Calculation of quadratic mean diameter

Given, you have estimates of:

1. Basal area per acre (BAPA, ft2/ac)
2. Trees per acre (TPA, #/ac)

Avery and Burkhart (1994) give a formula for calculating the quadratic mean diameter of a stand based on BAPA and TPA (see middle of page 290).

The derivation of this formula is give below.

The average basal area per tree (BA, ft2)

BA = BAPA / TPA

Using the formula BA = p D2 / 4, then the diameter of the tree of average basal area (a.k.a., quadratic mean diameter, Dq) is:

 Dq = [4 BA / p ]0.5 = [4 (BAPA/TPA) / p ]0.5

BUT, we want Dq in inches, therefore we need to include a conversion from feet (for BA) to inches (for Dq).

THEREFORE,

 Dq = [4 (BAPA/TPA) / p ]0.5 * 12 = [ (BAPA/TPA) / {(p / 4) / 144} ] 0.5 = [ (BAPA/TPA) / {0.005454} ] 0.5 = same as pg. 290

Return to
FOR322: Homepage | Outline | Syllabus | Assignments | Links | Archives
Eddie Bevilacqua's: | Homepage | Courses Taught| Curriculum Vitae| Publications | Research Interests |
Faculty of Forestry Homepage | ESF Homepage |