Percent Cylinder Occupation

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#1)  Percent Cylinder Occupation

Postby KoutaR » Wed Jan 23, 2013 12:57 pm

This is a question to all dbh and volume gurus of NTS. It is about the biggest spruce of this park (pictured above). We estimated its volume as 40 cubic meters quickly in our head (actually in Michael's head) at the tree. Now we think the estimation may be too low. We made the estimation assuming conical form, but old trees often have more parabolical form. If we use the circumference above the buttresses at 2.6 m (480 cm) as the base of a 56.2m tall paraboloid, we get 52 m3. When we add a few cubes for the buttresses and the branches we end up in almost 60 m3. Probably the real volume is somewhere between the conical and the parabolical estimate.

My question: How would you estimate the volume from these numbers and assuming the top is intact and the tree has a form similar to the American conifers familiar to you?

Height: 56.2 m
Circumference at different heights:
At 1.3 m: 671 cm
At 1.5 m: 631 cm
At 2.2 m: 503 cm
At 2.6 m: 480 cm (above the buttresses)

We know that more measurements are needed for a good estimation, so this is rather a best guess than an estimate.

Kouta
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#2)  Re: Percent Cylinder Occupation

Postby edfrank » Thu Jan 24, 2013 1:31 am

Kouta,

I have mentioned before the idea of Percent Cylinder Occupation.  he percent cylinder occupation listing is a measure of what percentage the measured volume of the tree represents compared to a cylinder equal to the circumference breast height (CBH) of the tree times the height of the tree. Trees with a fat base or a trunk that quickly tapers scores low on the list, trees that taper more slowly have higher values. Those trees with broken tops will have anomalously high values.  The table is not complete as it only lists a few of the largest species of western tree. The Sugar Pine and Western Hemlock are smaller than a number of other species, but were included as they are comparable to Eastern White Pine and Eastern Hemlock.

               
                       
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Looking at your numbers, the cylinder would be 4.8 meters in girth x 56.2 meters tall
radius = 0.764 m
cross section area  = 1.833 meters2
cylinder volume = 103.4 meters3

The average for the hemlocks, comparable is size is 40.9%, ignoring the anomalously low values for the other species for the other species, you have a percentage of 39.6% for 7 species.  

So my best estimate, for volume would be 40% x 103.4 m3 = 41.36 m3

This is somewhere between the volume of a cone (33.3%) and a paraboloid at (50%).

So this would make the tree somewhat smaller in volume that your estimates.  If you just look at the 5 largest volume hemlocks, their average is 44.84% which would be a volume of 46.36 m3.  

None of these calculations are including the material in the basal buttress where it is wider than cylinder radius of 0.764 m nor fro any of the branches.  

Edward Frank

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#3)  Re: Percent Cylinder Occupation

Postby KoutaR » Thu Jan 24, 2013 6:28 am

Thanks Ed! Our original estimate including buttresses and branches was 40 m3, so your estimates are about 5-10 m3 larger if we add a few cubes for buttresses and brances. But the percentages are for cylinders whose radii has been derived from CBH, not from girths at heights above the quickly tapering parts of the bases. I suppose the hemlocks also have basal buttresses or otherwise swollen or widened bases, though proably not so large as our spruce?  Should we use the CBH (6.71m) or some value between the CBH and 4.8m (like their mean) also for the Biogradska spruce? Above 2.6m (girth 4.8m) the spruce has almost no taper.

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#4)  Re: Percent Cylinder Occupation

Postby edfrank » Thu Jan 24, 2013 10:58 am

Kouta,

The basal buttresses extend up higher on some trees than others.  It is my impression, perhaps Will or Jess will comment, that the data for the hemlocks is generally above this basal buttressing.  So a similar value should be used for your tree.  The 480 cm values seemed the best choice of your data points.  The numbers used for the western trees may be suspect because I a unsure where the measures were taken with respect to this basal buttressing.  They were simply pulled from Bob Van Pelts book of Forest Giants.  

This is the data we have.  It was not collected for the purpose of these calculations and is therefore not ideal.  The numbers are for the most part pretty consistent and I would expect much more variation if some included much more of the basal buttressing than others.  I know from around here that the basal buttresses do not extend very far up the hemlock trunks, so I think the numbers generated are reasonable.  Will talks about the processes used for measuring these big hemlocks http://www.nativetreesociety.org/tsuga/ ... tocols.htm

Ed
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#5)  Re: Percent Cylinder Occupation

Postby Michael J Spraggon » Thu Jan 24, 2013 8:51 pm

So my mental arithmetic wasn't too bad after all!

