### 13, 14

```POINT SAMPLING
OR VARIABLE PLOT
CRUISING
Establishing Plots – Point Sampling
A cruise method where the sample trees are selected proportional to their
basal area. Thus larger trees sampled in greater proportions.
Fixed angle projected from plot center to determine ‘IN’ trees
As we learned before, Basal Area in square feet in expressed as below with
DBH in inches
Play video
Procedure
• The basal area factor (BAF) selected needs to yield an average of 4
to 8 trees per point.
• Smaller BAF will tally more trees per point, larger BAF will tally
fewer. In other words, use larger BAF for larger trees. Western
softwoods might use 20 to 60.
• In Kentucky, a BAF of 10 usually fits.
• Use only one BAF for a particular stratum. Just like the way we
don’t vary the plot size in fixed plot cruising.
Basal Area Factor (BAF)
Larger
trees
counted
“IN” at
longer
distances
Basal Area Factor
• indicates the number of square feet of basal area/acre each "in"
(measure) tree represents.
Smaller BAF causes smaller trees to be “IN” further from the sample point.
Which trees to tally?
Notice ‘hidden’ tree
How many points? Rule of Thumb
• If area in acres is: Number of points should be:
• Less than 10: 10
• 11-40: 1 per acre (this fits our lab area)
• 41-80: 20 + 0.5 * (area in acres)
• 81-200: 40 + 0.25 * (area in acres)
Basal Area Factor (BAF)
• Each sample tree, regardless of DBH, represents the same basal
area per acre for a given critical angle. This constant is the basal
area factor (BAF) of the angle gauge.
• In fixed area sampling, when using circular plots, the plot radius is
fixed for a plot of a given size. For example, the plot radius for a
fifth-acre plot is 52.7 feet. Each tree, regardless of size, on a fifthacre plot is associated with a plot radius of 52.7 feet.
Common BAF and PRF used in the United States
BAF
k
PRF
Can use to
calculate limiting
distance to
determine ‘IN’
trees
Which means:
For each inch of DBH, a tree can be 2.75 feet from the point to still
be included in the point’s tally.
Limiting Distance
• Since a basal area factor of 10 has a plot radius factor of we know
that any tree farther away than 2.75ft * DBH from our point center
will be considered out.
• We measure the distance from point center to the middle of the
tree (not the point facing side)
Limiting Distance
Variable Plot
Another way of looking at it
is as a multiplot.
Each tree has its own plot,
whose size is dependent on
the diameter of the tree
Those trees whose plots
overlap the center point get
measured.
How many trees at this
point will be tallied?
Slope Limiting Distance
• 1. Measure the diameter to the tenth of an inch
• 2. Determine the horizontal limiting distance from the face of the tree
(HLD = PRF X DBH)
• 3. Determine the percent of slope from the face of the tree at DBH to
where the wire pin or wooden stake penetrates the ground.
• 4. If the slope is 10% or greater, correct the horizontal limiting distance to
slope limiting distance (SLD). To obtain the slope limiting distance,
multiply the horizontal limiting distance by the appropriate slope
correction factor (SCF). (SLD = HLD X SCF)
• 5. Use a tape graduated in tenths of feet to measure the distance from
the face of the tree at DBH to plot center. The plot center is where the
wire pin or wooden stake enters the ground. These are two exact points
that can be measured "to" and "from". If the measured distance is equal
to or less than the slope limiting distance, the tree is "IN" and is sampled.
If no slope correction is needed, the horizontal limiting distance is
compared to the measured distance.
