Only the middle of the spine gets divided
A sewing layout has two fixed points before anything is divided: the kettle stitches, set in from the head and the tail. At the values in the form they sit half an inch in from each end of a 9 in spine, which leaves an 8 in span. Three tapes divide that span into four equal parts of 2 in, so the tape centres land at 2.5, 4.5 and 6.5 in from the head.
Notice that the gap from the head kettle to the first tape centre is 2 in and the gap between tape centres is also 2 in. That falls out of dividing the span into supports-plus-one parts, and it is why the arrangement looks regular even though the holes themselves are not evenly spaced: the real hole gaps at these values run from 0.625 in, across a tape, to 1.688 in between one pair and the next.
Mark eight holes at an even pitch down the whole 9 in instead and they land 1 in apart with the outer ones 1 in from the ends. Nothing is crowded, but every tape has moved, because an even pitch has no way to tell a kettle stitch from a support — it just puts holes where the division falls and leaves you to sew whatever is underneath them.
A tape takes two holes, not one
Sewing on tapes means the thread comes out of the fold on one side of the tape, crosses over it, and goes back in on the other side. So each tape is a pair of holes straddling its centre, offset by half the tape width plus whatever clearance keeps the thread off the selvedge. Half an inch of tape with a sixteenth of clearance either side puts the pair 0.625 in apart, at 2.1875 and 2.8125 in from the head for the first tape.
That is where three tapes turn into eight holes: two kettles plus six. Sewing on cords is one hole per cord and gives six, and unsupported sewing gives whatever you set. The page recounts the holes when you change the style, because the thread length depends on the count.
The thread nobody counts is the tails
Per section the thread runs the 8 in span, passes through the fold once at each of the eight holes for another 0.72 in, and spends half an inch at each kettle stitch. Multiplied by a 1.15 slack factor that is 11.18 in a section, so sixteen sections take 178.9 in of actual sewing — just under five yards.
Then the tails. Sewing four sections to a length means four lengths, eight tails, and 48 in of thread that never enters a fold. Doing the whole block in one length would need only 12 in of tail, so the changes cost 36 in — a fifth again on top of a continuous sew. Nobody sews sixteen sections on one thread, because a five yard length gets dragged through the fold 128 times and comes out furred, but it is worth knowing what the alternative costs before deciding how often to change.
What the number is not
It is a geometric floor with your own slack factor applied. It has no idea how hard you pull each stitch, how much thread you lose rethreading a needle that has come off, or that you will unpick the fourth section because the third one crossed. Every one of those is real and none is in the arithmetic. The honest use is to cut the length the page gives you and then note what was actually left over, until the slack factor is your slack factor rather than a placeholder.
Questions people ask
Where do the sewing stations go on a spine?
The kettle stitches go in a fixed distance from the head and the tail, and only the span between them is divided. With a 9 in spine, half-inch kettle insets and three tapes, the span is 8 in, it divides into four parts of 2 in, and the tape centres land at 2.5, 4.5 and 6.5 in from the head. The insets are your choice, not a standard, and they are the single input that moves every other position.
How many holes does each section need?
Two for the kettle stitches, plus the supports. Sewing on tapes gives two holes per tape because the thread has to straddle it, so three tapes make eight holes a section. Sewing on cords is one hole per cord, so the same three supports give six. Unsupported sewing is one per station. Change the style on the form and the count, the thread length and the marking list all change together.
How much thread does sewing a text block take?
At the values in the form — a 9 in spine, half-inch kettles, three tapes, sixteen sections, a 1.15 slack factor and six-inch tails changed every four sections — it comes to 6.3 yards. Just under five of those yards is sewing and the rest is tails. The figure is a floor plus your slack, so cut longer than it says.
Why does changing thread more often use more thread?
Because every new length needs a tail at each end that never goes through a fold. Sewing sixteen sections in four lengths costs 48 in of tails against 12 in for a single continuous length, so the changes add 36 in. The trade is real in both directions: a shorter working length abrades less as it passes through the folds, which is why almost nobody sews a whole block on one thread even though it uses less.
Does the tape width change the layout much?
It changes the hole positions but not the tape centres. The centres come out of dividing the span, and the pair straddling each one moves out by half the tape width plus the clearance. Wider tape spreads the pairs and narrows the bare spine between them, and the page prints that remaining gap so you can see when the tapes are crowding each other.