Those giant old growth trees at the bottom of the list would certainly have cylinder occupations far above 33% if you assume that they were approximately conical when they first reached full height. I would not be surprised if the CBH was taken at a height where the trunks were flared or buttressed.

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#6)  Re: Percent Cylinder Occupation

Postby edfrank » Thu Jan 24, 2013 9:37 pm

Michael,

Definitely the lower values in these trees reflect a flaring base rather than the general shape of the tree.  The value is only useful if girth is taken above the inflated base, or the resulting cylinder will be too large, and the occupation percentage will be too low.  It is an idea I proposed several years ago when first looking at general shape of the trees based up the tsuga search data Will had collected.  It was never pursued aside from a few calculations from miscellaneous data.  I think it is a worthwhile idea as it can be used to roughly estimate the volume of a tree with limited data.  There is still a range of possible volumes.  I think the 40% or so of the cylinder volume is a good first approximation for old growth big trees.  It is applicable to trees that essentially have a single trunk that extends from the base to the top.  I don't think it will be useful for broad crowned deciduous trees whose trunks split into numerous side branches as they approach the top.

Edward Frank
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#7)  Re: Percent Cylinder Occupation

Postby Michael J Spraggon » Fri Jan 25, 2013 3:46 pm

Well, let's apply it to one broad-crowned deciduous tree: the largest Trsteno plane.

Circumference at 2.0m: 10.75m. There is still slight buttressing and tapering above 2.0m all the way up to the first limbs, which I will assume negates the flaring and buttressing below. Original height before pruning: 48.5m.

Cylinder volume: 446.0m³. Cone volume: 148.7m³. 40% of cylinder: 178.4m³, which is not far off our estimate.

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#8)  Re: Percent Cylinder Occupation

Postby edfrank » Fri Jan 25, 2013 5:20 pm

Michael,

I think the numbers for the hemlocks should be similar to those for your spruce.  I only have a little data from a couple of trees that have been mapped for volume that are not conifers.  These are exceptional trees and might not be applicable to others.  I will check with Bob Leverett and see if he has modeled other trees.  (I think he did a big white oak Quercus alba, but if he did I don't see the numbers on the website).

               
                       
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In these cases the branches are enormous and add significantly to the total wood volume. The volume for most conifers for branches is a much smaller percentage.  

If you include branches on these trees you  can get volumes between paraboloid and cylindrical.  If you just look at the trunk volume the numbers are much different.

Sag Branch cylinder = 6602 ft3
Sag Branch Trunk = 2430 ft3
36.8%

Middleton Live Oak cylinder = 5770 ft3
Middelton Trunk =  970 ft3
16.8%

We need more data on the volumes of both broad leaf and conifers.

Edward Frank

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#9)  Re: Percent Cylinder Occupation

Postby KoutaR » Fri Jan 25, 2013 5:23 pm

Ed & Michael,

The diameters in Van Pelt's book are DBHs (diameter at BREAST height), indeed. Thus, they cannot be used in our calculation. Van Pelt himself says DBH has a limited value for describing giant western trees.

I looked at some online photos of the biggest eastern hemlocks and they really have almost no buttressing, so using 4.8m should be the best choice. I repeat the calculation:

40.9% x 103.4 m3 = 42,3 m3

If we add three cubes for buttresses and branches we end up in 45 m3. As there were big uncertaincies in the calculation I would state 40-50 m3. Do you agree?

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#10)  Re: Percent Cylinder Occupation

Postby edfrank » Fri Jan 25, 2013 5:52 pm

Kouta,

Yes I agree completely. The only trees I think are useful at this point are the hemlocks and the eastern white pine.  The hemlocks average out to 40.9%.  I know there is more white pine data, I just don't have it organized and would need to compile it.  There are many large eastern hemlocks and white pines in the old growth section of Cook Forest.  I am very familiar with these trees and can say that  breast height is typically above the basal flare.  

The one consideration here is that if the top of the tree has been broken very much below where the original tapered top would have been, then the percentage of cylinder occupation will be increased.  The largest percentage in the hemlock listing - the Jim Branch Giant - has such a broken top.  Some trees have the swelled base extending farther up the trunk, others have a top broken out and are shorter than an idealized form.  This is how any set of trees will look.  I am unsure how the overall shape changes as the tree matures.  

As I said before, this is the data we have.  The hemlocks to me seem to be the best representative of what might be expect from your spruce in terms of shape and volume.  The best girth for the calculation should be taken above the swelled base - thus the 4.8 meter option.  I could do better estimates and get a better idea of the ranges of volumes as the tree shapes varied in a mature conifer if we had more measurements.  This is, as far as I can see, the best option for addressing your original question, and my feeling it is as good of an estimate as is possible at this time.

Edward Frank
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