United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

Research Paper

RMRS-RP-60

November 2006

Comparison of Combinations of 

Sighting Devices and Target Objects for 

Establishing Circular Plots in the Field

Sylvio Mannel

Mark A. Rumble

Maribeth Price

Thomas M. Juntti

Dong Hua
Mannel, Sylvio; Rumble, Mark A.; Price, Maribeth; Juntti, Thomas M.; and Hua, Dong. 2006. Comparison 

of combinations of sighting devices and target objects for establishing circular plots in the field. Res. 

Pap. RMRS-RP-60. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain 

Research Station. 5 p.

Abstract—Many aspects of ecological research require measurement of characteristics within plots. 

Often, the time spent establishing plots is small relative to the time spent collecting and recording 

data. However, some studies require larger numbers of plots, where the time spent establishing the 

plot is consequential to the field effort. In open habitats, circular plots are easily established using 

a rope or tape. In tall or dense vegetation, however, considerable time can be spent ensuring that 

measures of plot radii are straight-line measurements. To rapidly establish fixed-radius plots in the 

field, common forest survey techniques can be used with a target object calibrated to the desired 

size of the plot. Although mentioned in past publications, the accuracy of establishing plots with 

these methods has not been evaluated. We tested the accuracy and precision in establishing fixedradius plots using different sighting device/target object combinations. A laser rangefinder aimed 

at 10.2-cm PVC pipe was most accurate and precise, but expensive, and required careful handling. 

Wedge prisms used with a 10.2-cm PVC pipe or cylinder were accurate, precise, inexpensive, and 

easy to use.

The Authors

Sylvio Mannel is an Assistant Professor, Mathematics and Science Department, Oglala Lakota 

College, Kyle, SD.

Mark A. Rumble is a Research Wildlife Biologist with the USDA Forest Service, Rocky Mountain 

Research Station, Rapid City, SD.

Maribeth Price is an Associate Professor in the Department of Geology and Geological Engineering, 

South Dakota School of Mines and Technology, Rapid City, SD.

Thomas M. Juntti is a Biological Technician with the USDA Forest Service, Rocky Mountain Research 

Station, Rapid City, SD.

Dong Hua is a Research Associate at ECO-MCS Lab, Institute des sciences de l’environment, Universit 

du Quebec Montreal, Case postale 8888, Succ. Centre-Ville Montreal, QC H3C 3P8, Canada.

Cover photos: View through a 10 BAF prism of 10.2-cm PVC pipe (top and lower 

right). Blue and red bands are at specific to the radius of circular plot. When 

the offset blue band in the prism aligns with the red band, the plot boundary is 

directly beneath the prism. A field technician demonstrates the field application 

(lower left) of the prism and target device.

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Contents

Introduction.............................................................................................................1

Materials and Methods.............................................................................................1

Results......................................................................................................................3

Discussion................................................................................................................4

Laser Rangefinder..............................................................................................4

Wedge Prism.....................................................................................................4

Angle Gauge .....................................................................................................4

Range Fork........................................................................................................4

PVC Pipe and Cylinder......................................................................................4

Management Implications........................................................................................5

References ...............................................................................................................5

Acknowledgments

We thank D. Baldwin for his creative ideas during the development of the range fork. This research 

was supported by NASA Food and Fiber Applications of Remote Sensing Program, Grant # NAG13-

99021, South Dakota School of Mines and Technology; USDA Forest Service, Rocky Mountain 

Research Station; and Oglala Lakota College. Dr. W. Shepperd and Dr. J. Squires provided helpful 

comments to this manuscript.

USDA Forest Service RMRS-RP-60. 2006 1

Introduction

Many natural science studies use plots with identifiable boundaries from which to collect measurements. 

Sometimes researchers need to establish a large number 

of plots where the time spent sampling within the plot 

is relatively short compared to time spent establishing 

the plot. Examples include characterizing vegetation 

for reference data when developing predictive models 

from aerial photographs or satellite images (Mannel 

and others 2006), or intensive sampling to characterize spatial patterns of vegetation surrounding items of 

particular interest such as a nest.

