## Pedestrian Impact Accident Reconstruction

The general equations for the calculation of the
speed required to “throw” an occupant a particular distance is generally (from
**ref 39**):

_{}

_{}

Where: V_{min}
= lower bound for projection velocity

V_{max } = 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.

More:

References