The Forestry Forum

What is a Prism for and how do you use it when cruising tree plots? :)

I knew!  I knew!  But I forgot :-[

I think Ron posted about prisms in the knowledge base - something about laying out an area and counting trees or dangling them from a string and watching all the cool colors - no, that was a different thread - go with the layout scenario.  I'm sure Ron will be along shortly with the tutorial.  ;)

Actually, Tom, in a prism cruise, there are no "plots".  Rather, a prism cruise is deemed a "point sample", because unlike the more familiar (and easier-to-understand) plot cruise, there are no plots in a prism cruise.  It would take more time to write a thorough description of point sampling than I could possibly devote, so instead I will loosely quote a lesson plan from my undergradutate curriculum:

"Point sampling
Probability Proportional to Size (PPS) or point sampling has been widely used in forest inventory. It is the method of selection of trees based on their size rather than their frequency of occurrence. In point sampling, inclusion of a tree in a plot depends on the basal area (cross sectional area of a tree at breast height) of the tree and its proximity (distance) to the sample point. With point sampling, you are most likely to sample big trees. Thus, in other words it is called probability proportional to size (PPS). Point sampling is known with different names – angle count sampling, plotless cruise, prism cruising, variable-plot sampling, variable-radius plot and most commonly, point sampling.
The procedure to sample trees in the forest stand is simple and easy to use in the field, therefore it became popular among natural resource managers and ecologists. The instruments used in point sampling are wedge prisms and angle guages.

The basal area factor (BAF) is the number of units of basal area per acre (or per hectare) represented by each tree tallied in point sampling. In point sampling;
• Do not need direct measurement of either plot boundaries or tree diameters to figure out which trees are in and what basal area per acre is
• Use a fixed angle to determine which trees are in
• Each tree has it's own plot with a radius proportional to its diameter. It means the probability of tallying a tree depends on its cross-sectional area (diameter) and the sighting angle used
• The imaginary tree plots vary with tree size, such that big trees have big plots and small trees have small plots.
• Plot size is such that each "in" tree represents the same amount of basal area per acre.
• The smaller the sighting angle of prism or angle gauge, the more trees included in the sample.

Wedge prisms are used to determine whether or not to count a tree at a point sample. The prisms we have for class are 10 BAF prisms. Trees are counted as in, if the offset image at breast height viewed through the prism and the actual image of the tree have some overlap. If there is no overlap, the tree is not tallied.   With a prism the PRISM is the center of the point and must be held over your point center marker.

(https://forestryforum.com/gallery/albums/userpics/15533/prism.jpg)

Borderline trees: For borderline trees, measure the dbh and the distance to the tree. The distance should be measured to the "center" of the tree, NOT THE FACE of the tree.   If the tree is equal to or closer than the limiting distance for its dbh, then it is tallied. Limiting distances for 10 BAF prisms and gauges are listed in the table below.  The table goes to 10ths of an inch. For an example, the limiting distance for a 15.4 in dbh tree is 42.35 feet . Any 15.4 in dbh tree 42.35 ft or closer to the sample point is counted.   If you forget your table, but have a calculator, you can determine the limiting distance in feet for a tree by multiplying the diameter (in inches) by 2.75 (for BAF 10 sampling only).  For instance, a 10.0" tree can be 27.5 feet away,

Common sources of error:

1. Not measuring borderline trees.  Do not count every other one.  Most people are biased one way or the other when they determine borderline trees, especially when they just start out.
2. Not holding the prism over plot center.
3. Missing "hidden" trees.  If a tree is behind another tree, carefully step to the side of your point center while keeping the same distance from the tree.  You should then be able to see if it's in, out or borderline.
4. Missing far away big trees.  It's important to look out in the distance for larger trees.  A 30.9" white pine can be 84.97 feet away and still be in!
5. Using a different prism or other measuring device than that which you normally work with."

Obviously, point sampling is a complicated procedure, and I'm sure that this description will probably lead to more questions than answers.  I would not recommend point sampling for anyone without hands-on experience and training.

I prefer the angle gauge over the prism.  They're cheaper and practically indestructible.  Anyone who is thinning down to a residual stocking level can use one.  They come in real handy. 

The angle gauge differs from the prism by using your eye as the center point as opposed to the prism.  Your not refracting light with the gauge.  There are still count, no count, and border trees.  But, instead of an offset, your tree will all be in a line.  If the tree is bigger than the gauge, its a count.  If it is smaller than the gauge, its a no count.  If the gauge and the sides of the tree match, its a borderline tree.

For the average landowner, he can go out and figure out which trees he wants to keep, and which should go.  Most people use a BAF (basal area factor) 10 gauge or prism.  That means each tree that counts represents 10 sq ft of basal area/acre.  If the actual basal area of the stand is something like 114 sq ft, then you're only going to have 11 or 12 count trees.  It isn't exact for each area, but gives a good idea.

So, you have a little basic knowledge of your current point.  You want to know if you should thin or let it alone.  If your optimum stocking is 70-90 (pretty much the case in many hardwood stands), then you should be trying to get 7-9 crop trees that count at your point.  Sometimes that's easy, sometimes its not. 

For the easy part, select the best 7, then try to thin from the others.  You want to thin those that are the poorest quality. 

