A forest inventory assesses the quality, quantity, and value of trees in a forest. Inventory focused on standing timber (live timber) is called a timber cruise. Inventories are also done for other objectives, such as wildlife habitat assessment or biodiversity conservation. When there is insufficient time or resources to measure all trees in a forest inventory, sampling is performed. Sampling involves selecting and measuring a subset of trees to estimate information about the entire forest (population). Forest sampling is integral to conducting forest inventories. The trees that are measured (tally trees) are typically selected by using two popular sampling techniques: plot and point sampling. This publication will help landowners and forestry professionals become knowledgeable about forest sampling for a timber cruise, emphasizing the point sampling technique.

## Introduction

It is important for landowners and forestry professionals who work for the landowners to understand the methods to conduct forest inventories/timber cruising. Landowners who understand the basics of timber cruising can assess timber/forest resources and make informed decisions while buying or selling timber. Similarly, forestry professionals who can conduct a timber cruise can help landowners get fair value for their resources, design a better forest management strategy, and increase their credibility in the market.

## Plot Sampling

Plot sampling, also called fixed area sampling, requires tallying and measuring all the trees within an area using circular or rectangular plots of consistent size (figure 1). Tallied trees are measured for variables of interest such as diameter, height, crown width, etc. In plot sampling, the sampling probability is proportional to frequency (species occurrence).^{1} For example, if the forest has a high number of 10 in. DBH (diameter at breast height, which is 4.5 ft.) trees, the sample will be likelier to have a high number of 10 in. DBH trees. Many small trees that contribute less to a forest’s timber volume and value are likely to be sampled, which is important for wildlife habitat assessment, carbon assessment, biodiversity conservation, understanding forest regeneration, and writing forest management plans.

## Point Sampling

In timber cruising, larger-sized trees contribute more to the volume and value of a forest; therefore, a more popular sampling technique that accounts for larger-sized trees is point sampling. Point sampling (also called variable radius plot sampling, Bitterlich plot, angle-gauge plot, prism cruising, plotless cruising, and angle-count sampling) is a technique that selects trees based on size and not frequency so that sampling probability is proportional to size.^{1,2} Larger trees are more likely to be sampled than smaller trees; therefore, point sampling is a popular method for timber cruising, as larger trees contribute to merchantable volume and are of higher value. Also, the closer a tree is to the sample point/plot center, the more likely it is a tally tree.

Point sampling uses a variable radius plot rather than a fixed area plot, meaning that the area around a point/plot center that includes tally trees is variable. This variability is based on tree DBH and the angle gauge or prism used for the point sampling (table 1, figure 2a and 2b).

**Table 1.** Plot radius (feet) of various-sized trees (DBH) for common prisms with 5, 10, and 20 basal area factor (BAF).

DBH (inches) |
5 |
10 |
20 |
---|---|---|---|

1 | 3.90 | 2.75 | 2.25 |

2 | 7.80 | 5.50 | 4.49 |

3 | 11.70 | 8.25 | 6.74 |

4 | 15.60 | 11.00 | 8.98 |

5 | 19.50 | 13.75 | 11.23 |

6 | 23.39 | 16.50 | 13.47 |

7 | 27.29 | 19.25 | 15.72 |

8 | 31.19 | 22.00 | 17.96 |

9 | 35.09 | 24.75 | 20.21 |

10 | 38.99 | 27.50 | 22.45 |

11 | 42.89 | 30.25 | 24.70 |

12 | 46.79 | 33.00 | 26.94 |

13 | 50.69 | 35.75 | 29.19 |

14 | 54.59 | 38.50 | 31.43 |

15 | 58.49 | 41.25 | 33.68 |

16 | 62.38 | 44.00 | 35.92 |

17 | 66.28 | 46.75 | 38.17 |

18 | 70.18 | 49.50 | 40.41 |

19 | 74.08 | 52.25 | 42.66 |

20 | 77.98 | 55.00 | 44.90 |

Today, most point sampling uses a prism (figure 3a). A prism is a device that subtends a fixed angle of view based (figure 2a) on the basal area factor (BAF), which decides the angle the prism subtends/projects toward the target tree. Angle gauges (figure 3b) were once standard when this method was introduced in the United States in the 1950s. In point sampling, an observer sights trees at DBH from the plot center or sample point through a prism (figure 2a). Trees that are large enough (due to size or distance from the sample point) to fill the angle are tallied or measured (figure 2a). The higher the BAF of the prism, the larger the subtended angle and the lower the number of sampled trees because a large tree is needed to fill the larger angle. BAF also decides how much basal area (cross-sectional area of trees at 4.5 ft., a measure of tree density) per acre is contributed by each sampled tree; the higher the BAF, the higher the trees per acre contributed by each tally tree. BAFs of 5, 10, and 20 are commonly used for sampling. Each BAF has a plot radius factor (PRF), which is the radius of a plot for each inch of tree diameter (table 1).

