I remember seeing an article where some clever fellow had created a
formula for calculating the size of the cuts required to make a box
from a single piece of wood. The point of this was that it told you the
most efficient way to make the largest box possible from a board of
given dimensions with no waste.
Does anyone remember where I might find this?
I guess the idea of making a box just cause you've got some scraps just
doesn't appeal to me. I tend to make things I can use or to give away, not
just for the sake of using algebraic equations to maximise the use of scrap
wood.
To each their own.
John Emmons
"Edwin Pawlowski" <[email protected]> wrote in message
news:[email protected]...
>
> "John Emmons" <[email protected]> wrote in message
> > conversely, decide what size box you want and then buy enough wood to
> > build
> > it...
> >
> > John Emmons
>
> Anyone can do that. Recently I wanted to make a box but the dimensions
were
> not critical. I guessed at a size and had some scrap that was, well,
scrap.
> Using this formula, I could have better utilized what I had.
>
> I could have come up with a particular size, Figured the wood I'd need.
> Drive 90 miles round trip to the wood store, Instead I used what I had
and
> in less time than the trip to the store, I was done.
>
>
In article <[email protected]>,
<[email protected]> wrote:
> Does anyone remember where I might find this?
The original link was
<http://www.netexperts.cc/~lambertm/Wood/nowaste.html> but that appears
to be a dead link.
I have a printout from that site and did save a copy of the html page
and the gif showing how to lay out the cuts on a board.
I've posted it at <http://www.balderstone.ca/nowaste/nowaste.html>
Mark Lambert, if you're reading this... Please let us know where your
site has moved to and I'll pull this off mine. I googled for you but
didn't find your new site.
djb
In article <[email protected]>, Guess who
<[email protected]> wrote:
> The images don't seen to be linked, Dave. Could you check that
> please? I most likely misunderstood the original question, so I'd be
> interested for sure in seeing what it's about.
That's noted on the page I posted where I wrote "The only graphic I
have a full version of is the one below at the right."
I only have one full sized image of the board plan. That is linked.
The other images are not linked. Sorry, but I won't be making any
effort to rectify that.
djb
In article <[email protected]>, John Grossbohlin
<[email protected]> wrote:
> Ah... therein lies the problem. When I saw all the dead links I didn't
> bother reading the page as I figured it wouldn't make sense if I couldn't
> view the graphics!
The missing graphics are pictures of the box the author made and are
not critical to the technique nor particularly illustrative.
If posting the page is of no value, please let me know and I'll pull it
and save the disk space on the server as well as the bandwidth. No
problem.
I'm not sure I see the problem or possibly, I'm not assuming correctly. Why
wouldn't you you simply cut two pieces of the width you want the box and
divide the remainder by four?
Don
"Cadillacjoe" <[email protected]> wrote in message
news:RzEBd.12678$hc7.6482@trnddc06...
> "Australopithecus scobis" <[email protected]> wrote in message
> news:[email protected]...
>> On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:
>>
>> > I remember seeing an article where some clever fellow had created a
>> > formula for calculating the size of the cuts required to make a box
>> > from a single piece of wood. The point of this was that it told you the
>> > most efficient way to make the largest box possible from a board of
>> > given dimensions with no waste.
>> > Does anyone remember where I might find this?
>>
>> Well, it was a standard problem in my high school analysis class... You
>> have to make the second derivative of dx/dy equal zero, or something like
>> that. Not a big help, I know.
>>
>
> I remember those problems. I believe it was the first derivative though
> since dx/dy is the slope of the tangent line to the curve. Therefore the
> only time when the slope of the tangent to the curve would be zero is
> during
> a local maximum/minimum. It is a simple quadratic using the ratio of
> surface area to volume, probably just as easy to use algebra.
>
> --
> Joe
>
>
Yeah, I searched the archives before I posted. No joy. I could figure
it out myself (the formula, that is), but I was just hoping not to have
to reinvent the wheel. I guess I'll get out my spokeshave....
r
J T wrote:
> Fri, Dec 31, 2004, 5:55pm (EST-3) [email protected] (r) wants to know:
> I remember seeing an article where some clever fellow had created a
> formula for calculating the size of the cuts required to make a box
from
> a single piece of wood. The point of this was that it told you the
most
> efficient way to make the largest box possible from a board of given
> dimensions with no waste.
