Frustum of a cone for firewood. . .

[Metals406]

Calculating Cord-Wood using the mathematical equation for the "Frustum of a cone" is very accurate; especially accurate when dealing with certain tree species.

Some of those trees being Engelmann Spruce, Tamarack, Western Larch, Ponderosa Pine, Lodgepole Pine, Sub-alpine Fir "piss fir", and some Grand Fir/Doug Fir. . . Any fairly evenly tapered tree will work. If the trees' taper is less consistent, measure smaller sections.

If you're getting a Firewood Permit from the FS, you might as well get a "Cord" of wood. There's 128 Cu. Ft. of wood in a Cord, unfortunately, you'll get air gaps in a stack 4'X4'X8' (or any 3 dimension combination). . . But that's the quickest way to figure out what you got stacked.

A FS Permit in these parts is $20.00 for 5 cords--and that's also the minimum amount you must purchase. I will also spend a lot of time and fuel hunting down the wood, thanks to the FS's affinity for locking every gate, and "Tank Trapping" roads. Then you have chains, guide bars, air filters, saw maintenance/ware and tare, files, fuel mix, fuel, and bar oil. . .

I want a Cord, when I write it down on the permit.

Here's all you have to memorize:

V= π (r1² + r2²) h/3

So lets break it down simple stupid. . .

I have a nice buckskin Larch I just dropped. Now I'll dream a little bit, and say it's 72" on the butt, 110' long, and 8" when I cut the top. Now let's enter real values in our formula:

V= 3.14 (pi) (1296 + 16) 110/3

Now solve to get Cu. In.~~~ 3.14 X 1312 X 110/3 = 151,054.9 Cu. In.

Now divide Cu. In. by 12³, and you get = 87.42 Cu. Ft. Or 68% of a Cord

It makes it way quicker to have a Construction Master, or scientific calculator on hand--but any calculator will do. . . Or you can do it all long hand.

If you're thinking, "That would take too much time and effort", I'd say not really. You measure two ends of your tree, and the calculation takes less than 1 minute with a calculator.

Once that same tree was split and stacked, you might come up with 95% of a cord? You just shorted yourself 27%.

I don't want to argue with anyone, that's not why I'm posting this. If you agree, great. . . If not, move forward and keep-on-keepin'-on.

 

[Metals406]

8 views, and no comments?

 

[Rookie1]

Thats all above me. I get/cut firewood from private property around here. I dont even know how to get a hol of the Ohio forestry service. Im sure it will help some here.

 

[Laird]

8 views, and no comments?

I hate math.....But admire those who are proficient at it.

 

[Metals406]

Thats all above me. I get/cut firewood from private property around here. I dont even know how to get a hol of the Ohio forestry service. Im sure it will help some here.

The formula works for any situation, not just for State Lands.

Definitely gives you a more accurate accounting of the wood you keep/sell.

I have a hunch if someones firewood customers knew how accurate you measured a cord, they'd buy from you just on that.

It's not a hard math thing. . . The smallest radius is multiplied by itself, then the largest is multiplied by itself... Add those two numbers together, times 3.14, times the length of the log, divide by three... That's Cu. In.~~now divide by 12 to the third power (or 12X12X12= 1728). Easy peasy.

 

[Rookie1]

I think Ill save the formula for future use.

 

[Metals406]

I think Ill save the formula for future use.

Cool! I hope my further explanation made it easier to understand? A Construction Master calc makes it really brainless.

Give it a try? You just bought a tree from me, and it's 20" on the butt, 2" when I cut the top, and 86' long between the top and butt cut. . . How many Cu. Ft. did you just buy?

 

[TJ-Bill]

I tried working it out using your formula but my crayon got dull and I couldn't make out my numbers, plus I was running out of room on my napkin.. I'll just leave the hard math to you and I'll go back to drinking my beer and coloring my pictures!

 

[Metals406]

volume= 5.26 cu. Ft. Or 4% of a cord

The answer is above^^^ highlight it with your mouse to see it.

 

[Metals406]

I tried working it out using your formula but my crayon got dull and I couldn't make out my numbers, plus I was running out of room on my napkin.. I'll just leave the hard math to you and I'll go back to drinking my beer and coloring my pictures!

