A peeling recipe, from the dry sheet backwards

Every rotary veneer mill has a recipe written on a whiteboard somewhere near the lathe. Three numbers: what the lathe is set to, in thousandths; what the spur knives are set to, in inches; what the green clipper is set to, also in inches. Fifty-four for a sheet that will finish at forty-eight. A hundred and two for a panel that will finish at ninety-six. A lathe "set a little heavy". The numbers are right, mostly, and almost nobody on the floor can tell you where they came from, because they came from the last person who ran the line and before that from the person before them.

They came from shrinkage. Veneer is peeled green — sapwood can be over a hundred percent moisture content, more water than wood by weight — and it is scored and clipped green, and only then dried to a few percent. Between the lathe and the dryer outlet it shrinks, by an amount that depends on the species and on the direction, and every one of those three settings is the dry number plus that shrinkage plus whatever the mill wants for trim and variation. So I built a calculator that does the arithmetic behind the whiteboard: RotaryPeelCalc. Pick a species, enter what the dry sheet has to measure and the moisture content it has to measure it at, and the three settings come back. This post is where the numbers come from.

Three settings, three directions

Wood does not shrink evenly. It shrinks most across the growth rings — tangentially — about half as much through them, radially, and almost not at all along the grain. For lumber that is a nuisance, because a board can be cut at any angle to the rings and you have to work out which value applies to which face. For rotary veneer it is a gift, because a lathe cuts tangent to the rings by definition, and a rotary sheet is flat-grain everywhere. The mapping never changes.

The clip width runs across the grain, so it shrinks tangentially, and by the most: 7 to 10 percent green to oven-dry for the species below. The peel thickness is through the sheet, radial, 4 to 7 percent — smaller, but a lathe is set in thousandths and four percent of a hundred thousandths is four thousandths, which is a real number. And the score length runs along the grain, where the Wood Handbook puts shrinkage at 0.1 to 0.2 percent for normal wood: a tenth of an inch on an eight-foot sheet. Three settings, three directions, three very different magnitudes, and the tool works each one separately for that reason.

Nothing moves above fiber saturation, and it is a straight line below

The physics fits in one equation, and it is equation 4-9 in chapter four of the USDA Forest Products Laboratory's Wood Handbook, which is the reference for wood movement in North America. Wood holds water two ways: free water in the cell cavities, and bound water in the cell walls. Drying takes the free water first, and nothing moves while it does. Only once the cavities are empty — the fiber saturation point, about 30 percent moisture content — does the bound water start to go, and the wood shrinks in proportion to how much of it goes. So shrinkage from green to any moisture content x is the full green-to-oven-dry shrinkage, scaled by how far below saturation you have gone:

Sx = S0 × (1 − x / 30)

S₀ comes from the handbook's Table 4-3, which lists it per species, per direction. Two things follow that a calculator exists to get right and a whiteboard cannot.

Any moisture content at or above 30 percent means no shrinkage at all. Type 35 into the tool and it does not give you a negative number; it tells you the sheet is still green at that moisture content and asks for the dryer outlet figure.

The table's percentages are of the green dimension, not the dry one — it says so in the footnote. So the green size for a dry target is the target divided by one minus the shrinkage, not multiplied by one plus it. At the six percent poplar shrinks at 8 percent moisture, the two differ by a fifth of an inch on a clip: multiplying gives 50.89, dividing gives 51.07. Small, and exactly the kind of thing that is wrong on every whiteboard that has a formula on it at all.

public static function greenFor(float $target, float $shrinkage): float
{
    return $target / (1 - $shrinkage / 100);
}

Deriving the whiteboard

Take the classic case: coast Douglas-fir, the western plywood species, peeled a tenth of an inch for a four-by-eight panel and dried to 5 percent for a phenolic glue. Table 4-3 gives it 7.6 percent tangential and 4.8 radial. At 5 percent moisture content that is 6.33 percent across the width and 4.00 through the thickness.

Run the industry's 54-inch clip through it and the sheet dries to 50.58 inches — about two and a half inches over the 48 the panel needs, which is the squaring trim and the margin for the sheets that shrink more than average. Run the tenth-inch dry target through the radial figure and the green peel is 0.1042 inches: a hundred and four thousandths, before the lathe's own allowance. And run 96 inches through the longitudinal figure and the green length is 96.12 inches — which means that of the industry's 100 to 104 inches, an eighth of an inch is shrinkage and the rest is end trim and spur allowance. The whiteboard was right. It just never said why, and it never said what changes when the species does.

