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If the unpointy top bit at 75' had an effective diameter even of only 6" (0.5'), the frustrum-of-a-cone volume would go up quite a bit more to 84.4 cu ft and the weight up to 2868 lb, or 1.43 US (short) tons. Very weighty.
I gave up trying on the web to find out the predicted volume of a white (?) spruce's branches and leaves, given the known dimensions of the trunk, though I'm sure it's out there. There are lots of formulae for estimating trunk volume, but most foresters are concerned with harvestable trunk wood and not with branches/leaves, which as we know in these parts are now mostly biomassacred.
This did turn up an interesting and widely confirmed observation though, made by Leonardo da Vinci as to why trees aren't overly top-heavy and so don't simply splinter under the weight of their own branches: he had noticed that the total thickness of branches at a particular height in a tree is equal to the thickness of the parent trunk at that height -- a still-believed approximation even in use by graphics illustrators to draw supposedly realistic branching trees, but still lacking a clear physical explanation.
There's an associated formula and possible modern explanation for Leonardo's rule, stemming (sic) from a tree's need to limit the effect of excessive wind shear summed on the canopy leaves, at
http://www.wired.com/2011/11/branching-tree-physics/
Steve (Hfx)
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of pce@accesswave.ca [pce@accesswave.ca]
Sent: Wednesday, May 18, 2016 7:06 PM
To: naturens@chebucto.ns.ca
Subject: [NatureNS] A weighty tree
A storm a few years ago brought down a big spruce in the forest behind
our house. In falling, the tree bumped up against, and landed on,
various other neighbouring trees, pressing some of them flat and causing
others to lean at odd angles.
I was wondering just how much a big tree like that might weigh, so today
I went out and measured it.
The broken-off part (above the stump) is about 75' long (forgive the
Imperial measure), and the circumference at the base of the broken-off
part is 5'7". Modelling the stem as a cone, that gives a volume of 60.6
cubic feet. Using a typical density for green (i.e. not dried) spruce of
34 lb/cubic foot, I get a weight of the stem alone of slightly over 2000
lb., or one ton.
Of course the branches and needles would add more weight, but I don't
have a good figure for that. It would depend upon just how bushy the
tree was. I'd be happy to say somewhere around 500 pounds, though.
A big tree!
Peter Payzant
Waverley
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