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I stand corrected.
Thanks Steve for pointing out the grievous error I made in mistakenly substituting the dimension of the wide end 12' in place of H in the frustum formula. Correctly the figure to be substituted for H (height or length between ends) should of been 40' not 12'. That error caused me to come up with a figure that was a long ways short of what the true weight was.
One thing is for sure a rolling log of 190,000 lbs might not stop with just one house.
I can just see that helicopter lifting his capacity of maybe 40,000 lbs with 150,000 lbs of sawdust blowing around.
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<i>> To: <a href="/cgi-bin/mail?to=schrader@beaches.net&replyto=9703130819.AA15255@spectre.ag.uiuc.edu&subject=Re:%20Re:%20Re:%20Analyzing%20tree%20weight%20formulas">schrader@beaches.net</a></i>
<i>> Subject: Re: Analyzing tree weight formulas</i>
<i>> Date: Wednesday, March 12, 1997 6:07 AM</i>
<i>> </i>
<i>> George,</i>
<i>> </i>
<i>> thanks for your interesting article. I would like to make just a few comments.</i>
<i>> </i>
<i>> Please let me know if I missed something fundamental here (and I apologize if I did!)</i>
<i>> </i>
<i>> >...bases with this sum multiplied by .2618 times the altitude</i>
<i>> </i>
<i>> </i>
<i>> I usually work at around sea level altitude but yesterday I worked in the mountains (picking seed of Euc. regnans) at about 2000 metres (+ the trees were between 150 and 200 feet). How does the altitude affect the volume of wood? ;)</i>
<i>> (I suspect 'altitude' is a slang for height in USA)</i>
I have never seen a Euc or Redwood for that matter. The tallest tree I have ever been in has been Norfolk Island Pine in Miami, Florida USA that was about 140'. The only seeds I want to pick off trees like that are on the ground. I can remember eating lunch in a not so large White Oak in St. Louis, Mo. I thought it was massive. Seems I have some wonders to behold.
<i>> By my figuring your crane (and the other author's helicopter) crane just tipped over and crushed a house! I think you may have made a mistake in using your own formula - V = .2618H ( D2 + d2 + Dd ) = .2618 @ H @ ( D2 + d2 + Dd ) - you have used 'D' in place of 'H' (?).</i>
<i>> </i>
<i>> Using 'H', as in 0.2618 x 40 you get an result something like 2638 f3 (cubic feet) which works out to be around 190,000 lbs! or 3.3 times your estimate of 57,001.1904 lbs! (btw I think using decimal places in the outcome of this type of estimation (especially to the fifth place) is not necessary and tends to imply that it is that accurate).</i>
I had used a calculator and copied the figures from it and had neglected to delete the decimals.
<i>> I think the problems have come in using the 'cord' in the estimation. As you point out not everyone is sure of what a 'cord' is and the guy you quote obvious has a different idea too. Why not just convert stait to cubic feet (or better still - cubic metres!)?</i>
<i>> Interestingly enough though, using his estimate of 20 cords and your definition of the weight of a cord you come up with 194560 lbs! - the closest yet!?</i>
<i>> </i>
<i>> I reckon either the original tree in question was a giant redwood!</i>
The original tree was supposed to be a Euc.
<i>> I'm not posting this to the news group because I'm not interested in embarrassing you or in 'point scoring'. I will leave it to you to make any 'erratum' (before someone actually hires a helicopter to lift their tree!). </i>
I thank you for the consideration about saving me some embarrassment but personally I would much rather know why I was wrong.
<i>> Would it be much different to use just the average between the two end diameters instead of using the frustum of cones? e.g.: Pi (3.14) x r2 (radius squared) x L (length) where r2 is the average of D and d ? - math is not my strong point!</i>
Math isn't my strong point either.
Mikes result averaging the end sizes yielded 2,543 Cubic feet.
Mine using the frustum formula yielded 2,638 cu. feet
That leaves a difference of 95 cu. ft. @ 72lbs or 6,800 lbs in Live Oak weight. I think that computes to an error of 3 or 4 percent over all. Averaging the ends appears to be 96.3 % accurate, close enough for our standards, I think.
Mike Oxman <a href="/cgi-bin/mail?to=oxman@chatlink.com&replyto=9703130819.AA15255@spectre.ag.uiuc.edu&subject=Re:%20Re:%20Re:%20Analyzing%20tree%20weight%20formulas">oxman@chatlink.com</a> contributed that point of averaging the end sizes with this following formula for a cylinder.
