X3R is a new free-piston driven reflected shock tunnel (RST) facility, derived from the X3 free-piston super-orbital expansion tube at the University of Queensland (UQ). X3R is the first dual-mode impulse facility in Australia, and is also the first dual-mode free-piston impulse facility originating as an expansion tube. Conversion and operation of the facility in a reflected shock tunnel mode was originally envisioned as a means to increase the scale and duration of Australia's hypersonic testing capability, which was previously limited in both aspects in comparison to other international impulse facilities. This thesis was completed to coincide with the physical X3R facility hardware design and development, to produce an operating condition capable of generating and maintaining a Mach 7, 50 kPa dynamic pressure test flow for 10 ms. It was initially postulated that this could be efficiently achieved using the pre-existing X3 facility hardware, new components designed specifically for reflected shock tunnel mode, and a new operating condition. Due to its parallel operation as an expansion tube, X3R featured a driver tube length that was 60% that of the shock tube in RST mode. These geometric proportions are unique compared to other facilities of this kind throughout the world, which typically feature driver tubes that are at least twice the shock tube length. Operation of a reflected shock tunnel with such a relatively short driver tube makes it extremely challenging to efficiently utilise the 'full' slug of test gas. The primary challenge was generating a pulse of gas from the driver with sufficient duration to fully shock the test gas and sustain critical flow processes until 10 ms of test flow at the target conditions had been generated. The solution to this challenge was careful configuration of the free-piston driver and quite unconventional driver operation. Theoretical analysis showed that a very low compression ratio was required to maximise the volume of the driver gas. Given the low compressive heating, this resulted in a much higher helium fraction that would be normally required to produce a free-piston driven 1400 m/s shock through air. The low compression ratio then required significant piston energy to compress the gas, leading to extended periods of high facility and piston loading. Sustaining a relatively steady driver gas pressure to drive the downstream flow processes required piston speed to be maintained immediately after diaphragm rupture. This driver gas 'hold time' was shown to depend on piston mass; the higher the driver gas pressure, the heavier the piston needed to be to sustain a given test time. Once this fundamental dependency had been identified, it was determined that if piston mass and test flow dynamic pressure were fixed, there was a maximum test time that could be achieved. Conversely, if piston mass and test time were specified, there was a fundamental limit to the achievable test flow dynamic pressure. For the initial configuration analysed in this thesis, it was found that, ...