  We estimate the energy input into the solar corona from photospheric
footpoint motions, using observations of a plage region by the Hinode Solar
Optical Telescope. Assuming a perfectly ideal coronal evolution, two
alternative lower bounds for the Poynting flux are computed based on field line
footpoint trajectories, without requiring horizontal magnetic field data. When
applied to the observed velocities, a bound based solely on displacements
between the two footpoints of each field line is tighter than a bound based on
relative twist between field lines. Depending on the assumed length of coronal
magnetic field lines, the higher bound is found to be reasonably tight compared
with a Poynting flux estimate using an available vector magnetogram. It is also
close to the energy input required to explain conductive and radiative losses
in the active region corona. Based on similar analysis of a numerical
convection simulation, we suggest that observations with higher spatial
resolution are likely to bring the bound based on relative twist closer to the
first bound, but not to increase the first bound substantially. Finally, we put
an approximate upper bound on the magnetic energy by constructing a
hypothetical ``unrelaxed'' magnetic field with the correct field line
connectivity.
