By the way ,you can see individual channels inside photoshop with ctrl+1 ,ctrl+2 ,ctrl+3 for red green and blue and ctrl+~ (that will be tilda ... left to 1)for full rgb, and you can copy them as follows : for red -> ctrl+1(go to red channel) , ctrl+a (select all) , ctrl+shift+c(copy visible) , ctrl+~(go to full rgb) and ctrl+v (paste), after this combination of shortcuts you will have the red channel of the current selected layer as a new layer on top.
If i rotate the cylinder 90degrees like below
the normal map will look something like this
and on separate channels
This time the red channel is flat at 128 ( like green channel was before ) since all the faces in the high are now parallel with the red arrow (and when the normals are decomposed the tangent components will be zero mapped to 128); the green channel ( binormal ) will look similar to the red channel before (but rotated 90 degrees CCW) and the blue channel looks the same as before but rotated 90 deg.
Ok ... after all this math and moving back and forth between last couple of images relax your eyes with some renders :)