Math Question About Cants & Roundwood

[Gypo Logger]

If an 8" cant has 64 sq. inches, how many square inches does a 10" round log have? A 10 inch log is about 31 inches in circ., and an 8" cant is 32" if measured distance on all four sides. So what is the equation for sq" of a cylinder on the face of the round log? And how does an 8" cant relate to a 10" dia. log volume wise?
What confuses me is that an 8" cant is about as big as a 10" dia. log if measured distance around, but I know I got lost in the math somewhere, so please straighten me out if you can.
Thanks in advance,
John

 

[rbtree]

The formula is Pi xRadius squared, so a 10 inch log= 3.1416x5x5, or 78.5 square inches

 

[sedanman]

Pi x r2 or 3.147x (5x5) 3.147x25=78.675 square inches.

 

[sedanman]

rbtree, You beat me by a fraction of a second. Waht do I get for second place?

 

[rbtree]

One of gypo's slow saws? He doesnt need em really more than the three days a month he does any real work.

 

[BlackSmith]

area of a circle = dia. x dia. x .7854

 

[Gypo Logger]

Thanks Roger and Sedanman, that was the answer I was looking for. So if an 8x8 has 64 sq.", and a 10" log has 78. 675 sq. ", and I made a conservative cut in 2.45 sec., in a 10" log, then that means I won, and I didn't have to go to Dan's to prove it. Thanks again, you bunch of sh!t disturbers! LOL
John

 

[eyolf]

yes, but which cuts faster...the 10" round or the 8"square cant?

Or maybe you could use the chainsaw?

If you use a 346xp to cut off your broomsticks, isn't it a pain to sweep out the kitchen when you're done?

Ole Svendsen drives over to the border at International falls and there he asks the officials:
Is it closer to Winnipeg, or by bus?

 

[Gypo Logger]

I think it's closer by bus says, John Lambert Vancouver 10 speed.

John

 

[Bill G]

The tooth has the ability to remove the same amount of material no matter the shape square or round. With that being said shape will not make a difference as long as the surface are is the same. If you are just looking at nominal size that is different. A 8 inch round is faster that a 8 inch square.

Bill

 

[Art Martin]

John,

You forgot to add one factor. You are not cutting square inches, you are cutting cubic inches. Add the width of the kerf to get volume. It makes a difference as the size gets bigger, other factors enter in also such as chip removal, friction loss, length of bar and chain and maintaining rpm's, etc.

Art

 

[tony marks]

i knew dat. them fellers just beat me to posting the answer. really

 

[ehp]

Another way is if the log is 10 inch diameter is bore times bore times . 7854 so that means 10times 10 times .7854 = 78.54 square inches just another way to skin the cat

 

[spencerhenry]

log area

the simplest formula no matter how you slice it is, pi(3.1415927)*r*r. r = radius or half of diameter. volume of material removed from the kerf, is 3.1415927*radius*radius*width of cut. that is the theoretical volume removed. operator error will add to the kerf. as far as round vs. square, i really dont have an opinion.
ok thats not true, but i wont offer my opinion because i havent spent any time evaluating it.
sam

 

[glens]

John, while a cant you might be using might actually be square in cross-section, it's pretty rare a round is actually round, right?

Probably "close enough" would be to figure the area of any size "round" is about equal to a "square" with a side 8/9 the diameter.  In reverse, the area of any square is about equal to a circle with a diameter 9/8 the square's side.

8" square equals 9" round, more or less.

Just remember 1¹/₈ (or ⁹/₈) and the square is smaller.

Glen

 

[Gypo Logger]

Thanks for the help with the math.
However, since dia. may be here nor there on a round log and measuring the circ. is more accurate, what is the equation for sq"., if only the circ. is known? To answer my own question would it be:
(circ" divided by pi)x DxD X .7854?
Thanks,
John

 

[TonyM]

You're making it too hard on yourself.

Since circumference (C) is already pi*D, and D*D*pi/4 is the area

Then (C/pi)*(C/pi)*pi/4 = area

or simplify

C*C/4/pi = area

 

[glens]

John, you really should be asking your buddy Doug about these math problems.

Here's a little something to chew on (and it only works for shapes which are perfectly circular).

For a given value circumference, divide it by Pi to find the diameter, divide that by 2 to find the radius, square that and multiply it by Pi to find the area.  On my HP48 I can create a simple program to do all that thus (it's "Reverse Polish" language):

&nbsp; <<&nbsp; PI&nbsp; /&nbsp; 2&nbsp; /&nbsp; SQ&nbsp; PI&nbsp; *&nbsp; >>

Then after assigning the program to a button, I can key in a value and press the button to find the area of a circle for which that initial value was the circumference.

Here are some results (circumference on left, area on right):

&nbsp;&nbsp; &nbsp;1&nbsp; &nbsp; 0.07957747
&nbsp; 10&nbsp; &nbsp; 7.95774715
100&nbsp; &nbsp; 795.774715

&nbsp; &nbsp;2&nbsp; &nbsp; 0.31830989
&nbsp; &nbsp;4&nbsp; &nbsp; 1.27323954
&nbsp; &nbsp;6&nbsp; &nbsp; 2.86478898
&nbsp; &nbsp;8&nbsp; &nbsp; 5.09295818

(each of the above left-hand values, when putting each "0" behind them, moves the decimal point to the right two more places, exactly as for "1")



Glen