limb and tree measurement
limb and tree measurement
Hi there. my name is rick and i am wondering if there is an expert in measuring out there using a rangefinder and solo monocular that i could run a couple thoughts by.
my easy question would be about measuring a large limb. it seems to me when measuring the size on a limb you would take the dimensions using the smallest possible circumference that could be done that would include the crotch of the limb. whether it is vertical or at any other angle really would not come into play, is that correct? are there any other variables or conventions that i need to be aware of? and the limb is very elliptical, it's much taller than it is wide at the base. Do we consider or refer to that characteristic at all?
the second question is harder. i am using the successive cones piled on top of one another method to calculate total volume of sequoias and i think i am good with the v=(pi/12)(H)(d1sq+d2sq+d1xd2sq) for the successive conical sections but how do you work the base when it is on a sloped piece of ground? i have not really found a good/easy formula that i am happy with for getting a really accurate flared base volume.
also what are the rules/conventions for the peak? sometimes it looks like a nice cone, or there is a conical dead spike, but often there are what really are limbs above the end of the tree's trunk. And what should we do when there is a broken/topped tree? some like that i think i should legitimately ignore the foliage above as being limbs, not bole, and just end the calculation with the topmost conical section.
anyone out there who is experienced at this and could give me a couple pointers or advice on the right way to do it?
my easy question would be about measuring a large limb. it seems to me when measuring the size on a limb you would take the dimensions using the smallest possible circumference that could be done that would include the crotch of the limb. whether it is vertical or at any other angle really would not come into play, is that correct? are there any other variables or conventions that i need to be aware of? and the limb is very elliptical, it's much taller than it is wide at the base. Do we consider or refer to that characteristic at all?
the second question is harder. i am using the successive cones piled on top of one another method to calculate total volume of sequoias and i think i am good with the v=(pi/12)(H)(d1sq+d2sq+d1xd2sq) for the successive conical sections but how do you work the base when it is on a sloped piece of ground? i have not really found a good/easy formula that i am happy with for getting a really accurate flared base volume.
also what are the rules/conventions for the peak? sometimes it looks like a nice cone, or there is a conical dead spike, but often there are what really are limbs above the end of the tree's trunk. And what should we do when there is a broken/topped tree? some like that i think i should legitimately ignore the foliage above as being limbs, not bole, and just end the calculation with the topmost conical section.
anyone out there who is experienced at this and could give me a couple pointers or advice on the right way to do it?
Re: limb and tree measurement
Hi Rick,
Welcome aboard. I'll address your questions within the next couple days. You've come to the right place. Trunk modeling is our business.
Bob
Welcome aboard. I'll address your questions within the next couple days. You've come to the right place. Trunk modeling is our business.
Bob
Robert T. Leverett
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Re: limb and tree measurement
Rick,
Here is the promised response. First, if you go to Measurement and Dendromorphometry on the BBS, the following posts contain information on trunk/limb modeling.
1. Trunk Taper Equations
2. Reticle Testing
3. Use of reticle for measuring limb length
4. Elliptical conical frustums
5. Calculating the Lower Basal Wedge – Alternate Method
6. Simplified Equation For Lower Basal Wedge  Improved Model
7. Improved model for lower basal wedge volume
8. Trapezoid Method Continued
9. Limb Length Using Monocular w/reticle and Rangefinder
10. Limb Length Using 3D coordinates
On routine trunk volume modeling, calculating volume with a reticle is a matter of establishing a series of adjacent frustums starting at the base and moving upward. The norm is usually to treat each frustum as regular conical, but you can use other types of frustums, e.g. paraboloid, neiloid, or an intermediate form. We have Excel spreadsheets NTS to implement different strategies. If frustums based on a circular crosssection is not assumed, the alternative is usually elliptical.
As a starter, two attachments are offered. The first presents an Excel spreadsheet modeler with an actual example. It allows you to divide a trunk into adjacent frustums and calculate the volume of each for several frustum types, showing the result and allowing you to select which type you want to settle on. For example, the lowest frustum is likely to be neiloid. You might have more than one. Farther up the trunk, the best form selection is likely to be paraboloid for frustums of say 10 feet or more, and finally conical for the upper 1/3rd to 1/4th. The spreadsheet allows you to make choices. Erase the green cells to enter a new problem.
