Auto Accident, Calculating Force of Impact

F=ma.

4500 lbs x 66 ft/sec/sec = 297,000 ft.-lbs./sec x 1/0.5 sec = 594,000 ft. pounds

Assume it took 0.5 seconds to decellerate to zero fps (1/0.5 sec) and that the collision surface measured eight square feet.

Impact pressure would be 74,250 pounds/square foot.

This story doesn't add up very well.

No way is 45 mph a "minor impact." If the pickup was actually going 45 mph at impact, your car should have moved several feet, brakes or not. There should be chassis damage to both vehicles, not just paint damage.

This makes me doubt the 45-mph figure. Sounds more like 15 mph or something like that.

I agree with you. My brother was parked (waiting to turn) in an 04 mustang convertible when he was hit by a pick-up traveling approximately 50 mph. The mustang spun 270 degrees while sliding 30 or so feet. The damage is much more obvious than paint damage and I wouldn't imagine an impact of 45 mph being that much less severe. Also, he and his girlfriend were a little sore for a few days and had minor scratches from glass shards. Their only doctor bills were from the ambulance ride and the examinations.

Unlikely. The only vehicle I can think of that won't move when hit by a 4500 lb truck doing 45 mph is an M1A1 tank.

I am going on what the driver of the other vehicle said. It was a 45 mph zone. He was looking to his rear trying to change lanes. He stated that he was accelerating when he hit me. So maybe I added 2 + 2 and came up with 45!

After getting the car repaired, I asked the bodyshop to keep the inner part of the bumper (steel) for me. All the joints are bent and buckled.

Maybe I need to leave speed out of the equation as I have no first hand knowledge of the other driver's speed. My car may have moved some - but fortunately I stopped several feet from the car in front of me so I did not hit another vehicle. All I know is here I am 5 months later with considerable back pain under the care of a neurologist. Personal injury attorneys do not want to take a case where neither the car or the driver is not obviously disfigured! So I have to argue this case myself.

Don't bring up speed in court unless they ask you point blank, and even then be honest and say you don't know. (IANAL)

Between the bumper and your doctors testimony hopefully the drivers insurance company will settle for medical bills.

Hope you feel better soon.

From your mangled parts you might be able to reverse calculate some impact data. But you will likely have to do some benchmark testing of similar if not identical parts to identify the forces involved to make a similar distortion of your replaced parts. If you do have to bring this to trial, I would certainly bring the damaged car parts to court with an affidavit from your body shop that they came from your vehicle. You might ask them for an assessment how much force the impact would have to be for the damage done.

Move to Pittsburgh! Personal injury lawyers here love soft-tissue injuries. Who's to prove if it's sore or not.

Scout around for attorneys. This could be worth $50,000 in contingency fees for a good intimidating attorney, and the right attorney could earn this fee with just a few letters and a couple hours time.

If the steel bumper was significantly distorted, then the force was high enough that you could have sustained a back injury -- it doesn't matter what the speed was -- the record of a large force is there in the bumper. Be sure that the body shop certifies that the part you have was from your car. Going beyond that, to the actual forces involved is a long and costly process. Better to threaten suit, with the help of a good attorney, and settle out of court. Without an attorney, you have no leverage.

An attorney could have a lab determine (with another matching bumper part and a calibrated press) the approximate force required to bend the bumper as yours bent. But to go from there to the acceleration imparted to your vehicle, and from there to the acceleration imparted to you (after the absorption the seat structure) will require expert testimony, and is not going to be very convincing, because there are many variables involved, requiring an engineering assessment of the structures of the two vehicles. Computer crash simulations cost the manufacturers several hundred thousand dollars each, (even when the crash is according to a standard procedure against a standard barrier) so as you can guess, the math is quite complicated. Doing this on your own just won't work, and an attorney will not follow this process either, unless he was confident he was working on a $20,000,000 settlement.

