When a vehicle is airborne during its travel path, as shown above, it is generally called a vault. If the launch angle θ (degrees), the horizontal travel distance d (feet), and the vertical drop h (feet) are known, then the launch velocity V (feet/second) is given by:
This launch angle θ generally must be measured at the scene, and a reasonable estimate of the vehicle orientation is required since d and h are measurements to the vehicle center of gravity.
Since roadway grades and cross slopes are usually less than 10 percent (θ =5.7 degrees), cos2θ ≈1, and tan θ= the grade g (in percent) of the vehicle launch path, the general equation is simplified to:
Note that if d and h are small, an accurate determination of the vehicle impact orientation is essential. This particular accident configuration is, however, a rare occurrence, thus limiting the usefulness of this method for speed determination.
Another commonly used speed formula for a vault is:
This expression is based upon the assumption that the take-off angle θ is equal to 45 degrees and, therefore, does not yield a valid estimate of the actual speed. It does, however, give a reasonable estimate of the minimum speed after the launch that may be considered as a reconstruction boundary.
Other crash configurations that would produce a vault would include: a vehicle striking another vehicle or object, a vehicle flip proceeding a rollover, a motorcyclist ejected during an impact, or a pedestrian being struck by an automobile. Serious problems arise since, in many cases, there is significant loss of kinetic energy in the launching mechanism. The landing and/or take-off points for motorcyclists or pedestrians may be unknown. In nearly all cases the lack of any pertinent physical evidence indicating the actual launch angle would make any speed estimate an unsupported guess.
Since the vault method of speed determination would generally require the use of dubious estimates and assumptions, I have rarely found a situation where its use is justified. In fact, after “critical speed,” this is probably the second most misused reconstruction concept. However, since little or no kinetic energy is lost during the vault itself, the method can generally be avoided.
Derivation of the preceding equations can be found in the Analysis Procedures chapter of Highway Accidents: Investigation, Reconstruction and Causation available at: Amazon.com. Information about the book and author is available at: www.bmorrow.com.