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# The case of the defective deduction

When following a trail, the "sign" must be studied carefully. A superficial examination may lead to incorrect conclusions. Tire skidmarks are evidence that must be analyzed carefully in order to draw valid conclusions.

Consider a situation involving a 1983 Ford Escort that runs into the rear of another car stopped at a walkway in a school zone. The speed limit was 20 mph, and the Escort left skidmarks 28 feet long prior to hitting the other car. Other evidence indicated an impact speed of 14 mph.

An expert witness for the plaintiff testified that the driver of the Escort was speeding. This was based on the length of the skid and the impact speed. In a straight-ahead skid, it is not unusual for the skidmarks from the rear tires to be superimposed on the skidmarks from the front tires, leaving what looks like two single skidmarks. In this case you would need to subtract the Escort wheelbase (b = 94.2 inches) from the skidmark length to obtain the skid distance (d = 20.2 feet). You multiply the skid distance by the friction force (coefficient of friction "mu" times the weight "W") to obtain the energy loss due to skidding. Knowing the kinetic energy at impact (Wv2 /2g), and the energy loss due to skidding, you work backwards to determine the kinetic energy and thus the speed at the beginning of the skid. This gives a speed at the beginning of the skid of 24.9 mph.

Close examination of the skid marks showed no evidence of skid marks from the front tires. Normally, when skidmarks are superimposed, there will be some evidence of the presence of two skidmarks. Such indicators might be a point where the mark becomes darker, a change in ribmarks due to overlapping or different patterns, heavier edge marks from an underinflated tire, or a wider track due to offset. If tires are different, such factors as tread width, ribcount, rib spacing or rib width can help determine which tires made which marks. The lack of such evidence implies that the front brakes were not working. Vehicle inspection indicated that the front brakes were in fact not operating because of low brake fluid due to a leak that existed prior to the accident. Thus, the speed calculation above is incorrect.

With the front brakes inoperative, the retarding friction force comes only from the rear wheels. To determine the friction force on the rear wheels, it is necessary to calculate the weight carried by the rear wheels, "R." In a parked situation, you can determine R if you know the weight of the vehicle and the distance of the center of gravity from the front wheels (a). This information is readily available from the NHTSA data available online.

You sum moments about the point (A) where the front tires touch the ground, and solve for R. This shows that in a static situation the rear wheels carry 35% of the weight of the car. However, in a dynamic situation there is another factor that must be considered. Due to the deceleration during braking, the rear tires carry less weight. This is observed by noticing the dip in the front end when braking a car. There is a virtual dynamic force that must be considered. This dynamic (deceleration) force is equal and opposite to the friction force muR, and acts through the center of mass at a height "h" above point A. (Note that if all brakes are working and mu is the same for all tires, the dynamic force does not have to be considered since the total friction force is still muW.)

Summing moments about point A allows calculation of R and the friction force. The energy methods above may again be applied to show that the speed at the beginning of braking was 19.3 mph, and that the driver was not speeding.