Volume Modeling of the Big Pine at Lilydale

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Erik Danielsen
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Volume Modeling of the Big Pine at Lilydale

Post by Erik Danielsen » Thu Nov 16, 2017 2:48 pm

In preparation for doing some reticle work in the Adirondacks later this month, I decided to visit the biggest pine in my general area to get some practice with using the Vortex Solo Reticle and figure out how the math works. Cross-referencing a bit of reading on the forums, Bob's volume estimate explanations in the recent Adirondacks Report, and the material in the Simple and Advanced Reticle Methods workbook I got what I hope was a fairly complete notion of how to do the work in the field, grabbed my equipment, and headed up to Lilydale.

I'm hoping those familiar with volume modeling will look over my methodology and let me know if I'm getting the right idea and what I might do to improve or correct my methods, so the rest of this post will be a bit long and heavy on things like Frustums of a Nieloid form that I had never heard of prior to yesterday. Hopefully this might also prove informative for others who are trying to figure this out from a place of similar ignorance. For those of you who might want to skip all that and just hear the updated numbers, here they are:

The Big Pine at Lilydale - 42 20'58.4246" N, -79 19'26.3539" W

148.05' tall / 13.23'cbh / 52.48'acs - 319.93 AF points (95.8% of the state champ's total)

Volume: 885.24 ft3 in best model (minimum 855.41 ft3, maximum 915.1 ft3) revised 11/17, see third post
The Big Pine in full
The Big Pine in full
Now, for the methods. Even updating the basic measurements was difficult. A lot of debris has fallen around the base of the pine since the first time I wrapped a tape around it. I was new to measuring and using a standard tape measure, and I believe I selected a point lower than midslope as base at the time and got 13.8'cbh. When I visited with Tom and his brother some of the debris was fresh from a fallen top, and I believe this influenced our midslope selection. I didn't even realize it was the same pine at the time. We came up with 12.5'cbh on that occasion. Currently, there is even more debris than before, but I took more time to discern the most suitable midpoint, and feel comfortable with a determination of 13.23'cbh.
The base, with debris apparent. This was all absent in the early summer of 2014.
The base, with debris apparent. This was all absent in the early summer of 2014.
Sighting the true top is very difficult and I'm still not sure I have done so; the highest visible twig is hiding back t the edge of what at first seems to be the highest cluster of foliage. This twig may itself be just the outer member of another cluster, so it's possible that the true top could be a couple feet higher. It's a deceptively difficult tree to find good views of. I do think this is the same top that I was measuring to last november, so the new height probably includes both some growth and a slight downward revision of determined midlsope. Absent any crown breakage, this tree should be in the 150x12 club within 5 years (or maybe just a couple), if it isn't already.
If you zoom in, the highest visible point in the crown is circled in orange, with an arrow pointing to it.
If you zoom in, the highest visible point in the crown is circled in orange, with an arrow pointing to it.
Crown spread, at least, was a straightforward 8-spoke operation.

Finally I got to the reticle. I managed to mount both the reticle and rangefinder/clinometer to a single bracket, which was great, but hadn't anticipated that the little tripod I had lying around was both flimsy and a bit short. A good tripod would definitely make this process a lot easier. It was difficult to find a single viewpoint that would provide a good clean view all the way up to the crown (and a clear view of the base nearly impossible, as was wrapping a tape down any lower). From my starting position I first measured at the same height as the tape. The derived diameter (4.21') was exactly the same as the tapewrap, down to the hundredths place. So far so good!

Next I measured at a point 14' up the trunk, then 28' up the trunk, then 52.5' up. At this point it was necessary to switch to a position about 90 degrees to my first position to continue up the trunk. I measured again at the 52.5' mark from this new position, then a final measurement at 73.5' above the base. Above this point the crown became more heavily branched. This gave me 4 segments. Based on the process Bob described in the adirondack report, I calculated these as Frustums of a Paraboloid. Segment 1 was 101.823 ft3, segment 2= 128.3 ft3, segment 3=185.345 ft3, and segment 4= 147.724 ft3.

One thing that bugged me at first was that upon changing positions, the diameter at 52.5' high I got from the first position (2.951') was narrower than the diameter I got at 52.5' high from the second position (3.041'). This suggested that the trunk is an ellipse, and that I had collected most of my measurements viewing it from the "skinny" side. To compensate, I calculated an alternate volume for segments 1-3 using just the DBH diameter and the diameter at 52.5' high viewed from the "wide" side. This gave a volume of 497.8 ft3 for segments 1-3 collected, compared to 415.5 ft3 using the measurements from the "skinny" side. I averaged the two and got 456.65 ft3 to use as the "best" model of segments 1-3, and the minimum and maximum mentioned are based on using one or the other without averaging.