Best to keep it simple, and a good attorney can do this for you. The bumper is evidence of a significant impact. You are hurt. A good attorney will want a large enough settlement to make it worth his time. This could be a debilitating condition, possibly costing you millions in lost wages, he will likely say. The Insurance company will settle out of court if you can find a good threatening attorney. I doubt that you can make any real headway on your own.

BTW... If your vehicle did not move, as you have said, then you did not sustain any acceleration, (because acceleration means a change in speed, and speed is distance over time -- no distance, no speed.) By F=MA, if you did not sustain any acceleration, then you also did not sustain any force. Best not to say that your car did not move, and also best to get proof that it did, which should be in the police report.

Again, all this is best handled by an attorney.

GA

I agree that the OP should not offer to anyone but their attorney that the vehicle did not seem to move. However, MB has made a critical misapplication of Newton's laws to say that no acceleration observed means no force applied to a body. F=ma applies to only the net force applied to an object. The car seat or whatever was in contact with the body clearly applied an impulse force to the OP's body. The inertia of the body generated a matching force that matched the impulse so that no net movement happened. To make the matching force though, tissue damage occurred resulting in this long term pain.

However, MB has made a critical misapplication of Newton's laws to say that no acceleration observed means no force applied to a body.

This cannot be! I do not make mistakes. (As long as I say and do nothing.)

I was playing devil's advocate. If the plaintiff says that no car motion occurred, then the car did not accelerate. If the car did not accelerate, then the seat did not accelerate, and the driver-seat relationship was constant: the only forces applied by the seat to the driver were the normal supporting forces. Therefore, the plaintiff would not have been injured in the accident, and must have injured his back after the accident, by some other cause.

Tires slide at a little less than one G in ordinary sedans, so even a light collision will cause a braked wheel to skid. Those skid marks could be a key.

If I were the judge, I'd want to know the length of the skid marks. I'd want to know what the driver said about his back at the time of the accident. Did the driver go to the doctor immediately following the accident, or the following day? If more than a day elapsed, then I'd rule against the plaintiff. (8 out of 10 Americans suffer from back pain.) I'd want to see actual damage to the car beyond that to the bumper steel. Did the body shop have to straighten the bumper mounting points to enable the new bumper piece to fit? If not, then this was a pretty light tap. (A three pound sledge hammer blow can distort bumper steel, while transmitting little more than sound to the driver.)

My son was hit in a parking lot recently, by a pickup truck backing up into his car. $1500 to his inexpensive car. Nothing even remotely close to any injuries. As a judge, I'd want to see at least $5000 in repairs to support there having been the significant damage that would be associated with a significant impact.

If the plaintiff is sure that his back was injured in the accident, then he would certainly have had x-rays taken on the day of the accident or the next to support his case. What do the x-rays show?

Next case.

MB contends: *** Did the driver go to the doctor immediately following the accident, or the following day? If more than a day elapsed, then I'd rule against the plaintiff. (8 out of 10 Americans suffer from back pain.)*** As both a chiropractor and participant in Way too many automotive collisions, I can testify that most rearend collision victims, though dazed and confused, really don't hurt much till the following day, and the third day is awful. Low speed collisions (under 6 MPH) result in chronic neck pain for 10% or more of victims. Some of the chronicity is failure to address the subtle relationships at the top of the neck. A whole branch of chiropractic is devoted to upper cervical correction. It's a bit like replacing the bent bumper and not having the wheel alignment checked. The unscrupulous behavior of insurance companies in attempting to avoid their contractual obligations is familiar. Get the materials related to the incident all together in a coherent file, police reports, scene pictures, and Get a Lawyer! If it comes down to making inferences from the skidmarks,glass, and bent parts for a jury, a credentialed expert will have to be paid. BTW, did your seat back break?

If it comes down to making inferences from the skidmarks,glass, and bent parts for a jury, a credentialed expert will have to be paid.

Perhaps these folks could help. I note that they use the day after criteria also. "The next day they allegedly experience even greater pain..." "... the full extent of which may not be apparent until about a day after the accident." I'm a tough judge, but even so, if he was at the doctor's within two days (rather than my original one) of the accident I'll look favorably on finding for the plaintiff.

