Scramjet engine technology has the potential to transform commercial flight and mankinds' ability to access space. Major technology hurdles remain which must be investigated and resolved before the potential of the scramjet engine can be realised. The ability to scale a small geometric scale scientific test model to a large practical vehicle size with similar performance characteristics is one such challenge. In this study, the small scale geometric scaling characteristics of a scramjet engine, one such tool to aid in future experimental based investigations and overall scramjet development, is presented. The study specifically concentrates on investigating the similarity effects for a new type of scramjet engine, the axisymmetric inlet-fuelled radical farming scramjet engine, and is concerned with the Pressure-Length scaling laws in both plain air mediums and hypersonic shock tunnel facility test mediums.