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FOREST SERVICE HANDBOOK
ROCKY MOUNTAIN REGION (R2)
DENVER, CO
FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
Supplement No.: 2409.12-2014-2
Effective Date: 6/18/2014
Duration: This supplement is effective until superseded or removed.
Approved: BRIAN FEREBEE, Deputy Regional Forester Date Approved: 06/06/2014
Posting Instructions: Supplements are numbered consecutively by title and calendar
year. Post by document; remove the entire document and replace it with this
supplement. Retain this transmittal as the first page(s) of this document. The last
supplement to this title was 2409.12-2014-1 to 2409.12_10.
New Document
2409.12_30
Superseded Document(s)
2409.12_30 (Supplement
by Issuance Number and Effective Date
2409.12-2008-3, 5/13/2008)
9 Pages
9 Pages
Digest: In order by code, summarize the main additions, revisions, or removal of
direction incorporated in this amendment.
35 – Removes using comparison with reconnaissance plots for final cruise.
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
2409.12_30
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
33 – SAMPLE-TREE WITH COMPLETE TALLY
33.11 – Operational Features
Mark sample trees in the following manner to help with sample location and
identification during presale inspection or check-cruises:
1. Paint a continuous band around the tree at about eye level.
2. Paint the sample number legibly.
3. Paint the cruiser ID legibly.
4. Identify with flagging.
Sample tree cruising often includes breaking individual species into sampling strata
based on DBH-groups. Expect that some trees measured as samples may have a DBH
just slightly different from the estimate made when the tree was tallied, and just outside
the strata limit. When this happens use the following procedure to maintain the random
and unbiased nature of the sample process:
In all cases, keep a sample tree in the strata it was originally called in. Do not skip
the tree or make other adjustments when it's taped DBH is outside the strata limits.
These trees represent other tallied trees that may have been called outside their
"true" DBH-group. Their effect will be to increase strata CV, usually by a very slight
amount. If a follow-up crew will be measuring the samples, be sure to mark the
sample trees in a way that indicates their "called" strata.
34.21 – Sample Plot Location and Monumentation of Plots and Trees
Identify plot centers with a firmly implanted solid stake. Do not use a wire pin. Indicate
the plot center by marking the top of the stake with an indelible "X" or a nail. Use a grid
system based on a random start to locate plot centers on the cruise map.
Use the Mirage method as described below and in exhibit 01 when fixed plots land so
their boundary would overlap outside the sale area or into a different cruise stratum. As
shown, measure the distance to the boundary, B, and establish a correction plot center
by going this distance beyond the boundary. Tally each tree in the shaded portion of
exhibit 01 twice in the sample.
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
34.21 - Exhibit 01
Mirage Method When Used In Conjunction With Fixed Area Plots
If point sampling is used, although plot size varies with tree diameter, overlap is easily
detected; it exists when the radius of the plot associated with the tree exceeds the
distance B, from the sample point to the boundary. In point sampling field application,
making use of the mirage method, one need not actually determine whether overlap
exists; it is only necessary to proceed the distance B out from the boundary, sight back
toward the forested area with the angle gauge (prism, relascope, and so forth) and tally
all qualifying trees from the correction point. Of course, if overlap is present, certain
trees will be the same ones tallied from the original sample point. If there is no overlap,
no trees will qualify from the correction point.
Do not tally a tree from a correction point unless it has first been tallied from the sample
point. Only trees inside the unit are tallied from the correction point.
Exhibit 02 illustrates the use of the mirage method. If the plot boundary overlaps both
sides, and also completely overlaps the corner itself, a total of three correction plots are
needed. If the plot boundary overlaps both sides, but not the corner, establish two
correction plot centers D and D2. From each correction plot center tally those trees
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
falling inside the cruise area boundary. Two sets of trees will be tallied twice. Note:
When three correction plots are established (four total plots), some trees will be tallied
only once, some twice, some three times, and some four times.
34.21 - Exhibit 02
Mirage Method
34.22 – Establishing Plot Boundaries
Use the slope corrections factors shown in section 91, exhibit 02, regional supplement.
35 – POINT SAMPLING
The 3PPNT is an approved cruise method that works well in sales with low value forest
products, where all that is needed is a reliable estimate of the volume. The cruise
method is a two-stage sampling system, (1) select sample trees in proportion to tree
basal area in the sample point first stage, and (2) make a 3P estimate of the point in the
second stage.
In order to know how many plots are needed, a recon cruise should be done to
determine the CV of the timber. When that is known, it can be determined how many
total plots are needed and how many of those total plots need to be measured. A KZ
value can be arrived at to get the correct ratio of total plots and measure plots. Grid the
total number of plots on a photo or map of the cutting units. Establish the plot center
and determine how many trees are in the variable plot factor. An estimate is made of
the average tree height to arrive at an estimated volume per acre on that plot. When
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
the predicted volume per acre equals or exceeds the random number, it becomes a
measure plot.
The process to arrive at estimated plot volume is:
Pcf = BAF x #T x
H
3
Where,
Pcf = cubic foot volume per acre prediction for ith plot
#T = number of trees
H
 1 / 3 Total Height Average
3
Instructions for Matrix:
The only part that will be in the matrix before determining the number of plots for both
stages will be the range of 3P errors.
Plot Error
# Of Plots
3P Error
# Of Measured
Plots
10
12
14
16
Plot error is determined by taking square root of the desired error squared minus the 3P
error.
Plot error =
=
=
302  102
800
28.3
The number of plots is calculated by multiplying the t factor of 2 times the CV (obtained
from the recon cruise) divided by the plot error and squaring it. A CV of 100 is used in
the following sample calculation.
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
n
t 2CV 2 (tCV ) 2 (2 x100) 2 40,000



