Professor Patrick D. Weidman of the CU-Boulder Mechanical Engineering department found that very little had been done on the dynamics of levitating disks, let alone rotating and levitating disks such as an air hockey puck. This prompted him to conduct his research around the idea of levitating disks. Weidman presented on his research to CSM at the weekly AMS colloquium.
For the basis of his studies, he constructed an initial model based upon certain conditions– infinite surface above which the puck spins, radially infinite puck, etc.– and assumptions such as normal gravity and a constant, extremely small gap between the surface of the table and the puck. These assumptions helped to develop a set of ordinary differential equations that could then be used to model the shear stresses on the inner and outer walls of the puck, the azimuthal, or rotational, stress, and the flow/counterflow generated from the puck’s rotation. This, in turn, was put together with another model constructed for the pressure gradient of the situation to produce an estimation for a quasi-steady spin-down function.
However, wanting to take the next step in this study, Weidman revealed his most recent work on the subject that is still in progress today. He explained how he went back and made some slight adjustments to the formulas and the constants he had defined in an attempt to produce a model of a completely steady spindown function rather than just quasi-steady. Weidman did this by redefining certain constants and adding new ones to take into account axial dynamics of the puck, which were assumed negligible in the quasi-steady model, to produce a set of partial differential equations. However, what is holding the study up at this point is that the numerics of the new model show a constant velocity in the change of the spinning height whereas the model itself implies that the spinning height of the puck initially has zero velocity.
At this point in time the reason for the discrepancy is unknown, and although Weidman admits there could be a possible error in the numerics of the problem, he instead believes that there is likely a certain physical or dynamic constant unknowingly being left out of the equation that he has simply not determined yet. As part of his future work, Weidman hopes to have this issue solved and finally be able to produce a model for a completely steady spin-down situation.