Originally Posted by
roughkype
Hello,
If my reply was too strong (which it probably was to this thread) it's because I've gotten a little frustrated at the bandwagon of bad advice about getting a wider strop so you don't need the X-stroke.
You're thinking about this extremely precisely, which is impressive. I don't think the critical detail is in the edge being tangent to the direction of motion, at least not for stropping. As others have already explained, the reason for the X-stroke is simply to ensure even contact between all parts of the blade and all parts of the strop, over the time of the stropping session and over the lifetime of the strop/blade/stropper, whichever is shortest.
When honing with a rolling X, the point is to be sure the heel and toe of the blade get equal time on the hone. On a smiling blade, you need this modification or else only the blade's belly gets the hone's full effect and you'll end up with really uneven hone wear and unsatisfactory edges at the heel and toe.
With any X-stroke on the hone, you'll end up with striations that are slightly angled from perpendicular. If you do a 10-degree X, your striations will be at 80 degrees to the edge. With a rolling-X stroke your striations may be more perpendicular to the edge at each point (more nearly tangent to it, to be as exact as you), but that's more an artifact of the honing motion than a goal. The rolling X's goal, again, is simply to get all the parts of a smiling edge in equal contact with the hone.
For a smiling blade on the strop, you don't need the rolling motion, at least not with a hanging strop. This is because the strop will flex to stay in pretty good contact with the blade's contour. On a paddle strop you might want to mix a little pivot into the stroke, like a reversed rolling X. I'll have to ponder that, and play a little with my paddle strop, before offering anything more certain.
I hope this helps. I'm like you, I don't like black-box explanations.
Best wishes.