 49.94  50
E2
E2
28.32
800.89
The number of measure plots is done the same way except the 3P error and cruiser CV
are used.
n
t 2CV 2 (tCV ) 2 (2 x30) 2 3600



 36
E2
E2
10 2
100
Solve for all the combinations and finish filling in the matrix.
Plot Error
# Of Plots
3P Error
# Of Measured
Plots
28.3
50
10
36
27.5
53
12
25
26.5
57
14
18
25.3
62
16
14
Select the one that will take the least amount of time.
BAF = Basal Area Factor
T
= Number of trees counted on ith plot
H
= Estimated average height of counted trees on ith plot
The variable of interest at the first stage is volume per acre while the variable of interest
in the second stage is the measured to predicted ratio.
The predictions are made in cubic feet. The easiest way to do a 3PPNT cruise is to use
a field data recorder. FSCruiser will calculate the volume per acre prediction just by
entering the number of trees and an average height.
A matrix is used to arrive at a combination of total plots and measure plots. After
analyzing the combinations, choose the most efficient one.
Given:
Volume per acre CV = 100%
3P cruiser CV
= 30%
Desired error
= 30%
Plot Error
# Of Plots
28.3
50
27.5
53
26.5
57
25.3
62
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
3P Error
# Of Measured
Plots
10
36
12
25
14
18
16
14
The total desired error must be divided up between the plot error and 3P error. A good
place to start is approximately 1/3 of total error allocated to the 3P portion.
Once the number of plots is known, the KZ must be calculated.
Given:
The option with 57 total plots and 18 measure plots was selected. The recon
cruise showed there was an average of 6 trees per plot using a 5 BAF.
6 trees per plot x 5 BAF = 30 square feet basal area
1/3 total height = 12 feet
30 square feet x 12 feet ht. = 360 cubic feet per acre average
The sum of the KPIs for the sale = 360 x 57 plots = 20,520 cubic feet
20,500
 1138 ( KZ value)
18
By the time the cruise is done, the computer program will select a measure plot
approximately every 1138 cubic feet.
35.21 – Sample Point Location and Monumentation of Points and Trees
Establish map locations and monument point centers in the same fashion as described
for plot centers in section 34.21.
Use the Mirage method as described in section 34.21.
35.22a - Assessing Borderline and Other Questionable Trees
The parent text prescribes measuring limiting distance to the face of the tree. Data
recorder routines for limiting distance are based on this measurement, not on the
distance to the tree center. Section 91, exhibit 02 (regional supplement) provides tables
of factors to use in hand calculations for limiting distance.
37.24 - Calculating Sample Size
The following section provides a guide for determining the number of samples needed
for the Fixed-Area Plot with 3P Subsample Cruising Method. The process involves two
basic steps:
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
1. Based on precruise data, build an array showing a practical range of