Average the log (6' + 12' divided by 2) out to a cylinder 9 feet in diameter.
Use the Pi X Radius squared X Length formula for cubic volume of a cylinder.
4.5' X 4.5' = 20.25 X 3.14 = 63.585 Sq. ft. X 40' = 2,543 Cubic feet
2,543 divided by 128 cu ft. per cord = 19.87 cords
20 cords times 6,000 lbs per cord = 120,000 lbs = 60 tons
Mike of course used an estimate of cord weight at 6,000 lbs.
Truth is neither one of us is sure what Euc weighs per cu ft or by the cord. I think we are both guessing as to its real weight.
It has been a very interesting exercise anyway.
Do you know what Euc weighs or possibly where one might find out?
Thanks again for your critical attention and your kind thoughts.
<i>> regards,</i>
<i>> </i>
<i>> Steve Fitzgerald</i>
I have corrected the mistake in the formula below.
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George <a href="/cgi-bin/mail?to=schrader@beaches.net&replyto=9703130819.AA15255@spectre.ag.uiuc.edu&subject=Re:%20Re:%20Re:%20Analyzing%20tree%20weight%20formulas">schrader@beaches.net</a> ISA Cert. Arborist SO-0448
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A log with a 12 foot dia. On the big end, 40 foot of length, and 6 foot dia on the small end.
Using the frustum method from the second edition of Related Mathematics for Carpenters. By the way its no longer available its about 23 years old but you may be able to secure a Third edition of Practical Mathematics published by the American Technical Society.
To figure the volume of a evenly tapered log.
If the top of a cone is cut off by a plane parallel to the base the part remaining is a frustum.
Formula = The volume of the frustum of a cone is equal to the sum of the squares of the diameters of the bases, plus the product of the diameters of the bases with this sum multiplied by .2618 times the altitude.
Formula
You will need to substitute in the figures for the letters.
V = volume of log
D = big diameter end of log
d = small diameter end of log
H = Height or distance between ends of log
V = .2618H ( D2 + d2 + Dd ) = .2618 @ H @ ( D2 + d2 + Dd )
D = 12 = foot diameter on big end
d = 6 = foot diameter on small end
H = 40 = height or distance between ends
V = .2618 by 40 ( 12 to 2nd power + 6 to 2nd power +12 by 6 )
V= .2618 by 40 by ( 12 to 2nd power + 6 to 2nd power + 12 by 6 )
V = 10.472 (144 + 36 + 72)
V = 10.472 by 252
V = 2638.944 cu. feet
If the logs volume is 2638.944 cu feet and there are 128 cu feet in a cord than 2638.944 divided by 128 should equal how many cords are in the log.
2638.944 cu. ft. divided by 128 = 20.61675 cords.
The logs weight can now be determined by multiplying the actual weight of the species of wood by the number of cubic feet determined to be in the log.
Since Oak weighs 72 lbs per cu foot than the log would weigh 72 lbs. Times 2638.944 cu. ft. and the log in Live Oak would weigh 190,003.968 lbs
One thing that bothers me is that a cord is equal to 128 cu feet and with Live Oak at 72 lbs. A cord of Live Oak should weigh 72 by 128 = 9,216 lbs. Mike believes Euc is heavier than live Oak by about 20%.
Using the chart that shows live Oak to weigh 76 lbs per cubic foot. And the frustum formula to get a volume of the log of 2638 cu. ft.
A Live Oak log would weigh 190,003 lbs.
Since in the believe that he could be right about Euc weighing 20% more than Live Oak.
Adding 20% to 190,003 lbs. = using his observation as to the weight for Euc the log could weigh 228,004 lbs.
Personally I would suspect the specie weight per cu foot to be about the same as sycamore or Cottonwood as they are two of the biggest trees I know and their weight is about 50 lbs per cu foot.
2638 cu. ft. at 50 lbs per cu. ft. The log could weigh as little as 131,900 lbs.
Go Figure!!!!!!!!!!!!!!!!!
George <a href="/cgi-bin/mail?to=schrader@beaches.net&replyto=9703130819.AA15255@spectre.ag.uiuc.edu&subject=Re:%20Re:%20Re:%20Analyzing%20tree%20weight%20formulas">schrader@beaches.net</a>
ISA Certified Arborist SO-0448
American Tree Services 904 769 4060
Panama City, Fl.