For areas where it is hard to get 7, you can do other types of silvicultural work.  You could do a small clearcut, or a small seedtree or shelterwood cut.  You should have enough area that makes it effective.  You're looking at improving the regeneration in these areas, so you don't want to leave junk.  At your next thinning, you may want to remove the overstory to release your new regeneration.  It has all the makings of uneven aged management.

Remember this thread Tom?  ;D

https://forestryforum.com/board/index.php?topic=16165.msg231621#msg231621


Might want to scroll up a couple posts for more info in that thread.

So, in determining Basal area, out of 10 trees, 3 are 30 inch and are excluded by the prism and 3 are 5 in and excluded by the prism and 4 are "in" trees, this after examining all of the trees on the plot says that the plot holds 40 square feet of basal area?

How does this relate to number of trees?  Or, are the two not comparable?

Is the prism just a means for determining the size of the plot to be counted, or which trees get counted inside of a predetermined plot?

Hmm  MIght need someone to get a bunch more elemental here.  :)

Your 40 square feet would be the correct assumption.   You're only counting the "in" trees and excluding all others.

You can figure out the number of trees per acre, but it is better to do this with more than one data point to have any significance. 

Here's how point sampling works.  Each tree has a plot radius where it can be measured.  Think of it as a circle around a tree.  If you happen to be standing inside that circle, then you'll count that tree.  For BAF of 10, the plot radius in feet computes out to the dbh in inches x 2.75. 

So, for your 5" tree, it would have a plot radius of 13.75'.  That means if you stand closer than 13.75', you'll count that tree.  Stand further away, then you won't.  Your 30" tree will have a plot radius of 82.5'. 

What happens when you take a reading is that you are measuring all those trees that you are standing in their plot radius.  There are a lot of overlapping circles.  Larger trees make larger circles.  As you move, those overlapping circles move.  Some go away and new ones come into play.

Now, if you have the plot radius, you can figure your plot size in acres.  Figure up the area of the circle, then divide by 43,560.  1/plot size will give you the number of trees of that size per acre that tree represents. 

Oh-h-h!   I've got lights coming on everywhere. :D    So, the context with which I should be considering prisms or angle gauges is How many trees on that plot are of that particular size.

Elementarily, If I wanted to include a different size tree, I would recount the plot for the basal area of that tree and add it to the first, continueing to do this until I had counted the basal area of the range of sizes in which I was concerned.

So, if I were counting 5" trees, I would use the prism to determine how many were within the 13.75' radius circle.  Then I would move, perhaps, 27.5' and count the "in" trees in that circle, with each new circle increasing my percentage of sampling.

If I'm getting close, I need cogitate on this a bit and get it to sink in.  If I'm off base i'll go back and read a little slower.  ;D   :P 8)

Ron's 2.75 is what is called the limiting distance factor (LDF).

LD = diameter at breast height/(12 in_/foot x K)

where: K=sqroot(BAF/10890ft²_/acre) = 0.0303, where BAF is basal area factor, in this case 10 ft²/acre.

LD = Diameter/(12 in_/foot x 0.0303) equivalent to Diameter x 2.75  just a little math juggling. ;)

We were doing point centres at 25 meter intervals and 50 meters between strip lines and a huge old western red cedar fell in 4 plots.  And we were using a 12.25 m²/ha prism, actually a reloscope. ;D

For density, all you need is a spread sheet or Tree Factor tables for that prism BAF.

TF=BAF/(0.005454 X Diameter Class^2)

ooops another constant, 0.005454 comes from pi/(4 x 144 in²/ft²) area of a circle converted to ft² from in², since you measure diameter in inches. Just another constant to remember without going through all the math. ;D

Now take your calculated TF for that diameter 'class' and multiply by trees tallied for that diameter 'class' and divide by number of plots sampled to calculate the density. Now add them all up for total density. That's why it's nice to use a spread sheet. ;)

You are pretty close, Tom.  Imagine that you are sampling a tree with a limiting distance of 37.2 feet.  That is equivalent to a plot of 1/10th acre (a circle with raduis of 37.2 feets is 1/10th acre in size).  If there is one tree that is counted "in" at that sample point of that DBH (13.5") then that is one tree per 1/10th acre which is the same as 10 trees in 1 acre.  If there are three trees of that size that are 37.2 feet or less from your sample point, that is equivalent to 30 trees pere acre.

So at a sample point, the area represented by each tree is different depending on its size.  So, you figure each sampled tree separately to determine the area it represents and convert that to a per acre basis.  Say there are two trees counted "in" by the prism at the first sample point.  One is 13.5" DBH, and one is 16.0" in DBH.  The limiting distance on the 13.5" tree is 37.2 feet which is equivalent to a circle with an area of 1/10th acre.  So finding one in 1/10th acre is like finding 10 in one acre.  The 16" tree has a limiting distance of 44 feet.  A circle of 44 feet represents 1/7 acre (rounded).  So 1 tree in 1/7 acre is the same proportion as 7 trees on one acre.  So adding the two together, there are 10 trees per acre represented by the 13.5" DBH tree and 7 trees per acre represented by the 16" tree, so the total trees per acre represented at the sample point with 2 trees counted "in" relates to 17 trees per acre.   

The number of trees/acre represented by each tree counted "in" is a function of the size of each tree counted "in", so the total trees/acre is the sum of the total represented by each tree in the sample.  Got it ???.

