Stand Volume and Growth:
Getting the Numbers
3. Calculating stand volume and growth
Now that you’ve collected the plot information, you can take it home and translate it into numbers that will more accurately describe your stand. The numbers to generate include: Trees per acre Tarif number for the stand Average radial growth Stand volume Basal area and average stand diameter Volume projections
Trees per acre We will use the completed Tree Tally Card for Coleman’s Conifers (Figure 2) for the data in our computations, and consult the completed Volume Computation Form (Figure 4) for our completed stand volume and growth calculations. A blank Tree Tally Card (Appendix C) and Volume Computation Form (Appendix D) have been provided for you to copy and use in your own timber stand calculations.
To determine the average number of trees per acre, refer to your Tree Tally Card (Figure 2). Total the trees tallied for each diameter class and enter the number in the Total Plot Trees column.
The next step is to convert total plot trees into trees per acre. To do this, look up the plot correction factor in the bottom right table of Figure 2 for your plot size. Divide this by the number of plots in your sample to get the multiplication factor.
The multiplication factor simply expresses how many trees per acre are represented by each tree in a sample plot. To find how many trees per acre there are in each diameter class, multiply the value in the total plot trees column by the multiplication factor. Next, add the values in the trees per acre column to calculate total trees per acre. Transfer this information to your Volume Computation Form (Figure 4).
Tarif number for the stand The average tarif number for the stand is the average of the tarif numbers for all the tarif trees you sampled.
Determine the tarif number for each sample tree on the tarif tree section of your Tree Tally Card by looking up the value in a tarif access table for the desired tree species (Appendixes A1 through A6). These tables list a tarif number based on tree species, DBH, and total tree height.
In our example, we have recorded height to the nearest 5 foot increment and diameter to the nearest whole number. We then accessed the appropriate appendix and recorded the corresponding tarif number on the Tarif Tree section of the Tree Tally Card.
Next, total these values and divide by the number of tarif trees to determine the average tarif number of the stand. Palce this number at the top of your Volume Computation Form. This average tarif number identifies the taper of your trees, and it’s the key to determining volumes for your trees.
Utilization of the computer program, VARPLOT: Stand Measurement Software, will allow you to measure tarif trees to the nearest 1/10th inch in diameter and the nearest foot in height. In some instances, these more accurate measurements may give you slightly different figures than rounded numbers used in our example, but this will not always be the case.
THIS SECTION GOES ALONGSIDE THE TREES PER ACRE SECTION Calculating trees per acre Looking at Figure 2, the Coleman’s Conifers has a total of 80 trees on 10 plots. The multiplication factor is 2 (a plot size correction factor of 20/ the number of plots, or 10). For example, you have 14 trees with a 12-inch diameter, thus 28 (14 plot trees times a multiplication factor of 2) 12-inch trees per acre in the stand.
Getting the tarif numbers In the example, 10 tarif trees have been measured. By adding the tarif number for each of the sample trees (Appendix A1: Tarif access table for Douglas-fir) and dividing by 10, you find an average of 39.1. Rounding to the nearest whole number means you’ll use 39 as the tarif number for the stand.
Computing average radial growth The total of column 4 in the Tarif Trees section of the Tree Tally Card is 60. This means the average tree grew 6/10 (6.0/10 trees measured) in the 5-year period, or 0.60 inches radial growth. Diameter growth is then 1.2 inches (0.60 radial growth times 2).
Average radial growth (ARG) Determine the radial growth estimate for the stand by adding the core samples recorded in column 4 of the Tarif Tree section of the Tree Tally card (Figure 2). Compute the average radial growth by dividing the total by the total number of tarif trees measured. Remember: This is a radial – not a diameter – measurement (Figure 3 illustrates radial growth). Transfer this information to your Volume Computation Form.
Estimating stand volume The next step is to compute estimates of the stand volume from field measurements and the average tarif number
First, transfer the number of trees per acre, by diameter class, from the Plot Trees section of your Tree Tally Card to column 1 of the Volume Computation Form. Next, record average radial growth and your average tarif number at the top of the Volume Computation Form. Don’t worry about Average basal area/tree or Average stand diameter at this time, you’ll fill in these lines during the next step of the process.
Tree Volume Tables are located in Appendix B. The volumes you use will be the figures aligned in the column under the appropriate Tarif Numbers. For our example, we determined 39 as our average tarif number for the stand. The volumes we use will be located under the Tarif Numbers column 39.
If you want to estimate board foot volumes in 32-foot logs, use Appendix B1. Appendix B2 is for volumes in 16-foot logs, and cubic-foot volumes are located in Appendix B3. Record board feet in column 2 and cubic feet in column 4 of the Volume Computation Form.
To get the total board-foot and cubic-foot volumes per acre for each diameter class, multiply trees per acre (column 1) by volume per tree (column 2 or column 4) of the Volume Computation Form. Enter the total volumes per acre for each diameter class in column 3 and column 5. The sum of column 3 is your total board-foot volume per acre and column 5 is your total cubic-foot volume per acre.
Basal area and average stand diameter We’ve computed the basal area per tree in column 6 of the Volume Computation Form. To determine basal area per acre of trees by diameter class (column 7), multiply the values in column 1 (Trees per acre) by those in column 6 (Basal area per tree). Add column 7 for the total stand basal area and record at the bottom of the column.
To compute the average basal area per tree, we need the total stand basal area (column 7) and trees per acre (column 1). Applying the following formula gives us Average basal area per tree:
Average basal area/tree = Total basal area = Total (column 7) Total trees/acre = Total (column 1)
The corresponding diameter for a tree of average basal area is defined as the average stand diameter. To find this diameter, you must convert from basal area (ft²) to diameter (inches), requiring one additional formula:
Average stand diameter = √Average basal area per tree .005454
You can now transfer your Average basal area/tree and Average stand diameter in the appropriate space at the top of your Volume Computation Form.
THIS SECTION GOES ALONGSIDE ESTIMATING STAND VOLUME AND BASAL AREA AND AVERAGE STAND DIAMETER
Determining Stand Volume Assume you want to estimate board foot volumes in 32-foot logs (Appendix B2). The Tree Tally Card shows 4 trees per acre with a DBH of 8 inches. Using Appendix B2 and our average tarif number of 39 shows a volume of 40 board feet for each tree containing a DBH of 8 inches.
Multiplying 4 trees (column 1) by 40 board feet as determined in Appendix B2 (column 2) you calculate160 board feet volume per acre for trees in our 8 inch diameter class (column 3). Repeat this process for each diameter class. Adding the values in columns 1 and 3 shows a total of 160 trees per care with a volume of 23,900 board feet per acre.
Calculating basal area Multiplying 4 trees per acre (column 1) by .349 basal area per tree (column 6) you get a total basal area of 1.396 for trees with a DBH of 8 inches. Repeating this process for all the diameter classes and adding column 7 gives a Total Basal Area of 147.46.
Computing Average basal area/tree For the stand, the total basal area is 147.46 and you have 160 total trees per care.
147.46 = .922 average basal area per tree 160
Computing average stand diameter You’ve determined .922 as our average basal area per tree. The average stand diameter will be:
√.922 = 13.00 .005454