I investigate errors in speed obtained from yaw marks due to braking and other retarding forces (“effective braking”). I calculate precise yaw trajectories (using a 4th order Runge-Kutta approximation) and determine how speed obtained from the Critical Speed Formula (CSF) (based on errorless chord and middle ordinate measurements of the center of mass trajectory) depends on the amount of effective braking and the chord length used for chord middle ordinate measurements.
I calculate the error, defined as the difference between speed at the start of a yaw maneuver and CSF-determined speed, as a function of chord length and effective braking. Consistent with vehicle tests, I find that the error due to effective braking is generally less than 14%. However, additional vehicle tests are needed to allow precise estimates of CSF uncertainty and the range of braking for which the CSF is reliable. Some specific test results necessary to more reliably use the calculations are reliable estimates of the distance between the start of yaw maneuvers and the appearance of yaw marks, and this parameter's dependence on speed, road, and other conditions.
Comparison of my results with vehicle tests indicates that the reliability of the CSF-determined speeds results, to some degree, from the partial cancellation of two errors: 1) Effective braking results in lower speed at the point a vehicle begins leaving yaw marks than at the start of the yaw maneuver; 2) Effective braking causes the CSF to overestimate the speed of the vehicle at the start of the yaw mark (for the chord lengths typically used).
I suggest improvements to yaw tests that will allow more accurate determination of the uncertainty in estimating speed from yaw marks, and allow refinement of yaw measurements to reduce errors.