© 2019. The American Astronomical Society. All rights reserved. We present a numerical parameter survey of sub-Chandrasekhar mass white dwarf (WD) explosions. Carbon-oxygen WDs accreting a helium shell have the potential to explode in the sub-Chandrasekhar mass regime. Previous studies have shown how the ignition of a helium shell can either directly ignite the WD at the core-shell interface or propagate a shock wave into the the core causing a central ignition. We examine the explosions of WDs from 0.6 to 1.2 M o with helium shells of 0.01, 0.05, and 0.08 M o . Distinct observational signatures of sub-Chandrasekhar mass WD explosions are predicted for two categories of shell size. Thicker-shell models show an early time flux excess, which is caused by the presence of radioactive material in the ashes of the helium shell, and red colors due to these ashes creating significant line blanketing in the UV through the blue portion of the spectrum. Thin shell models reproduce several typical Type Ia supernova signatures. We identify a relationship between Si ii velocity and luminosity that, for the first time, identifies a subclass of observed supernovae that are consistent with these models. This subclass is further delineated by the absence of carbon in their atmospheres. We suggest that the proposed difference in the ratio of selective to total extinction between the high velocity and normal velocity Type Ia supernovae is not due to differences in the properties of the dust around these events, but is rather an artifact of applying a single extinction correction to two intrinsically different populations of supernovae.