Given the base and top diameters and height of a frustum, the second spreadsheet show predicted radii along the frustum for each of the expressed frustum types. This is more of a show and tell spreadsheet to illustrate the different taper rates given the base and top diameters and the height. For instance, how much different is a paraboloid from a cone for the given frustum. The first spreadsheet is the workhorse. It allows you to divide the trunk into 16 frustums. You can unprotect the spreadsheet and expand the number of rows if you are Excel proficient. Not that it also calculates the carbon held in the model. There is no password, so you can unprotect it. However, if you are not Excel proficient, I can create a version with more rows for you if you wish  a benefit of being in NTS. If you use the spreadsheet in a study, report, etc. just give an acknowledgement for where it comes from.
If you have questions, please don't hesitate to ask. I would also note that Michael Taylor, the VP of the Western native Tree Society (WNTS) is a member here. WNTS ia an arm of NTS as is ENTS. There's virtually no question you could ask Michael that he couldn't answer.
Bob
Here is the promised response. First, if you go to Measurement and Dendromorphometry on the BBS, the following posts contain information on trunk/limb modeling.
1. Trunk Taper Equations
2. Reticle Testing
3. Use of reticle for measuring limb length
4. Elliptical conical frustums
5. Calculating the Lower Basal Wedge – Alternate Method
6. Simplified Equation For Lower Basal Wedge  Improved Model
7. Improved model for lower basal wedge volume
8. Trapezoid Method Continued
9. Limb Length Using Monocular w/reticle and Rangefinder
10. Limb Length Using 3D coordinates
On routine trunk volume modeling, calculating volume with a reticle is a matter of establishing a series of adjacent frustums starting at the base and moving upward. The norm is usually to treat each frustum as regular conical, but you can use other types of frustums, e.g. paraboloid, neiloid, or an intermediate form. We have Excel spreadsheets NTS to implement different strategies. If frustums based on a circular crosssection is not assumed, the alternative is usually elliptical.
As a starter, two attachments are offered. The first presents an Excel spreadsheet modeler with an actual example. It allows you to divide a trunk into adjacent frustums and calculate the volume of each for several frustum types, showing the result and allowing you to select which type you want to settle on. For example, the lowest frustum is likely to be neiloid. You might have more than one. Farther up the trunk, the best form selection is likely to be paraboloid for frustums of say 10 feet or more, and finally conical for the upper 1/3rd to 1/4th. The spreadsheet allows you to make choices. Erase the green cells to enter a new problem.
Given the base and top diameters and height of a frustum, the second spreadsheet show predicted radii along the frustum for each of the expressed frustum types. This is more of a show and tell spreadsheet to illustrate the different taper rates given the base and top diameters and the height. For instance, how much different is a paraboloid from a cone for the given frustum. The first spreadsheet is the workhorse. It allows you to divide the trunk into 16 frustums. You can unprotect the spreadsheet and expand the number of rows if you are Excel proficient. Not that it also calculates the carbon held in the model. There is no password, so you can unprotect it. However, if you are not Excel proficient, I can create a version with more rows for you if you wish  a benefit of being in NTS. If you use the spreadsheet in a study, report, etc. just give an acknowledgement for where it comes from.
If you have questions, please don't hesitate to ask. I would also note that Michael Taylor, the VP of the Western native Tree Society (WNTS) is a member here. WNTS ia an arm of NTS as is ENTS. There's virtually no question you could ask Michael that he couldn't answer.