The unscrupulous behavior of insurance companies in attempting to avoid their contractual obligations is familiar.

The flip side of this is the unscrupulous ambulance chasers who inflate insurance claims. The system is inherently combative, and I suppose that the resulting checks and balances might be a good thing -- but it can be infuriating no matter which side you are on: Spill coffee on yourself and win a multi-million dollar lawsuit??!!

Do I really have to explain the difference between the concept of "observed" and "precise" or "measured". Have you heard about one of my favorite topics, measurement uncertainty?

Although I greatly appreciate the comments made by those who have taken their time to read my post, I would like to say that I am not asking for opinions on what they believe should have occurred given the facts I presented. I was there, I felt the impact, I was hurt.

I'm not presenting information to a jury and trying to convince them of the facts. What I am looking for is an equation to calculate the force of an impact with the numbers I provided. It seems that I may need to try several figures in the MPH area as that is actually an unknown.

Some years ago I was involved in an accident where my car was totalled, the air-bags did not deploy and I was NOT hurt. The make and model of the car were the same. I tell you that to demonstrate that each accident is different and it is not possible to judge the injury by the visible condition of a vehicle.

Answers.com says:

"The formula is 2mv/t, m is mass, v is velocity at impact and t is the time contact is made during impact. The hardest part about calculating the impact force is calculating t.

One way to calculate t is to estimate the stopping distance (the distance it takes to stop the object during collision), then the simple equations of motion can be used to derive t.

t=2x/(u+v) where v will equal 0 if object is stopped"

Unfortunately for you, you do not any proof that v is over 15 MPH. Indeed, you confirm this, as has been pointed out.

If you have a new car, it may have a "black box" that can be accessed. It would tell you exactly how much energy you took.

I'm not disputing that you may have been injured. You just can't prove it with physics.

If injuries are valid it seems odd that a lawyer and his/her experts can't help you. They work with this many times a day.

There must have been law changes within the last year or two that make it either easier or more profitable for lawyers to suck the blood out of us obtain settlements in the courts. About once a week I have to change the station of my car radio due to the endless 1-800-ask-gary commercials followed by 1-900-hit-by-car, 1-800-411-pain and other national and local lawyer commercials. I have no clue who "Ros" actually is, but I wish Gary had refused her case so I wouldn't have to hear her dozens of times a week.

Is it possible with the brakes on a rear impact has double and sharper the effect on the spine? http://www.youtube.com/watch?v=RP7xZzknX0k&feature=channel (see at 4.59 of video) Sudden acceleration due to impact and sudden decceleration due to brakes. Momentum rocking the upper body to and fro sharply? Hope you recover soon. Regards.

One major resource of information about collision effects on the body is Art Croft, DC. www.srisd.com The police report should have measurements of any skid marks; these provide a basis for measuring the energy of the collision. If your brakes were locked and he hit you at that speed, you skidded forward. Measure the marks and consult a traffic cop who has taken the accident reconstruction class. There are accepted ways to interpret these marks. Sometimes these courses are taught at local community colleges. Consulting the instructor, and taking the class if you can make the time, would help. People are often profoundly injured in low speed (5mph) rearenders. A whole branch of Chiropractic is devoted to restoring the subtle relationships at the top of the neck after such injuries. That a rear end collision requiring automotive bodywork, much less at a speed anywhere near 45 doesn't deserve payment is Allsnake MUS.

If a vehicle hit you from behind at a full 45 mph, your car would be thrown tens of feet, damage to the vehicles would be extensive, and through inertia would have resulted in your foot no longer "applying the brake". Assuming that you stayed in a straight line, the car would have likely rolled for several tens of feet more before you even thought of reapplying the brakes...if you could.

I have seen cars hit from the side, and therefor having a much higher coefficient of friction (meaning harder to move) than in your case, pushed, slid, catapulted, and/or flipped for 30 to 150 ft. from a lowly 45 mph impact.

The calcs above are essentially accurate for the forces stated.