> Does anyone remember where I might find this?
>
> I remember seeing that too. Here. So, I'd suggest checking the
> archives.
>
>
>
> JOAT
> People without "things" are just intelligent animals.
Sat, Jan 1, 2005, 5:52am (EST-3) [email protected] (r) says:
Yeah, I searched the archives before I posted. No joy. I could figure it
out myself (the formula, that is), but I was just hoping not to have to
reinvent the wheel. I guess I'll get out my spokeshave....
I recall, I had saved that post. But, then decided I'd never be
using it, and discarded it. I don't make boxes that often, and when I
do, usually wind up not cutting all the pieces from one piece of wood
anyway.
JOAT
People without "things" are just intelligent animals.
Fri, Dec 31, 2004, 5:55pm (EST-3) [email protected] (r) wants to know:
I remember seeing an article where some clever fellow had created a
formula for calculating the size of the cuts required to make a box from
a single piece of wood. The point of this was that it told you the most
efficient way to make the largest box possible from a board of given
dimensions with no waste.
Does anyone remember where I might find this?
I remember seeing that too. Here. So, I'd suggest checking the
archives.
JOAT
People without "things" are just intelligent animals.
John Emmons wrote:
>
> I guess the idea of making a box just cause you've got some scraps just
> doesn't appeal to me. I tend to make things I can use or to give away, not
> just for the sake of using algebraic equations to maximise the use of scrap
> wood.
>
> To each their own.
I think that should be "To eaches their owns" or "To each his/her
own" : )
But I digress.
What if the board you have is a special board - one with a very nice,
unusual grain pattern and you want to make a coherent, wrap around
grained box? I had a wild grained oak board I'd cut from a fallen
branch
on a friend's ranch. The grain pattern was unusual enough to warrant
a name - The Van Gogh Board because of the frenetic, contrasting wavy
grain pattern.
Alas, the top didn't look right so I went with a sycamore top.
charlie b
"r" <[email protected]> wrote in message
news:[email protected]...
> Yeah, I searched the archives before I posted. No joy. I could figure
> it out myself (the formula, that is), but I was just hoping not to have
> to reinvent the wheel. I guess I'll get out my spokeshave....
I have the diagram someone posted on ABPW stored on my drive, but, sadly, my
ISP just doesn't allow its members to post there. Used it for the kids at
the shop.
I tried an upload. Who knows, it might make it.
"George" <george@least> wrote in message
news:[email protected]...
>
> "r" <[email protected]> wrote in message
> news:[email protected]...
> > Yeah, I searched the archives before I posted. No joy. I could figure
> > it out myself (the formula, that is), but I was just hoping not to have
> > to reinvent the wheel. I guess I'll get out my spokeshave....
>
> I have the diagram someone posted on ABPW stored on my drive, but, sadly,
my
> ISP just doesn't allow its members to post there. Used it for the kids at
> the shop.
>
>
It's a nice way to teach a lot of things when you're working with a shop
class. Calculus is not one of them, however.
"John Emmons" <[email protected]> wrote in message
news:[email protected]...
> conversely, decide what size box you want and then buy enough wood to
build
> it...
On 31 Dec 2004 17:55:31 -0800, "r" <[email protected]> wrote:
>I remember seeing an article where some clever fellow had created a
>formula for calculating the size of the cuts required to make a box
>from a single piece of wood. The point of this was that it told you the
>most efficient way to make the largest box possible from a board of
>given dimensions with no waste.
>Does anyone remember where I might find this?
The largest volume of a [sorry for this] parallelopiped happens when
it's a cube, all sides equal. Disallowing kerfs etc, if the wood is
much longer than the width there would be too much waste doing that,
so it gets more complicated.
I'm heading for bed having been sick for two weeks, but will get back
tomorrow to show how to cut for maximum volume in that case ....if I
remember. Again there is no allowance for kerfs, so that will have to
be taken into account later as well. It involves a bit of math
finding max volume given some variable dimensions. It's not too
tough, but I'm under the weather just now.