Bob
 Attachments

 VolumeOfConeparaboloidNeiloidFrustumsDoakie8272018 copy 2.xls
 (4.6 MiB) Downloaded 10 times

 RadiiForDifferentFrustumForms.xlsx
 (146.45 KiB) Downloaded 10 times
Robert T. Leverett
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Re: limb and tree measurement
bob; thanks for the response. i will look at the spread sheets and see if they will assist. and i want to read about the basil wedge subjects mentioned in your response, that is one of the major points of contention in my mind that i have to get straight.
i will be going up to look at some trees over the long weekend. i have made up a form for myself to fill out taking down, i think, all of the pertinent details. i think it has on it all that i really need to measure. perhaps when i get back with it we can run thru some actual cases numbers. i was just going to crunch the numbers manually using the equations (noted on the form) not an excel program as i have not used that before.
thanks muc, more after the weekend...
i will be going up to look at some trees over the long weekend. i have made up a form for myself to fill out taking down, i think, all of the pertinent details. i think it has on it all that i really need to measure. perhaps when i get back with it we can run thru some actual cases numbers. i was just going to crunch the numbers manually using the equations (noted on the form) not an excel program as i have not used that before.
thanks muc, more after the weekend...
 Attachments

 Tree Calculations Chart.docx
 (15.68 KiB) Downloaded 14 times
Re: limb and tree measurement
Rick,
Nifty WORDbased worksheet format. It would be easy to convert to Excel where calculations would be automatically done for you. Not a big deal though.
Looking at the frustum lengths on your worksheet, there's a good chance that they will conform more to a paraboloid frustum than the conical one called for in your worksheet. Traditional forestry would treat the frustum as a log and apply a formula that assumes a paraboloid shape. In addition, for the frustum between chest and 60 feet, there's a good chance that the crosssectional area isn't exactly circular. If you suspect this, You could go 90 degrees to the set of measurements taken from chest and 60 feet and take a second set and then apply the following formula.
In the formulas, R1 and R2 are the semimajor and semiminor axes of the chesthigh base and r1 and r2 are the counterparts at 60 feet. For small, wellbehaved trees, the extra set of measurements are usually not worth the effort, but for behemoths such as what you are dealing with, shape matters.
BTW, what is the origin of the sin .58 in your diameter formula?
Bob
Nifty WORDbased worksheet format. It would be easy to convert to Excel where calculations would be automatically done for you. Not a big deal though.
Looking at the frustum lengths on your worksheet, there's a good chance that they will conform more to a paraboloid frustum than the conical one called for in your worksheet. Traditional forestry would treat the frustum as a log and apply a formula that assumes a paraboloid shape. In addition, for the frustum between chest and 60 feet, there's a good chance that the crosssectional area isn't exactly circular. If you suspect this, You could go 90 degrees to the set of measurements taken from chest and 60 feet and take a second set and then apply the following formula.
In the formulas, R1 and R2 are the semimajor and semiminor axes of the chesthigh base and r1 and r2 are the counterparts at 60 feet. For small, wellbehaved trees, the extra set of measurements are usually not worth the effort, but for behemoths such as what you are dealing with, shape matters.
BTW, what is the origin of the sin .58 in your diameter formula?
Bob
Robert T. Leverett
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Re: limb and tree measurement
what i have been trying to do is take measurements at points where there is a slope break in the silhouette of the tree rather than at the traditional 60, 120, 180 feet heights. it seems like it would provide a truer estimate. and i usually wrap a tape measure around the tree 3 times, one level at chest height, once level at the highest ground height in addition to getting the perimeter at the ground's actual slope. that way i can have probably more exact numbers at the biggest volume section. i am not sure how to deal with the wedge below highest level of the ground that is left. sometimes that is a pretty big number, especially in a couple of the atwell mill trees. i will run the numbers on a couple trees using your above formula and see what they come up with. i have measurements on a couple trees that are noted in flints book and i will see if i come up near his numbers.
the sin .58 is from me testing the solo on some known width things, like garage doors and such when i was checking it out. it also is singularly close to multiplying by one, which makes me wonder if the solo designers mathematically set up the gradient lines so that i actually don't need that. i have not chased them down on that yet to ask tho. how do you translate your viewfinder grid lines into diameter's?