Circular plots have the lowest edge-to-area ratio, 

are prevalent in the literature, and may be less biased 

compared to plots of other shapes (McKelvey and others 

2002). Typically, a rope or tape measure is secured to 

the plot center and the circumference or plot boundary 

is delineated (Cox 1990; Lounsbury and Aldrich 1986). 

Establishing fixed-radius plots using ropes or tapes is 

easy in grasslands and open areas. But in tall or dense 

vegetation, considerable time can be expended ensuring 

that the rope or tape measure is a straight line (Lounsbury 

and Aldrich 1986).

During a study relating satellite images to field plots, 

we encountered the need to establish a large number 

of fixed-radius plots in forest vegetation that were 

georeferenced at the center. We used a wedge prism 

and target object to establish fixed-radius plots. While 

evaluating the accuracy of this method, we encountered 

some alternative methods that used wedge prisms or 

angle gauges to establish the boundaries of circular plots 

(Korhonen 1979; Nyland and Remele 1975; White and 

Lewis 1982). Despite the ease associated with these 

methods for establishing circular plots, we had not 

seen them applied in the scientific literature nor did we 

find any papers that made accuracy assessments of the 

plot boundaries estimated using these methods. In this 

paper, we evaluate the accuracy and precision of two 

sighting devices in conjunction with three target objects 

for establishing the boundary of fixed-radius plots.

Materials and Methods

Wedge prisms are commonly used for variableradius plots to quantify forest vegetation (Bell 1993; 

Moorhead 1990; Varnedoe and others 2000). The user 

holds the prism at a comfortable distance from the eye 

toward a tree while looking through the prism and over 

the prism. The image viewed through the wedge prism 

(typically a tree) is displaced to the side of the image 

viewed over the prism, and if the images overlap, the 

item is included in the variable-radius plot. Using this 

technique, the larger the object (typically tree diameter), 

the further it can be from the prism and be included in 

the variable-radius plot. Angle gauges are viewed at a 

distance from the observer’s eye that is maintained by 

string or lamp chain held in the teeth of the observer 

while extending the arm. If the object viewed extends 

beyond the gap in the angle gauge, it is included in the 

variable-radius plot. For each of these sighting devices, 

the investigator can calculate a plot radius associated 

with each object that was measured.

Wedge prisms are commercially available in 5-, 10-, 

or 20 ft2/ac English basal area factor (BAF) and 2-, 3-, or 

5 m2/ha metric BAF. For our application, we solved the 

equation to calculate the plot radius using the following 

formula for English BAF wedge prisms or angle gauges: 

d= 

r 2 × 4BAF

43560 − BAF where d represents the diameter or 

width of a target object and r represents the plot radius. 

We constructed target objects for which d corresponded 

Comparison of Combinations of Sighting Devices and Target 

Objects for Establishing Circular Plots in the Field

Sylvio Mannel

Mark A. Rumble

Maribeth Price

Thomas M. Juntti

Dong Hua
2 USDA Forest Service RMRS-RP-60. 2006

to a specific plot radius. We note here that the units of 

r and d can be either English or metric; however, they 

must be consistent.

We tested the accuracy of wedge prisms and angle 

gauges for establishing fixed-radius plots using four 

target objects. Three of the target objects we developed 

were a range fork, a cylinder, and horizontal discs. The 

two-pronged fork was constructed from 3.8-cm PVC 

pipe with d measured from the center of each prong so 

that the prongs would completely overlap at the correct plot radius (fig. 1A). The cylinder was constructed 

from two 1.9-cm plywood discs of diameter d with 

brightly colored plastic stapled around the circumference 

(fig. 1B). The fourth target object, a 10.2-cm PVC pipe 

(fig. 1C), had two bands of 5.1-cm duct tape of differing colors at the specified distance d apart (Nyland and 

Remele 1975, White and Lewis 1982).

