# Need help with miter angles



## thyde1108

Ok, I have a tough math problem for you guys. I am building a butterfly house for my wife's science classroom, and from a design standpoint, I would like the room to be a pyramid. I'm using scrap lumber to build it and the four pieces that I want to extend from each corner to create an apex are 2" wide by 3/4" thick. The base is approx. 26" wide with the radius from the center to the corner being 17.5". What angles do I use to have the four pieces meet a 12" height and the hit perfectly to form a pointed apex? 

I hope I described that well. I attached a very rough 2D drawing to maybe explain it a little more. I've searched a lot online to find calculators, but I can't seem to find one that gives me what I need. If you don't know how to calculate yourself, I would love to hear of a site you use for calculations. 

Thank you!


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## Dave Paine

I am smiling as I am thinking about a science teacher not knowing how to calculate the intersection of two planes.

OK, you are the one not your wife, but I am still smiling at the irony. :smile:

I happen to have a handy dandy Excel file which will allow you to enter the parameters.

I am not able to attach an Excel file (invalid file type error), and you do not have enough posts for me to send you a PM.

So if you want the Excel solution, email me tyke at ptd dot net.

If you want to do the mathematics yourself, here is an article with the gory details.

http://www.woodcentral.com/bparticles/miter_formula.shtml


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## thyde1108

Dave Paine said:


> I am smiling as I am thinking about a science teacher not knowing how to calculate the intersection of two planes.
> 
> OK, you are the one not your wife, but I am still smiling at the irony. :smile:


I know, I know. I could ask her, but I'm trying to build it without her seeing it first, so I'm left to fend for myself and this is not my strong suit. I'll email you, and thanks for the reply!


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## Steve Neul

The angle on the apex would be 45 degrees if it is square like shown. The angle would just converge in the center of each rail. I would use the same angles on the other end as well. On the triange at the bottom if the top angle is 2 pieces mitered at 45 degrees making a 90 degree angle then the bottom angle would be 45 degrees also. Turn your picture this way and look at it. You are still dividing a 90 degree angle by 2.


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## thyde1108

Steve Neul said:


> The angle on the apex would be 45 degrees if it is square like shown. The angle would just converge in the center of each rail. I would use the same angles on the other end as well. On the triange at the bottom if the top angle is 2 pieces mitered at 45 degrees making a 90 degree angle then the bottom angle would be 45 degrees also. Turn your picture this way and look at it. You are still dividing a 90 degree angle by 2.


I appreciate the reply - unfortunately my drawing is not to scale. I'm just not an artist! It's actually far from square like the drawing indicates. I think Dave's spreadsheet will get me where I need to go. But again, thank you!


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## GeorgeC

thyde1108 said:


> Ok, I have a tough math problem for you guys. I am building a butterfly house for my wife's science classroom, and from a design standpoint, I would like the room to be a pyramid. I'm using scrap lumber to build it and the four pieces that I want to extend from each corner to create an apex are 2" wide by 3/4" thick. The base is approx. 26" wide with the radius from the center to the corner being 17.5". What angles do I use to have the four pieces meet a 12" height and the hit perfectly to form a pointed apex?
> 
> I hope I described that well. I attached a very rough 2D drawing to maybe explain it a little more. I've searched a lot online to find calculators, but I can't seem to find one that gives me what I need. If you don't know how to calculate yourself, I would love to hear of a site you use for calculations.
> 
> Thank you!


If you want someone on the forum to provide angles then you will first have to provide the dimensions of each of the pieces in your sketch. It is hard to relate the dimensions you give to the sketch.

George


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## jschaben

:smile:

The bevels where the 4 corners meet at the peak will be 45°. The triangle as drawn is 12" high


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## LuckyNumber7

My interpretation of what you are asking... Looks like a 34.5º miter and a 45º bevel will get you fixed up. Guess I'll have to make some kindling tomorrow at work to check and see if SU is right


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## Hammer1

I don't see any reason for any frame for the roof on such a small box. Just cut some boards or plywood to form the roof. If you are math challenged, use some cardboard to practice and guess your way through. Plenty of info on making a four sided pyramid but you need to know some basic geometry.