For example, the PRF for a one-inch tree viewed through a 10 prism is 2.75 ft., while a 10 in. tree has a plot radius of 27.5 ft. The plot radius for each tree is termed the limiting distance. Each tree that is within limiting distance for its size will be counted as “IN” (tallied, figure 4a) or otherwise will be “OUT” (figure 4b). If a tree is outside the limiting distance, the shifted bole will not fall within the original bole. Sometimes, it is not clear whether a tree is IN or OUT, and these trees are called borderline trees (figure 4c). Usually, the suggestion is to use a BAF that gives five to twelve tally trees per sample point.^{1} To achieve the recommended number of samples, a smaller BAF might be useful in areas with scattered smaller trees, and a larger BAF might be useful in a dense stand. Another factor in selecting the prism BAF is visibility; a 30 in. tree will be tallied within 82.5 ft from the sample point while using a 10 BAF prism; in a brushy condition, it might be hard to see a tree at that distance.^{2} The process of using a prism is detailed in the next section.

## Working Through a Prism Cruise

Before using a prism for cruising, it is necessary to decide on the number of sample points and how to locate them in the forest stand for measurements (see cruise design section below). After deciding on the location of sample points, a prism is used to determine the trees to tally/measure. Selecting the correct basal area factor prism is important and is done by choosing a few random points and using 5, 10, and 20 BAF prisms to sample trees; choose the one that gives, on average, five to twelve trees (as mentioned above) per point.

### Cruise Design

Before designing a cruise, you must decide on the number of sample points in the forest stand. A common approach is to sample 5%, 10%, or 20% of the total area, especially with plot sampling. For example, if 20% of a 20-acre stand is sampled with 1/10-acre circular plots, you will need forty 1/10-acre plots or twenty 1/5-acre plots to sample 4 acres because 20% of 20 acres is 0.2 x 20 = 4 acres.

It is not possible to do similar calculations for point sampling since the plots will be of varying size, but a similar number of prism points can be used to sample the forest.^{2,3} As a general guide, use the same number of prism points as the number of 1/5-acre plots to sample five to twelve trees at each point^{1 }and a minimum of 30 prism points in natural stands and 20 in. even-aged plantations.^{1 }There is a statistical approach to calculating the number of points required for a precise sampling based on the variability of the data and acceptable estimation error,^{1} which is not discussed in this publication.

After determining the number of sample points or prism points, the next step is to choose sample point locations in the stands. A simple random sample is sampling points that are randomly placed. A systematic sampling technique called the line-plot system is more prevalent in forestry than a simple random sample (randomly placed sampling points). The line-plot system places sample points at fixed equal distances on compass lines. For varying sampling intensities, use fixed distances between sample points and lines (table 2).

**Table 2.** Distances between lines and points for varying cruising intensities while using a 1/10-acre fixed area plot or a 10 BAF prism for timber cruising.^{1,2,3}

Distances |
Cruising Intensity |
||
---|---|---|---|

– | 5% |
10% |
20% |

Between points | 4 chains | 2 chains | 2 chains |

Between lines | 5 chains | 5 chains | 2.5 chains |

For 5% intensity (table 2), follow the steps described below:

- As an example, a forester would start at a corner of the stand (northwest corner) and go one chain (66 feet) south along the boundary of the stand to establish the first imaginary compass line (figure 5a).
- To establish the first imaginary line, the forester would go inside the stand, towards a line perpendicular to the stand boundary (east in figure 5b) and follow the line to the opposite end. Establish the center of the first point, a chain from the boundary along the line (figure 5b).
- The following point center will be four chains from the first point along the same line, and so on (figure 5c).
- The second line would be south of the first line, five chains apart (figure 5d).

### How to Use a Prism

- Hold the prism above the center of the sample point (the prism should always be above the center) and then look through it at the DBH height (4.5 ft.) of every tree around a circle (360°). The tree’s bole in the prism’s view will shift due to refraction.
- If the shifted part is within the original bole, the tree is considered IN (tallied, figure 4a).
- If the shifted part is outside the original bole, the tree is considered OUT (do not tally, figure 4b).
- Sometimes, it is not clear whether a tree is IN or OUT, and these trees are called borderline trees (figure 4c) and require measuring the distance from the plot center to the center of the tree and comparing the distance to the limiting distance (plot radius) for the trees DBH. If a borderline tree is within the limiting distance, it is IN; otherwise, it is OUT. For example, if a 10-inch tree is borderline when using a 10 BAF prism, the limiting distance is the PRF (2.75 ft.) multiplied by the DBH (10 in.). In this case, the limiting distance is 27.5 ft. So, if the distance from the plot center to the tree is 28 ft., the tree would be OUT and not be counted.
- Collect data such as species, DBH, and height (merchantable or total) for each sample point for IN trees.