combinations for fixed-plots versus 3P sample trees.
2. Select the most efficient combination based on cruising costs and other
factors.
The following example illustrates the specific steps and calculations.
1. Given:
a. Presale measurement sale, conifer 3.5 MMBF (7000 Ccf), targeted
sampling error of 20 percent.
b. Estimated 3P CV is 25 percent.
c. Estimated 3P sampling error of 8 percent.
d. Estimated plot CV is 65 percent.
e. t = 2 for 95% probability.
2. Determine the desired sampling error for the sale as a whole.
3. Estimate the error for one of the sampling methods. 3P error is generally the
more easily estimated of the two errors. Use data from past cruises to estimate
the 3P error and CV. Display the error in the first row of an array, along with
several increments above and below the estimated error.
STEP-2
3P ERROR
7.0
7.5
8.0
8.5
9.0
STEP-3
NUMBER OF 3P
SAMPLE TREES
51
44
39
35
31
STEP-4
PLOT ERROR
18.7
18.5
18.3
18.1
17.9
STEP-5
NUMBER OF
PLOTS
48
49
50
52
53
4. Calculate the number of 3P samples needed to meet the estimated 3P error,
and then repeat this step for the other increments of 3P error. Display the
number of samples below the corresponding error.
3P Sample Trees  n 
(t ) 2 (CV ) 2 (2) 2 (25) 2

 39
E2
8.0 2
Region 2 Supplement: 2409.12-2014-2
EFFECTIVE DATE: 06/18/2014
DURATION: This supplement expires 5 years from the effective date unless superseded or removed
earlier.
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FSH 2409.12 – TIMBER CRUISING HANDBOOK
CHAPTER 30 – CRUISING SYSTEMS
5. Use the sale sampling error and estimated 3P error to calculate the fixed plot
error. Sample calculations for the mid-point 3P error are shown below:
Plot Error  ( Sale Error ) 2  (3P Error ) 2  (20.0) 2  (8.0) 2  336  18.3
6. Use past cruise data or reconnaissance information to estimate the CV for the
plot samples. Calculate the number of plots needed for each plot error shown in
the array.
(t ) 2 (CV ) 2 (2) 2 (65) 2
Fixed Plots  n 

 50
E2
(18.3) 2
37.43 - Calculating Sample Size
The example in the parent text is for t = 1. The following example illustrates how to
determine sample size for t = 2, which is the standard for tree measurement sales.
Definitions for the variables include:
n = total samples (count points plus measure points)
k = measure points
CV = coefficient of variation for volume/basal-area ratio (V-bar)
E = sale sampling error
r = ratio of cost of measuring a point to the cost of counting a point.
Step 1: Determine the ratio for the cost of measuring a point divided by the cost of
counting the point, and the value for estimated CV and target sale sampling error.
Values for the example are:
CV = 60 percent
E = 10 percent
r = 1.33
Step 2: Calculate the number of count points, k.
Number of count points  k 
(t ) 2 (CV ) 2  (0.433

 (2) 2 (60) 2  0.433

0
.
25
 0.25   90



2
2 
E
(10.0)  1.33
r



Step 3: Calculate the total number of points, n.
Total number of points  n  k (1.732) r  (90)(1.732)( 1.33 )  179.76  180 points