DanG, all them numbers make my head ache.  I built a spread sheet that takes all the math out of the calculations, and gives me the number of trees, sizes, volume, value, trees per acre, etc.  And built it for a  bunch of form classes, took a while, but cut down on time later.

Simply put, Tom, you take a talley book, establish a variable plot with a prism, count the  "in" trees and record diameter and height for each "in".  If your doing a plantation, your plot distance of 27.5 feet would be way to much.  While cruising for Champion and their eventual sale, we put one plot per 35 acres on plantations that had not been thinned.  thinned plantations and natural stands required more points, generally controlled by aerial photography and standard deviations.  You do enough standard deviation calculations until they show uniformity.  You then throw all your plots into the spread sheet and push the button.  For non-spread sheet users, a lot of calculations later, and there it is.  While your at it you bore a few trees and do a site index, unless it is already available.  So you end up with site index, basal area, form class, stand information, and your ready to write a plan, management or harvest.

That is a quick and dirty way to do, and it does not always work, have gone back and re-cruised stands when I was not comfortable with the data.  More points the merrier.

And WDH beat me to the punch.

Quote from: Texas Ranger on July 24, 2007, 10:04:26 PM
And WDH beat me to the punch.

That means that you have to buy breakfast next :D.

I think so.

The number of trees per acre is derived by counting the number of trees in the examining plot(limiting distance) relative to the sampling point.

The Sampling point is relative to the DBH.  The number of trees in the sampling point with the same DBH (in) Determines the density of that size tree based on the extrapolation of that Sampling point to reflect an acre Which is determined by learning what part of an acre the Sampling point represents.

Once the DBH can be assigned a Limiting Distance then the Sampling area can be defined to encompass all sizes of trees.  By knowing the Limiting Distance and the number of trees in the sampling area you can determine the number of trees per acre.

So, the purpose of the prism is to determine whether the tree is within the sampling area and has no relation to the size of the tree.  It is just an aid to tell you what to count.  If I understand this right, you could use a piece of string and draw a circle to accomplish the same thing.  

How far am I getting off base now?
Texas Ranger, If I were to take one of Grandmom's spread sheets to the woods, she'd kill me.  :-\  I might best stick with this prism thingy.

You have it, Tom. 

Also,definitely stick with the prism thingy in the woods and spread the sheets on the bed :).

The piece of string and the circle is a fixed point.  Prisms are variable points, or am I beating a dead horse?

the prism has a  relation to the size of the tree, Dodgy Loaners post with pictures indicates how you count the trees by the refraction of the image, how big the tree is in diameter is what allows the prism to work its magic.

then again, we may be going in circles here, shoot, I'll just come to Florida and bring my prism, no, on second thought, WDH, you do that. ;D

From a landowner standpoint, I wouldn't worry too much about the number of trees.  The prism captures the stand density at any given point.  It shows if your stand is too thick, too thin, or just right.  With that information, you can decide if you want to thin, what you want to thin, or to do nothing. 

You can also see if the stand has enough of good quality trees to take forward.  Or if it is mainly stocked with poor quality trees.  It works real good for doing on the ground thinning and checking to see if you are getting the results that you want. 

Foresters use them to conduct inventories.  That's where you take down all the pertinent data, such as species, dbh, and height.  From there, you can get number of trees, average diameter, suggested stocking level, and a whole lot more.  But, that's for doing number crunching.  Its not normally done on the spot.

Quote from: Tom on July 24, 2007, 10:29:27 PM

So, the purpose of the prism is to determine whether the tree is within the sampling area and has no relation to the size of the tree.  It is just an aid to tell you what to count.  If I understand this right, you could use a piece of string and draw a circle to accomplish the same thing.   

Tom, only use the string of fixed length for trees of the same diameter. Won't work for other sized trees. The string is different length for them. You have to calculate a new length (limiting distance) for each unique tree diameter. ;D

Here is how it works:

The prism is ground to a fixed angle, in this case a 10ft²/acre prism has an angle of refraction of 104.14 minutes expressed in decimal degrees (divide that by 60 to get degrees =1.7357 degrees ). In other words, light bends as it passes through the wedge of glass. Remember it's a wedge, thicker on one end than the other. ;) To calibrate the prism, or in other words to find that refracted angle of your wedge prism, use trig.

tan θ = width of tree/distance to tree  , express the tree width in feet. Do this for a tree that is just 'in' on the borderline. ;)

thus,

θ = arc tan (width of tree/distance to tree)

Ex: a 16" tree is 1.33 '

tan θ = 1.33 feet/44 feet
        = 0.030303  ooops, there's that constant k again. ;)

equivalent to k= 2 sin (θ/2)  remember them trig equivalents. ;)

so,
θ = arc tan (1.33/44)
   = 1.7357 degrees or (104.14 minutes)  :o How did they grind it to such a tiny angle?

for us metric dudes this works out to k=0.02828 because our prism of 2 m²/ha has a refracted angle of 97.22 minutes. ;D

Yup on that Swamp, and I use this wonderful little device that measures that distance electronically.  Makes it easy, all you have to do is estimate the center of the stem, and look at the tables.  Quick cruise.

And now for something totally different.............

(https://forestryforum.com/gallery/albums/userpics/11009/SD_Shapes.jpg)

All three shapes have a perimeter of 12 inches. All three could be stand perimeters drawn on a map.  ;D

I know y'all know what you are talking about, but it isn't coming across.  Don't these prisms have a label on them so that you don't have to do all that trig?

