  In this work, we report on the timing performances of the Time-Of-Flight
(TOF) apparatus of the FRACAS large acceptance mass spectrometer designed to
measure the fragmentation cross sections of a $^{12}$C beam in hadrontherapy.
The TOF system is composed of a Parallel Plate Avalanche Counter and
scintillating detectors to create so-called $\Delta$E---TOF maps used in the
fragment charge identification process. From tests with an alpha source and a
$^{12}$C beam experiment, we measured a coincidence resolving time for the
apparatus below 300 ps. Those results should lead in the final design to the
identification of all the fragments produced by the interaction of $^{12}$C
ions with thin targets for energies up to 400 MeV/nucleon.
