help in measuring for compound bevels

[elizabeth]

I guys. Have another question for you.

I'm ready to learn to make a tee-pee like (roof) top for my little boxes. I know it's got to be a compound bevel thing but have no idea how to measure. I've seen a formula for this in past threads but I didn't understand it. I think Cody mentioned it.

My difficulty is that I have ZERO math skills. Can't multiply without a calculator. I have to see and feel my way around dimensions. I draw a blank with decimals and fractions. For real! Angles, and measuring for them, allude me.

Would you be able to spell out the formula with a simple sample so I could plug in my own numbers? And I mean REALLY elemental. Like 2 + 2 = 5

Something I can do on the calculator, please, and tell me what buttons to punch where?

I'm embarrassed to have to fess-up to this but I really would like to make a small (from 1.5" - 6") 4 to 8 sided roof. Like in a round Gazebo.

Thanks!

[TDHofstetter]

The simplest way to do it... is to stop thinking in terms of "compound". Measure (or figure) one angle & set up for it, then measure (or figure) the second angle of the compound & set up for IT, while leaving the first angle's setup intact. Like with a compound miter saw, set up the TILT for one angle & don't disturb it while you set up the MITER for the other angle. The cut will be the correct compound angle.

Another thing that helps a lot (SOMETIMES) is not to think in terms of angles... at least not at first. Think instead in terms of "rise" and "run". Like thinking about building a staircase... don't think about cutting each notch at an ANGLE, cut it instead at a measured rise and run.

Once you know the rise & run, you can draw it onto a piece of scrap and measure the angle you've just drawn. Scale it up if necessary - like convert 1" to 10"... so every 2" would be 20", every 3" would be 30", like that. You can scale by any factor - 1:2, 1:5, 1:9-1/2.

EDIT: Um... and another thing that helps (cheating, maybe, but who's counting?) is that ol' SketchUp we talk about from time to time. It's a free download. Draw up whatcha' wanna' make, let IT figure out all the angle stuff.

[Leo Voisine]

Tim mentioned sketchup. Well I was thinking something similar.

Lets take some baby steps

One thing we need to know -- from the top of the side (wall) -to the tip of the roof peak - how tall is the roof?

Then is the base square - hexagon - round?

What are the dimensions of the base. you said 1.5" - 6", what does that mean?

So where I will be going here is to work with the compound angles on the component level. In other words to break the compound angle into to individual simple angles.

ONE angle - rise and run. Like the pitch on your roof on your house. For every 1 foot of horizontal distance (run) there is a vertical distance (rise). Commonly a roof will be called a 4 pitch. That is because for every 12 inch (1 foot) run, the rise is 4 inches. That is pretty shallow. I steeper pitch would be an 8 or (8-12) pitch. So - you need to decide what your pitch will be. That is one angle of the compound angle.

Second angle - the mitered cuts. This is pretty easy - it is just 360 degrees divided by the number of sections. so 6 sides will be 360 / 6 = 60.

Last angle - I am sure to get this wrong - so I will let someone else add this in. You will be cutting triangles, and those triangles will be cut at some included angle - based on the other angles. Thos triangles will be the sections. I can lay it all out in CAD - like sketchup, but off the top of my head I cannot explain a simple way to figure it out. Maybe as time goes on I can get something on paper - then I will share that.

Once all the numbers are figured out - then careful planning and layout - then careful cutting.

This is an interesting question - glad you asked it.

[TDHofstetter]

I might add, too, that to make things easiest... it's often a good idea to set up a raw piece of wood in exactly the orientation you expect it to be in as part of the roof - like leaning against the miter saw's fence - and then cut the side angles as simple miters. That's the easiest way to cut crown molding, instead of working out a compound angle - lean the crown against the miter saw's fence (or against a table saw's (or bandsaw's) miter gauge, then cut a simple miter.

[elizabeth]

OK, guys. Wait a second!

So "pitch" is the same thing as "rise"? I didn't know what rise or run meant. It's in my calculator but the instructions assume you know what is being explained. There are other commands on it, though I have no idea what they mean, that have to do with construction, including building a staircase. So this may help. But I've never built a roof nor cut crown molding, and I don't know the meaning of the terms used in this.

