  Ultra high energy cosmic rays (UHECRs) provide a natural source of particles
accelerated to energies beyond those that can be attained in the laboratory.
UHECRs have been observed with energies exceeding $10^{20}$ eV, which is
equivalent to 433 TeV in the center-of-momentum frame. Using this natural
source of particles physicists can extend the measurement of the $pp$ cross
section an order of magnitude above what is achievable in the lab, possibly
identifying hints of new physics. The proton-air cross section and other
properties of UHECR QCD physics are also important in their own right to the
study of the sources and composition of UHECRs, but hadronic modelling at these
energies is still reliant upon phenomenological and the theoretical
extrapolations based upon terrestrial accelerator data. UHECR data can be used
to improve these extrapolations of the proton-air cross section, but large
uncertainties remain for other hadronic model parameters. We present the most
recent measurement of the inelastic proton-air cross section at $\sqrt{s} = 95$
TeV measured by Telescope Array using high quality $X_{\mathrm{max}}$ data
collected in hybrid observing mode. This measurement is also used to infer the
total proton-proton cross section.