We used each target object and sighting object to 

establish plot boundaries of radii 9.22 m, 11.34 m, and 

13.41 m. The 11.34 m fixed-radius plot represented a 

0.04 ha plot (James and Shugart 1970) that has been 

used extensively in studies of avian ecology in forested 

environments (Noon 1981). At each plot radius, we 

also used a laser rangefinder (Impulse laser rangefinder 

user’s manual, 1998, Technology Inc., Englewood, CO) 

aimed at the PVC pipe.

We placed the target object at the center point of 

the desired plot and laid eight measuring tapes on the 

ground at 45° incremental compass directions. Four 

observers used the wedge prism and angle gauge with 

each target object, and the laser rangefinder and PVC 

pipe to estimate the plot boundary. When each observer 

indicated the plot boundary, we used a string and plumb 

bob from the sighting device to measure the estimated 

plot boundary on the tape.

We used analysis of variance (SPSS 2001) to evaluate 

the sources of variation from sighting devices, target 

objects, plot radii, and observers. Because of significant 

Figure 1. A. View of the fork target 

object through a wedge prism. The 

cutout shows the deflection of the 

forks and how they line up to indicate 

the correct plot radius. B. Cylinder 

constructed of plywood and brightly 

colored flexible plastic with diameter 

d such that when the deflected edge 

just touched the edge viewed over 

the prism it indicated the correct plot 

radius. C. A 10.2-cm PCV pipe with 

brightly colored duct tape spaced at 

distance d, which overlaps at the 

correct plot radius.
USDA Forest Service RMRS-RP-60. 2006 3

interaction among sighting device and target objects, 

we combined these treatments into six sighting device 

and target object combinations. Combining sighting 

devices and target objects into one treatment provided a 

balanced analysis. For our analyses, observers were the 

experimental unit. We then used analysis of variance to 

test for equality among the sighting device/target objects, 

plot radius distance, and observers. The response variable for tests was deviation between the observed and 

calculated plot radii. Tests were considered significant 

at α≤0.05. Precision is defined as the reciprocal of the 

standard error (Steel and Torrie 1980) associated with 

each sighting device and target object.

Results

No differences (P=0.48) were evident among observers in deviations from calculated plot radii using the 

sighting device/target objects. Significant differences 

were evident among sighting device/target objects 

(F5,15=16.2, P<0.01) and among plot radii (F2,6=15.4, 

P<0.01). The angle gauge overestimated the radius plot 

boundaries for the cylinder and PVC pipe (table 1) and 

the overestimation increased with the plot radius (fig. 

2). The laser rangefinder/PVC pipe provided the most 

accurate estimates for all plot radii. Wedge prisms provided accurate estimates of plot boundaries for all target 

objects. The interaction between sighting device/target 

object × plot radii was significant (F10,30=3.1, P≤0.01) 

and appeared to be caused by underestimation of the 

plot boundary using the wedge prism and fork.

The laser rangefinder was the most precise sighting 

device, followed by the wedge prism and the angle 

gauge. For wedge prism/range fork, angle gauge/cylinder, wedge prism/cylinder, and angle gauge/10.2-cm 

PVC pipe, the precision decreased as the size of the 

radius (plot) increased (fig. 2). Precision using the 

wedge prism/10.2-cm PVC pipe was consistently high 

at all plot radii and perhaps increased for the largest 

plot radius.

Table 1. Comparison of accuracy and precision of wedge prism, angle gauge, and laser 

rangefinder with sighting objects to establish fixed-radius plots.

