The development of proton primary air showers is described in terms of a model based on a hadron core plus an electromagnetic cascade. The muon component is neglected. The model uses three parameters: a rate at which hadron core energy is converted into electromagnetic cascade energy, and a two-parameter sea-level shower-age function. By also assuming an interaction length for the primary nucleus the model is extended to nuclear primaries. Both models are applied over the energy range of 1013 to 1021 eV. Both models describe the size and age structure (neglecting muons) from a depth of 342 to 2052 g/cm2.