  An accurate evaluation of the gravity acceleration from the timing of free
fall of anti-hydrogen atoms in the GBAR experiment requires to account for
obstacles surrounding the anti-matter source. These obstacles reduce the number
of useful events but may improve accuracy since the edges of the shadow of
obstacles on the detection chamber depends on gravity, bringing additional
information on the value of $g$. We perform Monte Carlo simulations to obtain
the dispersion and give a qualitative understanding of the results by analysing
the statistics of events close to an edge. We also study the effect of specular
quantum reflections of anti-hydrogen on surfaces and show that they do not
degrade the accuracy that much.