For the base, being unable to get a good view or wrap a tape below cbh, I calculated the rate of taper from the diameter at 14' to the diameter at 4.5', and extrapolated that downwards. Using the extrapolated base diameter (6.8347) I calculated the volume as a Neiloid Frustum (who is this Neil, anyways?) since it has a pronounced concave taper. This came to 92.93 ft3, and may be slightly conservative as the last 18" or so before ground level flares dramatically before becoming root.

Finally, since Bob used the volume of a frustum of a cone for the top segment in the Adirondack Report, I opted to do the same (though I hope in the future to get a better understanding of when cone vs. paraboloid are most appropriate). Taking a hypothetical top diameter of 0.1' as in that example, the top segment came to 154.9 ft3.

So, the final setup: Base= 92.93 ft3, Segments 1-3= 456.65 ft3, Segment 4= 147.72 ft3, and Top= 154.9 ft3. The final total is 852.2 ft3.

Using dbh and height with a form factor of 0.42 as an alternative gave an estimated volume of 865.69 ft3, which makes me feel like the final total is a good respectable figure, but I can definitely see some ways this measurement could have been collected more solidly (better tripod, more segments, different calculations for non-round trunk or measuring the full trunk from both directions to average) and look forward to any insights on aspects I'm undoubtedly missing.
Last edited by Erik Danielsen on Fri Nov 17, 2017 9:42 am, edited 1 time in total.

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dbhguru
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Re: Volume Modeling of the Big Pine at Lilydale

Post by dbhguru » Thu Nov 16, 2017 7:03 pm

Erik,

I replied by email, but thought others might like to see my answer. It is attached.

Bob
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Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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Erik Danielsen
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Re: Volume Modeling of the Big Pine at Lilydale

Post by Erik Danielsen » Fri Nov 17, 2017 9:41 am

Thanks for the feedback, Bob.

I came to realize that in attempting to mimic the "above eye-level" formula I had gotten the concept backwards and subtracted an approximate radius from my slope distances, since I had been measuring to the trunk's outer edge rather than its closest point. Instead I should have used the original slope distances with the simple reticle formula. I have recalculated the volume to reflect this and will edit the original post.

The recalculated volume is 885.24 ft3 (min 855.41, max 915.06). For reference, the volume I originally posted was 852.2 ft3.

As Bob pointed out, calculating the volume for frustums of an ellipse rather than just averaging out the difference in diameters from different directions would produce a slightly higher volume than this. This would probably put this tree right in the neighborhood of 900 ft3. Not too shabby for Chautauqua County's tallest (known) tree.

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dbhguru
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Re: Volume Modeling of the Big Pine at Lilydale

Post by dbhguru » Fri Nov 17, 2017 2:41 pm

Erik,

If we use a form factor of 0.43, then the volume calculates to 887 ft^3, or only 2 cubes more than what you got. For single-trunk pines in the age range of Lilydale, a form factor between 0.42 and 0.44 usually works. Your modeling substantiates the form factor range for mature pines. For the stoutest of trunks, we can see 0.45 or even 0.46, but that is about as high as we'll see when we apply the factor to the entire trunk.

Bob
Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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dbhguru
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Re: Volume Modeling of the Big Pine at Lilydale

Post by dbhguru » Fri Nov 17, 2017 6:26 pm

Erik, et. al.,

I had an error in the Excel encoding of the neiloid frustum formula. The attachment below corrects the error, plus adds a couple more columns for clarity.

Bob

Orig Post

Attached is an Excel spreadsheet that employs the reticle-based monocular to model trunk volume. I've included it in response to Erik's intention to do reticle-based modeling on NY's big pines.

A future version of the Excel spreadsheet will incorporate calculations for both circular and elliptical frustums. This one is based solely on circular trunk cross-sections. I also plan to include a calculator to identify the locations on the trunk where each measurement is to be taken. This is especially challenging where in moving to a point 90 degrees from the first shot, you lose track of the target point on the trunk. If we are going to test for an elliptical cross-section, we need diameter measurements at the same point at 90 degrees to one another.

We hope to apply this spreadsheet-driven methodology for the new big white pine site in the Adirondacks, which already has the greatest concentration of 12-foot+ CBH pines that we know of, and the team of Erik Danielsen, Elijah Whitcomb, Jared Lockwoood, and my son Rob is nowhere near finding all the biggies.

This remarkable site already claims New York's tallest tree at 163.2 feet. And the count of 12-foot circumference pines currently stands at 16, if I have counted right. I think the count of 150-footers stands at 7.

Getting the word out on the importance of these big pines is going to take some work. Ideally, Paul Smiths College can be an ally if they can take a serious interest in non-managed forest. Remains to be seen.

Bob
Attachments
Reticle Volume Modeling.xlsx
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Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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