There is no reason to fix k as certain number. We do not know what our real space is. In summary, the Hyperbolic NonEuclidean World has k that is not so big. Nothing at all. Effective factor is how many times distance d is as big as unit length k , and not d itself.
Hyperbolic degree depends on k .
If k is a trillion light year, our surrounding, including all heavenly bodies you look up is perfectly Euclidean. Also e influences hyperbolic degree . But it has nothing to do with a model just like k . As a result, a model show Hyperbolic NonEuclidean World regardless k and e . That is, you can not find hyperbolic degree on a model.