The buoyant rise and the resultant vertical distribution of wildfire smoke in the atmosphere have a strong influence on downwind pollutant concentrations at the surface. The amount of smoke injected vs. height is a key input into chemical transport models and smoke modelling frameworks. Due to scarcity of model evaluation data as well as the inherent complexity of wildfire plume dynamics, smoke injection height predictions have large uncertainties. In this work we use the coupled fire-atmosphere model WRF-SFIRE configured in large-eddy simulation (LES) mode to develop a synthetic plume dataset. Using this numerical data, we demonstrate that crosswind integrated smoke injection height for a fire of arbitrary shape and intensity can be modelled with a simple energy balance. We introduce two forms of updraft velocity scales that exhibit a linear dimensionless relationship with the plume vertical penetration distance through daytime convective boundary layers. Lastly, we use LES and prescribed burn data to constrain and evaluate the model. Our results suggest that the proposed simple parameterization of mean plume rise as a function of vertical velocity scale offers reasonable accuracy (30 m errors) at little computational cost.