How about this:

I want to make a 2" W X 3" L X 2" High box with a little roof that "rises" no more than 1". I'll be mitering four triangles at 45 degrees (these are flat pieces) 360 / 4 = 45. Then I have to angle their edges so they can be joined on tippy toe. How wide and long does each piece need to be and what is the angle of the edge? I can set my blade and miter gage to cut each piece once.

If you could fill in the blanks for me I can adapt this example to any other size (I think )

I'll also check out the site you mentioned.
Thanks!

[TDHofstetter]

Pitch = (rise divided by run), usually expressed as a ratio instead of a fraction - 1" rise in 12" run is written 1:12, and referred to as "1:12 pitch" or sometimes as the (incorrect but common) abbreviated "1 pitch".

You realize that the roof won't meet at a single point, right? That it'll have a short edge (1" long) between two points... because one wall is 2" long and the other wall is 3" long?

Since it'll be at 45 degrees, there's a special number we can use to make the calculation quick: 1.414. Visualized from the end, /\, each half (one piece of the roof), or / and \, will have a 1" rise in a 1" run. Its length (diagonal height) will be 1.414 x its run or rise, which means its length will be 1.414"... almost exactly 1-13/32". Since they all rise at the same angle, or pitch, they'll all be exactly the same length (diagonal height). So... the simplest simplest thing to do is make a tiny quick sled for your miter gauge, with a pocket exactly 1" long. You'd cut your roof pieces 1-13/32" long, then stand them up in the pocket so they lean against the miter gauge's fence. Since the pocket is exactly 1" long, they'll lean at exactly 45 degrees. Now if you look straight down at the top of the miter gauge, you'll see quickly that you only need to make two quick simple 45-degree miters and each piece will be finished.

Two of the pieces will be triangular - the pieces for the ends. The two side pieces will have all the same angles, but they'll be 1" longer, in the shape of an isosceles trapezoid:

en.wikipedia.org/wiki/File:Quadrilaterals.svg

[Leo Voisine]

Well, it "could" be made to meet at a single point - but that would be more comfusing, and I would need to lay that out with CAD.

The result would be that the ends and sides would have different pitches.

[elizabeth]

Sorry, guys. I'm hopeless at this. I didn't know the four pieces wouldn't meet at the center. I thought they would meet to form a star. How did they ever build domes in ancient times? (They obviously didn't play hookie during math classes! )

I've downloaded SketchUp and am learning my way around it.

My calculator can figure pitch, run,rise, diagonal if two dimensions are known and it will cycle to angle. I'm just not sure how to enter the values and unclear what the results mean.

I'm going to study your answers and try to figure it out.

Thanks again!

[TDHofstetter]

Here's how they built domes...

en.wikipedia.org/wiki/Truncated_rhombic_triacontahedron

Here's how the roof comes together if it's at 45 degrees all the way around:



EDIT: This is what you've got a mind to make?

[elizabeth]

YES! I followed the link to Wikipedia and it's called a Kite? Like a cone! It's what I would love to do. Like the roof of a Gazebo.
YEAH, Tim!!!! Thanks for understanding! Are we there yet?

[dicklaxt]

Here is the answer if you can get the Math Professor to explain it,how about it Prof Tim??

mathcentral.uregina.ca/QQ/database/QQ.09.04/steve2.html


dick

[TDHofstetter]

May 6, 2010 15:10:03 GMT -6 elizabeth said:

YES! I followed the link to Wikipedia and it's called a Kite? Like a cone! It's what I would love to do. Like the roof of a Gazebo.
YEAH, Tim!!!! Thanks for understanding! Are we there yet?

Like... this?

en.wikipedia.org/wiki/Kite_(geometry)

I'm not quite picturing it... in my mind a gazebo's got an octagonal roof like that last sketch up there ^^^.

EDIT: If we ARE on the same page... makin' that octagonal "cone" shape... yeah. It's not hard. Think of it like this:



You can make a shape like that, true? Eight sides, easy miters. All ya gotta' do is figure the true length of each piece (if it's gonna' tilt at 45 degrees, the length will be 1.414 x the flat-to-flat radius (distance from centerpoint to flat surface) of the octagon. Bevel the bottom edge at 45 degrees so it'll stand on the octagonal box below it, then stand it up at 45 degrees in the miter saw to make those two basic miter cuts. If ya need, I'll sketch ya the miter box setup.

