Measuring Fusions

General discussions of measurement techniques and the results of testing of techniques and equipment.

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To what extent do you agree: I want to adopt this equation for measuring the coast redwood.

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Total votes : 8

#31)  Re: Measuring Fusions

Postby dbhguru » Wed Jul 15, 2015 9:18 am

NTS,

 Zane Moore's approach to evening the playing field in big tree volume competitions may have applicability to the more customary point competitions by showing us the way to reducing the circumference points from fused trunks of coppice forms.

 If we have a tree that we definitely believe to be from one root system, but subordinate trunks have developed from the root collar and fused with a main trunk, each up to some height, do we exclude all of subordinate trunks, include those that make contact with the main trunk at 4.5 feet, or roll dice? Remember, here we assume on tree - just a complex form. The following formula discounts subordinate stems and is set up for basic reticle measurement of the diameters of each stem an the point of splitting from the main trunk plus the measurement of the whole structure at 4.5 feet or lower if that is where they all come together. In the formula below, Di represents the ith diameter where i=1 is for the main trunk. si=height where the ith trunk splits from the main trunk, h = total height of main stem to top of tree. s1=h to include the whole contribution of the main stem, n =total number of stems including the main trunk.

               
                       
FunctionalCircumference.png
                                       
               


Note that this approach follows Zane's lead. It is algebraically equivalent to: computing the cross-sectional areas of each stem at the point of separation and the apportioning the total cross-sectional area at 4.5 feet or lower, if that is where they all are fused, between the n stems. Then the areas of the subordinate stems are discounted by the factors si/h, remembering that s1=h. The areas of the main and discounted subordinate stems are added together and then the equivalent circumference computed from that combined area. The process can be expressed in terms of diameters since my assumption is that they will be measured via the reticle, except possibly for the combined group at 4.5 feet or lower. The composite measurement may be done with a tape in terms of circumference and then converted into equivalent area based on a circle.

When I return to Massachusetts, I'm going to test the formula out on some eastern deciduous trees. We owe Zane a vote of thanks for pointing the way to possibly solving a thorny problem that has heretofore had no satisfactory solution.

Bob
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#32)  Re: Measuring Fusions

Postby Don » Thu Jul 16, 2015 4:21 pm

John-
You're hitting on a point (and doing a great job of it) that I keep trying to make...photographers have been trained, or are intuitively "focused" on the feature that captures their attention.  What we are talking about here, is using photography to document a tree, and four "quadrant-ed" images capture a tree's base (in the case of redwoods, from base to 12-16' or enough to capture any "fusion" issues.

Speaking of fusion, as used in this thread, could we come upon a definition of what we mean?  What I think is meant by "fusion", is the 'butting up against' one stem with another, and with continued pressure over years, decades, even centuries, basal enclosure that 'extends' up the base and obscuring the nature of the "fusion".

Am I close?
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#33)  Re: Measuring Fusions

Postby Don » Thu Jul 16, 2015 4:33 pm

Bob/Zane/John/Mario-
Just to make sure I'm following you, in a big picture sense, we are progressing from:
1) a measure of a tree's "bigness" as determined by the anachronistic AF Formula, where Total Points = Girth + Height + Crown Spread (avg. breadth and depth)
2) a measure of a tree's "bigness" as determined by a more advanced AF Formula, where we look at the crown spread as a cross-section of square inches/feet; to
3) a measure of a tree's "bigness" as determined by it's volume (presumably of it's stem(s) up to an as yet defined height (topmost foot seldom seen on 300+ footers).

Here again, I am trying to continue finding common goals, and recognizing that while we might have differing objective, try to agree on definitions, phrases...
-Don
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#34)  Re: Measuring Fusions

Postby dbhguru » Thu Jul 16, 2015 10:07 pm

Don,

 Actually, the formula that I previously presented, which borrows from Zane Moore's treatment of volume, is just an embellishment on the anachronistic AF method of judging tree size. The formula seeks to create parity between single stem trees and legitimate coppices with respect to the circumference measurement. We've talked about that many times. The formula needs testing, which I hope to do on returning to Massachusetts.

