Variable radius plot sampling, also known as point sampling, is an awesome technique to use for fast, efficient cruising. Variable radius plots also provide a quick estimate of basal area. Because forest volume is closely related to basal area, cruising with variable radius plots makes it possible to do a backoftheenvelope volume estimate for the stand, if you know the approximate ratio of volume to basal area for your forest type. In this blog post, we will clarify best practices for this technique and troubleshoot some common problems that can occur if it isn’t used properly.
When cruising with variable radius plots, it’s important to use the right basal area factor (i.e. the right size prism) for your forest type, or your estimate of trees per acre could end up far higher or lower than your expectations (and reality). Before you cruise with point sampling, it’s important to understand that under certain conditions, the ease of point sampling comes with a cost in precision in the calculation of trees per acre. Higher BAFs, clumpier forests, and lower minimum diameters result in lower precision in the measurement of trees per acre. (The mean estimate is still accurate, but the confidence interval around that mean is expected to be wider than, for example, a mean from the same number of plots cruised using a lower BAF prism.)
Using this method, every ‘in’ tree in your plot represents a constant value of basal area per acre. For example, if you’re cruising with a BAF 10 wedge prism, that value is 10 square feet. The contribution of any given tree to your calculation of trees per acre, however, varies. Think of it this way: around every tree there is an imaginary circle. The radius of that circle depends on the basal area factor of the prism you used and the diameter of the tree. Small trees have very small circles around them; larger trees have very large circles. If the imaginary circle around the tree would overlap with the center of your plot, that tree appears ‘in’ through your prism. In fixed area plots you multiply, for example, the number of trees in a 1/100th acre plot by 100 to get an estimate of trees per acre. Not so with variable radius plots. Imagine the circles around trees in your variable radius plot are small fixedradius plots. A tree in a very small plot would represent a much higher estimate of trees per acre than a tree in a large plot.
Periodically, we get questions from Plot Hound users who are surprised by what seem like ‘unreasonably high’ trees per acre estimates from their cruise report. In most cases, these high tpa estimates are the result of measuring smalldiameter trees using a relatively large basal area factor for example, cruising with a BAF 20 prism. In this context, the high estimate of trees per acre isn’t necessarily accurate, but it should be expected, because the basal area factor chosen might not have been suited for that forest. For the most accurate results, use a larger BAF value in stands with predominantly larger trees, and a smaller BAF for stands with smaller ones.
Here’s a quick example of how to calculate trees per acre from a variable radius plot. When you download your cruise data from Plot Hound, you’ll see that we’ve calculated and included the ‘Tree Expansion’ value for you. This indicates the number of trees per acre that stem represents, within its plot.
Plot Number

Sampling Method

Cruiser

Diameter (in)

Species Common Name

Species Scientific Name

Tree Expansion

1

BAF 10

Nan Pond

4

sugar maple

Acer saccharum

114.59

1

BAF 10

Nan Pond

3

sugar maple

Acer saccharum

203.72

2

BAF 10

Nan Pond

8

red maple

Acer rubrum

28.65

2

BAF 10

Nan Pond

8

red maple

Acer rubrum

28.65

2

BAF 10

Nan Pond

9

red maple

Acer rubrum

22.64

2

BAF 10

Nan Pond

4

american beech

Fagus grandifolia

114.59

3

BAF 10

Nan Pond

19

red maple

Acer rubrum

5.08

3

BAF 10

Nan Pond

8

red maple

Acer rubrum

28.65

3

BAF 10

Nan Pond

8

american beech

Fagus grandifolia

28.65

The expansion factor equation for a given tree using a variable radius plot is BAF / basal area for the stem, or,
10 / (0.005454 * dbh2)
Then, we calculate the total TPA in each plot  by adding the expansion factor for all trees within a plot. In this example, we have:
Plot 1: 114.59 + 203.72 = 318.31 TPA
Plot 2: 28.65 + 28.65 + 22.64 + 114.59 = 194.53 TPA
Plot 3: 5.08 + 28.65 + 28.65 = 62.38 TPA
Because plot 1 had smaller trees in it, the trees per acre estimate for plot 1 is much higher than the other plots. When they are measured, they represent a large contribution in terms of trees per acre.
Then we average the TPA from each plot to get the average trees per acre for the stand  in this case, 191.74 trees per acre.
The basal area is much easier to calculate. It’s simply the basal area factor used multiplied by the number of trees in each plot.
Plot 1: 10 * 2 trees = 20 ft2
Plot 2: 10 * 4 trees = 40 ft2
Plot 3: 10 * 3 trees = 30 ft2
The average basal area for the stand is 30 ft2 per acre.
Variable radius plots are a quick and simple way to record inventory, which makes them very appealing. Just remember: it’s worth taking a minute to think about the forest type you’re cruising before you grab your prism and head to the woods. Using the appropriate basal area factor will help you get the most accurate representation of your forest from your cruise.