A theory of wheelchair wheelie performance.

The results of this analytical study of wheelchair wheelie performance can be summarized into two wheelchair design equations, or rules of thumb, as developed in the paper. The equation containing the significant parameters involved in popping a wheelie for curb climbing is: fh = 0.8 mg theta c.g. [A] where fh is handrim force, m is the mass of the wheelchair + user less rear wheels, g is acceleration of gravity (9.807 m/s2), and theta c.g. is "c.g. angle," i.e., the angle between the vertical through the rear axle and a line connecting the rear axle and the system center-of-gravity. Equation [A] shows that reducing the mass and/or the c.g. angle will make it easier to pop a wheelie. The c.g. angle is reduced by moving the rear axle position forward on the wheelchair. Wheelie balance is the other aspect of performance considered; where the user balances the wheelchair on the rear wheels for going down curbs or just for fun. The ease with which a system can be controlled (balanced) is related to the static stability of the system. The static stability is defined as: omega 2 = mgl/J [B] where J is the mass moment of inertia at the center of gravity of the system about the direction perpendicular to the sideframe. For better wheelchair control during wheelchair balance the static stability should be reduced. Measurements of the value for the polar mass moment of inertia for a typical wheelchair + user of m = 90 kg was found to be J = 8.7 kg-m2. In order to decrease the value of the static stability, Equation [B], one can increase J or decrease m and/or l, where l is the distance from the rear axle to the c.g. of the system. It is also shown that balancing a rod in the palm of the hand (inverted pendulum) is a mathematical problem similar to the wheelie balance problem, and a rod of length 1.56 meters is similar to a wheelchair + user system mass of 90 kg. However, balancing a rod is done primarily by using visual perception, whereas wheelie balance involves human joint proprioceptors and visual plus vestibular (inner ear) perception. Thus, a simple test of determining the shortest length of rod one can balance in the palm of the hand (plus measuring handrim force capability and simple reaction time) may indicate if a wheelchair user will find it easy to do a wheelie balance.