Algorithm to bypass the area in the minimum time?

Question

Algorithms

The task is to bypass the rectangular room in the minimum time. It is necessary to cover the entire area, there are no obstacles. Is there something better than "snake"?
If it's important - start from the corner

Answer 1

If the turn is "free", all non-self-intersecting routes are equivalent.
If not, I don’t see an exact proof, but, apparently, it is also optimal (2h−2 turns).
UPD1. If, due to some peculiarities of cornering at speed, 180° turns are undesirable, then a spiral with the first segment along the long side.

Answer 2

There is a "bull move" - ​​like this:
1 2 3 4 5
12 13 14 15 6
11 10 9 8 7
I don't think it's better.