

H. S. DEPT. OF AGRICULTURE 



U.S. FOREi®«nM®ieWV»PI8fE 

 DEC 2" 1965 



MtHI SERIAL RECOBDS 



Research note ls-67/ 



LAKE STATES FOREST EXPERIMENT STATION,- U.S. DEPARTMENT OF AGRICULTURE 



3 « J 



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Alinement Chart for Numbers 



The chart given here eliminates or simplifies 

 many calculations involving relationships among 

 numbers of trees, diameters, and basal areas. 1 If 

 any two of these variables are known or can be 

 estimated, the other can be found. This chart has 

 many applications in forestry, both in the field 

 and in the office. Some examples are given below. 



Estimating Average Stand Diameters. — If the 

 number of trees and basal area per unit of area 

 are known ( the unit of area can be an acre, a 

 lOth-acre plot, or any other sized area), the diam- 

 eter of the tree of average ( mean ) basal area can 

 be simply estimated. 



Place one end of a straightedge on the NUM- 

 BER OF TREES scale, for example 220 trees per 

 acre, and the other end on the BASAL AREA scale, 

 say on 90 square feet. The average diameter is 

 read off the DIAMETER scale at the point where 

 the straightedge crosses — 8.7 inches in this ex- 

 ample. 



Estimating Basal Areas. — If the number of trees 

 of a given average diameter is known, their basal 

 area is readily found. Aline the straightedge on the 

 NUMBER OF TREES and DIAMETER scales and 

 read off the BASAL AREA scale. The basal area 

 for 400 trees averaging 6 inches in diameter is 

 78.5 square feet. Note that this same answer tells 

 us that the basal area in 40 trees is 7.85 square 

 feet; in 4 trees, 0.785 square feet. For the basal 

 area of one 3.9-inch tree, find the basal area for 

 1,000 trees, 83 square feet, and divide by 1,000. 

 Thus, one 3.9-inch tree has a basal area of 0.083 

 square feet. Any convenient number of trees can 

 be used in this manner to find the basal area of 



The formula used in constructing this chart was: 



BA = 0.005454 D 2 N 

 where BA is total basal area in square feet, D is 

 tree diameter breast high in inches, and N is num- 

 ber of trees on an area of known size. 



of Trees - Diameters * Basal Areas -~^/ 



a single tree or a group of trees of any diameter. 



Estimating Diameter and Basal Area Growth. — If 

 future values of any two variables can be esti- 

 mated, then the third can be found. One use of 

 this is to estimate stand diameter growth ( the 

 increase in diameter of the tree of average basal 

 area). For example, after thinning a red pine 

 stand to 90 square feet of basal area we have 

 220 trees averaging 8.7 inches in diameter. Over 

 the next 10 years these 220 trees are expected to 

 grow in basal area to 135 square feet, with no mor- 

 tality. Thus, in 10 years the average diameter 

 would be 10.6 inches (220 trees, 135 square feet), 

 a growth of 1.9 inches. 



Conversely, past ring counts may have indi- 

 cated a future 10-year average diameter growth of 

 1.9 inches in this stand, from 8.7 to 10.6 inches. 

 Knowing the present number of trees ( 220 ) would 

 enable us to estimate the future basal area as 135 

 square feet if there is no mortality, a growth of 

 45 square feet ( 135-90). 



This technique only approximates actual stand 

 diameter and basal area growth. It applies best to 

 stands with a narrow and even distribution of di- 

 ameter classes, such as a well-spaced plantation. 



Estimating Numbers of Trees To Be Cut In Thin- 

 ning. — Another use of this chart is to estimate 

 how many trees must be cut to thin to a given 

 basal area ( assuming a cut from above and below 

 that does not change the diameter of the tree of 

 average basal area by cutting). To illustrate, a 

 stand averaging 10.6 inches in diameter with 220 

 trees and 135 square feet of basal area per acre is 

 to be thinned back to 90 square feet. A stand with 

 90 square feet in 10.6-inch trees would have 147 

 trees. Thus, about 73 trees per acre would have to 

 be cut to thin the stand back to 90 square feet. 



Other applications of this chart may come to 

 mind, but these examples illustrate its use in sev- 

 eral problems commonly encountered in timber 

 management. 



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OCTOBER 1965 



4i 



/ ALLEN L.JLUNDGREN. 



F.^nnnmict / 



/ 



Economist 



MAINTAINED AT ST. PAUL 1, MINNESOTA, IN COOPERATION WITH THE UNIVERSITY OF MINNESOTA 