### Concepts to Remember While Using a Prism

Point sampling is an excellent tool for quickly obtaining numbers on basal area, stand density, and volume to make forest management decisions. However, there are a few things that any prism user should be aware of. The prism should always be above the plot center. The person holding the prism should rotate around the plot center (figure 6a). For trees leaning to the left or right of the observer, rotate the prism so that the vertical axis of the prism is parallel to the vertical axis of the leaning tree (figure 6b). If the area’s slope is more than 15%, correct for the slope. For slope correction, rotate the prism (tilt the top) at the same angle perpendicular to the slope (figure 6c). If your line of sight is obstructed, move sideways but maintain the same distance to the tree.

### Basal Area Calculation

Point sampling is convenient for basal area calculation. Basal area is a tree’s cross-sectional area (sq. ft.) at DBH. The basal area per acre (sq. ft./acre) is the sum of all individual tree basal areas per acre and is commonly desired for forest management. In point sampling, the total basal area per acre is estimated based on the number of trees in the sample. The basal area per acre is calculated by multiplying the number of trees in a sample point by the BAF:

**basal area (sq. ft. / ac) = # of trees tallied × BAF**

For example, if you tally five trees with a 10 BAF prism at the first point, the basal area would be 50 sq. ft. per acre (table 3). We typically sample more than one point and calculate the average basal area per acre of the stand from all sample points. To do this, multiply the number of tallied trees across all samples with the BAF and divide the product by the total number of sample points. For example, if there are forty tallied trees across five sample points in a 5-acre stand with a 10 BAF prism, the average basal area of this stand would be 80 sq. ft. per acre [(40 x 10) / 5].

The average basal area per acre of the stand can also be calculated using the average of each sample point. This calculation is also helpful in exploring statistics such as standard error and confidence interval.

### Stand Density and Individual Tree Expansion Factors

Stand density is another important factor when making forest management decisions. It can be calculated using data collected from a point sample using individual tree expansion factors. Each “IN” tree represents a finite number of trees per acre (the expansion factor), which depends on the DBH and the BAF used.

The individual_{(i)} basal area of a 10-inch tree is 0.005454 x 10^{2} = 0.5454 sq. ft. For example, a 10 in. tree, identified with a 10 BAF prism, results in a TF_{i} of 16.0 trees per acre (10 / 0.005454 x 10^{2}).

Stand density for a sample point can be calculated using the sum of TF_{i} for each tree in a point.

**Stand density (trees per acre, TPA) = TF _{i=tree 1 }+ TF_{i=tree 2} + … + TF_{i=final tree}**

In table 3, summing the expansion factors for all the trees results in 102.9 trees per acre, or rounded up, 103 trees per acre. For stand density, round the results to whole numbers. Stand density can be used to calculate the per-acre volume. If there are multiple points, perform the calculations (as detailed above and summarized in table 3) for each point and then take the average across all points to calculate either stand density or basal area for the stand.

**Table 3.** Example of a variable radius plot (10 BAF) data with basal area and expansion factor calculations.

Point Number |
Tree Number |
Species Code |
DBH (in.) |
Total Height (ft.) |
Basal Area(sq. ft./ac) |
Individual Tree Expansion Factor (TF_{i}) |
---|---|---|---|---|---|---|

1 | 1 | Loblolly Pine | 8.1 | 80 | 10 | 27.94 |

1 | 2 | Loblolly Pine | 10.7 | 81 | 10 | 16.02 |

1 | 3 | Loblolly Pine | 6.9 | 60 | 10 | 38.51 |

1 | 4 | Loblolly Pine | 13.3 | 94 | 10 | 10.37 |

1 | 5 | Slash Pine | 13.5 | 93 | 10 | 10.06 |

– | – | – | – | – | 50 sq. ft. / acre |
Stand density = 103 TPA* |

*Notes:* TPA = trees per acre; TF_{i} = tree factor (expansion factor) for tree _{i}. For point sampling, the Basal Area per acre represented by each tree is the same as the BAF. *The sum is 102.9 trees per acre, rounded to the nearest whole number.

### Volume Calculation

For volume calculation, find the volume per tree using a volume table or an equation and multiply it by the expansion factor for each tree to calculate the volume per acre that each sample tree represents. Volume tables and equations can be region- or state-specific. You can search for volume tables online, but general volume tables for pines and hardwoods in the Southeast can be found in publications by Saucier et al.^{4} and Clark et al.^{5} As an example, the first tree in table 4 has 10.3 cu. ft. volume from a volume table. This value is multiplied by the expansion factor (27.94) to get 287.78 cu. ft. If there are five trees at the point, perform the calculation for all five trees and sum up the values to get the volume per acre for the first point (table 4). For multiple points in the stand and the stand average, use the calculations in table 4 for all your points and take the average. In this example, the volume table is in cubic feet for each tree; other volume tables may use different units, such as pounds or tons.

