Service Forester's Handbook

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====== Use of Wedge Prism ======
The prism is a piece of a wedge-shaped rectangular glass which causes a
distortion of light, displacing the image towards the thinner edge.
It is used to estimate the basal area of a stand.

====Basal Area====

   1. Hold prism (not your eye) over the selected point at a comfortable distance from
   the eye, with the long side horizontal. Hold prism with right hand by lower part of 
   the thicker edge.
   
   2. With one eye closed, point with the upper part of the prism so as to divide the 
   tree in question at breast height. Refraction of light through the prism will cause
   the portion of the tree below breast height to appear separated. Count as 1 all of
   the trees whose figures are superimposed, as 1/2, or measure for accuracy those which
   touch only at the edge. If they do not touch each other they are not counted.
{{ :use_of_wedge_prism1.jpg |}}

   3. Turn in a circle, checking each visible tree, making sure not to count the same tree 
   twice.
   
   4. The number of trees counted, multiplied by basal area conversion factor of prism gives
   us the basal area per stand acre.
    
    BA/Acre = (Total number of trees counted X BAF of prism)/(Number of samples)
    
====Basal Area Factor.==== Set up a target exactly one foot wide. Fro an approximate 10 BAF prism,
sight about 33 feet from target. Move toward or away from target until right edge of target
(as seen in prism) jibes with the left edge of target (just above prism). Measure exact 
distance prism to target. Take several readings and use average.{{ ::use_of_wedge_prism2.png|}} 

Calculate BAF by formula:\\
BAF = (43560)/[(1+4)(D/W)<sup>2</sup>]\\ 
D is distance prism to target\\
W is width of target\\
or: BAF = (43560)/[(1+4)(D)<sup>2</sup>]\\
Where target "W"  is exactly 1 foot wide\\
or: BAF = 10890(W/D)<sup>2</sup>  \\
A close approximation\\

====Plot Radius Factor====
The distance from a sampling point to the borderline tree equals DBH times PRF. For a BAF 10.0 prism
the PRF is 2.75. A 10-inch tree times 2.75 gives a critical distance of 27.5 feet, a 14-inch tree
is 38.5 feet, etc. The number of trees per acre that each tallied 10-inch tree represents 18.35; 
each 14-inch tree is 9.35, etc.
The basic formula: PRF = √(75.625/BAF)
====Borderline Trees====
Always measure borderline trees more than a casual check on basal area. A short cut method counts
borderline trees as 1/2. 
    1. Measure horizontal distance from sample point to center of tree at BH.
    2. Get DBH. 
    3. Multiply DBH by prism PRF. When this product is more than taped distance, the tree is "In".
    
    Example: (PRF is 2.75, DBH 10.0)
    2.75 X 10.0 = 27.5 feet, taped distance is 27.2 feet; tree is "In". 
    
====Precautions====
   1. Prism must be in center of plot, not the eye. Walk around the prism; do not stand in one 
   place and move the prism around you.
   2. Always hold the face of the prism at right angel to eyesight, horizontally and vertically.
   (Except for leaning trees and when correcting for slopes).
   3. For leaning trees move prism forward then backward on its vertical axis according to the 
   inclination of the tree trunk.
   4. Correct for slope by rotating prism to the same amount of slope between the prism and the
   tree, but at right angles to the eye.
   5. If there is an object between you and the tree to be checked, move one step sideways, 
   keeping a constant distance between you and the tree.
   6. In dense strands be careful not to confuse or incorrectly associate the trunks. (If a tree 
   is "In" above the brush, it is "In" at BH). 
   7. Remember that each diameter size has its own plot radius, the radius varies directly with
   the tree diameter. Therefore, the largest and most valuable trunks are usually sampled more
   intensely than the smaller trunks.
     --The prism helps to train the eye to estimate the basal area of stands, use it. 
====Volume Per Acre====
__Volume:__ Volume is related to basal area and merchantable or total tree height. The average
basal area per acre in each height class multiplied by the volume factor gives us the volume per
acre. The factors can be for any scale- board feet by any rule, cubic feet, or cords. If the 
available factors cannot be relied upon, they can be developed as necessary.
====Volume Factors====
Estimate the volume per acre by multiplying the number of trees measured in each length class
by the following factors:*
^Pulpwood                                         ^^^Sawlogs                                                  ^^^^|
^Merchantable height^Cubic Vol.(w/bark)^Cords(w/bark)^Merchantable height1/^Int.1/4^Scribner^Doyle^Cubic(w/o bark)|
|10                 |7                 |.08          |1                    |7      |6       |4    |1.2            |
|20                 |14                |.16          |2                    |13     |11      |8    |2.0            |
|30                 |20                |.22          |3                    |18     |16      |12   |2.7            |
|40                 |26                |.29          |4                    |23     |20      |15   |3.4            |
|50                 |31                |.34          |5                    |28     |25      |21   |4.0            |
|60                 |36                |.40          |                     |       |        |     |               |
|70                 |39                |.43          |                     |       |        |     |               |
^v = 10 (sum of products/number of points          ^^^v = 100 (sum of products/number of points)              ^^^^|

* For a 10 factor prism\\
1/ Merchantable height is in 16 foot logs

====Local volume factors====
Pulpwood factors are fairly consistent. Sawlog factors are not very reliable in different localities.
The procedure to prepare local factors is as follows:
   1. Write down the sample trees according to diameter class and number of logs. (The total trees
   tallied divided by the number of points or samples.)
   2. Obtain the number of plots per acre from the table at page 54.
   3. Multiply in order to obtain trees per acre.
   4. Write down volume for each tree.
   5. Multiply to obtain volume per acre.
   6. Total volume per acre for each length class.
   7. Write down the basal area per acre (trees per plot for each length class multiplied by the
   basal area factor).
   8. Volume factor is the volume per acre divided by basal area per acre.
Refer to following example

===Basal Area Factor: 10===
^Dbh Class ^Trees per point ^^^Plots per acre ^Trees per acre ^^^Volume per tree^^^Volume per acre^^|
^          ^1-log^2-log^3-log ^               ^1-log^2-log^3-log^1-log^2-log^3-log^1-log^2-log^3-log|
|10        |0.136|0.136|      |18.349         |2.5  |2.5  |     |40   |60   |70   |100  |150  |     |
|12        |0.785|0.628|0.157 |12.739         |10.0 |8.0  |2.0  |50   |90   |120  |500  |720  |240  |
|14        |0.428|0.534|0.107 |9.355          |4.0  |5.0  |1.0  |80   |130  |170  |320  |650  |170  |
|16        |0.140|0.419|0.140 |7.163          |1.0  |3.0  |1.0  |100  |170  |230  |100  |510  |230  |
^Total     ^1.489^1.717^1.404 ^               ^Boardfeet per acre            ^^^^^^1020 ^2030 ^640  |
^                                         ^^^^^Basal Area per Acre           ^^^^^^14.89^17.17^4.04 |
^                                         ^^^^^Volume Factor                 ^^^^^^68.5 ^118.2^158.4|
Service Forester's Handbook

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