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Cubing stems by mid-diameter

How many cubic metres are there in 20 logs of 5 m with 32 cm average diameter?

Answer: Sawn timber is cubed according to length and mid-diameter without bark: the trunk is calculated as a cylinder with the diameter measured in the middle of the log. If you measure with bark, subtract twice the bark thickness. The calculator gives the volume per log and for a whole load or stack with identical logs, so you can verify a billing or assess a lorryload.

Formula

Midtdiameter uden bark = målt midtdiameter − dobbelt barktykkelse

Rumfang pr. stok (Huber) = π/4 × (diameter i m)² × længde i m

Rumfang i alt = rumfang pr. stok × antal stokke

The diameter is squared: 2 cm too much on a 30 cm log gives approx. 14% too much volume

Symbols and units in the formula
SymbolMeaningUnit
midtdiameterMeasured mid-diametercm
barkfradragDouble bark thickness (0 if measured without bark)cm
laengdeStick lengthm
antalNumber of identical logsstk
=Total volumem³
=Volume per piecem³
=Mid-diameter without barkcm
=Sticks per cubic metrestk/m³

Validity and source

Source
Huber formula with mid-diameter without bark (Raw Timber Handbook Danish Forest Society 2008)

Does not apply when

  • The mid-diameter is measured perpendicular to the trunk mid-log. If the log is oval, two diameters are measured crosswise and the average is used. Follow the rounding rules for length and diameter stated in the Raw Wood Manual or buyer's measurement agreement. Machine measurement in the harvester follows the certification scheme's own rules.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Measured mid-diameter32 cm
  • Double bark thickness (0 if measured without bark)2 cm
  • Stick length5 m
  • Number of identical logs20 stk

Giver

  • Total volume7.07 m³
  • Volume per piece0.353 m³
  • Mid-diameter without bark30.0 cm
  • Sticks per cubic metre2.8 stk/m³

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Sådan bruger du den

Når tømmer er afkortet og stablet ved vejen, kuberes det efter længde og midtdiameter uden bark. Du bruger det til at kontrollere en afregning, vurdere et læs eller planlægge transport.

Step by step

  1. Mål midtdiameteren vinkelret på stokken midt på længden. Er stokken oval, så mål på kryds og brug gennemsnittet.
  2. Måler du med bark, så træk den dobbelte barktykkelse fra.
  3. Rumfang pr. stok = π/4 × (diameter i m)² × længde.
  4. Gang med antal stokke.

Typical errors

  • At måle diameteren i enden af stokken. Toppen er tyndere og roden tykkere.
  • At glemme barkfradraget. Det kan give over 10 % for meget.
  • At bruge omkredsen som diameter. Del omkredsen med π.

Examples from everyday life

Rødgran-savtømmer

Du har 20 rødgranstokke på 5 m med 32 cm midtdiameter målt med bark. Barken er ca. 1 cm tyk, altså 2 cm i alt.

Measured mid-diameter
32 cm
Double bark thickness (0 if measured without bark)
2 cm
Stick length
5 m
Number of identical logs
20 pcs

It means: Stokkene har i alt 7.07 m³. Hver stok er 0.353 m³ med en midtdiameter uden bark på 30 cm.

Bøgekævler

Fire bøgekævler på 6 m har 52 cm midtdiameter målt med bark. Bøgebark er tynd, så du trækker 1 cm fra.

Measured mid-diameter
52 cm
Double bark thickness (0 if measured without bark)
1 cm
Stick length
6 m
Number of identical logs
4 pcs

It means: De fire kævler har 4.9 m³, altså 1.226 m³ pr. kævle.

Tyndingstømmer uden bark

60 afbarkede rødgranstokke på 4 m har 22 cm midtdiameter.

Measured mid-diameter
22 cm
Double bark thickness (0 if measured without bark)
0 cm
Stick length
4 m
Number of identical logs
60 pcs

It means: Stakken er 9.12 m³. Stokke pr. m³: 6.6 stk/m³.

Rule of thumb

En stok på 5 m med 30 cm midtdiameter er ca. 0,35 m³.

How to check the answer

Gang rumfang pr. stok med antal. Det skal give rumfanget i alt.