>> > I remember those problems. I believe it was the first derivative
>> > though
>> > since dx/dy is the slope of the tangent line to the curve. Therefore
> the
>> > only time when the slope of the tangent to the curve would be zero is
>> > during
>> > a local maximum/minimum. It is a simple quadratic using the ratio of
>> > surface area to volume, probably just as easy to use algebra.
Oh my god. I'm having a nightmare. I'm in my calc 3 class, I have a test
I didn't study for, and I'm naked....
I have a calculator that works in fractions, and a tape measure with the
16ths printed on it. I am such an idiot.
"r" <[email protected]> wrote in message
news:[email protected]...
>I remember seeing an article where some clever fellow had created a
> formula for calculating the size of the cuts required to make a box
> from a single piece of wood. The point of this was that it told you the
> most efficient way to make the largest box possible from a board of
> given dimensions with no waste.
> Does anyone remember where I might find this?
Umm, measure the length of the board and divide by 4.
Leon responds:
>"r" <[email protected]> wrote in message
>news:[email protected]...
>>I remember seeing an article where some clever fellow had created a
>> formula for calculating the size of the cuts required to make a box
>> from a single piece of wood. The point of this was that it told you the
>> most efficient way to make the largest box possible from a board of
>> given dimensions with no waste.
>> Does anyone remember where I might find this?
>
>
>Umm, measure the length of the board and divide by 4.
Nope. Still needs a top and bottom.
Charlie Self
"A politician is an animal which can sit on a fence and yet keep both ears to
the ground." H. L. Mencken
"John Emmons" <[email protected]> wrote in message
> conversely, decide what size box you want and then buy enough wood to
> build
> it...
>
> John Emmons
Anyone can do that. Recently I wanted to make a box but the dimensions were
not critical. I guessed at a size and had some scrap that was, well, scrap.
Using this formula, I could have better utilized what I had.
I could have come up with a particular size, Figured the wood I'd need.
Drive 90 miles round trip to the wood store, Instead I used what I had and
in less time than the trip to the store, I was done.
"Australopithecus scobis" <[email protected]> wrote in message
news:[email protected]...
> On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:
>
> > I remember seeing an article where some clever fellow had created a
> > formula for calculating the size of the cuts required to make a box
> > from a single piece of wood. The point of this was that it told you the
> > most efficient way to make the largest box possible from a board of
> > given dimensions with no waste.
> > Does anyone remember where I might find this?
>
> Well, it was a standard problem in my high school analysis class... You
> have to make the second derivative of dx/dy equal zero, or something like
> that. Not a big help, I know.
>
I remember those problems. I believe it was the first derivative though
since dx/dy is the slope of the tangent line to the curve. Therefore the
only time when the slope of the tangent to the curve would be zero is during
a local maximum/minimum. It is a simple quadratic using the ratio of
surface area to volume, probably just as easy to use algebra.
--
Joe
"r" <[email protected]> wrote in message
news:[email protected]...
> Yeah, I searched the archives before I posted. No joy. I could figure
> it out myself (the formula, that is), but I was just hoping not to have
> to reinvent the wheel. I guess I'll get out my spokeshave....
>
> r
>
> J T wrote:
>> Fri, Dec 31, 2004, 5:55pm (EST-3) [email protected] (r) wants to know:
>> I remember seeing an article where some clever fellow had created a
>> formula for calculating the size of the cuts required to make a box
> from
>> a single piece of wood. The point of this was that it told you the
> most
>> efficient way to make the largest box possible from a board of given
>> dimensions with no waste.
A little different spin on things...
While I can appreciate wanting to not waste any wood I'd be concerned that
the aesthetics of the box would suffer by simply maximizing the dimensions
and volume of the box via a maximization formula. Personally I'd rather
"waste" some wood and end up with something that looks "right" than end up
with no waste.
What is needed is a maximization formula that incorporates the golden mean
in the dimensions of all faces of the box... ;-)
John
"mark" <[email protected]> wrote in message
news:[email protected]...
> >> > I remember those problems. I believe it was the first derivative
> >> > though
> >> > since dx/dy is the slope of the tangent line to the curve. Therefore
> > the
> >> > only time when the slope of the tangent to the curve would be zero is
> >> > during
> >> > a local maximum/minimum. It is a simple quadratic using the ratio of
> >> > surface area to volume, probably just as easy to use algebra.