 As a brief digression, on July 21 and 22, I'll be assisting a team from the BBC, which is developing a documentary on New England forests. We'll be in MTSF. Fancy that, a BBC documentary, which when released will be seen around the world. I'll try to get a plug in for both NTS and AF. No control over that, however.

Bob
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#35)  Re: Measuring Fusions

Postby Don » Fri Jul 17, 2015 12:18 am

Very cool Bob!  We couldn't have a better spokesperson!!  Anything else you want to add to your itinerary?  ; ~ }
-Don
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#36)  Re: Measuring Fusions

Postby dbhguru » Wed Jul 22, 2015 8:12 am

Don,

  As you know, I've passed the derivation of the formula for functional circumference on to Michael Taylor. I have a hard time spotting my own errors. However, here is the derivation with added explanatory comments for anyone else who would take a crack at it.

               
                       
FunctionalCircumference.png
                                       
               


  The formulas in the left block set up the subsequent derivation. For example f and fi,  are variables introduced to simplify what follows. My ultimate objective was to express the functional circumference in terms of diameters since the reticle will play a big part in measuring the cross-sectional areas of the stems at the point of separation, with the possible exception of the composite stem. Remember that the underlying strategy, per Zane's approach to volume, is to compute the cross-sectional area of each stem at the point of splitting off the main stem. For two stems, this is a clear process. However, if there are more stems, then the height at the highest split should probably be taken and the cross-sectional areas at that point taken to derive the percentages to apply to the fusion at 4.5 feet (or whatever). Discussion on this point would be helpful.

 I see a limited use for this formula. It doesn't replace the case where we judge there to be two or more separate trees. This is meant for a natural coppice such as we see with a fair number of eastern species, cottonwoods, silver maples, box elders, etc. I would include species like pinyon pine, which often exhibit a sprouting form in dry regions.

  The formula will greatly discount shrubby forms where sprouting around the root collar accounts for most of the appearance of the shrubby tree. There is an ambiguous case where we may believe that the stems originate from slightly above the root collar so that there is at least a small section of single trunk (maybe only inches). We could then measure the circumference at this point, which would be well below 4.5 feet, but still not involve root collar or limb spread at the narrowest point of the area judged to be a single trunk. Basically, this is what our rules say now.

  Don, since you've been doing excellent research into what scientists are discovering about many complex forms such as baobab, me thinks our challenges have only begun for sorting through our options a la big tree contests. Bryant Smith and our other colleagues at America Forests are going to be thrilled. Maybe this can occupy a small part of tomorrow's discussion with the Eligible Species Group.

Bob
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#37)  Re: Measuring Fusions

Postby Don » Wed Jul 22, 2015 3:11 pm

Bob-
Couldn't sleep last night?
I didn't see any problem with your derivation...; ~ }

Relative to "challenges", interpreting cross-sectional shapes in light of what we know about how gymnosperms adapt to adjacent objects ("reaction wood", a la Wood Science and Technology) will help us judge better where to take (if possible) 'reticled' monocular/binocular readings, to feed that beast of a formula you derived...: ~ }

While I understand your focus on diameter, it's in the back of my mind that we have two objectives we're dealing with here...1)determine proportional cross-sectional areas; 2)determine proportional volumes...not that they aren't related, but that in the context of AF formula competition, we're interested in relative cross-sectional areas, and in the case of Zane's formula, he's interested in comparative volumes.

Like I say, they're not unrelated, as they are probably the closest thing we have to a segue into a conversation about how future 'gobsmackers' will be measured, and the units of measure that will determine those competitions, huh?

