  We present a technique for obtaining an effective packing fraction for
discontinuous shear thickening suspensions near a critical point. It uses a
measurable quantity that diverges at the critical point -- in this case the
inverse of the shear rate $\dot\gamma_c^{-1}$ at the onset of discontinuous
shear thickening -- as a proxy for packing fraction $\phi$. We obtain an
effective packing fraction for cornstarch and water by fitting
$\dot\gamma_c^{-1}(\phi)$, then invert the function to obtain
$\phi_{eff}(\dot\gamma_c)$. We further include the dependence of
$\dot\gamma_c^{-1}$ on the rheometer gap $d$ to obtain the function
$\phi_{eff}(\dot\gamma_c,d)$. This effective packing fraction $\phi_{eff}$ has
better resolution near the critical point than the raw measured packing
fraction $\phi$ by as much as an order of magnitude. Furthermore, $\phi_{eff}$
normalized by the critical packing fraction $\phi_c$ can be used to compare
rheology data for cornstarch and water suspensions from different lab
environments with different temperature and humidity. This technique can be
straightforwardly generalized to improve resolution in any system with a
diverging quantity near a critical point.
