The Traffic Accident Reconstruction Origin -Approach Angles Solution-

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Solution to the Approach Angles case "Ped Skid"

This is a solution to the "ped skid" Approach Angles problem. With the information provided in the case file, I believe that I have answered the primary question posed; "Was the suspect in excess of the 30 MPH speed limit when he locked the brakes?"

The Analysis

The problem established that the vehicle in question had in fact laid down the skid marks documented in the problem. They were described as starting as shadows, progressing to a "lighter mark", and then continuing to rest as a dark mark.

Including these "shadows", or as I would call them, "impending tire marks", in the total length laid down by each tire of the vehicle does not pose a problem in the analysis. This is due to the fact that during these impending tire marks, the vehicle is at it's maximum braking efficiency (near static friction) until the tires lose traction and begin to slide on the roadway at the locked wheel co-efficient. By including these impending tire marks in the total slide distance, we are still giving every consideration to the driver of the vehicle by using the locked wheel co-efficient of friction over the total skid distance, obtaining a lower speed.

In order to calculate an accurate co-efficient of friction for the roadway, test skids were conducted with the use of a patrol car with it's ABS braking system disabled. If I were to conduct the skid tests, I believe I would have added a third test to confirm without a doubt the results of the first two. My calculations for the tests listed were as follows-.

Test #1

Test Speed = 40 M/H

         Left Front = 56 feet        Right Front = 58 feet
         Left Rear = 53 feet         Right Rear = 56 feet

I first took the average of the skid lengths:

To establish the co-efficient of friction-

Test #2:
Test Speed = 40 M/H

                       Left Front = 53 feet                Right Front = 58 feet
                       Left Rear = 56 feet                 Right Rear = 57 feet

I, once again, took the average of the skid lengths

To establish the coeficient of friction

With the results being in essence the same, I utilized this figure (.95) as the co-efficient of the roadway and applied it to the vehicle in question-

The first step was to calculate the negative acceleration for the vehicle as it slid to a stop..

The given collision skids lengths:

         Left Front = 43 feet    Right Front = 47 feet
         Left Rear = 50 feet     Right Rear = 54 feet

Next, as I did with the test skids, I averaged the length of the collision skids:

With these values, I then calculated the velocity of the vehicle at the start of the tire marks-.

With the resultant velocity of 54.57 fps, I was able to calculate the speed of the vehicle at the start of the skids-

Many investigators and reconstructionists will argue that the skid distances used should be the "longest skid" measured. Crunching the numbers with these distances does not significantly change the final speed of the vehicle ... in fact it raises the vehicles speed to 38 MPH.

Thus ends my solution of this problem, with the answer to the initial question: The suspect was exceeding the speed limit for the location.

Dan Kemble is a nine year veteran of the Los Angeles Police Department, currently assigned to the Specialized Collision Investigation Detail. He has been investigating traffic collisions for the past eight years, and reconstructing collisions since 1995. Mr Kemble has completed approximately 440 hours of formal training in the collision investigation and reconstruction field. He is also a member of the Southwestern Association of Technical Accident Investigators (SATAI).

Mr Kemble opened a consulting business, "Southwest Collision Reconstruction" in 1997.

He can be reached at

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