The count across the roll is a step function
A 42 in roll with half an inch off each selvedge gives 41 in of usable width. A 14.946 in blank with a quarter inch cutting gap needs 15.196 in of that width, and 41 divided by 15.196 is 2.7 — so two blanks fit across, and 10.6 in of the roll is thrown away on every row.
That fraction is where the cost hides. Two hundred and sixty cases at two across is 130 rows, 1,397 in of cloth, 38.8 yards before the allowance and 40.8 after it. Getting a third blank across the same roll would need the blank down to 13.5 in, which is nearly an inch and a half narrower — not a trim, a redesign. But it would drop the requirement to 87 rows and 38.6 yards, and it would raise the share of cloth that ends up on a book from 66.2 percent to 70.
What grain direction costs, at these numbers
Cloth grain in a case wants to run head to tail, which means the 10.5 in dimension has to lie along the roll and the 14.946 in dimension across it. Turn the blank ninety degrees and 10.75 in fits three times across 41 in instead of twice, so the same 260 cases take 87 rows of 15.196 in — 38.6 yards against 40.8.
So respecting the grain costs 2.2 yards here, or 5.7 percent. That is small enough that the arithmetic is not really the argument, which is the useful thing to know. On a different blank against a different roll the same question costs a third of the cloth, and the page recomputes it rather than repeating this figure. It also has no view on whether to take the saving: cloth turned sideways behaves differently when it is pasted and when the humidity moves, and that is not a number.
Waste is mostly the roll, not the cutting
At the defaults, 260 blanks hold 283 square feet of cloth and the roll gives up 428. The gap is not sloppy cutting: it is 10.86 in of unused roll width on every row, the selvedge trims, the quarter inch between rows, and five percent for flaws. Cutting gaps are the smallest term in that list by a wide margin.
Which is why the blank width is the number to attack if the cloth bill matters. Half an inch off the turn-in is worth more than any amount of careful nesting, because it acts on the step function rather than on the crumbs.
Things it cannot see
Pattern matching, nap direction and mill flaws all cost length and none of them can be predicted from a form. A flaw in the middle of a roll can waste a whole row rather than a piece. The allowance percentage is the only place any of this can live, and the honest way to set it is to record what an edition actually consumed and use that figure next time.
Questions people ask
How much book cloth does an edition take?
It depends almost entirely on how many blanks fit across the roll, which is a whole number. At the values in the form — a 14.946 by 10.5 in blank, a 42 in roll with half-inch selvedge trims, 250 copies and 10 spares — two fit across, it takes 130 rows, and with five percent for flaws that is 40.8 yards. Change the blank by an inch and the answer may not move at all, or may move by a fifth.
Does the grain direction cost extra cloth?
Sometimes a lot, sometimes nothing. At the defaults here, locking the grain head to tail gives two blanks across the roll instead of three and costs 2.2 yards on 260 cases, which is 5.7 percent. The page computes both layouts and prints the difference every time rather than quoting a rule, because the answer is set by how the blank and the roll happen to divide.
How much of a roll ends up on a book?
At the values in the form, 66 percent. The rest is 10.86 in of unused roll width on every row, the selvedge trims, the cutting gaps and the flaw allowance. The unused width dominates, which is why trimming the blank is worth far more than cutting more carefully.
What allowance should I add for flaws?
Yours, from what your last edition actually consumed. The field defaults to five percent as a placeholder. It has to cover slubs, printing faults, squaring the end of the roll and any pattern matching, and none of those is predictable from dimensions. If you have never measured it, the safe direction to be wrong in is upward, because a second roll rarely matches the first.
Should I buy one long roll or several short ones?
The page does not answer that, but it gives you the input: the yards per case figure tells you how far any given roll length goes. The thing worth knowing is that cloth from two different rolls can differ visibly in colour and finish, so a run split across rolls is a run with two slightly different books in it.