it also occurs to me that the angle of the view on the solo gridlines will be slightly smaller at the edge of the viewfinder than the center. do i have to worry about or maybe put in a multiplier to correct for it if i measure a 100 hash mark width versus a 10 hash mark width? do you know much about solo's?
the sin .58 is from me testing the solo on some known width things, like garage doors and such when i was checking it out. it also is singularly close to multiplying by one, which makes me wonder if the solo designers mathematically set up the gradient lines so that i actually don't need that. i have not chased them down on that yet to ask tho. how do you translate your viewfinder grid lines into diameter's?
it also occurs to me that the angle of the view on the solo gridlines will be slightly smaller at the edge of the viewfinder than the center. do i have to worry about or maybe put in a multiplier to correct for it if i measure a 100 hash mark width versus a 10 hash mark width? do you know much about solo's?
Re: limb and tree measurement
hey, in the case of a circular/non elliptical tree your above formula is exactly the same as the one on my sheet isn't it? After replacing the radii with diameters that is. the above formula is for a simple conical frustum yes? i was thinking that if i took frequent data points on the trunk and did them specifically where i saw shape changes i could do a pretty good estimate using the conical frustum sections and would not have to worry about paraboloid or neiloid shapes.
i would think however for the lower trunk if i saw a large curvature on it and i wanted to be particularly exacting that a neiloid not a paraboloid frustum would be more appropriate. that more closely resembles the flare at the bottom under 60 feet i think. but that formula is a little more complex, doable with the same measurements however. maybe the top sections would be better done with a paraboloid equation...?
i would think however for the lower trunk if i saw a large curvature on it and i wanted to be particularly exacting that a neiloid not a paraboloid frustum would be more appropriate. that more closely resembles the flare at the bottom under 60 feet i think. but that formula is a little more complex, doable with the same measurements however. maybe the top sections would be better done with a paraboloid equation...?
Re: limb and tree measurement
Rick,
I own a Vortex Solo RT 8x36 along with three other monoculars. All of them use the following formula for calculating the width of a flat target: W = MD/F where M = reticle reading, D = distance to center of target, and F = manufacturer's factor. I added an adjustment for circular trunks to get W = MD/(F0.5M). In the case of the Vortex, F is 1000. My Bushnell Legend UltraHD 10x 42mm should be the same, but needs an adjustment. Its factor is 1021. Using this factor, I just completed 5 tests. Here are the results.
I am always amazed at just how good these instruments are. Now to your comments/questions.
Looking for points of inflection is the right way to do it. Find where the taper changes. The wedge is covered in BBS post referred to as 5, 6, and 7 in my list from a previous post. The formula shown in the July 4th 2:20PM post is for an elliptical conical frustum. Reticle readings at the edges of the reticle versus in the middle are an issue that I've not spent much time with, but maybe now is the time.
In terms of whether you want to switch from a cone to a paraboloid, you could choose an intermediate point, measure it and use the trunk taper equation (1 in the previous list) to see if the radius matches the expected value for a paraboloid. This strategy only makes sense for long frustums. For short ones, cone is fine.
Bob
I own a Vortex Solo RT 8x36 along with three other monoculars. All of them use the following formula for calculating the width of a flat target: W = MD/F where M = reticle reading, D = distance to center of target, and F = manufacturer's factor. I added an adjustment for circular trunks to get W = MD/(F0.5M). In the case of the Vortex, F is 1000. My Bushnell Legend UltraHD 10x 42mm should be the same, but needs an adjustment. Its factor is 1021. Using this factor, I just completed 5 tests. Here are the results.
I am always amazed at just how good these instruments are. Now to your comments/questions.
Looking for points of inflection is the right way to do it. Find where the taper changes. The wedge is covered in BBS post referred to as 5, 6, and 7 in my list from a previous post. The formula shown in the July 4th 2:20PM post is for an elliptical conical frustum. Reticle readings at the edges of the reticle versus in the middle are an issue that I've not spent much time with, but maybe now is the time.
In terms of whether you want to switch from a cone to a paraboloid, you could choose an intermediate point, measure it and use the trunk taper equation (1 in the previous list) to see if the radius matches the expected value for a paraboloid. This strategy only makes sense for long frustums. For short ones, cone is fine.
