1. Point Sampling or Variable Plot Cruising

2. 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

3. 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.

4. Basal Area Factor (BAF)
Larger trees counted “IN” at longer distances

5. 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.

6. Which trees to tally?
Notice ‘hidden’ tree

7. 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: * (area in acres)
81-200: * (area in acres)

8. 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 fifth- acre plot is associated with a plot radius of 52.7 feet.

9. Common BAF and PRF used in the United Statesk
PRF

10. Plot Radius Factor
Can use to calculate limiting distance to determine ‘IN’ trees

11. Plot Radius Factor = 8.696/SQRT(BAF)
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.

12. 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)

13. Limiting Distance

14. 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?

15. 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.

16. Slope Limiting Distance
Slope Correction Factor X Horizontal Limiting Distance = Slope Limiting Distance
SCF X HLD = SLD

17. Slope Correction

18. Point Sampling Tools

19. Cruise Angle – 4 BAFs, $10

20. Cruiser’s Crutch
4 BAFs
Compensates for slope
~$30

21. Cruise Gauge App – >1 BAF, $10

22. iBitterlich

23. Laser – corrects for slope, > 1 BAF, $1500

24. Panama Basal Area Angle Gauge – 1 BAF, $40

25. Relaskop – corrects for slope, > 1 BAF, $1800

26. Thumb as an angle gauge Let thumb width = 0.85”
Eye to thumb distance = 25”
BAF = ft2/acre
Try this at home

27. Prisms – easily lost, 1 BAF, $20 to $70

28. Ways to hold a prism

29. Looking through the prism
Procedure
Looking through the prism

30. Procedure

31. Correct Positioning - Point SamplingX

32. “IN” Trees (determined then measured)
Fixed Plot
Variable Plot

33. 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.

34. 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

35. Null Plots
Must be tallied as having no trees for correct expansion factor to apply to whole site.

36. 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.

37. 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.

38. 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?

39. 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.

40. Point Sampling Summary
It is not necessary to establish a fixed plot boundary; thus greater cruising speed is possible.
Large high-value trees are sampled in greater proportions than smaller stems.
BA and volume per acre may be derived without direct measurement of stem diameters.
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.
Does not work well in heavy underbrush.

41. Point Sampling
Calculations

42. 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 3
Total 10 20 7 27 12 8 25 40 14 5 15 16 4 11 28 46 19 93

43. Trees per acre – single tree example
.oo5454 X DBH2 = ft2 Area of tree
If DBH = 12 then
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

44. 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

45. Trees per acre - Example
Frequency of stems tallied by DBH and Height classes
Height (no. of logs)
DBH(in.) 1 2 3
Total 10 20 7 27 12 8 25 40 14 5 15 16 4 11 28 46 19 93
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

46. Volume-Factor Approach (Part 1)
Create a table of the calculations from previous slide
18.35 X 39 = 716
And so on 
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)
DBH(in.) 1 2 3 10
716
1156 12
752
1248
1618 14
1318
1739 16
1360
1833

47. 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 X 1156
+ 8 X X X 1618
+10 X X 1318
+ 4 X X 1833)
/12 points = 9258 board feet per acre

48. Volume/Basal-Area Ratios Approach (Part 1) Basal Area = .005454 (DBH)2
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
Basal Area by 16-ft logs
DBH(in.) 1 2 3 10
.545 12
.785 14
1.069 16
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

49. 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 X X X X X X X 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.

50. Catch all that?