I started off thinking that the prism would mysteriously identify the size of tree to be counted.  Then I saw that it seemed to be used to identify the sampling area.
Then I thought it identified the sampling area, but also the relative LD to an acre.

Now, and it might make more sense, I'm back to Basal Area and a sampling area defined by the Limiting distance ...relative to the gauge or prism.

I need to study this a bunch more.  I guess, if anything, I see that I won't be utilizing one of these tools.  But it it sticks in my craw that I can't understand how they work.

Simple? Why didn't ya ask? ;D

Usually on the prism there is an inscribed number, such as '2'  or '2 m' for metric 2 m²/ha prism or a '10' or '10 f' for a 10 ft²/acre prism. So, forget plot size and concentrate on sample size. Depending on the local standard, you may be required to put in 1 plot per ha or 1 plot per 5 acres or some other number. The more the variablity you encounter in your woods, the more samples you need. To start with, you have to group similar sites together and come up with the area of each. Then take your dandy prism, stand at point centre and use a stick, planted firmly in the ground and fixed vertically, to rotate about that point and tally trees by species and diameter class. A diameter class in usually a spread of 2 cm or an inch between one class and another. List species in a column on the left of the page and diameter classes along the top of the page.

Each tree that is 'in' represents 10 ft²/acre regardless of size. And as you know, there is likely to be more 4 inch trees than 50 inch trees in your woods. ;) That's why TF (tree factor) tables, or the equation, is used to determine density from your samples. Your sampling predicts how many trees of each diameter class is expected to be growing in your woods. So the higher the frequency you encounter a particular sized tree in your samples the greater the density of the diameter class.


Beyond that,
In my area when I have a stand with 26 m²/ha, it is handy to 25 cords/acre. Some sites will be lower, some higher. Remember the site influences heights, regardless of species or density.  You have to have a feel for your local situation to make shortcuts if accuracy is not paramount. Sometimes close is good enough. ;D

Stick to the prism for basal area and growing density like Ron said.  If you want trees per acre, do a simple count on a 1/10th acre plot and multiple by 10.  99.9% of people and 98% of foresters don't truly understand why a prism works, only that it does ;D.

Yup, I agree with WDH and Ron. I like to go over this stuff once in awhile to jog my noodles. About the only place I know that requires you to know the theory is in BC when you write your Timber Cruiser/Evaluator exam. I think starting next year it's going to be mandatory to document seminars and write refresher exams periodically to maintain your registration as a timber cruiser/evaluator. Up to this point it has been voluntary. There is even a provincial standard cruising manual for BC and cruise cards used on crown lands. Been there done that. I believe member Tillaway worked the same forest up there I did in BC for a short stint.

Well Tom, I can say with a high degree of certainty that there have been a few folks print this topic off. I've even got it bookmarked along with similar threads.  I'm also quite certain some of the printers are also foresters. ;D  8)

I appreciate this thread. I have 8 prisms, that came from the estate of one of the Forest Service Statisticians/Mensurationists. I've been trying to decipher the pencil marks on the paper wrappers, and have such hierogliphics as
3 delta     BAF 9.33
3 delta  BAF 9.76
3 delta  BAF 9.70
4 delta BAF 16.31
6.00 delta BAF 39.6
7.00 delta 38.0 (looks like Sq)
7      delta  38.0 (looks like Sq)
8.00 delta  BAF 64.80

I'm trying to fit these numbers into what y'all have been saying. Have found it interesting.
Do these numbers correspond to the percent sample? The 3 delta prisms have the least taper. 
None have any etching or numbers/letters on the prisms themselves, only the wrapper.

When the Forum auction fires up next, I will put some of these up for bidding. 

Beenthere, the thinner the wedge the lower the BAF. That fits with what you described so far. Now, if the prism have no markings then determine their BAF (basal area factor) as follows. ;D

We know: tan θ = 1.33 feet/44 feet = K

is equivelent to: K=sqroot(BAF/10890ft²/acre)

So find K. Take a prism and a pointed stick (in my case a garden weasel handle) and look through the prism so that the broad side of the prism is near the eye. Keep both eyes open. Walk toward or away from a tree until the image of the tree in the naked eye and that of the image seen through the prism with the other eye just touch. This is an 'in' tree, but borderline. Jab the stick in the ground directly under the prism viewpoint. Hopefully your prism was held up to your face and not arms length. ;) So once the stick is jabbed into the ground and almost perfectly straight or level, measure the distance to the centre of the tree (to it's side) at 4.5 feet, keeping the tape level. Then measure the tree diameter so the calipers are pointing toward the prism view point. Now do the math. Convert diameter in inches to feet.


tan θ = 1.33 feet/44 feet = K in this example 0.030303

and...

K=sqroot(BAF/10890ft²/acre)

so BAF = K² x 10890ft²/acre

if you want to find the angle of the wedge...

θ = arc tan (1.33/44)
   = 1.7357 degrees or (104.14 minutes)


got it?  ;)

Here's my figures for my metric prism

diameter of white birch 0.295 m, make sure calipers point toward point centre. ;D

distance from tree 10.4 m , measure to the centre of tree by pulling the tape to the side of the tree.

tan θ = 0.295 m/ 10.4 m = 0.02836

BAF = K² x 2500 m²/ha

       = 0.02836² x 2500 m²/ha

       = 2.0 m²/ha  rounded

θ = arc tan (0.295/10.4)

  = 1.6247 degrees (97.48 minutes)  off by 0.26 minutes :D

to convert metric to US BAF...

