To get a perfectly straightened unwrap from quad-strips, the Follow Active Quads method exists.
This will take the selected geometry and unwrap it as a rectangular strip, no matter what angle they have on the model. It is particularly helpful on objects with even but somehow spatially warped surfaces, like pipes, floor maps, etc. and truly invaluable if you need 100% straightened unwraps. These often make texturing a lot easier.
It has two options for the Mapping Type:
Even will make all UV-Squares the same size,
Length will take the average length into consideration
To use Follow Active, select desired polygons. Ensure that one of them is the Active Selection. The algorithm will make this one the border piece in the unwrap. Also, as its name suggests, it will not run without an Active Quad.
Follow Active Quads has a couple of quirks, though:
For one, it does not like Triangles or N-Gons. It will split those from the quad strips.
For another, if you have already unwrapped, the Follow Active Quads will sometimes give you skewed results. In that case,
- select the strip you want,
- choose Unwrap > Reset
- with the same selection Unwrap > Follow Active Quads