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## Lola Ranch

Hammer1 said:


> I don't see any reason for any frame for the roof on such a small box. Just cut some boards or plywood to form the roof. If you are math challenged, use some cardboard to practice and guess your way through. Plenty of info on making a four sided pyramid but you need to know some basic geometry.


All the info you need is available on a framing square. This is straight forward roof framing. You are cutting hip rafters. 

Bret


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## thyde1108

I appreciate all of the responses. Maybe I'm reading I to it too much but what's really creating my confusion is that I want the boards to be laying flat - not on end. Does that make sense? I need more surface area to staple my screen netting. Again, maybe the same rules of geometry apply but it's just not hitting for me.


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## Dave Paine

thyde1108 said:


> I appreciate all of the responses. Maybe I'm reading I to it too much but what's really creating my confusion is that I want the boards to be laying flat - not on end. Does that make sense? I need more surface area to staple my screen netting. Again, maybe the same rules of geometry apply but it's just not hitting for me.


Technically the geometry is the same. You have planes with are intersecting. Once you figure out the angles from the spreadsheet, then it is just a matter of whether the compound cut is made on the edge (narrow) or face (wide) portion of the board.


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## thyde1108

Dave Paine said:


> Technically the geometry is the same. You have planes with are intersecting. Once you figure out the angles from the spreadsheet, then it is just a matter of whether the compound cut is made on the edge (narrow) or face (wide) portion of the board.


Thanks Dave.


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## CasinoDuck

I'm angled challenged myself.

This get's me through it.


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## MissionIsMyMission

R U talking about something like this...only going all the way to a point???


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## thyde1108

MissionIsMyMission said:


> R U talking about something like this...only going all the way to a point???


Yes! Two other differences:

1. They ate not solid sides connected all around - there will be screen between them to see I to the cage.

2. The sides are not equal. Two sides are longer than the other making it a rectangle not a square. 

I know that each stick, if you will, has 45 degree angles on each side which forms the solid point if you lay them flat on the ground. What I'm struggling with is the bevel angle so as the sticks are elevated from the center to form the pyramid the bottoms don't hit each other - the tips meet to form a perfect point. Make sense?


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## Dave Paine

thyde1108 said:


> Yes! Two other differences:
> 
> 1. They ate not solid sides connected all around - there will be screen between them to see I to the cage.
> 
> 2. The sides are not equal. Two sides are longer than the other making it a rectangle not a square.
> 
> I know that each stick, if you will, has 45 degree angles on each side which forms the solid point if you lay them flat on the ground. What I'm struggling with is the bevel angle so as the sticks are elevated from the center to form the pyramid the bottoms don't hit each other - the tips meet to form a perfect point. Make sense?


The angles to cut are not what you think. One angle is not 45 deg IN THE PLANE of the cut.

I cannot tell the dimensions from the thread.

Send me the dimensions and I will cut the wood for you.


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## thyde1108

Dave Paine said:


> The angles to cut are not what you think. One angle is not 45 deg IN THE PLANE of the cut.
> 
> I cannot tell the dimensions from the thread.
> 
> Send me the dimensions and I will cut the wood for you.


Hi Dave. I'd still like to cut them, I just can't decipher from the spreadsheet where I am to find the angles. The dimensions of the "box", or the 4 corners where the pillars will head towards the apex are:

27 7/16" x 25 15/16" The pillars would angle upwards towards an apex of 12", give or take. I can go up or down slightly if it makes it easier.

Does this help? I appreciate the assistance, I really do. I don't want to frustrate anyone.


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## Dave Paine

thyde1108 said:


> Hi Dave. I'd still like to cut them, I just can't decipher from the spreadsheet where I am to find the angles. The dimensions of the "box", or the 4 corners where the pillars will head towards the apex are:
> 
> 27 7/16" x 25 15/16" The pillars would angle upwards towards an apex of 12", give or take. I can go up or down slightly if it makes it easier.
> 
> Does this help? I appreciate the assistance, I really do. I don't want to frustrate anyone.


Tim, the last detail is to dimensions of the wood. I think you said you wanted the "flat" side being up.

