Determining the radius a locomotive can turn

I am curious how designers of steam locomotives/civil engineers who laid out the track, determine the minimum practical radius that a steam locomotive can turn?

What factors are considered? I would imagine the length of the rigid wheelbase would be one, but are there others?

What design features can be built into locomotives if the terrain dictates sharp curvature?

Can different wheel arrangements be made to take tighter curves by reducing the size of the drivers and thereby the overall length of the rigid wheelbase if speed is not an issue?

For example, could the 30 inch gauge Rio Turbio 2-10-2s have handled the same curvature as the Rio Grande K-series 2-8-2's if the 2-10-2s were unchanged except for the track gauge?

Are there other factors that went into the design/engineer process that determined the curvature that had to be used and what designs could be used in the locomotives.

Thanks for any and all input on these questions.