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Is there an equivalent to planing (or paring) with the grain or against the grain when planing end grain?

In my experience, the answer is a definite yes. If I plane the end of a board in one direction I get a perfectly smooth shiny finish, and if I plane in the opposite direction I might get a slightly rough finish, with much less shine.

However, I want to understand this better. What is the best direction? Is it related to going parallel to or across growth rings? Towards or away from the centre of the tree? What is the reason for the difference?

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    You're answered your own question as far as whether there's a favourable direction (or can be). What you've observed should be down to the subteties of grain direction in the cut end of the board, where the grain is perfectly square to the end or leaning towards you you'll experience more resistance and there's a greater chance of tearing. If the grain leans away from you, even just a little bit, the resistance will be lower and the smoothness of the surface should be better.
    – Graphus
    Jul 26, 2017 at 16:32
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    P.S. Regardless of the above you should notice this less and less as your sharpening improves. Extremely sharp edges on your plane iron, along with a very light cut, will reduce the significance of grain variation.
    – Graphus
    Jul 26, 2017 at 16:37
  • I think there is only a favorable direction when the grain is not truly perpendicular to the cut across the cutting plane. Which is most likely 100% of the time in practice.
    – jbord39
    Jul 26, 2017 at 21:20
  • @jbord39 LOL, I don't think it's quite that bad, plenty of straight-grained wood in the world.
    – Graphus
    Jul 27, 2017 at 6:46
  • Thanks for the comments. It seems the answer is actually a lot simpler than I had thought - in fact it's obvious once pointed out. But the fact is that I've never seen anyone in books or videos mention that there can be a preferred direction for planing end grain (maybe because their planes are sharper than mine), so the answer is still useful.
    – MarkH
    Jul 27, 2017 at 15:27

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I know the question is about grain direction and this may be obvious, but it's safer to plane over the edges from the outside towards the center of the piece. This avoids breakout. It can be a good idea to use a sacrificial piece, or by chamfering the edges before planing endgrain.

Assuming that edge breakout can be eliminated, if the direction of grain is orthogonal to the sole of the plane (perfectly 90degree to the sole of the plane in X/Y) then the direction of planing doesn't matter so much. If the grain tilts one way or another, then the more the the grain is oriented towards the direction you move the blade to, the smoother the cut will be.

As mentioned in this comment, you should find that a very sharp iron cuts finely regardless of direction. But even in cases where sharpening skill or equipment (or patience) doesn't produce a plane iron that is laser-sharp, I've found that skewing the plane (i.e. at a non-90degree attack angle, e.g., moving the plane body Northwards, while keeping the plane pointed NE or NW) always seems to leave a smoother endgrain surface.

edit: added skewing reference. thank you.

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    I'm very much not a fan of planing end grain in from both edges, but everyone's mileage varies (and to be honest after sanding it can really make zero difference so I shouldn't be that fussy about it). Re. your final point, this is referred to as skewing the plane in case you didn't know? It's the classic way to reduce planing resistance, it works as it effectively lowers the angle of attack due to a weird trick of geometry.
    – Graphus
    Mar 26, 2019 at 7:02

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