Methodology

Rolls, Sheets and the Lap Between Them

Why covering an area with rolls is a strip count rather than a division, why the lap is bought twice over, and why turning the strips the other way can change the order.
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A roll covers in strips, not in area

Dividing an area by the area of a roll is the intuitive move and it is wrong, because a roll cannot be laid as an arbitrary shape. It has a fixed width, so it lays as a strip, and the question is how many strips the surface needs — which depends on the surface's width measured ACROSS the direction the strips will run, and on nothing else.

That single change explains most of the shortfalls in ordering sheet goods. A surface 4.3 m across, covered by a roll 1 m wide, needs five strips. The area division would have said four point three rolls' worth and somebody would have ordered five anyway — but on a surface 4.0 m across needing four strips, the area division and the strip count agree, and the habit survives until the day it does not.

s=⌈Wwr-ls⌉
The number of strips equals the ceiling of the surface width divided by the roll's width less its side lap.
s
strips needed across the surface
W
surface width, measured across the direction the strips run
w_r
the roll's nominal width
l_s
the side lap — width consumed where one strip overlaps the next

The lap is bought and never seen

Every overlapping strip gives up part of its width to the strip beside it, so the EFFECTIVE width is the nominal width less the lap. That is the second reason an area division fails, and its magnitude is easy to state: a roll a metre wide lapped a hundred millimetres covers nine hundred millimetres, so eleven per cent of every roll is buried under the next one.

Eleven per cent is not a waste factor and should not be folded into one. A waste factor covers offcuts, mistakes and awkward corners, and varies with the job. The lap is a designed, unavoidable, entirely predictable consumption that happens on every square metre of a perfectly executed installation — and rolling it into a waste allowance hides it from the one person who might otherwise notice that a wider roll would cost less per covered area.

Long runs pay it a second time. Where the surface is longer than the roll, the strips need a head lap as well, and that consumes LENGTH on the same principle. A surface needing two rolls end to end down each strip buys the head lap once per join, so a tall wall or a long slope costs proportionally more than a short one of the same area.

N=s⁢⌈L+(k-1)⁢leLr⌉
Rolls equal the strip count times the ceiling of the run length, plus the end laps it needs, divided by the length of one roll.
N
rolls to order
s
strips across, from the formula above
L
the length of one strip — the run down the surface
k
pieces needed to make up that run; one join fewer than pieces
l_e
the end or head lap between consecutive pieces in a strip
L_r
usable length on one roll

Turning the strips changes the answer

Because the count depends on the width measured across the strips, it is a function of the DIRECTION they run — and on a rectangular surface the two directions give different answers.

Run the strips the long way and there are fewer of them, each longer, with fewer side laps and more end laps. Run them the short way and there are more strips, each shorter, with more side laps and possibly no end laps at all. Neither is universally cheaper: which wins depends on the ratio of the surface's sides, the roll's length, and which lap is wider.

The choice is usually not free, either. Roofing underlayment runs along the slope's contours so that water sheds over each lap rather than into it. Landscape fabric and erosion blankets run down the slope so the seams do not become channels. Air and vapour barriers run whichever way lets the laps be taped continuously. So the answer here is a quantity for a chosen direction, and where the direction is set by the physics rather than by the arithmetic, the physics is what states it.

Where it fails: the lap is the product

For a membrane, an air barrier, a vapour control layer or a geotextile, the lap is not packaging — it IS the performance. A taped lap is the joint that keeps the assembly continuous, and a lap trimmed to save material is an assembly with a designed-in leak.

Two rules govern it and neither is arithmetic. The lap must be wide enough for whatever bonds it — a tape needs a surface on both sides of itself, a welded seam needs a weldable overlap, a mechanically fastened lap needs room for the fastener plus an edge distance. And the lap must SHINGLE: the upper piece over the lower, so that water and air pressure act to close the joint rather than to open it. A correctly sized lap installed the wrong way round performs worse than none, because it channels.

Geotextiles carry the same rule with a second condition: on weak subgrade the required overlap widens, because the fabric is being asked to carry tension across a seam that is not sewn. A figure lifted from a firm-ground detail is the wrong figure on soft ground, and the soft ground is where the fabric was needed.

Where it fails: a sheet is a roll fixed in both directions

Sheet goods — board, ply, plasterboard, insulation board — are the same problem with one more constraint: the length is fixed too, so the offcut at the end of a run cannot be used to start the next one unless something else on the job happens to need exactly that piece.

That is a PACKING problem rather than a coverage one, and it does not obey a coverage formula. A wall 3.1 m high consumes two sheets of 2.4 m and produces a 1.7 m remnant; unless there is a 1.7 m need elsewhere, that remnant is waste of seventy per cent of a sheet. The area division says 1.29 sheets.

So the sheet calculators here work in whole sheets against the actual dimension rather than against the area, and where offcuts genuinely can be recombined, that is a separate method with its own page — see the cut-list and bin-packing paper, which is about exactly the case this one cannot handle.

The alternative: a seam plan rather than a count

The alternative to counting is drawing. A seam plan sets out where each strip lands, which is the only way to answer the questions a count cannot: whether a seam falls over a joint it should not, whether the last strip is an unusably narrow sliver, and whether shifting the first strip by half a width removes a whole row of cuts.

For a large single-ply roof or a below-grade tanking job this is normal practice and the quantity falls out of the drawing rather than the other way round. For a bedroom floor it is overkill.

The count on these pages is the estimating figure — enough to order against, honest about the laps, and explicit that it assumes strips of full width across a surface with no obstructions in it. Where the surface has penetrations, upstands or a shape that is not a rectangle, the seam plan is the real answer and the count is the budget.

Calculators that use this method

Basis

  • AASHTO M288, Geotextile Specification for Highway Applications. Minimum overlap by subgrade strength, and the point that the requirement widens as the ground weakens.
  • ASTM E2357, Standard Test Method for Determining Air Leakage Rate of Air Barrier Assemblies. Assemblies are tested as built, laps included, which is why a trimmed lap is an untested assembly.
  • ASTM D226 / D226M and ASTM D1970 for asphalt-saturated felt and self-adhering underlayment, and the lap dimensions each is tested with.
  • International Building Code and International Residential Code roof underlayment provisions, which set minimum side and end laps against roof slope — shallower slopes require wider laps, because water travels further sideways before it drains.
  • Single-ply membrane manufacturers' seam requirements. These are product-specific and govern over any general figure; a welded seam and a taped seam do not need the same overlap.
  • The cut-list and bin-packing paper on this site, for the sheet-remnant case this method deliberately does not attempt.
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