@IkariShinji> actually you only need a grayscale map for rotation. A value of 0 or 1 is equal to the Tangent. A value of 0.5, turns the anysotropic direction 180º so it’s also equal to the Tangent (at least has the same result). 0.25 or 0.75 are perpendicular to the tangent, 90º angle.
@moony> the rotation input is exactly for a texture map. The usage of the UVmap in the Tangent Node is more for, when you have a complex object, where you need to change the tangent of your texture map in a way that you don’t have to change the texture map itself.
Just like in the ‘carbon fiber’ example, it will be probably a tiled texture (a checker texture with a (0,0,0) and (.25,.25,.25) as colors in the rotation input should give you the desired result).
And for some parts of you object you will need it to be a bit rotated… So, instead changing your texture, you can use the TangentNode(UVmap) to orient the texture on your surface.
The problem you showed in your examples is because your base Tangent is the Blender’s Default which is radial (around the Z axis of the object’s coordinate system), and not very suitable for a orthogonal mapping as in carbon fiber, at least for a face pointing to Z…
Try to unwrap the object, use that uvmap as the tangent (through the tangent node), and use the greyscale texture as your rotation.