BAF_US = 4.356 x BAF_metric

                              = 4.356 x 2
                           
                              = 8.7 rounded

 (https://forestryforum.com/gallery/albums/userpics/11009/SD_prism.jpg)

Here's what mine says:

cm

2 m


Made by Cruise-Master Prisms of Sublimity, OR.

10 factor prism being used to determine stand basal area. 

(https://forestryforum.com/gallery/albums/userpics/10001/management_trip_7.jpg)

Prisms and basal areas are just consistency standards.  Much like site index or site classes they are most useful (unless you are a timber cruiser) as giving benchmark growing stock levels in square feet per acre.  Just like doctors write prescription in Latin, if we foresters didn't have basal areas and talk prism angles, anybody could be a forester. <grin>  The statistics for variable plot cruising are the same as fixed plot cruise errors, but the variable plots coefficient of variations are affected by tree counts within your squinted eyes looking through a piece of imperfect glass.......

Gee, Ron, I don't see a prism.  Looks to me like you are getting ready to flip a coin to decide if a particular tree is 'in' or 'out'.  :D

Of course my eyesight leaves a bit to be desired.  Went cruising my woods with my district forester yesterday to spot invasives.  He kept gazing out and saying 'There's some autumn olive, there's some Japanese honeysuckle, look there's some Japanese knot weed.  See that ailanthus?  I had to get within a few feet to see the honeysuckle and knotweed.  It is gong to be and adventure to spray the right plants when it comes time. 

I don't think a prism is in my future  ::)

It's at the end of the 25 inch string.  ;) The prism needs to be kept over plot center for accuracy. I usually mark plot center with my walking stick (ski pole) and hold the prism over it and then start counting the trees starting with the first one off my right shoulder from my cruise direction.

All border line trees are measured from plot center with the tape measured distance then read off a table to dertmine if that diameter tree is "in or out".

Just to clarify the method used to record data we use here in NB. We use a set of standard volume tables that represent 4 site indexes for softwood and 4 for hardwood, tree taper is factored in. So in a few plots within your stand we measure a few heights and use them to estimate others in the plot. We don't measure heights at every plot, just when your uncertain of the estimates of your heights. I usually document the height per plot of the dominants, just the average for sw and hw. For suppressed trees I use a lower site index because they are overtopped trees and stunted and they get grouped into pulp. My % pulp for softwood is 30 % and for hardwood it's 60 %, but I'll adjust if the wood is really poor. That part can be kind of dodgy because you never know until you open a tree up, how much heartwood is in hard maple or how much rot on the but of a fir. You can tell if something is going on there, but for someone to say 'oh that's got 50% heart' without opening up a tree it's pure speculation. An 'inky' borer can confirm if the but has rot, but how far up the tree does it go? Your not going to bore every tree or you won't be in business long. ;) So I write a little disclaimer regarding that difficulty. Out in BC they estimate most trees by measuring some trees in every plot and record diameter and height. Sounds similar for most states. Then they use volume equations that factor in taper. Some of you folks are probably estimating the height where the last log can be bucked. The computer program they use in BC makes use of tree pathology codes to deduct for waste as well.

So Tom, if you want to use a prism I think this might help.

First, know the area of your woods and group your woods into stands of trees with similar species and ground type (swamp land , dry upland). Get yourself a good aerial photo and ground truth the scale. We can explain that later. With a grease pencil, outline the stand perimeters by texture and color on the photo. Get yourself a measuring device, such as a hip chain and a good compass with declination dial on it. Now to make the location of the points random, go a set distance and bearing to each point. Mark the cruise pattern on your photo with grease pencil and note the Azimuth changes, so you can compass your way and know with some certainty where your at. We don't want to loose ya out there in the swamp. ;D If you have a small stand of wood, say 5 acres, put at least three points in and not on the edges of the stand perimeter.

Second, take your compass and set the declination to your local area, and from a starting point and distance you choose, measure and compass to point one which you marked on the photo.  ;D After you get there adjust the compass for the path along the cruise line you drew on the photo.

Third, now that your there at point one, mark the centre with a broom handle you remembered to bring along. ;) Now to keep track of where you start tallying trees you can have a handy can of paint with you and spray a little dot on the tree you counted 'in' and measured it's diameter at 4.5 feet and height (for height measurements, that's another discussion ;) ) Make sure the dot faces the point centre so you can see it when at the point centre. ;)

If your tree is hard to see or borderline get the tape out. We will assume you have a 10 ft²/acre prism here.

To see if the tree is 'in' use.

LD = Diameter of tree x 2.75, if your measured distance is longer, then tree is 'out'

On to the next one and so one and measure each tree diameter and height (or estimate) as you count them 'in'.