So stock dimensions and orientation, then I can calculate the angle-of-the-dangle for you. :yes:

The first time I did this was cutting bar top molding. This lies at e.g., 20-25 deg. The 90 deg mitre we needed to cut was very different angles in the saw. The end result was it looked like 90 deg after assembly.


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## thyde1108

Dave Paine said:


> Tim, the last detail is to dimensions of the wood. I think you said you wanted the "flat" side being up.
> 
> So stock dimensions and orientation, then I can calculate the angle-of-the-dangle for you. :yes:
> 
> The first time I did this was cutting bar top molding. This lies at e.g., 20-25 deg. The 90 deg mitre we needed to cut was very different angles in the saw. The end result was it looked like 90 deg after assembly.


The stock is 2" wide x 3/4" thick. And yes, flat side down. Would it be possible to include the calculation so I can learn for future projects? If its too much or time consuming, don't worry about it. Thanks!


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## Roger Newby

Lola Ranch said:


> All the info you need is available on a framing square. This is straight forward roof framing. You are cutting hip rafters.
> 
> Bret



Listen to Bret..................the square has all the information you need and learning to use one is a heckuva good lesson. :thumbsup:


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## Dave Paine

Roger Newby said:


> Listen to Bret..................the square has all the information you need and learning to use one is a heckuva good lesson. :thumbsup:


I am not looking to start a debate. This is not as simple as a framing square. This is a problem about intersection of two planes. The angles we see in the finished assembly are not the angles we need to set in a Compound Mitre Saw to achieve the angle we see.

Tim, I did the calculations, and I did some tests on scrap pieces of particle board. I forgot an extra detail is whether your SCMS is left tilt, right tilt or like mine, can do both.

I will post pictures tomorrow. Getting late for me on the east coast.

You did not help yourself by the base not being square. This impacts the bevel at the top. Two different setting needed.

Can you make the base a square?

It will really be easier for me to cut the wood and send it to you.


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## thyde1108

Dave Paine said:


> I am not looking to start a debate. This is not as simple as a framing square. This is a problem about intersection of two planes. The angles we see in the finished assembly are not the angles we need to set in a Compound Mitre Saw to achieve the angle we see.
> 
> Tim, I did the calculations, and I did some tests on scrap pieces of particle board. I forgot an extra detail is whether your SCMS is left tilt, right tilt or like mine, can do both.
> 
> I will post pictures tomorrow. Getting late for me on the east coast.
> 
> You did not help yourself by the base not being square. This impacts the bevel at the top. Two different setting needed.
> 
> Can you make the base a square?
> 
> It will really be easier for me to cut the wood and send it to you.


Dave - I appreciate all of the work you've done. I also appreciate the other posts, but I think we're on the same page that this is not as easy admit sounds. I know I made it a very difficult challenge by it not being square, but as weird as it sounds I had to make it that way. I may just scrap the pyramid roof and go with a traditional roof pitch. I just thought the pyramid would look cool. 

Thanks again for the time you've spent on this - I may just try some trial and error and see what happens. 

Oh - I have a SCMS that can do both left and right up to 50 degrees.


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## Dave Paine

thyde1108 said:


> Oh - I have a SCMS that can do both left and right up to 50 degrees.


I think your saw may swivel left and right to 50 deg. It may not tilt left and right to 50 deg. My Bosch Slider tilts left or right to about 46 deg.


I normally resist having to document in minute detail complicated items like this. In my old company I was famous for doing something in much less time than it would take me to explain.

Since so many replies are not appreciating the complexity of how to calculate these compound mitre cuts, I will attempt to document for posterity of the forum.

For this explanation, the saw needs to be set to a LEFT tilt. The tilt can be used on the left for both cuts. 

The cut with the swivel to the left *STARTS *in the middle of the wood.

The cut with the swivel to the right *ENDS *in the middle of the wood. 

The swivel angle is not fixed, since the base is not square.

First we need to calculate some simple, but important lengths and angles. 

The base measurement is 
27 7/16 = 27.4375 in x 25 15/16 = 25.9375in.

This means the diagonal of the base would be 37.7567in.

The apex of the pyramid is 12in height.

The triangle represented by the apex is
Height = 12in, Length = 1/2 the diagonal = 18.8784in.

