A plank begins with a line. Every saw cut removes wood along the whole length of the log, and the bark and taper take away further parts before any plank exists.
Model diagram of the cross-section at the top end of the log. The dark ring is bark, the grey area is slabs and wane, the blue lines are kerfs, and the bar in the corner is 10 cm.
Drawing only: the displacement is not a dimension.
Sawn timber 46.8% · slabs and wane 32.3% · kerf 4.6% · bark 16.3% of the log’s 0.387 m³.
Sawing pattern
Cutting
The line is a strip of wood of this width, as long as the whole log.
The beam fits when its diagonal does not exceed the diameter of the wood under the bark.
The bark reduces the diameter of the wood at both ends by twice this value.
All pieces fit within the outline of the wood under the bark (diameter at the top end: 27.0 cm). The grey area is slabs and wane.
Balance: 100% of the log’s volume
Sawn timber (pieces from the plan)0.181 m³46.8%
Slabs and wane (the rest of the wood, including the taper wedge)0.125 m³32.3%
Kerf (sawdust)0.018 m³4.6%
Bark0.063 m³16.3%
Whole log (truncated cone, model)0.387 m³100.0%
Cuts: 8 · total length of lines in the cross-section: 126.6 cm · a 3.5 mm kerf over a length of 4.0 m turns approx. 0.018 m³ into sawdust.
Values are rounded by the largest remainder method, so the parts shown always add up to the log volume shown. The volume balance does not assess the strength or structural suitability of the beams.
Pieces of sawn timber · length L = 4.0 m· the button takes the piece out onto the table
Piece
Cross-section
Qty
Each
Total
Central beam
18 × 18 cm
1
0.1296 m³
0.1296 m³
Top and bottom boards
25 mm × 12.9 cm
2
0.0129 m³
0.0258 m³
Left and right boards
25 mm × 12.9 cm
2
0.0129 m³
0.0258 m³
Total sawn timber
0.1812 m³
Choose a piece from the list or click it in the drawing. It will slide out onto the table, leaving a dashed outline and blue kerf marks in its place.
A log is not a cylinder
Sawing from the top uses the cross-section of the thinner end, because only that is certain along the whole length. The thicker end adds a wedge of wood, which in this model goes into the slabs. Below are four ways of calculating volume, all on one scale.
Diameter of the thinner end d = 30 cm
The strip of timber along the whole length is at most 27.0 cm in diameter (wood under the bark at the top end, bark 15 mm on the radius). The thicker end (40 cm) gives an additional wedge: in the model it goes into slabs and wane.
Model diagram. The length is shortened: the vertical axis (diameters) is exaggerated 3× relative to the horizontal.
bark
wood under the bark
cross-section band from the Sawing plan section
cylinder of diameter D
mid-diameter (Huber)
1 · Cylinder with the butt-end diameter π·L·D²/4
0.503 m³+29.7% relative to the cone
2 · Truncated cone, reference model π·L·(D²+D·d+d²)/12
0.387 m³reference
3 · Mid-diameter (Huber’s formula) π·L·d_mid²/4
0.385 m³−0.7% relative to the cone
4 · Cylinder with the top-end diameter π·L·d²/4
0.283 m³−27.0% relative to the cone
Bars: 100% = the longest of the four. The mid-diameter here is the mean of the two ends, not a measurement at the middle of the log. The cone is a model, not a description of a real trunk.
The butt-end cylinder (D = 40 cm along the whole length) overstates the volume by 29.7% relative to the truncated cone; the top-end cylinder understates it by 27.0%.
Two routes for timber, two separate accounts
This is not the journey of the log in the drawing above. On the left is the modern organisation of forestry work, on the right the tradition of rafting at Ulanów. Both accounts are shown at once, because the difference only becomes visible in comparison.
The modern forestry chain
Account from the V2 material (Antonin Forest District), to be rechecked
HarvestingFelling and cutting the logs to length with a harvester or chainsaws in the forest ranger district.
ExtractionCarrying the logs by forwarder to a landing by the haul road.
SortingGrading the raw material: sawlogs, pulpwood, firewood.
Loading and haulageTrucks with a loader crane or the railway take it to the plant.
PlantSawing, drying and processing are further stages. Not every trunk becomes a plank.
Rafting at Ulanów, a tradition
Account from the V2 material (Ulanów municipality website), to be rechecked
Felling and gatheringTimber from the forests of the San basin, in winter and early spring.
Building raftsTrunks fastened into raft sections and then into rafts at the landing places (bindugi) at Ulanów.
Floating downriverWith the current of the San and the Vistula to Gdańsk. V2 gives ‘several hundred kilometres’, with no route or speed.
Limits in timeAccording to V2: the last commercial float to Gdańsk in summer 1939, the return of traditional rafting in 1993.
HeritageV2 mentions the inscription of rafting on lists of intangible heritage. The scope and dates need checking.
What they share, what sets them apart. The only thing in common is that roundwood travels to the place where it is processed. Tools, organisation and time scale set them apart. The page does not follow the fate of a single log, nor does it give the time or cost of either route.
Limits of the model and what changed relative to V2
What the model calculates
The log is a truncated cone with diameters D (thick end) and d (thin end) and length L.
The bark is a constant thickness on the radius (5–30 mm), subtracted from the diameter at both ends.
The cross-section is the circle of the top end with the pith in the middle, the same along the whole length. The pieces have the dimensions shown in the drawing along the whole length L.
The kerf is a strip of the saw’s width along each line; its length is the segment between the pieces being separated.
Slabs and wane are the rest of the wood under the bark, including the taper wedge. Board widths are rounded down to 0.1 cm; boards narrower than 4 cm (an assumption of the model, not a standard) are not produced.
What the model does not calculate
Strength, quality grades, knots, curvature, cracks, moisture content, shrinkage, drying or optimisation in a real sawmill.
Price, time and transport emissions.
This is not a structural recommendation: a beam for a building must be assessed by a specialist.
A piece that does not fit within the outline of the wood may be shown on the table as a candidate, but it never counts towards the yield.
What changed relative to V2
Removed the three log presets A, B, C: they are replaced by a single default state and a restore button.
Removed the ‘Assembled/Spread out’ buttons: what remains is the spreading slider and the option to take out a single piece.
Replaced the switchable transport tabs with two columns visible at once.
Removed the embedded photograph of a raft from the internet: the page works offline, and the photograph is only a link.
Moved the four volume models from cards to bars on one scale, after the sawing plan.
Fixed in V2: raw dollar signs in headings, outdated values in the HTML without JS, rounding of board width to the nearest 0.1 cm (which could round up beyond the outline) and clipping of a negative remainder, which broke the balance total.
Kept the three sawing patterns, the dependencies on bark, kerf and taper, and the exclusion of beams that do not fit in the cross-section.
Sources
The links were carried over from V2. They were not opened or checked in this session, so they should not be treated as verified. External images, fonts and scripts are not loaded; the links work only when clicked.
Photograph of a rafting raft (not embedded): Klotbas, Wikimedia Commons, licence CC BY-SA 3.0. According to V2: a traditional raft at Ulanów, 2013; it illustrates the keeping alive of the craft today, not an archival float or the log from the model.
All drawings on this page are this version’s own diagrams, generated from the slider values; they are neither a measurement nor a map.
