The varying results from tangent measurements

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The varying results from tangent measurements

Post by dbhguru » Tue Jun 02, 2015 12:34 pm

Hi All,

As the AF MGWG struggles to elucidate measuring challenges for Cadre apprentices, it struck me that one aspect of comparing tangent with sine-based height measurements gets overlooked. For a particular tree, provided one can see the top and base from different locations, and assuming there is a horizontal top to base offset, one gets different heights from different locations using tangent method, but the same results using sine. I'm unsure if this is widely understood. I presume that most traditional measurers assume that if you get to a convenient location where top and base are visible that measuring the tree with the conventional tangent method yields the correct height, and that moving to a different location with equally good access would yield the same results. Not so! The attached Excel spreadsheet is meant to allow the user to play what-if games.

The measurer assumes a tree with a specified height, H, a set baseline distance to the trunk, D, and a specific top to base horizontal offset, S, e.g. 110, 100, and 15. Keeping the baseline fixed in distance, the user moves around the tree and takes readings and calculates the height using tangent. We assume visibility of top an base from all locations. One other statistic can be computed by the measurer, the horizontal angle ß between the top and base as seen at the position of the eye. This angle can be determined with a compass. So, we have the inputs H, D, S, and ß. The spreadsheet allows the user to plug in assumed values for H, D, S, and ß and see the impact on height, i.e. the height error that results from location. If S is 0, there are no errors. The formula in the spreadsheet for baseline error assumes S>0. Different values of ß are tried, keeping to the constraint that ß<=atan(S/D). If this constraint is not met the direction from eye at the angle ß missed the top.

So, as the measurer circles the trunk at the set distance of D (assumed to be the level distance), the angle ß changes.For a particular tree, we compute the error in the baseline and height as a function of ß. I'm thinking of a spreadsheet that shows the position of top and trunk with assumed values for H, D, and S and computes the tangent height from random locations marked by subscripted x values and associated height. The distances would be scaled. The resulting scatter of different values would likely open a few eyes.

If we dug up all our old posts on sine versus tangent, the list would be amazingly. But this is what it takes to shift folks off decades of measuring trees by the tangent method.

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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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Re: The varying results from tangent measurements

Post by Don » Wed Jun 03, 2015 2:06 am

Going back to old, old posts I recall conversations on trying to put a tree's lean at right angles to minimize the effect of lean on height...of course there were two locations (opposite each other) where that occurs. And I was aware of the tree seeming higher as I approach in the direction of the tree's lean, and how from an opposite direction, that same lean seemed lower.

But I don't think I ever conceptually animated it, as if I were circling it, and observed the tree's top APPEAR to rise and fall...

But taking four quadrant-ed TANGENT measures on the same tree and getting four (make that three, if aligned so) different readings; that would be diagnostic of a problem with the TANGENT follow the same path taking SINE measures and all of the readings approaching a common height would diagnostically support SINE-SINE as superior method.
Don Bertolette - President/Moderator, WNTS BBS
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