This is the upper left portion of the picture below. The green tape shows the swivel angles which will be calculated later.









We then use the lengths to calculate the included angle = 32.44 deg.
This is the bevel angle you would use at the BOTTOM of the pyramid. I would recommend you do not attempt a compound cut here. Too complicated and not worthwhile. Just sand to trim off the protrusion.

This angle is also the "B" value in the spreadsheet and the diagram below.

To recap, this is the diagram representing the intersecting planes.









The next step is to determine the corner angle "A" in the diagram. In this case we have two since the base is a rectangle.

From the base dimensions
27.4375 in x 25.9375in.
we can determine the included angles between the diagonals.
These are 93.22 on the long side and the complimentary angle 86.78 on the short side.

This is shown on the upper right in the picture below.

We take 1/2 of these angles for the "B" measurement in the diagram.

We now enter the "A" and "B" values into the spreadsheet.

For the short side the formulae calculate
X = Crosscut Angle (swivel) = 38.58 deg
Y = Blade Tilt = 21.62 deg

For the long side the formulae calculate
X = Crosscut Angle (swivel) = 41.76 deg
Y = Blade Tilt = 22.94 deg

The saw is now set for the short side values.
This picture is the swivel to the left.









This shows the left tilt angle 21.62 (very hard to get that accurate on the saw scale). I highly recommend marking the angles on each pieces, otherwise you will get very confused.









Since I was only using scraps, I did not change the settings for the long side. For this illustration use the same setting for both cuts is close enough.

I appreciate the required saw settings look nothing like we would expect for a normal cut in a single plane.

I used CA glue to join the two scrap pieces so everyone can see this really would go together as Tim wanted.

The scrap pieces are 2in wide and face side up. For the picture the assembly is supported by a 12 in rule. This is a centre finding rule, if anyone was trying to read the scale.









Tim, now it is your turn. I did the hard work. 

Class dismissed. Oops, that if for your wife to say. :laughing:

Good luck. :icon_smile:


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## thyde1108

Dave Paine said:


> Tim, now it is your turn. I did the hard work.
> 
> Class dismissed. Oops, that if for your wife to say. :laughing:
> 
> Good luck. :icon_smile:


Dave,

I can't thank you enough for the time you took in doing this. I feel incredibly guilty for it! My appreciation can't be expressed enough. 

I've been working on this and it all makes sense. I think I have the cuts complete. I hope I am right that the only measurement not listed is the actual length of each piece but the ole Pythagorean Theorem tells me they are 22.875" long as the height is 12" and the length is 18.875" (a2+b2=c2). At least I remember that from school!

The only thing at this point that confuses me is the bottom bevel at 32.44 degrees. That is not coming out for me. That creates a pitch much higher than 12". The reason I think I'm not thinking of this correctly is because of your comment about not using a compound cut. This seems like the most simple cut. Set the saw or even table saw at 32.44 degrees and cut on the long side. That must not be right. 

I'm still working out that issue, but I think I have the others right. Again thank you so much. All of these notes give me tons of knowledge moving forward.


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## Dave Paine

thyde1108 said:


> The only thing at this point that confuses me is the bottom bevel at 32.44 degrees. That is not coming out for me. That creates a pitch much higher than 12". The reason I think I'm not thinking of this correctly is because of your comment about not using a compound cut. This seems like the most simple cut. Set the saw or even table saw at 32.44 degrees and cut on the long side. That must not be right.


Tim, I am happy you did not give up. 

I am a sucker for a puzzle. I recall the only time I did such a cut, for some bartop molding. I was aware the cut was not as anticipated, but when I did the calculations, I was having a hard time believing the results, but they were correct. Intersecting planes is not easy. So many details. Swivel vs bevel is easy to mess up. DAMHIKT. 

The thread was quiet and I was feeling that my explanation may not have made sense to you.

The bevel angle I calculated at the bottom may be off since it does not account for the thickness of the base. I entered 12in as the height from a reference plane.

If the overall height is 12in, then you need to subtract the height of the base. It is not uncommon in such complicated assemblies to need to do a bit of tweaking.