>
> Oh my god. I'm having a nightmare. I'm in my calc 3 class, I have a
test
> I didn't study for, and I'm naked....
>
> I have a calculator that works in fractions, and a tape measure with the
> 16ths printed on it. I am such an idiot.
Don't feel too bad. I just finished a Calc 3 course so it is a little fresh
in my mind. I could've brought up partial derivatives or triple integration
for volumes. I think I will have nightmares about those problems for a long
time.
--
Joe
Who is about to start modern differential equations in two weeks.
"Dave Balderstone" <dave@N_O_T_T_H_I_S.balderstone.ca> wrote in message
news:020120052140039076%dave@N_O_T_T_H_I_S.balderstone.ca...
> In article <[email protected]>, Guess who
> <[email protected]> wrote:
>
>> The images don't seen to be linked, Dave. Could you check that
>> please? I most likely misunderstood the original question, so I'd be
>> interested for sure in seeing what it's about.
>
> That's noted on the page I posted where I wrote "The only graphic I
> have a full version of is the one below at the right."
Ah... therein lies the problem. When I saw all the dead links I didn't
bother reading the page as I figured it wouldn't make sense if I couldn't
view the graphics!
John
conversely, decide what size box you want and then buy enough wood to build
it...
John Emmons
"D. J. Dorn" <[email protected]> wrote in message
news:[email protected]...
> I'm not sure I see the problem or possibly, I'm not assuming correctly.
Why
> wouldn't you you simply cut two pieces of the width you want the box and
> divide the remainder by four?
>
> Don
>
> "Cadillacjoe" <[email protected]> wrote in message
> news:RzEBd.12678$hc7.6482@trnddc06...
> > "Australopithecus scobis" <[email protected]> wrote in message
> > news:[email protected]...
> >> On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:
> >>
> >> > I remember seeing an article where some clever fellow had created a
> >> > formula for calculating the size of the cuts required to make a box
> >> > from a single piece of wood. The point of this was that it told you
the
> >> > most efficient way to make the largest box possible from a board of
> >> > given dimensions with no waste.
> >> > Does anyone remember where I might find this?
> >>
> >> Well, it was a standard problem in my high school analysis class... You
> >> have to make the second derivative of dx/dy equal zero, or something
like
> >> that. Not a big help, I know.
> >>
> >
> > I remember those problems. I believe it was the first derivative though
> > since dx/dy is the slope of the tangent line to the curve. Therefore
the
> > only time when the slope of the tangent to the curve would be zero is
> > during
> > a local maximum/minimum. It is a simple quadratic using the ratio of
> > surface area to volume, probably just as easy to use algebra.
> >
> > --
> > Joe
> >
> >
>
>
On Sat, 01 Jan 2005 12:25:03 -0600, Dave Balderstone
<dave@N_O_T_T_H_I_S.balderstone.ca> wrote:
The images don't seen to be linked, Dave. Could you check that
please? I most likely misunderstood the original question, so I'd be
interested for sure in seeing what it's about.
>In article <[email protected]>,
><[email protected]> wrote:
>
>> Does anyone remember where I might find this?
>
>The original link was
><http://www.netexperts.cc/~lambertm/Wood/nowaste.html> but that appears
>to be a dead link.
>
>I have a printout from that site and did save a copy of the html page
>and the gif showing how to lay out the cuts on a board.
>
>I've posted it at <http://www.balderstone.ca/nowaste/nowaste.html>
On Sat, 01 Jan 2005 19:53:45 -0800, charlie b <[email protected]>
wrote:
>posted one answer to your question in
>alt.binaries.pictures.woodworking
Sorry Charlie. Some of my posts are not getting through. I answered
there. For max volume, two of th cuts have to be equal to the width.
The other four pieces should be of equal length for max volume.
On Fri, 31 Dec 2004 21:05:29 -0600, Australopithecus scobis
<[email protected]> wrote:
>On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:
>
>> I remember seeing an article where some clever fellow had created a
>> formula for calculating the size of the cuts required to make a box
>> from a single piece of wood. The point of this was that it told you the
>> most efficient way to make the largest box possible from a board of
>> given dimensions with no waste.
>> Does anyone remember where I might find this?
