The helicity injected tokamak (HIT) experiment uses coaxial helicity injection to drive current in a low aspect-ratio tokamak. In order to accurately calculate the equilibria of such objects, a model which includes the essential physics of the injector and edge region must be included. Such a model is also crucial in determining the performance of future helicity injector designs. We present a model for the helicity injector that treats the open field lines as being in a force-free equilibrium determined by the field line length, the applied injector voltage, and an effective resistivity , which can have both resistive and dynamic components. This model agrees well with data for plasmas with little or no closed flux, using a uniform as the fitting parameter.