We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall.
Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive
settling and the active swimming of a foil. This also allows us to partly answer the long-standing question
in cartoon physics—can carpets fly? Our analysis suggests a region in parameter space where one may
realize this dream and move the virtual towards reality.