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Anyone think they know enough to tackle this one? I’m not talking about the slant-sided box where everything is cut at 45s (though feel free to share your method there, if you’d like). I’m more interested in making a box that fits a prescribed space. Say you need to put a slant-sided box in a x by y by z space, and you need to know the miter and bevel cuts for it. I know of a few calculators out there, but other than telling me to plug in the numbers, who knows how to actually make this step-by-step?

I found a few videos here and there, and some websites, too, but couldn’t find a good description from start to finish...
 

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If you couldn't find an established answer, how do you expect us to help you with a vague description. Like Steve asked, a picture or drawing would help...
 

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Not a vague description - just a difficult problem. A slant-sided box is a square or rectangular box with a base that’s smaller in size than the lid. The walls slant out as they rise.

This box could be made the way one of the guys here suggests, drawing it out and calculating the angles. But that would get you one box. There are trigonometric formulas that allow a woodworker to adjust the plans to change the box’s height, say, without drawing it all out again. Who can make those, and then take it from that step to completion?

As I said, not a simple one to solve. Curious to see if anyone knows this.
 

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Ancient Termite
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I'm thinking that the box is like a planter, small at the bottom and large at the top.

Cut your sheet goods a bit over size, an inch or so.
Decide on the slope of angle of the sides. Set your miter gauge to that angle and leave it. Set the blade bevel angle to what you desire. (90 or 45°) Cut all the pieces on one side only. Move the miter gauge to the other slot and cut the remaining side.

Unless you are very experienced, understand the physics involved and have two good push blocks that will hold the sheet goods flat, DO NOT USE YOUR FENCE WITH THIS CUT. One push block isn't enough.

I had to do something similar but I cheated. I have a miter gauge with positive stops and I could go from 7½° left to 7½° right with repeatability. (The blue one from Rockler with the poker chip design.)
 

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Not a vague description - just a difficult problem. A slant-sided box is a square or rectangular box with a base that’s smaller in size than the lid. The walls slant out as they rise.

This box could be made the way one of the guys here suggests, drawing it out and calculating the angles. But that would get you one box. There are trigonometric formulas that allow a woodworker to adjust the plans to change the box’s height, say, without drawing it all out again. Who can make those, and then take it from that step to completion?

As I said, not a simple one to solve. Curious to see if anyone knows this.
Hi Matt,

Welcome to the forum...:laugh2:

I'm under the presumption that you are looking for "old school" solutions to such a quandary...???...No CAD modeling short cuts (that makes it easy for me now...LOL..:vs_laugh:)

And yes, there are indeed "trigonometric formulas" for such real world project challenges. We see them all the time in roof collisions within timber frames. I've taught basic math (substitute occasionally now no more full time) and work as a Designer, Timberwright and tradtional woodworker...so have the math and the applications events you described happening in the "real world," just as you are describing...

If you would be so kind, provide a scenario where you think this would apply (even if fictitious :smile2:) but it must have sizes and numbers. The more "step by step" your details of the condition, the better I can (perhaps?) break it down for you. I will see what "cobb webs" I can dust off to give you a step by step formulaic plan to use in that scenario...I'm sure with that I can (or I can find) what you are looking for...

Again...Welcome,

j
 

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where's my table saw?
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who knows how to make it?

Anyone think they know enough to tackle this one? I’m not talking about the slant-sided box where everything is cut at 45s (though feel free to share your method there, if you’d like). I’m more interested in making a box that fits a prescribed space. Say you need to put a slant-sided box in a x by y by z space, and you need to know the miter and bevel cuts for it. I know of a few calculators out there, but other than telling me to plug in the numbers, who knows how to actually make this step-by-step?

I found a few videos here and there, and some websites, too, but couldn’t find a good description from start to finish...

You will need to generate the angles by:
1. Using an online calculator which you can plug in the various dimensions, the easiest by far. :smile2:

2. Draw out the project in 3 views using specific dimensions for that one project. :|

3. Use TRIG to calculate all the angles, the most difficult, especially for those who didn't pass with an A in high school. :sad2:



You can't just throw some panels on the saw and start cutting without a dimensioned plan, including the miter and bevel angles.
This online calculator will do it for you:
http://www.pdxtex.com/canoe/compound.htm


Once you have the miter and bevel angles, set up your table saw to correspond with them, bevel being the tilt of the blade and miter being the angle of crosscut. Remember that the miter gauge markings are subtracted from a 90 or square cut for your angles. This can be confusing to a novice who may think the markings are the actual angles, they are NOT.


For accurately measuring the bevels/blade tilt, a digital angle gauge or Wixey should be used. An old school plastic see thru protractor would also be useful.



Once the pieces are cut and are checked against their mating components, you will find clamping them the next biggest hurdle, since any clamps want to slide up the angled surfaces. Some folks "hot glue" temporary clamp blocks on the corners to give the clamps a resting place, probably the best solution. Strap or ratchet clamps will also ride up the sides, so not good. Other folks use painters tape on the corners laid out flat and then "fold" up the sides into a complete rectangle/square.


