Volume of Log - Calculation

I would like to have someone check my rather simple way of working out the cubic meter volume of a log.
I assume that 2piR is the formula, so
300 mm diameter log = 2 x 3.14159 x 150 mm = 940 mm square, or 0.094 m cubic over 1 meter.
If the log is 6 meters, am I right to assume 0.0940 x 6 m = 0.55 m cube?
When I use the calculator that is off this site, it works out near to.

If I buy the log at $16 per meter, then I'm looking at $177 per cube?
This is where I fall down, seems way too cheap, when the same timber in 100 mm x 25 mm is at $3,740 per cube.
The price list states it is sold "per lineal meter, 300 - 349 large end diameter $16.00 per meter". I am assuming I'm looking at this the wrong way.

I also need to know the conversion rate of cutting this down, I am right to assume a 60% recovery and 40% waste as a good starting point?
I know this depends on the method and machine used, however I am looking for a "rule of thumb".

Does all this sound about right, or am I taking the wrong path?
Thanks in advance.
(I've used the word ASSuMe 3 times in this, obviously I have no idea :D )

Hi Clinton

It's a long time since I used to do log volumes in my head, and I have forgotten the method. However I will see if I can track it down. The one thing I did notice, however, is that you are working on the large end diameter. You need the average of large and small ends, or preferably the mid girth diameter. Also, is the measurement over the bark or bark free?

Recovery percentage depends on quite a number of factors, including the type of timber, is the log straight or bent, any rot, cracks, etc, as well as the factors you mentioned. Some timber has quite a large volume of sapwood, which may not be usable, again depending on the species.

Thanks John, if you could dig that up I would appreciate it.

It is bark free. I am looking at building poles, and don't know the small end diameter, or an average just yet. I believe that it is straight, and without cracks, rot and splits as it is structural. Sapwood is minimal, i.e. less than 10%.
Again, I would appreciate it if you could dig out the methodology.

I am trying to compare apples with apples, and usually work things out to a cubic meter $ value, as I find this helps me to appreciate to overall cost.

G'day.

Look up 'lineal meter' and 'super foot' I think that you will find that they are actually a cubic measure IE; a standard board size.


Snip...
A superficial (super) foot measured timber for the purpose of payment. It referred to a section, 12 inches square and 1 inch thick and payment was based on value per 100 super feet.

Also....
http://www.mtg.unimelb.edu.au/tools/conversion.htm

Quote:

---

Originally Posted by Clinton1

I would like to have someone check my rather simple way of working out the cubic meter volume of a log.
I assume that 2piR is the formula, so
300 mm diameter log = 2 x 3.14159 x 150 mm = 940 mm square, or 0.094 m cubic over 1 meter.
If the log is 6 meters, am I right to assume 0.0940 x 6 m = 0.55 m cube?

---

The formula is "pi Rsquared" not "2 pi R" plus you need to use all measurements expressed in metres (not cm or mm)

So your equation should be
pi x .150 x .150 x 6

Work on 50% recovery

Echnidna's right, the volume of a cylinder is Area x Length, and Area (for a circle) is pi x r x r, or pi x r-squared, where r is the radius. For r=.15 m I get
Area = 3.14 x .15 x .15
= 0.071 m-squared

For a length of 1 m, the volume is 0.071 m-cubed, and for a length of 6 m the volume is 0.071 x 6 = 0.42 m-cubed.

A price of $16 per metre would amount to 16/0.071 = $225 per m-cubed.

Not familiar with the terminology of "large end diameter", but if the radius of the log varies you could find an average diameter (radius) and use that as above. Not familiar with "recovery rates" either.

Use small end diameter not average diameter.
You cant cut timber larger than the small end.

Quote:

---

Originally Posted by echnidna

Use small end diameter not average diameter.
You cant cut timber larger than the small end.

---

Depends if you cut the full length of the log or cut it into shorter lengths. Sawmillers use average girth. (Or did in my day)

Quote:

---

Originally Posted by JohnM

Depends if you cut the full length of the log or cut it into shorter lengths. Sawmillers use average girth. (Or did in my day)

---

In the sawmill I'm in we currently use the SED (which is not technically correct as we use the smallest diameter which may not be at the end) and the scanning system we use can also be setup for a recovery or cut pattern sort which means cutting the boards to shorter lengths as said.

There is another part to the formula that we use when manually checking, that takes into account the taper of the log (which we set as 8mm/m) so a more accurate volume is obtained than just using the SED or an mid point diameter. So the longer the log the higher it's average diameter is when taper is included so obviously higher volume...it's stuff all but when you chop up 6000+ logs per day it is substantial.

Reg

Thanks all.

As you can see my maths is not my strong suit, one of those 'not in use things' (or at least thats what I'll claim).
Anyway, a mate is getting ready to build on his farm. The intent is to build a few sheds as storage and we are trying to figure out the pro's and con's of cutting timber on the farm or buying it. 6 meter poles at $96 each, as opposed to felling, cleaning it up and dragging it through the bush to the site. Time is a factor as well as both of us will be doing it at the expense of our pay packets or holiday time. (Although this sort of thing is what I like to do on holidays - live on a farm and do some work:) )

It seems that I can buy the building poles at Zenwoods figure of $225 per cube, when the furniture grade timber is at @$3700 per cube.
I am thinking of getting some in for myself with a view to cutting out 200 x 50 planks and seeing what I can recover from the flitches.
My mate intends to have a Lucas mill by the time the sheds go up. The 200 x 50 are usually sold at @$36 per meter, clean and clear.

I am thinking I can recover some good stuff, and I believe that the building poles are clear felling 'waste', and it seems a shame to not utilise it. Have to think about 'supporting' clear felling operations though.
Hmm

Anyway, thanks to all those that assisted

Theres a log cubic metre calculator here

http://www.blocklayer.com/WoodCalc.aspx