>
>Well, it was a standard problem in my high school analysis class... You
>have to make the second derivative of dx/dy equal zero, or something like
>that. Not a big help, I know.
No need since it will turn out to be quadratic and you can do that
with high school algebra. Calculus is simpler though, the HS method
being a bit longish.
"John Emmons" <[email protected]> wrote in message
news:%[email protected]...
>I guess the idea of making a box just cause you've got some scraps just
> doesn't appeal to me. I tend to make things I can use or to give away, not
> just for the sake of using algebraic equations to maximise the use of
> scrap
> wood.
>
> To each their own.
I would not call a 7" wide by 60" long piece of cherry scrap. The system is
to eliminate scrap. But at times, the dimension of the box are not all that
critical. If you want a "catch all" for your bureau, what is the big deal
if it is 10 x 6 or if it is 9 1/2 x 5 3/4 as long as it looks reasonably
proportional?
If you feel it is worth a 90 mile drive to get the exact dimension, feel
free to do so. When I buy wood for a project I always get a little extra.
This is a good way to utilize that top grade wood so it does not become
scrap.
To each their own.
On Fri, 31 Dec 2004 17:55:31 -0800, r wrote:
> I remember seeing an article where some clever fellow had created a
> formula for calculating the size of the cuts required to make a box
> from a single piece of wood. The point of this was that it told you the
> most efficient way to make the largest box possible from a board of
> given dimensions with no waste.
> Does anyone remember where I might find this?
Well, it was a standard problem in my high school analysis class... You
have to make the second derivative of dx/dy equal zero, or something like
that. Not a big help, I know.
--
"Keep your ass behind you"
vladimir a t mad {dot} scientist {dot} com
On Sun, 02 Jan 2005 10:49:31 +0000, John Emmons wrote:
> I guess the idea of making a box just cause you've got some scraps just
> doesn't appeal to me. I tend to make things I can use or to give away, not
> just for the sake of using algebraic equations to maximise the use of scrap
> wood.
>
> To each their own.
Quite. I do get my jollies from squeezing every last chip from lumber. So
far, 4.8 bf of 5/4 ash has yielded: 28" frame resaw, 28" frame saw, stair
saw, panel gauge, huge mallet, drill press fence (check on the end,
useless for anything else), a couple pair of bar gauge heads, and just
today, a skew rabbet plane. I'm down to 1 piece ~9.5" x ~1" x 5/4". I'll
think of something...
Oh, and I used a Rockler coupon for the ash, 20% off..
--
"Keep your ass behind you"
vladimir a t mad {dot} scientist {dot} com
On 1 Jan 2005 05:52:33 -0800, "r" <[email protected]> wrote:
>Yeah, I searched the archives before I posted. No joy. I could figure
>it out myself (the formula, that is), but I was just hoping not to have
>to reinvent the wheel. I guess I'll get out my spokeshave....
OK, I 'm happy to be corrected, since I'm not in the best of shape,
but here's my first effort, not allowing fo kerf cuts:
Box length L, width D.
The box has to have two sides as squares If not, the only length for
one of those sides must be less than D. That is, with one side D,
there are only two others to consider. So, divide the rest of the
length as follows:
D D x x y y
Now you can get messy with this, or since D is alread max and
constant, look to maximising the area x*y. That's simple, and occurs
when the side are equal.
So, give or take [some wood allowance always], measure twice the board
width along the length for two of the ends. Then divide the remainder
ito four equal parts. If you want all the math I'll put it here, but
it might get to be more boring than the personal junk nobody wants to
hear about "Gee, I hurt my thumb. Has anyone else done anything this
dumb?". So I'll leave it.
There it is:
D D x x x x
That's the theory. The practice is to allow for type of assembly:
butt, box, mitre ... . So add a bit to each accordingly.
"Guess who" <[email protected]> wrote in message
news:[email protected]...
> On Sat, 01 Jan 2005 12:25:03 -0600, Dave Balderstone
> <dave@N_O_T_T_H_I_S.balderstone.ca> wrote:
>
> The images don't seen to be linked, Dave. Could you check that
> please? I most likely misunderstood the original question, so I'd be
> interested for sure in seeing what it's about.
>
I ran into the same thing tonight...