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?
Fri, Dec 31, 2004, 5:55pm (EST-3) snipped-for-privacy@cox.net (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.
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.
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.
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.
Umm, measure the length of the board and divide by 4.
Leon responds:
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
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....
rJ T wrote:
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.
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.
I tried an upload. Who knows, it might make it.
The original link was 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
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
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.
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.
Sat, Jan 1, 2005, 5:52am (EST-3) snipped-for-privacy@cox.net (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.
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?
D>>
conversely, decide what size box you want and then buy enough wood to build it...
John Emmons
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.
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.
posted one answer to your question in alt.binaries.pictures.woodworking
charlie b
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