Bob
Robert T. Leverett
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Re: limb and tree measurement
great, i will just take a lot of reading points when there is a greater amount of taper change. that makes it easy. i already started doing that actually. i found i didn't have enuf calculation lines on the bottom of my form and had to write in more in the margins over the last weekend...
i think the monocular i have is the same Solo RT 8x36 you use, i will look and confirm tonite, but it sure looks like it when i googled it. so i can try out my formulae with your width calculator equation and manufacturers factor also.
what i have been doing for the circular trunk adjustment is to work the diameter up using the rangefinders distance so i can see the approx. diameter and then do it again with the distance corrected for the radius of the tree. i basically run the equation once just to estimate the radius and then do it again to get the real answer with the estimated radius from the first work up added to the distance. i can do it a third time if it changes the radius significantly. with my trunk diameters being on the large side i figured that would be important. and its actually easier than it sounds, you just multiply in the distance last, getting your estimate, divide it out to remove it, and then multiply it again using the corrected distance.
do you think that will be better than adding the .5m to the equation divisor or is there a reason why you do the .5m? would you approve of my current modus operandi?
i suppose i will have to just check on the readings at the edge of the reticule by measuring things from different distances and see if i need a factor added for excessive reticule widths. that'll be a good weekend project for me. : )
thanks for all the help and useful advice by the way!
i think the monocular i have is the same Solo RT 8x36 you use, i will look and confirm tonite, but it sure looks like it when i googled it. so i can try out my formulae with your width calculator equation and manufacturers factor also.
what i have been doing for the circular trunk adjustment is to work the diameter up using the rangefinders distance so i can see the approx. diameter and then do it again with the distance corrected for the radius of the tree. i basically run the equation once just to estimate the radius and then do it again to get the real answer with the estimated radius from the first work up added to the distance. i can do it a third time if it changes the radius significantly. with my trunk diameters being on the large side i figured that would be important. and its actually easier than it sounds, you just multiply in the distance last, getting your estimate, divide it out to remove it, and then multiply it again using the corrected distance.
do you think that will be better than adding the .5m to the equation divisor or is there a reason why you do the .5m? would you approve of my current modus operandi?
i suppose i will have to just check on the readings at the edge of the reticule by measuring things from different distances and see if i need a factor added for excessive reticule widths. that'll be a good weekend project for me. : )
thanks for all the help and useful advice by the way!
Re: limb and tree measurement
Rick,
Here is the source of the 0.5M factor.
So, you can see that if the target is truly circular, the adjustment is mathematically provable. I have an Excel workbook that offers eight reticle methods and their mathematical derivations. The workbook is 4.5 Mbytes, so I don't like to post it here. However, if you email me via the BBS, I can send you a copy. You can also send me an email directly to dbhguru@comcast.net, my regular email address. BTW, you experimental method for adding in the extra radial distance I fine, but the 0.5M is the theoretical adjustment. If you suspect that the trunk is not circular, you can use one of the other methods in the workbook that lift that assumption.
Since you are in California, I'm hoping that Michael Taylor will weight in. He has an unlimited amount of experience to offer.
Bob
Here is the source of the 0.5M factor.
So, you can see that if the target is truly circular, the adjustment is mathematically provable. I have an Excel workbook that offers eight reticle methods and their mathematical derivations. The workbook is 4.5 Mbytes, so I don't like to post it here. However, if you email me via the BBS, I can send you a copy. You can also send me an email directly to dbhguru@comcast.net, my regular email address. BTW, you experimental method for adding in the extra radial distance I fine, but the 0.5M is the theoretical adjustment. If you suspect that the trunk is not circular, you can use one of the other methods in the workbook that lift that assumption.
Since you are in California, I'm hoping that Michael Taylor will weight in. He has an unlimited amount of experience to offer.
Bob
Robert T. Leverett
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre
Cofounder, Native Native Tree Society
Cofounder and President
Friends of Mohawk Trail State Forest
Cofounder, National Cadre