Desperately seeking a formula to cut sheathing for any hip roof! Can anyone help?

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Mine is to measure what the first piece is, then I know the angle and the gain for all the rest.

Welcome to the

Taunton University of Knowledge FHB Campus at Breaktime.

where ...

Excellence is its own reward!

What Piffin said...measure it once, you've got it for the rest of the roof.

Edited 10/26/2008 1:53 pm by

mmoogieDesperately seeking a formula to cut sheathing for any hip roof! Can anyone help?

Do you have a Construction Master Calculator? If so w/without trig?

For any roof, all you need is your common rafter and hip length to tell you what your sheathing will be. Your framing square already has the answer for hips running at 45°

Edited 10/26/2008 2:10 pm ET by

FramerThanks Framer! You put me onto a solution. I took your advice and drew up a scale model of a 5:12 hip roof in SketchUp so that I could measure to make the cuts on a 4 x 8 sheet of plywood. The mitre cut came in at between 44.25" and 44.3125" and I chose the larger feeling that I would be off by only 0.004" strong at the short point. Then I sectioned the roof to measure the bevel angle, which came in at a little less than 16.5 degrees. I'll use 16 degrees for the bevel. Sometimes looking at a problem through anothers eyes will yield an answer. Thank-You Framer, and thank-you FHB.

I took 4' at the slope at the 5/12 pitch and solved for the horizontal dimension. I came up with 44 5/16" - Pretty close to what you came up with. Like others have said, If you cut one piece off and it works well, mark that as "PAT" and use it for your pattern. .BTW - You aren't SERIOUSLY gonna bevel the plywood, are ya ???

A bothersome person is like a booger that you can't thump off.

The bevel is very important! I'm interested in modeling a pyramid. I think of it as a hip roof with a slope of 15:12. I cannot imagine open seams. I am the "new guy" and I just want to get it right! I have yet to pull apart a hip roof where the hips were not backed, or where there was a common framed against the ridge. I appreciate the work of these unknown Carpenters and their level of craftmanship. And, so far, along with reading, this is how I've been learning the craft. Thank-You muchly for your comments. Now-a-days, feed-back is adding to my adventure. And thank-you FHB.

I can't imagine why you would think that a bevel is important. What kind of roofing will you be using?

We judge ourselves by what we feel capable of doing, while others judge us by what we have already done. [Henry Wadsworth Longfellow]

The bevel is very important! I'm interested in modeling a pyramid.

Is this for a model or is it for a real life size roof?

I think of it as a hip roof with a slope of 15:12. I cannot imagine open seams.

The way you made it sound was that you were beveling the sheathing.Why would the plywood have to have a perfect seam on a hip roof that's getting covered with tarpaper and shingles? If you want to do it for peace of mind, fine, but there's no need at all to bevel a hip. You can get a perfect seam without beveling the hip if you want too.

I am the "new guy" and I just want to get it right! I have yet to pull apart a hip roof where the hips were not backed,

Since you are the new guy, you have to learn that not beveling a hip is right. Beveling a hip is just a waste of time, it';s only cosmetic and gets covered.

Beveling the bottom of the hip for a cathedral ceiling is another story and that's important, but you're not talking about that.

Joe Carola

I use a Construction Master Calculator with Trig. You don't need the trig for this right now. If you want, I can give it to you.

All you need to do for any pitch hip roof running at 45° is to look at the first line on your framing square "Common Rafter Length Per Foot Run" where it says 13" for a 5/12 pitch. Divide 12 by any number in that column for any pitch and multiply it by 48" and that will be the measurement for the plywood angle.

12/13 = .923077x48" = 44-4/16"

Construction Master.

5[Inch] [Pitch]

48[Inch] [Diag]

[Run] = 44-5/16"

Forget beveling the sheathing, there's no need at all to bevel sheathing. That bevel angle is good for when you have a cathedral ceiling and you have to run beadboard or something else under the rafters for a finished product.

What Piffin and the others say are true and work perfect, but this way takes 5 seconds to get the answer and you make your mark without going on the roof and measuring to get the mark. Takes way to much time to do that compared to knowing a simple math solution.