Which suggests that at a certain measure of 'gobsmacked-ness', we would determine "big tree-ness" by their volume, rather than by the current single American Forests' formula?  While the correlation between tree volume and AF Tree 'points' is somewhat tenuous, somewhere upwards of 500 AF formula points, the correlation begins to unravel the 3%/3points rule for co-champs, and brings to the fore the question, how would we determine 'gobsmacking' co-champs in a "volume world"? Would 3% still hold up well, or?
-Don
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#38)  Re: Measuring Fusions

Postby dbhguru » Thu Jul 23, 2015 9:02 am

Don,

 I hear you. Actually, if you notice column #2 of the derivation, the use of the A variables are cross-sectional areas. Where I transition to diameter, I carry the full areas so that we don't lose the area connection in subsequent steps, which are just algebraic simplifications. Transitioning to functional circumference is carries the area contribution. That all likely sounds like gobbledegook, and there may be a logic error in there, which is why I called on Michael to analyze the proof. However, it it holds up, we still need rules to apply it, i.e when do we want to compute a functional circumference? I've assumed that we are applying it to what we think started as a single organism and through its natural coppicing behavior sent up more stems from around the root collar. which we would discount to some degree by the Zane factor.  Forms that we judge to be multiple separate trees would not be subject to this formula. Thoughts?


  Looking forward to the AF meeting today with the other Group.

Bob
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#39)  Re: Measuring Fusions

Postby Matt Markworth » Sat Jul 25, 2015 1:22 pm

Zane,

I really like your equation and the idea of discounting subordinate stems makes a lot of sense. It's very thought-provoking. Thanks for sharing!

Bob,

I think that calculating a functional circumference for certain species holds a lot of promise.

Here I have taken 3 "trees", combined them into 1 "tree", and calculated a functional circumference attempting to follow your methodology. As long as I've included all of the necessary input data, please let me know if the math works out with your formula. This example is a good illustration of how a stem with less taper (Trunk C) will have a bigger relative impact than a stem with more taper (Trunk B).

Even though the circumference at 4.5 units above the base and the area at 4.5 units above the base of the 3 separated "trees" aren't included in the calculation, I've included the numbers as a point of interest. Had the "trees" grown together instead of separately they may not have grown as big, so there are a lot of variables affecting an attempt at comparing the 3 "trees" to the 1 "tree", but nonetheless there might be some promise in this type of paper model to show characteristics of fusions.

3 Trunks:

               
                       
3 trunks.jpg
                                       
               


Fusion of 3 Trunks:

               
                       
fusion.JPG
                                       
               


Cross Section of Base:

               
                       
base.jpg
                                       
               


Trunk A (separate "tree") circumference at 4.5 units above the base: 17.5 units
Trunk B (separate "tree") circumference at 4.5 units above the base: 10.7 units
Trunk C (separate "tree") circumference at 4.5 units above the base: 8.2 units
Total: 36.4 units

Trunk A (separate "tree") circumference at 26 units above the base: 13.35 units
Trunk B (separate "tree") circumference at 26 units above the base: 6.6 units
Trunk C (separate "tree") circumference at 26 units above the base: 6.28 units

Trunk A (separate "tree") area at 4.5 units above the base: 24.37 square units
Trunk B (separate "tree") area at 4.5 units above the base: 9.11 square units
Trunk C (separate "tree") area at 4.5 units above the base: 5.35 square units
Total: 38.83 square units

Trunk A (separate "tree") area at 26 units above the base: 14.19 square units
Trunk B (separate "tree") area at 26 units above the base: 3.46 square units
Trunk C (separate "tree") area at 26 units above the base: 3.14 square units

Fusion circumference at 4.5 units above the base: 21.4 units

Fusion area at 4.5 units above the base: 35.34 square units

The main trunk is 120 units tall. Both subordinate trunks separate from the main trunk at 26 units above the base.

The circumference and area of the trunks where they separate from the fusion are the same as the circumference and area numbers shown above that indicate the circumference and area of the trunks at 26 units above the base.

Reduced area at 4.5 units above the base: 26.55 square units

Functional circumference at 4.5 units above the base: 18.27 units

Matt

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#40)  Re: Measuring Fusions

Postby dbhguru » Sat Jul 25, 2015 5:31 pm

Matt,

  Good exercise. I ran your numbers through the functional circumference formula and got slightly different results. It may be rounding, or maybe I entered a number incorrectly. Please find attached an Excel spreadsheet that substitutes all the numbers. Maybe you can see where the slight difference in our results comes from. As you point out, a more columnar subsidiary trunk will have greater impact on the final result, other things being equal.

   More simulations would be nice.

Bob
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