We provide a quantitative description of a method to measure neutron-induced fission cross sections in ratio to elastic hydrogen scattering in a white-source neutron beam with the fission Time Projection Chamber. This detector has measured precision fission cross section ratios using actinide references such as $^{235}$U(n,f) and $^{238}$U(n,f). However, by employing a more precise reference such as the H(n,el) cross section there is the potential to further reduce the evaluation uncertainties of the measured cross sections. In principle the fissionTPC could provide a unique measurement by simultaneously measuring both fission fragments and proton recoils over a large solid angle. We investigate one method with a hydrogenous gas target and with the neutron energy determined by the proton recoil kinematics. This method enables the measurement to be performed in a white-source neutron beam and with the current configuration of the fissionTPC. We show that while such a measurement is feasible in the energy range of 0.5 MeV to $sim$10 MeV, uncertainties on the proton detection efficiency and the neutron energy resolution do not allow us to preform a fission ratio measurement to the desired precision. Utilizing either a direct measurement of the neutron time-of-flight for the recoil proton or a mono-energetic neutron source or some combination of both would provide a path to a sub-percent precision measurement.
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