We present a methodology for the determination of the detection efficiency of a solid state nuclear track detector for radon and its short-lived daughters. First, particular attention is paid to the -particles having energies and angles of incidence that lead to observable tracks after an adapted chemical etching. These results are then incorporated in a mathematical model to determine the theoretical radon detection efficiency of a polymeric detector placed in a cylindrical cell. When applied to LR115 and CR39 detectors, the model reveals the influence of the position of the radon daughters inside the cell. Radon daughters tend to link up with natural atmospheric aerosols and then settle on the cell's inside wall. This model allows to determine, among other things, the cell size for which the detector response is independent of the fraction daughters plated out.