A passenger car traveling too fast on a curved path will slip sideways and rotate into a spinout. If the lateral coefficient of friction f, adjusted for any cross slope, and the instantaneous radius R (feet), of the vehicle’s center of gravity travel path are known, then the theoretical critical speed S (miles per hour) is given by
In most cases, even on dry pavement, there is no physical evidence prior to the spinout. Therefore, the vehicle path radius that is not necessarily the highway curve radius, cannot be determined. Occasionally a narrow black cornering mark will be found, but since this mark can occur at speeds well below critical speed, it is not reliable evidence.
Spinouts can be, and often are, caused by a quick steering input that will drastically reduce the instantaneous path radius, or by braking action that will suddenly reduce or eliminate the available lateral friction capacity. These driver actions, generally undetectable, make use of this critical speed formula totally invalid.
A serious, but all too common, misuse of this formula is when it is applied to the path of a yaw mark. A yaw mark is not a cornering mark and is not traveling on the same path radius as the vehicle at the initiation of the spinout. The rotating tire leaving the yaw mark may also be generating a centripetal force, altering the vehicle path, and thus making the use of the critical speed formula inappropriate.
A vehicle with a high center of gravity will roll over, rather than spinout, when traveling too fast on a curved path. The theoretical speed is given bywhere x is the horizontal distance from the vehicle center of gravity to the outside edge of the outside tire and h is the height of the center of gravity above the pavement. Determination of the actual vehicle path radius R at the initiation of the rollover is compromised by the same uncertainties as the critical speed spinout analysis.
In addition, finding the static height h of the center of gravity of a truck and its load may be difficult since the information is rarely available. Due to tire bending and compression, suspension yielding and possible load shifting, the value of h may increase and the horizontal distance x may be significantly decreased at impending rollover. Therefore, this critical speed formula is rarely applicable for the determination of a truck’s speed at rollover.
Using the critical speed formula is probably the most misused method for determining the speed of a vehicle at the initiation of a non-impact spinout. Estimating a post-spinout effective friction factor is generally a preferred method or, at least, should be used as a comparison check on the results obtained from the critical speed formula.
Derivations of these Critical Speed formulae and information on related topics can be found in Highway Accidents: Investigation, Reconstruction and Causation available at: Amazon.com. Information about the book and author is available at: www.bmorrow.com