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Prompted by a comment in this answer:

What is better for a roof, plywood or OSB?

Why is it stronger to install roof sheathing horizontally? Yes, it ties in more rafters, but in what manner is that stronger?

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The same policy goes for roof sheathing as for hanging drywall, you get more strength by spanning more rafters/joists/studs and offsetting the joints. This solves two points of weakness.

The main one is the structure turning into a parallelogram where the studs are no longer perpendicular to the ground. When you think of using a diagonal brace to support a wall, you want to get both ends as far apart as possible. If you install vertical, then that gives you the support of a diagonal brace spanning 4' worth of studs. But by staggering the joints and going horizontal, you get the equivalent 12' or more of studs braced.

The other form of support you get is for vertical load on a roof segment. If you stand between two rafters and the sheathing was laid vertically, you are closer to a seam where the nails could pull away under load and you can fall through. Holmes on Homes had an episode where they were replacing a leaking roof and the builder laid a patch where the owner decided not to go with the skylight option. The patch was laid vertically, and they almost fell right through the roof.

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That makes a lot of sense - I wasn't considering the pull force on the side nails when set vertically. Although, doesn't that mean the outside edges of the horizontal board are just as weak as the outside edges of the vertical one? After all, if you're standing between two joists next to a seam, a seam is a seam, right? Though I do see how horizontal reduces said number of vertical seams. –  The Evil Greebo Oct 5 '11 at 13:14
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With vertical seams are offset, the weak spots are spread out rather than being concentrated along a single rafter. But yes, I believe they also have the same concern. By using T&G, you can get more support from the sheathing above and below. I believe they also align the grain of some sheathing to be stronger along the length of the board. –  BMitch Oct 5 '11 at 13:25
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Nailing sheets longitudinally greatly increases the length(s), nails, and nail-downs allocated to edge nailing, the most problematic fastening that is required--you have one (eight-foot) line of rafter midline nailing for every two (eight-foot) lines of sheet and rafter edge nailing.

With transverse sheathing, the sheet length and nail count allocated to edge nailing is reduced by half and the rafter centerline nailing (and nail count) is increased by one third.

Additionally, longitudinal panel attachment leaves each panel spanning between two rafters and bolstered between by only one. By comparison, a transverse panel bridging two rafters, but only along half the length, and bolstered between by three rafters provides for a stronger, stiffer, more rigid overall system. It is that stiffness that, from the reliability standpoint, is instrumental in assuring least movement and flexing (with least consequent degradation) of the roofing materials, and of the roofing materials attachment.

Here is more to illustrate the above and the advantages conferred by horizontal and disadvantages otherwise. Note that "panelization" (the stiffening or a framework--namely of ridge, rafters, plate, etc--by spanning them with panels) has been given greater prominence. Ultimately, it is that aspect of panel fastening for stiffening that is at the heart of the OP question. Note also that horizontal makes more efficient (and cost effective) use of supplies: fewer nails to better effect; less cut waste of plywood or OSB. In statistical terms, it could be said that horizontal strikes a better balance between edge and spaced out fasteners; that it represent a more uniform attachment distribution...which optimizes a panel's panelization stiffening effect, and the mutual holding effectiveness of the nails.

horizongal good, vertical not so good

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I know what you're saying, but the scope of this site includes DIY-ers, and your choice of words might prevent your answer from being as easily understood to the general audience. At the very least, translate the terms you're using to the ones used in the question to cater that person, eg. "Nailing sheets longitudinally ("horizontally") greatly increases ... " –  Joe Oct 25 '12 at 13:17
    
Thanks, Joe. I have read numerous @theevilgreebo posts and, accordingly, don't believe him to be strictly "dyi novice." (In fact I suspect his "challenge" might have been intended to be a bit greebulous (at worst), tongue-in-cheek (at best). That said, thinking of rafters as longitudes (just like on a map, sheathing oriented in line with them would be longitudinal/vertical. Tansverse was meant to indicate panels oriented with their longer dimension going across the rafters. My apologies for any inconvenences or head scratches cause by my posting. –  Lex Oct 26 '12 at 1:07
    
+1 great answer and diagram. –  Matthew Oct 26 '12 at 17:01
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