Average deviation (m)

Sighting device/target object from plot radius ± SE

Angle gauge/cylinder 0.352 0.0289

Angle gauge/10.2-cm PVC pipe 0.434 0.0304

Wedge prism/cylinder 0.003 0.0174

Wedge prism/fork -0.094 0.0162

Wedge prism/10.2-cm PVC pipe 0.070 0.0164

Laser rangefinder/10.2-cm PVC pipe -0.007 0.0037

Figure 2. Deviations ± SE from the calculated plot radii for six combinations of 

sighting device/target objects used to 

establish fixed‐radius plots.
4 USDA Forest Service RMRS-RP-60. 2006

Discussion

The advantage of all of the techniques we tested was 

that the plot boundary only needed to be established for 

objects of interest that were near the boundary. Thus in 

a forest, the plot boundary only needed to be estimated 

for a few trees in each plot.

Laser Rangefinder

The laser rangefinder aimed at a 10.2-cm PVC pipe 

provided very accurate and precise estimates of the plot 

boundaries. We encountered some difficulty holding 

the laser rangefinder without movement while aiming 

it. To quickly aim the laser rangefinder, a target ≥10.2 

cm was required. Plots with large radii might require 

target objects ≥10.2 cm in diameter. Nonetheless, the 

laser rangefinder was bulky, expensive (>$2,500), and 

required careful handling under field conditions. The 

accuracy of less expensive laser rangefinders (± 1.0 m) 

or optical rangefinders is not acceptable for establishing 

plot boundaries.

Wedge Prism

The wedge prism was easy to use and provided 

accurate and precise estimates of plot boundaries. 

Each target object we evaluated had advantages and 

disadvantages (table 2). We found the wedge prism 

worked best with the cylinder. The wedge prism and 

10.2-cm PVC pipe also provided accurate and precise 

estimates for the 9.22-m radius plot. Pipes < 10.2 cm in 

diameter are difficult to see (Korhonen 1979), and we 

found it was more difficult to line up the colored tape 

rings on the PVC pipe when the plot radii were >9.22 m. 

A larger pipe could alleviate this problem (Nyland and 

Remele 1975). Since wedge prisms could be attached 

to the observer’s field jacket with a string, it was easy 

for the observer to collect and record measurements. 

One wedge prism did not have the correct refraction 

as engraved on the prism from the manufacturer. We 

don’t know how pervasive this is, but we recommend 

testing prisms with a calculated distance before taking 

them to the field.

Angle Gauge

The angle gauge was difficult to hold steady. The 

plot radii were over estimated with angle gauges and 

the associated precision was lower. The impossibility 

of focusing on a near and far object with one eye closed 

complicated the use of this sighting device. We also 

were concerned about personal hygiene associated with 

holding the lighting chain or string in our teeth when 

using this sighting device.

Range Fork

The range fork worked well with the wedge prism. 

It was easy to determine when the forks were lined 

up except with the 13.41-m radius plot. We attributed 

the ease of lining up the forks to their length. Longer 

and larger diameter PVC forks were more visible at 

greater distances. The fork also required someone to 

hold and turn the fork toward the observer as they 

moved around the plot boundary. The forks must be 

precisely perpendicular to the observer; any deviation 

from perpendicular to the observer underestimated the 

plot radius. This explains the underestimation of plot 

boundaries in our test.

PVC Pipe and Cylinder

The 10.2-cm PVC pipe and cylinder could be viewed 

from all directions, without any rotation, and could 

be used by one person in the field. The cylinder and 

10.2-cm PVC pipe could be used with a spike on the 

Table 2. Advantages and disadvantages of target objects when used with a wedge 

prism as the sighting device for establishing fixed-radius plots.

Fork PVC Pipe Cylinder

Precision1 Good Good (r ≤11.4 m) Good

Visibility Very good Good Good

Convenience Good Very good Poor

Measurements from all sides No Yes Yes

Single person application No Yes Yes

1

 Precision inverse of standard error of deviation from calculated radius.
USDA Forest Service RMRS-RP-60. 2006 5

end of a pole when data was recorded by one person. The 

wedge prism used with the cylinder was accurate and 

precise, but the cylinder was bulky and inconvenient.