Slope Limiting Distance
Slope Correction Factor X Horizontal Limiting Distance = Slope Limiting Distance
SCF X HLD = SLD
Slope Correction
POINT SAMPLING
TOOLS
Cruise Angle – 4 BAFs, \$10
Cruiser’s Crutch
• 4 BAFs
• Compensates for slope
• ~\$30
Cruise Gauge App – >1 BAF, \$10
iBitterlich
Laser – corrects for slope, > 1 BAF, \$1500
Panama Basal Area Angle Gauge – 1 BAF, \$40
Relaskop – corrects for slope, > 1 BAF, \$1800
Thumb as an angle gauge
Let thumb width = 0.85”
Eye to thumb distance = 25”
k 
Diameter

0 . 85
 0 . 034  gauge _ constant
25 . 0
BAF  10890  k
2
 10890  ( 0 . 034 )  12 . 59
2
BAF = 12.59 ft2/acre
Try this at home
Prisms – easily lost, 1 BAF, \$20 to \$70
Ways to hold a prism
Procedure
• Looking through the prism
Procedure
Correct Positioning - Point Sampling
“IN” Trees
(determined then measured)
Fixed Plot
Variable Plot
Problem Trees
• Forked Trees - Use measurement rules to determine if measuring
one or two trees and to determine diameter. Then calculate limiting
distance.
• Leaning Trees - Angle gauges are always used by looking at the
diameter of a tree at breast height. When a tree is leaning to the
left or to the right, as viewed from point center, the angle gauge is
tilted so it is oriented along the axis of the tree rather than
vertically. If the tree is leaning toward or away from point center,
the angle gauge is held as it would be for a vertical tree. If a limiting
distance calculation is required for a leaning tree, the distance from
point center to the tree is measured to the center of the tree at
breast height, just like it is for vertical trees.
Problem Trees
• Down trees -- Trees of this nature are determined to be "in" or "out"
depending upon the location of DBH in relation to the plot center
and the appropriate limiting distance. That is, all measurements are
made between the plot center and DBH and the tree is "in" or "out"
regardless of root location, etc.
• Hidden trees -- It is possible that a tree or some other object
obscures the view of a tree behind it. A cruiser must be careful to
recognize this possibility and check to see if there are any hidden
trees which could be "in" trees. If there is an obscured tree which
might be "in", the cruiser moves away from point center in a
direction perpendicular to the direction to the tree just far enough
to be able to clearly see the tree at breast height. The same rules
then apply as for any other tree.
• Distant Large Trees
Null Plots
• Must be tallied as having no trees for correct expansion
factor to apply to whole site.
Boundary Points –
Half points
The simplest method for
dealing with boundary points
is also the most prone to
bias. Basically, an imaginary
dividing line is drawn through
the point center in such a
way it does not cross the
boundary. Only those trees
whose center point is on the
side of the line away from
the boundary are considered.
Since this represents only
half a regular point, every
tree that is "in" is recorded
twice.
Boundary Points –
Quarter points
If a point center falls near a
corner or other area where
even a half point is not
possible, the quarter point
method can be used. This
method is basically the same
as the half point method
except two imaginary lines
extend at a right angle from
the point center in such a
way that they do not cross
the boundary. The only trees
considered are in the area
between the two imaginary
lines. Since this represents
only a quarter of a point,
every tree that is "in" is
recorded four times.
Boundary Points Mirage Points
1. Establish plot
2. Measure all trees within
the plot that are in the unit
3. Measure distance from
plot center to boundary
4. Set mirage plot center on
the same line at an equal
distance outside of unit
boundary
5. Establish a second plot of
equal size from mirage plot
center
6. Rerecord all trees in the
mirage plot which are also in
the original plot
Mirage points should not be used where the boundary
is curved or irregularly shaped. In addition, someone
must be able to actually stand at the mirage point
center. What situations would exclude the use of this
type of point?
Boundary Points Walkthrough points
Least Biased and Easy to use
Works for curvy boundaries
For any tree that is "in",
measure the distance from
the point center to the tree
then measure that same
distance beyond the tree. In
other words, walk through
the tree the same distance
the tree is from point center.
If the ending point is outside
the boundary the tree is
recorded a second time. It
also works even if a person
can't go beyond the
boundary.
Point Sampling Summary
1.
It is not necessary to establish a fixed plot boundary; thus greater
cruising speed is possible.
2. Large high-value trees are sampled in greater proportions than
smaller stems.
3. BA and volume per acre may be derived without direct
measurement of stem diameters.
4. When volume-per-acre conversions are developed in advance of
fieldwork, efficient volume determinations can be made in a
minimum of time. Thus the method is particularly suited to quick
cruises.