That's pretty much a how to process.
 

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being mathematically challenged, I find it helpful to make a
full size template out of cardboard, if it is feasible.
a member recently made a similar project and it looked great.
 

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Discussion Starter #10
Jay C. White Cloud - Thanks for the offer. If the slant-sided box is 10” wide, 25” deep, and 6” tall, how would you do the calculations?
 

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where's my table saw?
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I'll let Jay answer that ....

But I think he will need more dimensions. Like size of the box at the top and bottom which will determine the angle of the slant. Draw the thing out full size with those 3 dimensions and see how far you can get ...... :|
 

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Jay C. White Cloud - Thanks for the offer. If the slant-sided box is 10” wide, 25” deep, and 6” tall, how would you do the calculations?
Hi Matt,

It's funny, some OP's and their questions will stick with me into the day's work (or play...LOL!!!...in my case) as today was fill with punching mortises into huge timbers for a Dutch Barn project to..."unfold"...in the next few months...

Your query Matt, and John Smiths comment are both serendipitous, because today was filled with me trying to figure out where I placed something I was reading/studying and I can't seem to find it. It relates to 折り紙 (Origami)...or...more precisely...折り紙設計 (Origami Sekkei) which is known in English as "Technical Origami" or "Technical Paper Folding," sometimes called "architectural origami." There is another word/method to but that is the one that has escaped me, and I can't find it in my notes. It is the method that many Japanese woodworkers use to model their projects...and...what John Smith was most logically and accurately getting at...

I thought of you today, because this truly is the "analog" and "empirical" modality to figure out a project. It starts with modeling in paper before all else. Its been around so long as to really be unknown in orgin. Academics debate it, but the bottom line is, ever since a human could hold a large leaf or a piece of leather and think of something they wanted to make, we began "folding" things to create models and/or practical items of use in textile before the "hard form."

If I find the word and its applied methods, I will share it...In the mean time...instead of "paper" I just quickly use CAD, and when I "plug" your numbers in...as Woodnthings has suggested...there isn't enough information with only 6", 10" and 25"...unless I apply my own imagination and creativity to concept of your query...Which also would mean I have to make some logical conceptional extrapolations...but...since this is your project (or concept) I think it is best if you expand on what "numerical parameters," you wish to apply to this learning exercise?

With just your current information (and no imagining on my part...LOL) what we get is seen below...



As you can see, those number just give us your basic ubiquitous...box...:vs_laugh:...So I either need some angles (?) or I would require the ends and sides to be defined within the context of trapezoids with the dimensions of each side given and these would have to reconsile with the other sides in concert also...or dictate there geography...I'm fine with either...
 

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where's my table saw?
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Like I said ......

But I think he will need more dimensions. Like size of the box at the top and bottom which will determine the angle of the slant. Draw the thing out full size with those 3 dimensions and see how far you can get ...... :|

Jay, needs the angles /slopes of the sides OR the dimensions of bottom, since we have been given the top. Folded paper/thin cardboard is one approach. We used Strathmore in school for models sometimes scored and folded, other times just cut and taped together.

https://www.bkstr.com/savannahstore/shop/boards-and-panel

Now don't forget, a sloped line is longer than a vertical line between two horizontal planes so when you make your folded layout, that needs to be accounted for. You can't use the 6" dimension on a diagonal, it won't work. Some TRIG or experimentation is required.
 

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my head still hurts just reading all the responses.
[I failed math in High School and have only gotten worse since then].

and I still ask myself: is this question just an exercise for a
high school math project ??
a college thesis engineering project to get the degree to build a super high-rise ??
or - an actual project for the wife just to plant some flowers in.

who knows ?

I just performed the simple google search for "Flower Box with Angled Sides
Images" and all kinds of stuff popped up on how to cut Compound Miter Cuts.
maybe Matt (O/P) should try that and see if he can solve the riddle.
 

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what you are looking to do includes compound angles. they can be calculated using trig, but are readily available for those mathematically challenged on websites for "compound angle calculators"


http://www.pdxtex.com/canoe/compound.htm - so enter the slope of the sides, say 10 degrees, keep the 90 degrees in the "included angle" box, and tap calculate. it will provide the miter (end) angle, and the angle to make the cut on the board.


imagine a 4 sided box (square or rectangle), obviously the sides would be mitered to 45 degrees. as the sides splay out from 90 degrees, 2 things change - the angle of the miter AND the cut as it relates to the board. instead of being 90 degrees, it now will be cut at an angle other than 90 degrees.




fyi, the side lengths and heights will be provided by you, as you dimension your lumber and prepare for the cuts.
 

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If I’m understanding, it’s similar to to a tapered flower pot, something like John depicts.

In which case there are 2 angles, one the taper and one the bevel, which are easily determined.

Regardless, my approach to something like this is a full size drawing and a digital angle bevel to guide my saw set up, then a mock up & dialing in angles.

Once the reality of the piece is determined and all the angles recorded, I figure all the trigonometry and math I neither need nor desire to know is already figured out, right?
 
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