LOL. . . Grab a calculator. . . I just timed myself, and I had an answer in 12 seconds.

 

[BlueRidgeMark]

I see one problem with this:


A cord is NOT 128 cubic feet of wood.



A cord is a stack of wood 4x4x8, or any other combination that yields the same volume of tightly stacked wood.

Not 128 cubic feet of wood.

128 cubic feet of tightly stacked wood.

The definition of a cord INCLUDES the air spaces. It is NOT 128 cubic feet of solid wood.

 

[Haywire Haywood]

I measure wood by the load... I throw it in until the truck and trailer are full and I then have a "load" of wood. No calculators needed... LOL

Ian

 

[BlueRidgeMark]

Works for me, too!

 

[Steve NW WI]

Looks like a good system, but would require a ton of calculations here on multi limbed hardwoods with a ton of bends in them.

Thanks for the info, though.

Steve

 

[Metals406]

I see one problem with this:


A cord is NOT 128 cubic feet of wood.



A cord is a stack of wood 4x4x8, or any other combination that yields the same volume of tightly stacked wood.

Not 128 cubic feet of wood.

128 cubic feet of tightly stacked wood.

The definition of a cord INCLUDES the air spaces. It is NOT 128 cubic feet of solid wood.

I disagree. . . I can stack two piles of wood together, each measuring 4'X4'X8'. . . One with larger air gaps than the other, and one will contain more wood than the larger gapped pile.

I don't know about you, but I burn wood not air. If I was buying a cord from a vendor, I wouldn't hold him to my anal formula. . . But for my own use or selling--the customer would surely take notice when I explained they were getting 128 Cu. Ft. of wood. . . They'd probably only want to buy from me because of it.

To each his own though. . . Thought I'd throw this thread out there for anyone interested.

 

[Metals406]

Looks like a good system, but would require a ton of calculations here on multi limbed hardwoods with a ton of bends in them.

Thanks for the info, though.

Steve

Yes, you hardwood guys would have a little more work ahead of you, but it would still be pretty easy. Bends don't mess with the calculation, as you just measure the length along the bend.

This formula is ideal for conifers, they tend to have a long, even taper--so a guy wouldn't have to make multiple measurements.

There are other uses for the formula as well. . . Once you quickly established cubic feet, wet/dry wood weight charts would give you a fairly accurate weight of a log.

I've heard of a mill worker using the formula to check the computers accuracy in calculating log volume as well.

 

[xtm]

Lotsa times when I help a friend or neighbor take down one of their trees, they give me the wood to burn. They usually think that they are giving me a tremendous amount of wood - when it may only be a pickup load or so. I don't know how many times I've stood under a rather small-sized tree I'm getting ready to take down and had someone ask, "How many cord will you get outta that?" :hmm3grin2orange:

Not that I don't appreciate a free batch of firewood, but this will be a useful calculator for informing them actually how much wood they are giving me. Might be harder to calculate on a tree with large limbs, but still do-able.

Thanks,
xtm

 

[Metals406]

Lotsa times when I help a friend or neighbor take down one of their trees, they give me the wood to burn. They usually think that they are giving me a tremendous amount of wood - when it may only be a pickup load or so. I don't know how many times I've stood under a rather small-sized tree I'm getting ready to take down and had someone ask, "How many cord will you get outta that?" :hmm3grin2orange:

Not that I don't appreciate a free batch of firewood, but this will be a useful calculator for informing them actually how much wood they are giving me. Might be harder to calculate on a tree with large limbs, but still do-able.

Thanks,
xtm

Yet another good use for it. I personally like how easy it is to remember too.

 

[Wood Doctor]

I have a simple formula that works and requires no math:

Haul two truckloads of firewood to the customer in my Ford Ranger with my racks on the sides (see avatar).

That's a cord of wood and a few bones left over for Fido and a very satisfied customer. :greenchainsaw:

 

[Metals406]

I have a simple formula that works and requires no math:

Haul two truckloads of firewood to the customer in my Ford Ranger with my racks on the sides (see avatar).

That's a cord of wood and a few bones left over for Fido and a very satisfied customer. :greenchainsaw:

That works too.