If you don't have a spreadsheet program like EXCEL 2000 or something (I think OpenOffice has a freebie), be prepared for long hand calculations for the next steps. ;D

(https://forestryforum.com/gallery/albums/userpics/11009/SD_CruiseTally.jpg)

Here is a long hand calculation of your tally to find density and basal area. Well the basal area part can be done in your head by adding all the tally up, multiply by Basal Area Factor (10 ft²/acre) and divide by # points tallied. And density can be sped up by making up a table of tree factors for each diameter class of that BAF. This is different for prisms of different BAF's. ;)


BAF                                      diameter
+++++++++++++++++++++++++++++++++++++++++++++++
                 +     10     +    12     +    13     +   14   +   15
+++++++++++++++++++++++++++++++++++++++++++++++
      10           18.3352 + 12.7328 + 10.8492 + 9.3547+ 8.1490

TF = BAF / (0.005454 x Diameter²)


To do your volumes it's more work unless you use an average height of that diameter in that particular stand (site). I would group the suppressed ones from the upper canopy trees and have two, maybe three if you group codoms from dominants, volume calculations per diameter and species per stand (site). Maybe when your tallying you can have a code for suppressed (1), Co-dominant (2), Dominant (3) and have average height for each group in that stand (site). Something similar to this...

(https://forestryforum.com/gallery/albums/userpics/11009/SD_CruiseTally2.jpg)

Well, anyway this is the not so pretty way because it's all manual calculations.  Better find some wide paper and a big table. ::) Hope the wife don't chase ya off the dining room table.  :D :D :D

Sample cruise photo:

(https://forestryforum.com/gallery/albums/userpics/11009/SD_cruisephoto.jpg)

Ground truthing reveals that the photo has a scale of 1:10000. So for a rough idea of stand area, we can use a transparency with dots spaced 1 inch apart. Drop the transparency onto the photo at random, count the dots inside each unique stand number and some math

Ground Area = # dots x (10000² in² x ft² x acres)/(12² in² x 43560 ft²)

or

Ground Area = # dots x 15.94 (round to 16) acres.

If you find the plot centres are a lot closer than the dot grid spacing, reduce the dot grid spacing to get more accurate area estimates.

If any dots land on the perimeter, count every other dot on the perimeter.

Example:

Drop the spacing down to 1/4"

so.........

Ground Area = # dots x (10000² in² x ft² x acres)/(12² in² x 4²x 43560 ft²)

Ground Area = # dots x 0.996 (rounded to 1) acres

;D

Typical Area Dot Grid

(https://forestryforum.com/gallery/albums/userpics/11009/SD_dotgrid.jpg)

The dots in this case are actually spaced at 0.8 cm apart. (reciprocal of 1.25 cm) That way, each dot represents a hectare. ;)

SD, that is the old fashioned way ;).   You are dating yourself ;D.

Yeah I know, but does Joe land owner have all the fancy GPS/GIS and equipment? ;D


I think if Tom and Dang got together as a cruising team and cruised their ground and survived the ordeal with all this math and paperwork, in this blistering heat, it would definitely be worth more than a shared bottle of beer wouldn't it? ;)

DanG right it wood ;D.  We used to measure our productivity in acres cruised/day or in plots/day.  With those two, it would be acres cruised/mint julep :D.  By the way, the heat here was brutal today............. :-\.   

As I read your post about the cruise methodology, I got tired just thinking back about doing that so many times ;).  With all the fancy GIS/GPS tools and spreadsheets and such, it is much easier than it used to be.  However, many of the young foresters today might have difficulty doing things the old way.  Using the compass and your pace to do a type map is probably not taught these days.  Just find the satellite photo on the internet and point and click to outline the boundaries to get the acres magically from the computer.  Getting the accurate acres (hectares  ::)) used to be quite a lot of hard field work :).

I wonder if someone has written a JAVA GIS program for the Terraserver website? ;D Most of these programs I think are commercial products, ARCIMS by ESRI comes to mind. That means something else to learn. Give me my map and dot grid. Through them up in the air, where they land, count the dots. Try that with the computer.  ;D :D

When we cruised the west coast an 8 point day was very good, a 12 point day was rare and made DNR suspicious about quality, 6 was a minimum target. Takes anywhere from 40 mins to 1 hr 25 minutes per point with all the tight chaining for horizontal distance, reference tree and centre stake marking, pathology and measuring, sometimes even clearing of salal vines.  ;)

Cruising for Champion was interesting in light of the daily achievement.  We would try for 20 (flat land and plantations), but usually got just over 10, with travel time, and cutting our way through to the points.

In relitively open older stands i can get 20-30 day.  Tom your string idea is what plot cruising is that 37.2 foot string is your 1/10 acre!  It is confusing that is why there is an entire class devoted to the subject of cruising.

-Nate

In open stands, yes, 20-30 a day, but, been to South Carolina, and you don't have NEAR the brush we do in Texas.  On some plantations we had a machete man in front of the compass man.  On a two man crew.  To DanG old to go in the woods by myself and let the buzzards be the ones that find me.

Thats why i put the little disclaimer "older open stands".  We have a coastal plain that has the growth of bushed and vines so thick that you cant see, just like your talking about. I have not been in these relly bad first thin stands but i have been in some upper coastal plain stands where i could only get arount 10 a day.

-Nate

Same ol' same ol', far as I can tell.  I cruised a 22 year old plantation a couple of months ago, like walking in a park.  Right next to it a 15 year old unthinned, you can lose your religion in one of those.

I have decided some cruising is a young mans sport, but still love it.

This gets my vote to belong in the top 10 most informative FF threads!

