Ratio of decidable problems
See Chaitin's research into Omega that shows, as I understand it, that undecidable problems are [paraphrasing] quite numerous, rampant or dense among statements chosen at random. However you have to be careful how you define $U(N)$ and $D(N)$ because they may be actually uncomputable functions. There is also some connections to busy beaver research. Identifying decidable and undecidable statements seems quite analogous to proving that busy beavers halt or do not halt. (e.g. some of all statements are in the form, “busy beaver [x] halts”).