  The Telescope Array (TA) collaboration has measured the energy spectrum of
ultra-high energy cosmic rays with primary energies above 1.6 x 10^(18) eV.
This measurement is based upon four years of observation by the surface
detector component of TA. The spectrum shows a dip at an energy of 4.6 x
10^(18) eV and a steepening at 5.4 x 10^(19) eV which is consistent with the
expectation from the GZK cutoff. We present the results of a technique, new to
the analysis of ultra-high energy cosmic ray surface detector data, that
involves generating a complete simulation of ultra-high energy cosmic rays
striking the TA surface detector. The procedure starts with shower simulations
using the CORSIKA Monte Carlo program where we have solved the problems caused
by use of the "thinning" approximation. This simulation method allows us to
make an accurate calculation of the acceptance of the detector for the energies
concerned.
