The general equations for the calculation of the speed required to “throw” an occupant a particular distance is generally (from ref 39):
Where: Vmin = lower bound for projection velocity
Vmax = upper bound for projectile velocity
μ = Coefficient of friction between the pedestrian
and the roadway ( normally 0.60 to 0.80)
S = Distance traveled from point of impact o rest
g = Gravitational acceleration constant, 32.2 ft/sec^2
In Ref 40, the relationship was extended to include the provision for a launch height less than the landing height;
Where: H = difference in height from impact to rest
As a part of the continuing research at McHenry Consultants, Inc. in conjunction with McHenry Software, a simple Launch program has been created to determine the minimum possible speed required for a projectile launch. The program was created to permit investigation of the possible variations in assumption about throw distances and the ratio of the distance traveled in air, distance traveled on the ground, the assumed coefficient of the ground surface, and any possible elevation difference between the launch point and the landing area.
Figure 22 Equations used in McHenry Software Launch Program
The normal equations and assumptions for a Simple ballistic trajectory of an occupant travel of a distance R is that the occupant is assumed to stop at the landing point. A problem with that assumption is that for most launch angles the occupant will have a horizontal component of velocity at the landing point. Therefore the occupant will continue to travel after landing.
Figure 22 is the assumptions and equations used in the Launch program. The figure depicts a more likely scenario for a pedestrian impact with a vehicle or a occupant ejected from a vehicle, The occupant is normally at a elevation different than the landing area. For example an occupant may be struck by a car in a standing position and land in a prone or laying position. This would require a 2 to 3 foot elevation change between the impact and landing position.
Also considered in Figure 22 is the distance traveled from the landing point to the point of rest. The occupant does not follow a simple ballistic trajectory. At the landing the horizontal component of the launch continues. Many assumptions are required for this scenario. At what approximate elevation does the launch occur? What is the friction coefficient for the landing area? What range of values for the friction coefficient is associated with the landing area? What is the probable launch angle for the particular accident? What effect would a variation in the assumed launch angle and/or the assumed friction coefficient of the landing zone have on the approximate launch velocity?
To compute all these variations would require a substantial amount of calculator activity. Fortunately we have included a program called Launch in the Tools menu of the m-Edit Environment. The program requires for input:
Total Horizontal Travel, Feet or Meters
Terrain Surface Friction Coefficient, G-Units
Elevation of Launch, Feet or Meters
and optionally the Launch Angle, degrees
The program will iterate to find the minimum velocity required to satisfy all the user inputs. Likewise the user can vary the inputs to test the ranges of probable input variables to establish a range of speed estimates.