[Ruffnek]

Tim, you're making my head hurt.

[TDHofstetter]

Let's walk through it step-by-step:

[Mark]

But, isn't it goin' on a rectangular box?

Mark

[TDHofstetter]

From the original post:

I'm embarrassed to have to fess-up to this but I really would like to make a small (from 1.5" - 6") 4 to 8 sided roof. Like in a round Gazebo.

[elizabeth]

May 6, 2010 16:45:29 GMT -6 Ruffnek said:

Tim, you're making my head hurt.

Tim: This is fabulous. Thank you!!! My head is swimming. The graphics are great, but can you spell out the sequence of the math for me? (Like: 2 X 2 + 6 - 3 = ?) I've never been able to do math. Particularly the problems like Peter has 3 apples, Paul 6, Peter gives 2 to Roger, etc.... Can't wait to give it a go.

And Mark: Yes. It will be a rectangular box but I'll also make square ones and octagonal ones. I'm intending to put the Octagonal roof on any kind of shaped box. Once the roof is done I will glue in (on the inside) a rim that will fit the box shape and dimensions. For the little boxes I'm making I want a whimsical look.

Dick: You're right, I need Tim to spell out the math for me.

And, if I can learn the formula I can adapt it to the other shapes Tim has posted!!!!

As my skill improves I want to make a box in the shape of a Porcupine (for real ).

[Joe Lyddon]

Yep, that was a super presentation...

Looked real simple as it was explained...

I do think I will have to take another aspirin and read it some more though... picturing the saws doing their thing, etc.... ;D

Good job, Tim! (as usual)...

[elizabeth]

Hey, Tim! Some clarification, please

I think I'm first going to do a simple 4 sided "roof" like the one in your reply # 5, May 5Th. It'll be longer than wider, like your first graphic.

I'm reading the instructions and also looking at your diagram on reply #13.

I'm still getting confused with the terminology. Would you be able to label the run, rise and pitch on the diagram? I'm trying to adapt the dimensions to the little boxes I just made.

Then: I don't know what you mean by a "pocket" in my quick sled. I'm getting confused with length and width.

Also, forgive me , your last diagram shows a solid wedge. I was hoping to make a roof with and "attic". In other words, my pieces are thin, and there will be a cavity inside the "roof". Shouldn't I be cutting these flat on the table with the miter set at 45, and the saw set at 45?

So, if my box is 1" W by 2" long, and I want a 1/2" long slope, but I want a rim of 1/4" (a Sofit) how wide and long do I cut my blanks before I miter and bevel at 45?

I'm so sorry. I'm a real dingbat but I spent the better of two hours today reading and manipulating little pieces of wood trying to understand both you and Leo.

Your dreams. Thank you!

[TDHofstetter]

Here's your run & rise:



...and here's a sketch of a pocket - and the way to make for an attic:



I think you'll find this way of cutting 'em a LOT easier than trying to cut a compound angle with the stock lying flat. Most people do. You see... if you cut it flat, with the miter and bevel both at 45 degrees, the miters won't match up - that drives a lot of people nuts until they either figure out the much more complicated math to get the miter RIGHT or they wind up with a setup like this one. Been there, got the beer cans.

EDIT:

So, if my box is 1" W by 2" long, and I want a 1/2" long slope, but I want a rim of 1/4" (a Sofit) how wide and long do I cut my blanks before I miter and bevel at 45?

Ok - your end roof pieces will be...

Roof 1" wide
Peak 0.5" high
Slope 0.707 x width = 0.707" long

Add a soffit and you have to think differently - the soffit makes all the roof pieces wider. So... figure a 1/4" soffit, add one soffit to each side, so your end pieces will be 1/4"+1"+1/4" (1-1/2") wide.
The soffit will dangle downward 1/4", since it's at 45 degrees, so the peak is 0.75" high.
The slope is 0.707 x width = 1.060" long.