"It is likely a half length curve of O, a standard offering. It would take 16 halves to make a circle. (normally 8) . Each has 22.5° of arc vs standard 45°. "
Actually, they are more than 22.5 degrees. So-called "half" sections are bigger than what you would get by cutting a standard section in half. (Which would result in a piece of track with a tie sliced down the middle, or with two ties that wind up being closer together than any two ties on a full section.) If you lay a half-section on top of a full section, the first and second ties will line up. A little bit of rail will hang out the end. That means that two half sections when placed end to end are slightly longer than one full section. If you try to put 16 of them into a circle, your engineers and passengers will be disappointed.
I don't have the exact dimensions handy for the curves, but here are the dimensions for straights that demonstrate the concept:
O-27 Straight: Full = 8.75 Half = 4.8" (exact half would be 4.375")
O -31 Straight: Full = 10" Half = 5.5" (exact half would be 5")
This was probably done for two reasons: Lining the ties up on a machine that installed them onto the rails, and those weird track arrangements that we need to install to get sidings the correct distance apart for pairs of operating accessories. There's also something rattling around in the old brain about figure 8 layouts, and getting crossings to play nicely with switches, but I'll let the next guy tell you about that.