Joe Carola

Edited 10/27/2008 8:17 am ET by

FramerFramer, your O.K. Thank-you for the lesson on the Framing Square! That is one of the holes in my education. I usually throw some mud over it, tape it, and it goes away. I bought a CM when they were first introduced, and loved it. I no longer use them. I've gone back to the old scientific. Now if I want the slope, I take the inverse tangent. I'm a calculated carpenter. None the less, I've had this nagging problem with sheathing. For example, the last two roofs I pulled apart were Dutch Hips. Both of them were porch roofs. Both of them were sheathed with 1x boards, and both of them had mitered bevels. When I left those jobs, I was not satisfyied, because I did not know how to reproduce the work, save for pulling a good board and copying it! Fast forward to yesterday when you and Pifin opened my eyes. Again, thank-you!

I've gone back to the old scientific. Now if I want the slope, I take the inverse tangent. I'm a calculated carpenter.

For a 5/12 pitch 22.62° roof, you do this.

48"x Cos(22.62) = 44-5/16"

As far as the framing square is concerned, the answer is right there. For the 5/12 pitch is says 13. If you measure 12" in off the left corner of a sheet of plywood for example, measure up 13" and connect that to the corner. The hypotenuse will read 17.69" or 17-11/16". That 17.69" is the "Hip or Valley Length" measurement on your framing square.

Just continue the diagonal of the triangle until it hits the top of the sheathing and that's your cut. Take that piece and use it as a pattern.

Visualize the 17.69 diagonal (Hip Length)and the 13" rise (Common Rafter Length) and the 12" (Run) as a small hip roof. You can use those numbers on your framing square for every pitch running at 45°.

Joe Carola

Hi Framer! I'm still on the trail. Just when I thought I had it, I realized I had it backwards, do to my limited abillity to visualize. So, here's what I came with! This jpg. is an X-Ray iso of the 5/12 using the values from the framing square. Everything checks out! I may not be wrapped too tight, but at least I can see through the cellophane! Thanks Framer!

Sorry about that! I forgot the attachment!

That's it.

Joe Carola

Subjects been pretty well covered, but I'll still put in my two cents.

Since you would all ready have your jacks figured, I just use a 2' or 4' as the bottom leg of my "formula" and then the allready figure rafter length ( with no subtraction for hip material) and those two numbers act as the legs in the Asq +Bsq=Csq (obviously don't know how to spell plathagrium therum?) Its pretty easy to explain to the labor also.

My question is, if you are doing a cone roof, how do you figure th radius's and such to sheet. Did one a few years a go and built a small mock up for cheek cuts and all, about a 10' radius plate with something like a 30/12 pitch. We were about 25' in the air bending 1/4" sheets around and triming in place. I think I did one temp and then used it as a pattern with limited success. triple sheeted it, looked great, but still like any bodies input that has a better way.

Love the formulas, but love my construction pro more, lol

Edited 11/4/2008 9:21 pm ET by

ryderCubeSquare,

http://www.josephfusco.org

http://joes-stuff1960.blogspot.com/

Good to see both Joes out again, THIS is where a lot of us get to learn.

Thanks guys,cheers,Phil."If 'tis to be,'twil be done by me."

Joe, if I understand you correctly, you say find the slope of the hip rafter by dividing the rise by the run (16.97056275) and then taking the inverse tangent. Then press SIN, then press TAN-1 and what I get is the backing angle for the hip rafter. The backing angle is then the bevel angle for the sheathing! I didn't know that! Wow! I cannot thank-you enough for helping me!

O.K. That gives exactly what I asked for to a certainty of eight decimal places. Can the mitre angle for the sheathing also be formulated, or should I be satisfied with measuring? Wait a minute! I've got it!

Example: On a 5:12 roof the common rafter length is 13" per foot of run, as you pointed out on the framing square. Thus, the inverse tangent of the Run divided by Length of rafter per foot of run, yields the mitre angle for the sheathing! Yes?

O.K. That gives exactly what I asked for to a certainty of eight decimal places.

Can the mitre angle for the sheathing also be formulated,or should I be satisfied with measuring? Wait a minute! I've got it!Any angle can, if you just visualize it as a triangle. I gave you the numbers as 13" for the rise(on the framing square), 12" for the run and 17.69(on the framing square) as the hypotenuse.

All I do is visualize those numbers as if the hip was framed already and looking at it in plan view as a triangle and you have the numbers you need to get the sheathing cuts and the sheathing angle.

Let's say you didn't use the framing square table and you wanted the sheathing angle, all you have to do is use the common rafter length and common run to get it or common rafter length and hip length to get it.

