Chapter 3 showed how to flesh in the run-out trajectory by drawing a spline curve between the key points, and then how to subdivide the trajectory into piecewise linear segments, such that the end points on the segments were positioned on the spline curve. It even showed how to adjust certain of the segment end points along the spline curve such that they would coincide with the key points, in order that calculations pertaining to such points would also pertain to the key points. Chapter 4 shows how to perform those calculations, so that the vehicle’s motion can be discovered as it exits the crash. The analysis can also be applied to the vehicle’s precrash motions, once the conditions at impact are known.

Each segment is a straight line, so the segments should be short enough to make their assemblage a good representation of the actual trajectory. In each segment, the average drag factor (which depends on the average crab angle and the segment lock fraction and friction coefficient) is constant. Thus, the loss in velocity for each segment may be calculated from the familiar formulas of energy conservation. Potential energy change due to elevation change is included in this calculation. The time interval to traverse the segment is also computed. Starting at the final vehicle position, moving backwards through the trajectory segment by segment, and chaining the calculations together, the final result is the linear and angular (yaw) velocities at the trajectory’s start—where the vehicles separate from each other. Spreadsheets work very well for this purpose. The vehicle separation velocities provide the basis for reconstructing the crash itself. An example reverse-trajectory spreadsheet is shown.

To validate the reverse trajectory calculations, it is necessary to compare them with actual trajectories of out-of-control vehicles, preferably as they run-out from a crash. Such data are rare indeed, but the 12 car-to-car crash tests of the Research Input for Computer Simulation of Automobile Collisions (RICSAC) program were performed just for that purpose. Numerous data collection and recording issues pertain. Chapter 4 presents those issues, along with the results for 23 of the trajectories.