I'd guess the postings here pretty well cover the same if not more, crucial real world information covered in a 10 week undergrand forestry course...

Thanks for sharing,
Greg

That's for sure, Greg.  Ole Tom sure knows how to stir up a learnin' fest  8)

Like Tom, and others, and probably most of us.... If there is something that draws our interest we like to pull it apart and take the mystery out of it.  ;D 8)

Hmmm, the GIS statistics of the aqua colored perimeter............using metric

(https://forestryforum.com/gallery/albums/userpics/11009/SD_Arcpad-Area.jpg)


And by dot grid?............ count the dots inside the black perimeter.

(https://forestryforum.com/gallery/albums/userpics/11009/SD_Dotgrid-Area.jpg)

Some more random drops of the dot grid come up with the following counts.

4 inside, 4 on perimeter = 6 (count every 2 perimeter dots)
5 inside and 3 perimeter = 6.5
5 inside and 2 perimeter = 6
5 inside and 1 perimeter = 5.5
6 inside and 2 perimeter = 7
5 inside and 1 perimeter = 5.5
6 inside and 1 perimeter = 6.5
5 inside and 1 perimeter = 5.5
4 inside and 3 perimeter = 5.5
4 inside and 4 perimeter = 6
4 inside and 2 perimeter = 5
6 inside ....................  = 6
=====================
5.91 (average)  ;D  :D :D :D

I got broke in on a dot grid.  I bet most of the new generation of foresters have never used one.  SD, we are archaic.

I still use one. Very reliable. ;)

yup

I think I lost mine. ::)  They work pretty darn good and the price is right.

Hey, Jeff and Tom. I expect to see the results of a 'mini' cruise on an under explored corner of the Brokenclaw (Ian's name, not mine) woodlot. Not one of them trail side cruises though, won't do. ;D  ;) :D

I can vouch that they're still teaching dot grids. A lot quicker to pick up than the GIS software.

 smiley_thumbsup

I suspect that they do as I see them used from time to time. They are or were and maybe still are used in more disciplines than just forestry. Some aren't even used to find area, they are used to layout elements in a publishing program. ;)

Just a review of the formulas used in calculating Density and Basal Area in a spreadsheet layout of your cruise data by prism sample.

Density = tally x BAF/ (0.005454 x Diameter²)
                              # points sampled

BA = 0.005454 x Diameter² x Density

The constant of 0.005454 comes from converting inches² to feet².
       pi feet²        
4x144 inches²

A stand with basal area of 100 ft²/acre determined by sampling with a prism of basal area factor 10 ft²/acre has an average of 10 trees per sample point.

I refuse to Prism Cruise any more. I will use a prism to get basal area for thinnings. I have not done a line plot cruise in years. I prefer a 10% strip cruise or even a 20% in small stands or when a stand has rapid changes in timber type. I no longer carry a tally book or a hand-held. I use a tape recorder with a microphone with on/off function. I make my tree "calls" into the recorder as well as every ditch, creek , fence I cross. At the end of every line I check to ensure the recorder is working (never hadf a problem yet). I can cover a few more acres per day and do my take off in the air conditioned office. When marking timber it is really handy not to keep up with a tally book or hand-held. The recorder fits perfectly in the left inside pocket of a filson vest. (In a ziploc bag for weather resistance)

I figure it's enough to go through the paces during the day and right it all down then, rather than live it all over again that evening or the next day listening to a tape recorder. I know the whole day isn't recorded, but what time did you save? You might as well write it down (or type into GPS/Windows Mobile datasheets) and it's more reliable. Just sit the unit in the charge cradle and hit send, open the cruise program and click and print the reports. :) It will only take once, maybe twice for the recorder to malfunction to test your enthusiasm. ;D

Each timber type gets a minimum of 3 or 4 points, if the stand is quite variable, usually more points are added (closer spacing). A map is usually sketched on paper along strip lines or GPS'ed position  (some have camera to geolocate a photo of a stream), aerial photo or GPS used to set up preliminary stand perimeters, ground features and "truthed" when walked.

Could someone please tell me how to calculate the tree units once I've done the work in the field. I've done it before but I forgot....and may I ask for the very simple version...

Thank you!!!

Sunflower4dayz

What are you asking for? The density and basal area per acre? Volume would depend on your local conditions and standardized volumes for the site, species and crown class (dom,int, sup).

The tree factor equation is built into the density formula above. Finding density is your first step to get to the others. And you need your prism BAF of course. If you don't know it, you can find it by measuring as accurately as possible the distance to a bordline tree and the diameter of that tree at breast height with calipers pointing to point centre. Just use a yard tree and step away until it is borderline. Formula is in this thread earlier.

sunflower4dayz , hope you found your answer.  ;)

Welcome to the forum anyway.  ;D

Tom here is a way to demonstrate what Ron talked about when using a prism and determining "in" or "out" trees. The yellow circles are trees, the blue circles are limiting distances of trees of different diameters. The red dot in the middle is the point centre where the prism is held for the circular sweep. If you didn't have a prism, you could calculate manually the limiting distance from a tree centre in order to count it. So, if the blue line does not capture the point centre then it's not an "in" tree. The bottom tree is marked borderline because it's just on the outer reach of the point centre.