5. Does not work well in heavy underbrush.
POINT SAMPLING
Calculations
Basal Area per Acre
• BA per acre = (total trees tallied/no. of points) X BAF
• Sum total for cruise and also sum by species
• (93/12) X 10 = 77.5 sq ft per acre
Frequency of stems tallied by DBH and Height classes from 12 point samples
BAF = 10
Height (no. of logs)
DBH(in.)
1
2
10
20
7
12
8
25
7
40
14
10
5
15
16
4
7
11
46
19
93
Total
28
3
Total
27
Trees per acre – single tree example
•.oo5454 X DBH2 = ft2 Area of tree
•If DBH = 12 then
•.005454 X 144 = .785 ft2 area for that tree
•BAF / ft2 Area of tree = trees per acre
•Using a BAF of 10
•10 / .785 = 12.7 trees per acre represented by
each 12 inch DBH tree
Trees per Acre
• Trees per acre = no. trees tallied X per-acre conversion factor
--------------------------------------------------------total no. of points
• Must be calculated for each
Tree size then summed for entire
tract
Trees per acre - Example
Frequency of stems tallied by DBH and Height classes
Height (no. of logs)
DBH(in.)
1
2
10
20
7
12
8
25
7
40
14
10
5
15
16
4
7
11
46
19
93
Total
•
•
•
•
•
28
3
Total
27
10-in. class = 27(18.35)/12 = 41 trees per acre
12-in. class = 40(12.74)/12 = 42 trees per acre
14-in. class = 15(9.35)/12 = 12 trees per acre
16-in. class = 11(7.16)/12 = 7 trees per acre
Total
= 102 trees per acre
Volume-Factor Approach (Part 1)
• Create a table of the calculations from previous slide
Board-foot volume by 16-ft logs
DBH(in.)
1
2
3
10
39
63
12
59
98
127
14
141
186
16
190
256
Board-foot volume per acre
Height (no. of logs)
• 18.35 X 39 = 716
• And so on 
DBH(in.)
1
2
3
10
716
1156
12
752
1248
1618
14
1318
1739
16
1360
1833
Volume-Factor Approach (Part 2)
Board-foot volume per acre
Height (no. of logs)
DBH(in.)
1
2
3
10
716
1156
12
752
1248
1618
14
1318
1739
16
1360
1833
Volume per acre = (20 X 716 + 7 X 1156
+ 8 X 752 + 25 X 1248 +7 X 1618
+10 X 1318 + 5 X 1318
+ 4 X 1360 + 7 X 1833)
/12 points = 9258 board feet per acre
Volume/Basal-Area Ratios Approach (Part 1)
Basal Area = .005454 (DBH)2
Board-foot volume by 16-ft logs
DBH(in.)
1
2
10
39
63
12
59
98
14
16
Basal Area by 16-ft logs
3
DBH(in.)
1
2
3
10
.545
.545
127
12
.785
.785
.785
141
186
14
1.069
1.069
190
256
16
1.396
1.396
For 10 inch, 1 log tree the ratio = 39/.545 = 72
Populating the table with the remaining calculations…
Board-foot volume per sq ft of basal area by 16-ft logs
DBH (in.)
1
2
3
10
72
116
12
75
125
162
14
132
174
16
136
183
Volume/Basal-Area Ratios Approach (Part 2)
Board-foot volume per sq ft of basal area by 16-ft logs
DBH (in.)
1
2
3
10
72
116
12
75
125
162
14
132
174
16
136
183
Volume per acre = (sum of ratios/no. of trees) X BA per acre
Sum of ratios =
20 X 72 + 7 X 116 + 8 X 75 + 25 X 125 + 7 X 162 + 10 X 132 + 5 X 174 + 4 X 136 + 7 X 183 = 11126
Recall BA per acre was the easy calculation at the beginning of all this –
BA per acre = total trees tallied/no. of points X BAF = 93/12 X 10 = 77.5 sq ft per acre
Volume per acre = 11126/93 X 77.5 = 9272 bd ft per acre
Differs from 9258 found earlier due to rounding errors.
Catch all that?
```