The same recipe, eight hardwoods

Which is the point, because the mills around here peel hardwoods. The tool ships the species a central Kentucky veneer line sees — walnut, red oak, white oak, hickory, hard and soft maple, cherry, poplar — and hardwood veneer for a urea glue is dried to 6 to 8 percent, not 5. Here is the same 54-inch clip at 8 percent for all eight, straight from the table with no drying factor and no allowance.

Every species clears 48, but not by the same amount: cherry has three and a fifth inches to spare and hickory has a little under two. Turn it around and ask what clip a 48-inch dry sheet needs, and the shrinkage-only answer runs from 50.64 inches for cherry to 52.00 for white oak and hickory — an inch and a third of difference from one species to the next on the same clipper. The peel spreads the same way: hickory wants about three thousandths more than cherry for the same dry sheet, before the lathe allowance. One clip setting is not one recipe, and a mill that runs cherry on Tuesday and hickory on Wednesday with the same number on the board is giving away width on one and squeezing it on the other.

At 8 percent, inches, from Wood Handbook Table 4-3 and nothing else. Maple is two rows because hard and soft maple are 1.7 points apart tangentially, and a mill that peels both needs both. Notice that poplar with the default allowance lands on 54.07 — which is the check that the default is reasonable. I did not pick three inches because it felt right; I picked it because it reproduces the number every mill already uses, for the species most of them peel most.

What the book does not know

Table 4-3 was measured on small clear blocks drying slowly and freely. Veneer in a jet dryer at 350 °F is neither small, nor drying slowly, nor free, and the differences run in both directions. Lutz, in the 1974 Forest Products Laboratory paper that is still the most complete public treatment of veneer drying, measured eighth-inch yellow-poplar shrinking 6 percent in width at 150 °F, 5½ at 250 and 4½ at 350 — against the 6.8 percent the equation predicts at 5 percent moisture. A hot dryer sets the wood before it has finished moving, and a modern one can deliver two thirds of the book width shrinkage. Thickness goes the other way: hot drying takes more off the thickness than the book says, and in collapse-prone species like overcup oak and sweetgum dramatically more.

And individual sheets vary. The handbook puts the coefficient of variation of transverse shrinkage at about 15 percent, and says outright that predicting the shrinkage of one piece is impossible while predicting the average of many is not. The oversize on the whiteboard exists because of that variability — Lutz notes that mills which dry the ribbon and clip dry do it partly because they no longer have to oversize for it.

So the tool does three things about what it cannot know. It carries a drying factor for width and one for thickness, defaulting to the book value of 1.0, with the page saying plainly that hot dryers typically land between 0.7 and 0.9 of book on width and that the only way to learn a mill's number is to measure it. It shows a conservative setting at 1.15 times the shrinkage beside the mean one, so you can see what "most sheets make size" costs against "the average sheet makes size". And every allowance it adds is printed next to the number it changed, with the word "default" on it until you overwrite it. The three defaults — 3 inches on the clip, 6 on the score, 3 thousandths on the peel — each have a source stated on the page, and none of them is a measurement of any mill, and the page says that too. Plausible numbers on a public page get read as fact unless the page says where they came from. The next version takes a measured green and dry pair per axis and back-solves the effective shrinkage — the seam is built and tested; the inputs are not there yet.

Score length: computed, then dismissed

The tool works the length out properly, because it would be odd not to, and then tells you it barely matters. A 96-inch sheet loses about a tenth of an inch along the grain. The four to eight inches the industry adds are end trim and spur allowance, and the page says so under the number rather than letting a hundred-and-two-inch setting look like it was derived from physics. The one thing to know is what the setting is: the spur-knife spacing, which is the green length of the sheet. The bolt is chucked longer than that and the spurs trim it.

So I built it

Same shape as the two calculators before it. The maths lives in PHP, under test, and does not know the web exists: the equation, the eight rows of the table, the parsing of 1/10 and 100 and 54 1/16 into inches, and the formatting back out to the nearest sixteenth or to thousandths, because that is how a clipper and a lathe are set. The transcription of the species table has a test of its own, since a column slip in a table of decimals is silent: for every row, tangential has to be at least radial, and volumetric has to be near their sum, and a shifted decimal fails both. The page is the query string, so a recipe for white oak at 6 percent is a link that opens to the same three numbers every time — which is what a shift handover wants, and what a whiteboard cannot do.

If you run a lathe and one of these numbers is wrong for your line, I would like to know which one, and by how much. That is the whole of what the next version needs.