The Stunt Person – Part 2
The following equation can be used to calculate the kinetic energy of the motorcycle on landing
The energy which must be absorbed by the cardboard boxes is shown in the following equation:
η is the efficiency factor for the shock absorption of the boxes, L is the load during “deflection” of the
boxes, and S is the stroke, or the distance travelled during deflection. This is the height of the cardboard
boxes that is at the root of this problem. At this time, the shock absorption of the motorcycle’s tires and
suspension will be neglected. The above equations were developed for use with aircraft. The W in the
first equation is the weight of the vehicle, offset by some amount of lift. It is assumed that the
motorcycle will generate no lift. L usually represents the average load per landing gear strut. In this case,
there is only one stack of cardboard, so L will be equal to W, and can be factored out of the equation.
For initial calculations, the efficiency factor is assumed to be 0.45, roughly equal to an air spring shock
absorber. Solving for S gives us:
This can in turn be simplified to
where
since gravity and efficiency
factor are assumed to be constants for the purposes of these calculations. As  approaches 1, S
decreases, and as  approaches 0, S increases significantly. Numerically, =.0345s2/ft when =0.45.
It was stated earlier that a vertical speed on landing of between 8 and 17.5 ft/s would be desirable.
Using the above equation for stroke, and a vertical speed of 8 ft/s, S=2.21ft. At 17.5ft/s, S=10.57ft. The
stroke would be lessened by including the effect of the motorcycle’s tires and suspension.
While the cardboard is deflecting, the motorcycle decelerates from Vvertical ft/s to 0ft/s. Assuming a
constant rate of deceleration,
deceleration of the motorcycle is
pressure, and A=area. Using this relation,
and the time t to decelerate to zero is equal to
. The
. F=Ma and also F=A Where M is mass, a is acceleration,  is
. A in this case represents the contact patch of the tires
on the cardboard, and  is the pressure in lbs/ft2 that the cardboard will experience while slowing the
fall of the motorcycle. Assuming a contact area of 2in2, =7037.3 lbs/ft2 when Vvertical =17.5ft/s.
References:
Raymer, Daniel P. Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and
Astronautics, Inc., Washington, DC, 1992.