Engineering approximations are often derived by regression to empirical functional forms, which can result in all kinds of dimensional weirdness, including floating point powers. In principle these could be accommodated within a dimensional analysis framework. In practice, floating point powers are impossible for a compile-time library. On the other hand, we do support rational powers and, for engineering approximations, you might as well use a rational approximation to the powers since it is unlikely that they will be exactly equal to some irrational value... Matthias
There's just plain going to be times when you have to break out of the dim/unit analysis model. For instance, in fluid flow analysis, what I do, you often have empirical functions...guesswork...it is not at all uncommon to take a quantity to some variable power that might itself be a quantity. There's no way to enforce dimensions on this.
Is this really right? Are you sure there isn't a constant lurking around that resolves all the dimensions properly? Surely, these formulas have to be adjusted appropriately if you use different units.
Can you provide a concrete example?