More on run/rise/pitch vs. length and width

[elizabeth]

Help Tim and friends!

Sorry to bother you again. Made my sled and took it for a spin today. Followed all I learned and tried adjusting your calculations to my actual box width and length.

Here are the details and how I figured:

Box: 1 4/32 Wide X 1 10/32 long.
want a roof 1/4" high

Run = 1 4/32 divided by 2 = 9/16
Rise = 1/4"
diagonal = 39/64 (To me that meant cutting a board 20/32 wide and two pieces 1" 10/32 long, and two pieces 1" 4/32 long.)

But: I wanted an overhang (sofit) of 1/16"

1/16" X 2 = 1/8 that I needed to add to each piece lengthwise and in height. so:

the end pieces were 1/8 + 1" 4/32 = 1" 1/4 long
the side pieces were 1/8 + 1" 10/32 = 1" 7/16 long

The Rise then is 1/4 + 1/16 (sofit) = 5/16
Run = 1" 1/4 divided by 2 = 5/8
Diagonal = 45/64 (I rounded to 22/32)

It didn't work. The pieces didn't close at the top.

Following Tim's formula (HELP TIM!!!!!)

1.414 divided by 4 = .3535 (23/64) slope x 9/16 (run) = 13/64

BIG DIFFERENCE IN NUMBERS!!!

So what did I do wrong? Are the pieces I need to cut 23/64 wide X the length of the box sides?

I obviously missed something. The first test I made was with a square box, not a rectangular one.

Can you spell it out, PLEASE?

Thanks!!!!

[TDHofstetter]

Oho, you're very close. You were doing just fine until you figured the soffit into the diagonal height. You won't add it in twice for each roof piece, only once... and add just a smidge more because you're at a low pitch (1/4" high at the peak). In this case, the smidge will be insignificant (less than 1/128" more), so just add the single 1/16" for the soffit.

The change in rise, too, will be pretty insignificant because of the low slope - the rise will only be between 1/64" and 1/32" greater.

Here - lemme sketch it up for ya. Paper is FAR cheaper than wood...



The smaller triangle is the critical dimensions of the roof without soffit, the larger is the roof with soffit. See how little the rise changes with the low slope? In a case like this, it helps to draw it up in both views (side and end), then add the soffit to the drawing before calculating for the hypotenuse... in this case SQURT(0.274"² + 0.719"²) = 0.769", or 49/64".

We can't use the easy 0.707 and 1.414 here because the roof won't be at 45 degrees (45-degree angles are special).

Oh... one more thing I might point out. To figure the soffit itself... draw the basic roof with no soffit. You know the soffit's run (1/16", but what'n heck is its rise? Well... you already know the ROOF's run & rise, so you multiply the ratio of that roof's run to rise (0.656"/0.250") by the soffit's run (0.063).

(0.656"/0.250") x 0.063 = 0.024 (the soffit's rise). Draw it in, dimensioned.

NOW you have the true total rise and run of the roof-with-soffit, so you can calculate the hypotenuse.

Ain't geometry fun? Someday we may take ya alla' way into TRIG...

Do keep in mind that all four roof pieces won't have the same dimensions...

[elizabeth]

Oh, thank you. What do you mean the pieces won't have the same dimensions? Won't the two ends be the same and the two sides be the same?

Maybe I should just do it at 1/2" rise so I can use your formula?

I'm so sorry to be so thick on this but I have no math background. I studied to pass the tests in school and the moment I put my pen down I promptly forgot everything I memorized. I'm the same way with grammar!

[TDHofstetter]

Oh, each pair of pieces will have the same dimensions as each other... I just meant that the four pieces won't all be identical. Gotta' cover the "just in case it gets forgotten" scenario, ya know.

No problem with the talkthroughs. At some point, one of us will say something "magical", just the right words in just the right way, and suddenly it'll all fall into place. Could be we're just waiting for synapses to develop.

I have confidence - you'll get it. After all, I've watched your progress thus far...

[elizabeth]

Thank you so much. I'm also waiting for synapses to develop. ;D ;D It's neither in my nature or genes to think this way.

