The Combined Speed Formula

SxS = S1xS1 + S2xS2 + S3xS3

•With a multiple phase accident where a vehicle may have undergone several speed changing events, it is necessary to use the combined speed formula (above) to estimate the original speed of the vehicle.

•If for example, a vehicle looses 30 mph in sliding before impact, 20 mph in the collision and 10 mph in sliding to a stop after the impact, the original speed of the vehicle is then:

S x S = 30 x 30 + 20 x 20 +10 x 10 = 900 + 400 + 100 = 1400, so that S = 37 mph

Notice that we cannot simply add the speed decrements together, they must be combined using the formula. This frequently leads to lower speed estimates than might be anticipated when looking at the various speed numbers before they are combined. The reason is that speed energy- what's really being computed in the partial estimates- varies with the square of the speed. Thus 20 mph is four times the (kinetic) energy of 10 mph (20 x 20 =400, 10 x 10 =100), not twice as much. The speed from skid marks formula - S = 5.5 x sqrt ( cd x distance ) - is a computational aid which assumes a zero final velocity, that is, that the vehicle has stopped at the end of the skid marks; if the computed value is to be taken as the original speed of the vehicle.. It does not yield speed drops simpliciter. Thus, 20 feet of locked wheel skid marks represents about 20 mph if the vehicle is stopped at the end of the marks. Suppose however that the vehicle is doing 60 mph when it leaves 20 feet of skid marks. Its speed at this point is:

S = sqrt (3600 - 400) = sqrt 3200 = 56.6 mph !

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