Gaines,
You are absolutely correct. Older pines, in particular, change their trunk curvature. The formula has limited applicability. Bob ----- Original Message ----- From: "Gaines McMartin" <[email protected]> To: [email protected] Cc: [email protected] Sent: Monday, January 11, 2010 9:42:55 AM GMT -05:00 US/Canada Eastern Subject: Re: [ENTS] Projected heights Andrew, Bob, Don, etc.: I think you need to be very careful with these projections. The problem I have with any model based on any existing white pine trees is that the theory that there were 250 (or whatever) foot tall white pines in the past is besed on the idea that those trees were much older than the tallest we see today. From the white pines we see today we can be fairly sure that trees of similar ages did not grow significantly taller--we have enough data to say that trees of the age of the present tallest white pines are at or very near the maximum possible for any white pine not signigicantly older. But there were, in the past, white pines that at least had the opportunity to grow taller for something like 400 years. None of the present tallest white pines, as far as I know, approach that age. If they do, they have reached their maximum height. But, of course, if the very tall white pines in virgin forests, like the one preserved in the Cook Forest, were 400 years old and not 250 feet tall, we could look and see if they are growing on the best kind of growing site. It is on the assumption that the much older white pines of the past had a longer time to grow very tall, and were growing on a superior growing site, that the theory of 250 white pines must be based Now my concern is that the older a white pine gets, the more its trunk taper near the top changes. The taper near the top of old--200 year or so--white pine trees increases as their age increases even more. I don't think you can really do a good model of the form of a very, very old white pine, and do height projections, based on data from other old, but not nearly so old white pine trees. --Gaines Mcmartin -------------------------------------------------------------------------- On 1/10/10, Andrew Joslin <[email protected]> wrote: > To deal with the variations in a real world non-uniform white pine trunk > taper would it be possible to pick a tree that we have volume data on, > (either a Smokies, Mohawk or Cooks tall white pine), use it as a model > case, apply its irregular form/taper to the values required for a Royal > Navy mast and see where the height falls so-to-speak? This would have a > fairly high margin of error since we know the form of a white pine top > so variable, might be able to get within 15-20 ft. which is better than > nothing. But... if this exercise was done across say 20 of the tallest > white pines in the east the margin of error might be reduced to > something usable. > > Is there a way to come up with a value for average thickness of bark and > cambium/sapwood at the base of the trunk and at the upper end for a > mature white pine to factor in approximately what the top and bottom > diameter of the log section needed to be before it was shaped into a > mast sized log? Maybe it's too early in this thought process to start > trying to work on that variable. > > Not being very mathematically inclined I can only suggest possibilities > but can't actually come up with the algorithms. > -AJ > > Bob wrote: >> Don, ENTS, >> >> The following formula projects the remaining height of a tree >> using a main log and an assumption about overall trunk form. I will >> use computer symbols for the mathatical operators. >> >> Let >> >> R1 = radius of lower end of log >> R2 = radius of upper end of log >> L. = length of log >> H. = height of remainder of tree >> P = form factor >> >> P = 0.5 for paraboloid >> P = 1 for cone >> P = 1.5 for neiloid >> >> Then >> >> H = [L * R1^(1/P)] / [R2^(1/P)- R1^(1/P)] >> >> If you apply this formula, you quickly see than assuming a conical >> form leads to a greater height than assuming a paraboloid form. >> >> The actual trunk form may change several times, so that this >> approach to projecting remaining height probably can't be reliably >> used for many conifers - especially older ones. I'll give examples in >> another email. Typing on this iPhone is a pain in the #%*. >> >> Bob >> >> Sent from my iPhone >> >> >> > >