If I have been able to pass on a little knowledge in your project, then I am very pleased. Sharing knowledge is what this forum is about. :thumbsup:


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## Dave Paine

Tim, overnight thought. I did forget to include the length of the pieces. Sorry just an oversight.

My calculation came out with 22.37 which is close to 22 3/8.

To confirm.
Distance corner to apex = 18.8784in.
Height of apex = 12in

Hypotenuse (length of piece to be cut) = (18.878^2 + 12^2) ^ 0.5
= (356.394 + 144) ^0.5
= (500.394) ^ 0.5
= 22.37

I used ATAN(12/22.37) to get the 32.44 bevel angle for the bottom.


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## Midlandbob

Look at these sites
-
http://benkrasnow.blogspot.ca/2008/09/determining-proper-angles-to-cut.html
-
http://jansson.us/jcompound.htm

The second seem to be a compound angle generator. I just google "angles to cut for a pyramid".
-
Hope they help


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## thyde1108

*Finally complete*

Sorry for the long delay - this project got derailed a few times. I had some offline conversations with Dave Paine so he's aware that I had to scrap the pyramid roof idea. I hated it, but in the end poor early planning led to the demise of that. However, I did finish the project with a standard roofline and wanted to show off the final product. Again, I used scrap MDF so the quality of the material isn't great, but the joinery is solid. My wife wanted me to paint it Tiffany Blue (I guess she figured that was the quickest way to get that color box) and I'm happy with the final product. So was she, her faculty cohorts, and her students. The only thing missing are door handles (she hasn't picked those out yet) and the chrysalis the caterpillars make. Hopefully in a couple of weeks, there will be 4 monarch butterflies flying around!

I decided to round off the exterior sides of the doors so they could swing hingeless. I just cut a long metal rod into small pieces, slipped a washer over each one and glued them into the frame and door to hold the door in place. I used dovetail joinery for the frame, and since it was going to be painted, I cheated by countersink screwing the top to the box frame, puttied the holes and painted over. So there are no visible ways to see it held together. That was something I wanted since Google searches over other projects like this showed a lot of nails/screws/hinges. I wanted a seamless box.

Anyway, here are the pics (sorry they're sideways. Not sure why they loaded that way. They're upright on my desktop!). Thanks for everyone's support and an extra shout out to Dave Paine for the obvious time he took to help me. I wish I could have made the pyramid roof happen for both of us, but in the end it's done.

Thanks!
Tim


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## Dave Paine

Tim,

Thanks for the update. I am happy to see the final project. I also love seeing a thread about a project having a conclusion. :icon_smile:

If you had made a new thread people would not know that the pyramid shape was the original plan. 

I have had my own share of projects where the original idea "evolved" during execution. Sometimes due to getting new inspiration, sometimes the inspiration being forced upon me by various "Murphyism's". Necessity can indeed be the mother of invention.

It does look good even with a straight roof line.

Nice work to avoid the fasteners. :thumbsup:

I hope you are able to take a picture with the monarch's just before they fly off for parts way down south.


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## jharris2

That turned out very nicely Tim.

Looking forward to your next build.

Jeff


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## thyde1108

jharris2 said:


> That turned out very nicely Tim.
> 
> Looking forward to your next build.
> 
> Jeff


Thank you! Should have a butterfly soon.


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## thyde1108

Sorry for the delay. In the end, out if 10 eggs, my wife ended up with one butterfly. Here she is:

I'm officially closing this one out! Working on my son's queen size bed now out of walnut.


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## jharris2

Very cool! 

Jeff


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## JRoberts2589

MissionIsMyMission said:


> R U talking about something like this...only going all the way to a point???


MissionIsMyMission, 

That is exactly what I am looking for, how to build my own dust collection ports. 

Can you tell me how you made that? What angles did you use?

I have been trying to draw this in Sketchup to try and figure out the angles.

Thanks,
JRoberts


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## BigJim

JR, that post is about 3 years old.


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## MissionIsMyMission

JRoberts, 

There's an Excel Spreadsheet that I found online that will give you the formula to calculate the angles. 
This link should get you started.

http://jansson.us/jcompound.html


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## JRoberts2589

*Thanks*

Thanks, Mission.

I really appreciate your reply. I am probably trying to do something that would take much less time and effort to buy. :blink:


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