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International 1/4-Inch Log Rule

The international 1/4-inch log rule determines the volume of lumber from a log, accounting for the taper that exists in all logs, saw kerf (or the loss of wood as sawdust) and wood removed on the outside of the logs for slabs.

The volume of lumber depends on the diamter, length and taper. It increases quadratically with diameter and cubically with length, and decreases with taper.

Formula

QuantityVariable["V", "Volume"] == Quantity[1, "BoardFeet"]*(Quantity[-1.9284000000000001, "Feet"^(-2)]*QuantityVariable["d", "Diameter"]*QuantityVariable["L", "Length"] + Quantity[7.1712, "Feet"^(-3)]*QuantityVariable["d", "Diameter"]^2*QuantityVariable["L", "Length"] + Quantity[0.3214, "Inches"^(-1)]*QuantityVariable["L", "Length"]*QuantityVariable["t", "LengthRatios"] + Quantity[-0.1992, "Inches"^(-2)]*QuantityVariable["d", "Diameter"]*QuantityVariable["L", "Length"]*QuantityVariable["t", "LengthRatios"] + Quantity[-0.9648, "Feet"^(-2)]*QuantityVariable["L", "Length"]^2*QuantityVariable["t", "LengthRatios"] + Quantity[7.1712, "Feet"^(-3)]*QuantityVariable["d", "Diameter"]*QuantityVariable["L", "Length"]^2*QuantityVariable["t", "LengthRatios"] + Quantity[1.91232, "Feet"^(-1)]*QuantityVariable["L", "Length"]*QuantityVariable["t", "LengthRatios"]^2 + Quantity[-0.0996, "Inches"^(-2)]*QuantityVariable["L", "Length"]^2*QuantityVariable["t", "LengthRatios"]^2 + Quantity[0.0013833333333333332, "Inches"^(-3)]*QuantityVariable["L", "Length"]^3*QuantityVariable["t", "LengthRatios"]^2)

symbol description physical quantity
V volume "Volume"
d diameter "Diameter"
L length "Length"
t taper "LengthRatios"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["International 1/4-Inch Log Rule"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["International 1/4-Inch Log Rule"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "International 1/4-Inch Log Rule"], {QuantityVariable[ "L","Length"] -> Quantity[10, "Feet"]}]
Out[3]=

Source Metadata

  • Date: 1906

Publisher Information