Eaurp Guz's roughly 1:30 scale live-steam model of Slaibsgloth Coal Railroad No.32, a ~1.6 meter gauge 2-8-8-2 garratt steam locomotive built on planet Mellanus in (earth-)year 2346 and retired in 2379 (two years ago) for service bringing coal carriages from the coal pits up to the interchange at the Glooiw & North Eastern. It is unusual for a coal burning steam engine to remain in revenue service--the majority that remained in use after the development of Diesel-Hydraulics were decommissioned with nuclear-powered railway electrification in the 2360s, and the ones that remained were mostly converted to oil burning. The Slaibsgloth steam engines meanwhile persisted right up until the closure of the coal mine. Glooiw & North Eastern has acquired the 40 locomotives. Their fates are uncertain but railway preservation groups remain optimistic.
When Guz first came aboard the Cerritos she was overworking herself constantly, which lead to her being so tired that she was leaving residues on the consoles and generally doing sloppier work. It turned out that Guz had been working double shifts, and when Billups found out he put a stop to that. That's when Guz turned to a hobby she'd done a lot of before joining starfleet--model rocketry. Armed with far more advanced tools than she'd had on Mellanus, she made accurate working model replicas of real historical prewarp spacecraft from a variety of planets and would fly them in real space whenever possible.
Eventually, she also found a new appreciation for her childhood love of trains, and her model-making skills and tools translated well to model railroading as well. She has a little shelf layout in storage that she occasionally tinkers with, and she runs large scale model trains on the holodeck. She could run full-scale holographic trains on the holodeck too of course, but it wouldn't be nearly as satisfying. And then there's the 1:5600 scale BM-gauge railroad she's building on a microscope slide! (Bµ gauge is "Byte micrometer" gauge or a track spacing of 256 µm)
Guz eventually wants to build a roughly 1:80 scale modular layout of the Slaibsgloth Coal Mine, with smaller scale electric-powered models of the Slaibsgloth coal-burning steam engines and enough track to wrap around a room and give them a good run, but unless she can rally support for a Cerritos chapter of the Starfleet Rail Transport Modelling Club or she can get her own crew quarters, it's a pipe dream--or maybe something for her retirement.
Replicators and advanced computer aided design tools reduce the amount of time it takes to get modelling projects done by whatever factor is desired. Technically Guz could probably replicate fully assembled working models as long as they fit in the replicator bed, but where's the fun in that? But she's still only got so much time in an off-shift, and doing it 'properly,' scratch-built using machine tools like 'real' modellers on Mellanus, or manually defining all of the geometry in a CAD program like modellers on Earth, would take too much time.
see also: alt versions of the locomotive.
