<p>The Stunt Person</p><p>Possible important factors in determining the number of cardboard boxes necessary to protect the stunt person are as follows:</p><p>Weight of motorcycle/stunt rider combined.</p><p>Height needed to clear the elephant/max height attained by the motorcycle during the jump.</p><p>Velocity/Acceleration of the motorcycle.</p><p>Thickness of cardboard.</p><p>Shock-absorption factor of the cardboard.</p><p>The figure above is a rough sketch of the stunt set-up. The stunt driver will drive off the ramp, clear the elephant, and land on the pile of cardboard boxes on the far side. The driver must maintain a set speed which is high enough to give reasonable clearance above the elephant, while at the same time slow enough to minimize vertical speed on landing. Aircraft vertical speeds on landing are often around 8.3 -13.3 ft/s. Most aircraft employ hydraulic or spring shock-absorption systems. The T-10C Parachute used by U.S. Army paratroopers has a descent speed of 17.5 ft/s. Paratroopers use their bodies as shock absorbers. If feasible, it would be desirable to limit the vertical speed to 8.3 ft/s or less. If possible, a vertical speed of 17.5 ft/s should not be exceeded.</p><p>According to the source listed below, elephants range in height from 5-14 ft, with a typical height of around 11 ft. For the purposes of these calculations, it will be assumed that the elephant is 11 ft tall; with a 5 foot factor of safety, the clearance height for the motorcycle is 16 feet.</p><p>A Harley Davidson motorcycle would look good in the finished scene, but such motorcycles tend to be heavy. The lightest current production model has an operating weight of 581 lbs. The heaviest model weighs 889 lbs. A Kawasaki Ninja weighs 484.4 lbs. Assuming a weight for the driver of 200 lbs, the combined weight of the driver and cycle is between 684.4 and 1089 lbs.</p><p>Corrugated cardboard manufactured by Uline comes in 48x48 inch sheets which are 5/8ths of an inch thick and have a burst strength of 1,100 ft/in2.</p><p>For simplicity of calculation, this problem will be approached initially as a projectile motion problem.</p><p>The elephant is placed at the point where vertical height of the motorcycle will be the greatest. X 0 and </p><p>Y0 are at the high end of the ramp, with HR being the height above ground at that point. HB is the height of the stack of boxes.</p><p>Projectile Calculations v0 (ft/s) He (ft) vy0 (ft/s) q (degrees) vx0 (ft/s) R g (ft/s^2) 44 16 8.018363 10.5 43.26322 21.54659 32.2 y at R/2 t at R/2 0.998356 0.249017</p><p>With an initial velocity of 44 ft/s (30 mph) and a ramp angle of 10.5 degrees, the motorcycle gains a maximum altitude of slightly less than 1 ft (y at R/2). To meet the 16 foot height necessary to clear the elephant, HR must be 15 feet. If HB=HR, then the final vertical speed of the motorcycle when it impacts the boxes will be roughly 8 ft/s. However, as HB decreases, vertical speed increases. x y t vy 0.00 0.00 0.000 8.02 1.08 0.19 0.025 7.21 2.16 0.36 0.050 6.41 3.24 0.51 0.075 5.60 4.33 0.64 0.100 4.80 5.41 0.75 0.125 3.99 6.49 0.84 0.150 3.19 7.57 0.91 0.175 2.38 8.65 0.96 0.200 1.58 9.73 0.99 0.225 0.77 10.82 1.00 0.250 -0.03 11.90 0.99 0.275 -0.84 12.98 0.96 0.300 -1.64 14.06 0.91 0.325 -2.45 15.14 0.83 0.350 -3.25 16.22 0.74 0.375 -4.06 17.31 0.63 0.400 -4.86 21.63 -0.02 0.500 -8.08 25.96 -0.98 0.600 -11.30 30.28 -2.28 0.700 -14.52 34.61 -3.89 0.800 -17.74 38.94 -5.82 0.900 -20.96 43.26 -8.08 1.000 -24.18 52.53 -14.00 1.214 -31.08</p><p>It is desirable for HR to be less than or equal to HB. The height of the boxes must be sufficient to absorb the impact of the motorcycle, but must also be kept to a minimum, as per the original problem statement.</p><p>References:</p><p>Elephant Information Provided by Wikipedia: http://en.wikipedia.org/wiki/Elephant </p><p>Motorcycle information provided by: http://www.harley-davidson.com http://www.kawasaki.com/Products/Motorcycles.aspx</p><p>Cardboard Box information provided by: http://www.uline.com/BL_1855/Corrugated-Pads-Heavy-Duty</p><p>T-10C Information: http://www.pioneeraero.com/index_standard.htm</p><p>Physics Equations:</p><p>Halliday, Resnick, Walker; Fundamentals of Physics, Fourth Ed., John Wiley& Sons, Inc. New York, 1993.</p>