  A number of experiments are currently working towards a measurement of the 21
cm signal from the Epoch of Reionization. Whether or not these experiments
deliver a detection of cosmological emission, their limited sensitivity will
prevent them from providing detailed information about the astrophysics of
reionization. In this work, we consider what types of measurements will be
enabled by a next-generation of larger 21 cm EoR telescopes. To calculate the
type of constraints that will be possible with such arrays, we use simple
models for the instrument, foreground emission, and the reionization history.
We focus primarily on an instrument modeled after the $\sim 0.1~\rm{km}^2$
collecting area Hydrogen Epoch of Reionization Array (HERA) concept design, and
parameterize the uncertainties with regard to foreground emission by
considering different limits to the recently described "wedge" footprint in
k-space. Uncertainties in the reionization history are accounted for using a
series of simulations which vary the ionizing efficiency and minimum virial
temperature of the galaxies responsible for reionization, as well as the mean
free path of ionizing photons through the IGM. Given various combinations of
models, we consider the significance of the possible power spectrum detections,
the ability to trace the power spectrum evolution versus redshift, the
detectability of salient power spectrum features, and the achievable level of
quantitative constraints on astrophysical parameters. Ultimately, we find that
$0.1~\rm{km}^2$ of collecting area is enough to ensure a very high significance
($\gtrsim30\sigma$) detection of the reionization power spectrum in even the
most pessimistic scenarios. This sensitivity should allow for meaningful
constraints on the reionization history and astrophysical parameters,
especially if foreground subtraction techniques can be improved and
successfully implemented.