The standing volume for the plot in table 4 is 1,471.7 cu. ft. per acre. In timber harvesting operations and for forest management decision-making, volumes are represented as weight in tons. Conversion factors from cubic feet to tons are species-specific. For southern yellow pine species (softwood) for pulpwood in South Carolina, the factor is 36 tons per thousand cubic feet (MCF).^{6} The volume of 1.47 (1,471.7 cubic feet) MCF is equivalent to 52.9 tons (36 tons per MCF × 1.47 MCF = 52.9 tons). For hardwood, the conversion is 39.6 tons per MCF. Please refer to the table on page 20 of Winn et al.^{6 }for more details_{.}

**Table 4.** Example of volume per acre calculation with point sampling (10 BAF).

Point Number |
Tree Number |
Species Code |
DBH |
Total Height |
Volume Per Tree to 4 in. Top (cu. ft.)* |
Trees Per Acre or Expansion Factor |
Volume Per Acre |
---|---|---|---|---|---|---|---|

1 | 1 | Loblolly Pine | 8.1 | 80 | 10.3 | 27.94 | 287.78 |

1 | 2 | Loblolly Pine | 10.7 | 81 | 19.9 | 16.02 | 318.80 |

1 | 3 | Loblolly Pine | 6.9 | 60 | 5.7 | 38.51 | 219.51 |

1 | 4 | Loblolly Pine | 13.3 | 94 | 31.6 | 10.37 | 327.69 |

1 | 5 | Slash Pine | 13.5 | 93 | 31.6 | 10.06 | 317.90 |

– | – | – | – | – | – | – | 1471.7 cu ft. per acre |

*Volume value comes from tables 10 and 46 from Saucier et al. (1981)_{.}^{6}

## Conclusion

Point sampling is helpful for timber cruising because it is biased towards larger trees, which contributes more to the quantity and value of timber. It is also a quick way to measure basal area per acre because it does not require diameter measurements. In point sampling, there is no need to establish plot boundaries; therefore, it is faster than plot sampling. Some disadvantages are difficulty seeing trees through a prism in dense underbrush and errors in very steep slopes due to improper slope correction.

## References Cited

- Burkhart, HE, Avery TE, Bullock BP. Forest measurements. 6th ed. Long Grove (IL): Waveland Press; 2019.
- Kershaw JAJ, Ducey MJ, Beers TW, Husch B. Forest mensuration. 5th ed. Hoboken (NJ): John Wiley & Sons; 2016.
- Henning, JG, Merker DC. Conducting a simple timber inventory. Knoxville (TN): The University of Tennessee Agricultural Extension Service; 2009. E12-4915-00-009-09 09-0110 PB1780-1M-2/09. https://trace.tennessee.edu/utk_agexfores/39/.
- Saucier JR, Phillips DR, William JG. Green weight, volume, board-foot, and cord tables for the major southern pine species. GA: Research Division Georgia Forestry Commission; 1981 [accessed 2023 Oct 20]. Georgia Forest Research Paper GFRP-19. http://www.gatrees.gov/resources/publications/research-papers/GFRP19.pdf.
- Clark, A, Saucier JR, McNab WH. Total-tree weight, stem weight, and volume tables for hardwood species in the Southeast. GA: Georgia Forestry Commission, Research Division; 1986 [accessed 2023 Oct 20]. Georgia Forest Research Paper GFRP-60. https://www.frames.gov/documents/jfsp/biomass_review/clark_saucier_mcnab_1986.pdf.
- Winn MF, Royer LA, Bentley JW, Piva RJ, Morgan TA, Berg EC, Coulston JW. Timber products monitoring unit of measure conversion factors for roundwood receiving facilities. Asheville (NC): U.S. Department of Agriculture Forest Service, Southern Research Station; 2020. e-Gen. Tech. Rep. SRS-251. doi:10.2737/SRS-GTR-251.

## Additional Resources

Keene KA, Barlow B. Benefits and drawbacks to variable radius plots. Auburn (AL): Alabama Cooperative Extension Service; 2019. FOR-2062. https://www.aces.edu/blog/topics/forestry/benefits-drawbacks-to-variable-radius-plots/.

Larsen D. Forest measurement and inventory sample design. Houston (TX): University of Houston-Clear Lake. https://www.uhcl.edu/environmental-institute/texas-envirothon/documents/study-guide/forestry-how-to-use-a-prism.pdf.

Why Do Foresters “Cruise” Timber. Wildlight (FL): Rayonier; 2022. Forest Management, Forestry 101. https://www.rayonier.com/stories/what-is-a-timber-cruise-in-forestry/.