Using Dimensional Analysis at Home!

My older son came to me with a question about speed limits on train tracks, and how they might change with curvature. He had one example, and wanted to know what would happen if he doubled the curvature. Assuming that acceleration was the key idea, we just wrote down the units, keeping a fixed acceleration, and a formula relating curvature and train speed popped out. Unfortunately Microsoft Train Simulator doesn't actually let your trains derail, so we were not able to test it out, uh, "empirically".