BTW: I just did a test with the actual dimensions of the box but with a 1/2" rise. The pieces all closed properly and I'm going to put it in real wood.

I didn't do the 1/4" rise because you said it was no longer a 45 angle. So I started thinking that I would have to change the setting on the miter gage? And if so, then the bevel at each edge would not be 45, nor the wedge I made? So, to move things along I increased the rise like you taught me. It doesn't look too top heavy so I'm going to plug ahead.

But, for future reference: Is 1/2" rise the lowest I can do to still have the 45 degree angle? My set-up is all based on a 45.

I'll take pics of my sled and what I've done so far. The sled works but theses pieces are just a tad too small for real comfort. I have to be very careful with the clamps.

Also, In the last threads, when we were discussing measuring and bevels you mentioned that if I measured right I could use the offcuts as another roof piece. I've tried doing that but discovered that if I had the pieces beveled first, then the offcut was backwards and unusable. I tried it without beveling the edges, and I can capture those pieces, but only if I flip the faces. Is this your take on it too or did I miss something again.

Thank you for your continued patience. I can't wait to show you my progress!!!!!

[TDHofstetter]

To get the roof sides to slope at exactly 45 degrees... the rise and run must be exactly identical. If the rise is less than the run, the roof will slope at an angle less than 45 degrees, if the rise is greater than the run, the roof will slope at more than 45.

The four "edges" of the roof can still be miter-cut at 45, though, provided they're stood on your sled leaning at the slope they'll have in the finished box.

-:-:-

To capture & use the offcuts as roof pieces, be sure to bevel both edges on the same face (so the soffit "looks down"). If you bevel them on opposite faces (so the soffit will have a fascia, "looking out"), the offcuts will be discardable scrap.

[elizabeth]

Thank you. Now I understand. I sure have cut many unusable pieces but I've managed to cut two roofs. Now all I have to figure is how to cut a "beak" on the inside of the roof so that the rim of the box sits inside it.

I haven't glued yet because I think it would be prudent to cut this little groove with the wood flat. Or, glue and support it somehow and use the Dremell for the groove. What do you think will give me the best result?

Of course, I still haven't figured out how to glue it!

I attach pics of the sled.

Thanks again!!!!

[TDHofstetter]

Boy, no doubt ABOUT it, you are a jigmaker extraordinaire! Remarkable, truly... and your inclination to make them little bitty things fulla' precise work, as well.

Lessee - to make that birdsmouth cut... I can see two ways of doing it reasonably. One way you've suggested already - Dremel work before the glueup, carefully planned & executed. The other way would be another special dedicated sled that references to the table saw's fence and uses the blade tilted to the roof's angle or its complement (whichever is at 45 degrees or less). It'd be tricky to do, though, especially without sawing clean through your sled. It'd be tricky, too, to hold the little pieces firmly and accurately in place while you grazed 'em with the table saw.

OK, a third way - a hand plane, a little bitty one specially built just for the purpose, with an iron specially ground for the purpose. The iron could be tilted to whichever angle you'd need for these various roofs. Almost more like a scratch stock than a hand plane... which... DANG. You KNOW... a scratch stock might do a pretty good JOB of it. Again jigged so the roof pieces would reference against a fence & slide along a table of sorts with the scratch stock sticking up out of it. Fence adjustable for different size roofs, scratch stock adjustable for different roof angles. The contributing steel could be a simple hacksaw blade, ground to shape.

[elizabeth]

I don't know what a scratch stock is. Having slept on this I think the easiest way to do it is to glue up first and then set up the router table with stops and make my cuts by lowering the roof onto the bit. I've done this before and it's easy. I can square the corners with a chisel. This way the roof is already tilted at the right angle and supported by itself. I'm going to test it with the mock-up roofs first.

I hope to get this done today and I'll let you know how I progress.

Thanks again!

[TDHofstetter]

Boy, that thought scares me... it'll be accurate, surely, but the thought of fingers next to that spinning cutter just jeebies the life outta' me.