Ignore the fact I miss labeled the prism point as the "plot centre". My circles are a little wobbly. ;D


(https://forestryforum.com/gallery/albums/userpics/11009/SD_Limiting_Distances.jpg)

From further reading in Husch, Miller and Beers (1982), beenthere's prisms are termed uncalibrated prisms. They were either home made or done by a lens shop that might make prescription lenses. A calibrated prism would be one manufactured for 10, 12, 14 etc ..ft²/acre and won't have fractions like 9.6 etc... Nothing wrong with them, as long as you calibrate them as the gentlemen obviously did to arrive at those BAF's. The prisms are usually cheaper to get made uncalibrated. The procedure I discussed earlier.

Good information in this old thread. I am also watching video's. I have not gotten to the point I understand all the math yet but I will.

My question is basic. I understand what I read and see on using a prism or angle gauge. I think I understand the reason for measuring multiple plots to get average. What I am struggling with is how far away from your point are you counting tree's? in other words, I am using a prism and rotating count in or out. How far ahead of me am I looking? Then, I move to another point and do the same. Am I now counting some of the same trees from my initial point? If another measuring point is on the border of the property do I only count what is on the property?

Sorry for being obtuse and I hope I asked that right.

The prism your using or angle gauge determines the plot size. The bigger the trees at DBH (diameter breast height) the further away they can be from the point your at to be counted. If your in big wood you'll have a larger diameter plot than in small wood. It's not really a plot, but based on a 'limiting distance' of each tree diameter based on the angle the prism is shaped and the refracted image seen within compared to the naked eye.

I've been in second growth hemlock that had old growth western red ceder left in it. I had one of those those big cedar in 2 or 3 plots, we used 50 meter spacing on grid.

Personally, I don't count border plots, unless the cover type and development stage of the forest doesn't change. If I'm standing in mature aspen/fir 80 feet tall and on the other side of the line it is now suckered aspen and fir regrowth then no sample if the tree diameters on my side of the line suggest the limiting distance goes beyond the boundary for those diameters.

Look up borderline tree on Wikipedia or other fine source:


     https://en.wikipedia.org/wiki/Borderline_tree (https://en.wikipedia.org/wiki/Borderline_tree)

That is how far you are measuring to with a particular prism or angle gauge, for a tree of a specific diameter. 

Lets assume I want to determine density of a 1 acre stand. I am using a 10 guage angle or prism. I can use 1/10 of an acre plot to measure. I determine the plot center and then measure out 37.2 feet. This would establish the diameter I an measuring. Then from center of the plot I count in and out within this diameter and multiply by 10.

Is that right?

Clearcut, thanks. I wil read that too.

That works for fixed area plots yes. But doing just one plot, there would be no average to account for variability. But for prisms and angle gauge you don't measure out a plot. The size of each plot is variable, depending on tree diameters. You need to make a table of 'tree factors' by diameter class. For 10 ft2/acre (BAF) prism it is BAF/(0.005454 x Diameter^2) then multiply tally of trees in each diameter by this number for that diameter. Then total them up for all diameters for density. The constant 0.005454 comes from pi/(4 x 144 in^2/ft^2), area of circle from in^2 to ft^2.   ^ symbol is to the power of.

The accuracy improves with sample size, stand typing, and known stand area. You can delineate stands and find their area easily in today's GIS software, even Google Earth can measure a polygon. Delineate stands based on texture and color.

You described a Fixed Radius Plot of 1/10 acre. Each tree measured represents 10 similar trees per acre. 

Plots measured with a prism or angle gauge are Variable Radius Plots, each tree's diameter determines the plot size. Plot size is a fixed ratio of tree diameter to plot size. Thus, you get a constant value for Basal Area for each tree counted, depending on the Basal Area Factor of the prism or angle gauge.  ie. 10 sqft of Basal Area per acre.

There are a number of advantages to Variable Radius plots, especially when inventorying timber. Probability is Proportional to Size, here you are selecting larger trees to measure, generally the tree that a landowner can sell, but trees are selected in an unbiased manner, useful for the statistics that describe your stand. Species composition, and a number of other variables can be estimated. 

The biggest advantage is speed. Basal area is closely correlated with volume. You can measure Basal Area with a simple count, and measure a representative sample of trees accurately for volume. Using this information, one can construct a local Volume-Basal Area Ration table, to rapidly and accurately calculate volume. 

Basal Area is also closely correlated with a number of other factors of interest such as habitat value,and fire modeling, among others. 

Your description of a fixed radius plot gives you the density of the plot, number of trees per acre. You would need to calculate the basal area of each tree and summarize to get Basal Area per acre. Basal Area is an expression of density that also incorporates DBH. 

In any statistical sample, the number of sample points — n — is crucial. More is better for a number of reasons. 

Quote from: SwampDonkey on April 14, 2009, 08:54:42 AM
(https://forestryforum.com/gallery/albums/userpics/11009/SD_Limiting_Distances.jpg)

I like SwampDonkey's visualization of the "variable radius plot".
In this method you measure from the tree to a distance that varies depending on the diameter of that tree, and if the center of your plot is included in that distance, the tree is "in". The prisms have been explained in depth previously, but let's just say until you need to check a borderline tree, it's trigonometry magic that keeps you from needing to physically take this measurement.

In a "fixed radius plot", you measure from the plot center a set distance with no maths involved (on flat ground.)
The fixed plot allows you to easily find trees per acre, whereas the variable plot allows you to easily find the basal are per acre.