to be accounted for as well. The downward slope of the Cadillac's nose indicates is was braking hard, (it has a black box as well) and immediately after impact that vehicles driver probably released the brake as well from the rebound. The subsequent photo looks like there may be a slope. If so, this is a major factor in getting underneath your Saturn. Without seeing more of the approach, the pavement type, access to the black boxes and interviews, it's just guesswork. Best thing is, you got away, sorer I'm sure. One thing, having taught this, knowing stops and intersections have a higher crash rate. Be aware of escape routes, that is, be attentive to the cars behind you. You can see one coming and move, or start to move out of the way. Before you start jumping me, realize it's requires an active participation. How many of you practice/train for driving every year? And driving back and forth from work doesn't count.