Forest Functions, Computer code to help foresters

Doyle Boardfoot Log Volume

This is one of the most widely use and well as one of the oldest log rules. The rule was developed by Edward Doyle in 1825. The rule states: "Deduct 4 inches from the diameter of the log, D, in inches, for slabing, square one-quarter of the remainder, and multiply by the length of the log, L, in feet." This is equivalent to squaring the log into a cant and calculating the board feet in the cant. Doyle assumed 25 % reduction for kerf and shrinkage. The rule can be stated as:

where $V$ is the volume in board feet, $D$ is the small end diameter of the log, and $L$ is the log length. Known issues include:

1. The formula is very simple.
2. The rule works best for logs between 26 and 36 inches in diameter.
3. Larger logs produce underruns.
4. Smaller logs produce overruns.

Example

Imperial Units

dia small = 10 in inches

L = 16 feet

Answer = 36 board feet




dia small = 28 in inches

L = 16 feet

Answer = 576 board feet




Board feet is a imperial units only system.

Code

Visual Basic

 
Function bfLogVolume(sdia As Single, length As Single, Optional voltype As String = "int") As Double
' Function to calculate the Doyle, scribner and International board foot volume of a log
' sdia is in inches and length is in feet
' by David R. Larsen, Copyright October 9, 2012
' Creative Commons http://creativecommons.org/licenses/by-nc/3.0/us/

If (voltype = "doyle") Then
    bfLogVolume = ((sdia - 4) / 4) ^ 2 * length
ElseIf (voltype = "scribner") Then
    bfLogVolume = (0.79 * sdia ^ 2 - 2# * sdia - 4#) * (length / 16#)
ElseIf (voltype = "int") Then
    If (length = 4#) Then
        bfLogVolume = 0.22 * sdia ^ 2 - 0.71 * sdia
    ElseIf (length = 8#) Then
        bfLogVolume = 0.44 * sdia ^ 2 - 1.2 * sdia - 0.3
    ElseIf (length = 12#) Then
        bfLogVolume = 0.66 * sdia ^ 2 - 1.47 * sdia - 0.79
    ElseIf (length = 16#) Then
        bfLogVolume = 0.88 * sdia ^ 2 - 1.56 * sdia - 1.36
    ElseIf (length = 20#) Then
        bfLogVolume = 1.1 * sdia ^ 2 - 1.35 * sdia - 1.9
    ElseIf (length = 24#) Then
        bfLogVolume = 1.1 * sdia ^ 2 - 1.35 * sdia - 1.9 + 0.22 * sdia ^ 2 - 0.71 * sdia
    ElseIf (length = 28#) Then
        bfLogVolume = 1.1 * sdia ^ 2 - 1.35 * sdia - 1.9 +  0.44 * sdia ^ 2 - 1.2 * sdia - 0.3
    ElseIf (length = 32#) Then
        bfLogVolume = 1.1 * sdia ^ 2 - 1.35 * sdia - 1.9 + 0.66 * sdia ^ 2 - 1.47 * sdia - 0.79
    ElseIf (length = 36#) Then
        bfLogVolume = (0.88 * sdia ^ 2 - 1.56 * sdia - 1.36) * 2
    ElseIf (length = 40#) Then
        bfLogVolume = (1.1 * sdia ^ 2 - 1.35 * sdia - 1.9 ) * 2
    Else
        bfLogVolume = 0
        MsgBox ("Unknown log length, options are: 4, 8, 12, 16, 20")
    End If

Else
    bfLogVolume = 0
    MsgBox ("Unknown voltype, options are: doyle, scribner, or int")
End If

End Function

Excel® Visual Basic Code


R Statistical Package Code

 
doyle = function( sdia, length )
{
# Function to calculate the Doyle Board Foot volume
# by David R. Larsen, Copyright November 2, 2012
# Creative Commons http://creativecommons.org/licenses/by-nc/3.0/us/

  doyle = ((sdia - 4) / 4 )^2 * length
  doyle
}

R Statistical Package Code


Python Code

 
#!/usr/local/bin/python
# Function to calculate the Doyle Board foot volume
# from small end diameter and log length
# by David R. Larsen, October 11, 2012
# Creative Commons,  http://creativecommons.org/licenses/by-nc/3.0/us/


def doyle( sdia, length):
    value = (( sdia - 4.0) / 4.0 )**2 * length
    return value

print "doyle =", doyle(sdia=10,length=16)
print "doyle =", doyle(sdia=28,length=16)

Python Code

Note the python files has a extra "txt" at the end to allow the files to be viewed in a web browser.