Management Implications

The laser rangefinder was the most accurate and precise method for establishing fixed-radius plots. However, 

laser rangefinders are expensive and require careful 

handling. Considering cost, ease of applicability, and 

accuracy, we recommend the wedge prism as the best 

sighting device. The wedge prisms used with a 10.2-cm 

PVC pipe is recommended as an inexpensive method 

for establishing fixed-radius plots by one person. For 

plots larger than 11.34 m, the wedge prism used with 

a cylinder was accurate and precise probably because 

the target object was larger. The range fork was easy 

to disassemble and carry. However, the range fork 

required two persons in the field, one to hold the fork 

perpendicular to the other using the wedge prism—thus, 

partially negating savings in field personnel time.

The time savings associated with using a sighting 

device/target object for establishing fixed-radius circular 

plots depends on how busy the plot is. It is difficult to 

use a rope pinned at the plot center in dense timber or 

shrubs. The rope must constantly be rethreaded through 

obstructing vegetation to check the items near the plot 

boundary for inclusion. Generally, this must be done 

whether or not an object near the plot boundary needs 

to be checked for inclusion. The sighting device/target 

object, however, is easily carried around the plot and is 

only brought into use when objects of interest lie near 

the plot boundary. For establishing a large number of 

plots quickly, we recommend wedge prisms or laser 

rangefinders and ≥10.2-cm PVC pipe.

References

Bell, J. F. 1993. Log scaling and timber cruising. Oregon State 

University Book Stores, Inc., Corvallis, Oregon, USA.

Cox, G. W. 1990. Laboratory manual of general ecology. 

W. C. Brown Co., Dubuque, Iowa, USA.

James, F. C.; Shugart, H. H. Jr. 1970. A quantitative method of 

habitat description. Audubon Field Notes. 24:727-736.

Korhonen, J. 1979. One-person circular plot establishment. 

The Forestry Chronicle. 55:51-53.

Lounsbury, J. F.; Aldrich, F. T. 1986. Introduction to geographic field methods and techniques, second edition. 

Bell and Howell, Columbus, Ohio, USA.

Mannel, S.; Price, M.; Hua, D. 2006. A method to obtain 

large quantities of reference data. International Journal 

of Remote Sensing. 27:623-627.

McKelvey, K. S.; Daniel, G. W. M.; Mills, L. S.; Griffin, 

P.C. 2002. Effects of plot size and shape on pellet density 

estimates for snowshoe hares. Wildlife Society Bulletin. 

30:751-755.

Moorhead, D. J. 1990. Evaluating and regulating timber stands. 

Pages 12-21 in: Gunter, J. E., coordinator. Georgia Forest 

Landowner’s Manual. University of Georgia School of 

Forest Resources Extension Bulletin 950. http://warnell.

forestry.uga.edu/warnell/service/library/b0950/b0950.

pdf.

Noon, B. R. 1981. Techniques for sampling avian habitats. 

Pages 42-52 in: Capen, D. E., editor. The use of multivariate statistics in studies of wildlife habitat. General 

Technical Report RM-87, USDA, Forest Service, Rocky 

Mountain Forest and Range Experiment Station, Fort 

Collins, CO, USA.

Nyland, R. D.; Remele, K. E. 1975. Prism Measures distance 

for plot boundaries. Applied Forestry Research Institute 

Research Note. 17:1-4.

SPSS. 2001. User’s guide. SPSS, Inc. Chicago, IL, USA.

Steel, R. G. D.; Torrie, J. H. 1980. Principles and procedures of 

statistics, a biometrical approach. McGraw-Hill Publishing 

Company, Second edition, New York, NY, USA.

Varnedoe, L. E.; Coder, K. D.; Moorhead, D. J. 2000. 4-H 

forestry field day manual. Georgia Cooperative Extension 

Service. http://pubs.caes.uga.edu/caespubs/pubcd/4-

Hpubs/4H-forestry.htm.

White, W. E.; Lewis, C. E. 1982. Establishing circular plot 

boundaries with a wedge prism and an adjustable target 

pole. Journal of Range Management. 35:677-678.

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