Let's say you had a rafter run of 10'(no ridge deduction) with a 5/12 pitch roof. You know the common rafter would be 10'10. You can divide that by 10' and hit the Tan-¹ button and get 47.29061°

Visualize that 10' 10" common rafter nailed up and the hip nailed up and the run coming in off the corner at 10', that's your triangle, now sheath it.

Does this make any sense?

Example: On a 5:12 roof the common rafter length is 13" per foot of run, as you pointed out on the framing square. Thus, the inverse tangent of the Run divided by Length of rafter per foot of run, yields the mitre angle for the sheathing! Yes?

Tan-¹ (13/12) = 47.29061°

Check yourself with all the numbers I gave you with the plywood drawing.

13 [Inch] [Rise]

12 [Inch] [Run]

[Pitch] = 47.29°

4' [Rise]

3' 8-5/16" [Run]

[Pitch] = 47.29°

Joe Carola

Wow! How lucky am I. Your the man! Obviously, your the real deal. After talking to you, my problem became simple. I now own the math skills to to solve the sheathing problem for any equaly pitched hip roof. I refuse to admit how long this problem has plagued me! Yup! There goes another satisfied carpenter! Thank-You!

Nice work, Framer,I like a guy who can get to the same answer from at least three different ways!The first hip roof that I cut was a timber frame. 5"x18" hip rafters.

Had to get help just to flip them over to mark the other side.I'd never cut a hip before, but I'd at least read about it, which put me ahead of everyone else on the crew. I was elected.I went home, read up until smoke was coming out of my ears, came back to work, and cut the roof.Backed the hips and all. That's beveled, not dropped!I sweated bullets on crane day, but it all fit.Next time, though, I'll call Framer, and sit in a lawn chair sipping a cool drink while he does it blindfolded.AitchKay

I like a guy who can get to the same answer from at least three different ways!

I always try as many ways as I can to come up with the same answer to check myself and then I use the fastest way. It's all about triangles.

Joe Carola

I'm glad I could help. Isn't this fun?

Joe Carola

Oh! I see. I had it exactly backwards! Using the formula the way I explained it to you yields a mitre of 42 degrees. Your mitre is 47 degrees. O.K. I'm gonna watch the relationships of the trig functions. I love the way you turn these triangles around.

I made a drawing of a 5/12 pitch hip roof using the numbers on the table of the framing square with a run of 1'. You will see the triangle that it makes as a finished roof. You will see the angles the plywood makes. How you mark it with your square is shown on the other drawing.

You'll see that the bottom says 47.29°. Visualize is as if it were a common rafter and you were to mark the top of the plywood in the drawing, you would mark the top plumbcut with a 47.29° on your speedsquare and the compliment of 42.71° on the bottom as if it were the seatcut of a common rafter.

Joe Carola

And once you have found the angle, whether by calculator or other means, it has made sense to me to make a marking stick from a length of something handy, and a couple nails.

The stick lays on the bias across the uncut panel, and the nails are stops to position it correctly. Listen for the callout from above, as in "seventy six and a quarter long," then mark and position the stick, draw line, and cut. To be effective even for doing short cuts, when the stick will want to be past the top edge end, you'll want a full panel sistered alongside the one to be cut, so there is a surface to hang that other nail to.

It is like the plywood-cutter's version of the draftsman's adjustable triangle.

View Image

View Image

"A stripe is just as real as a dadgummed flower."

Gene Davis 1920-1985

Gene,

We had this conversation about 3 years ago when Jim Allen/Blue eyed devil said that he does this. I drew this back then. Isa this something like what you're talking about?

Joe Carola

That's it, Joe. Three sawhorses, another full panel to the R of it, butted up tight and aligned, and you are ready to mark and cut, no matter what the "long" number called down.

View Image

"A stripe is just as real as a dadgummed flower."

Gene Davis 1920-1985

you say find the slope of the hip rafter by dividing the rise by the run (16.97056275) and then taking the inverse tangent. Then press SIN, then press TAN-1 and what I get is the backing angle for the hip rafter. The backing angle is then the bevel angle for the sheathing!

Tan-¹(5/16.907056) = 16.41644° (Hip plumbcut angle)

Tan-¹(Sin(16.41644)) = 15.78118° (Hip bevel and sheathing bevel)

Joe Carola

One place I've always been lacking, is in the abillity to visualize. However, I caught a glimpse when you called the slope angle the plumb-cut. Of course! At that point, I could see two legs of the triangle. Wow! Also, at that point, I think the CubeSquare got religion, as in "Oh, my God" which is to say this abillity to visualize is every bit as important as finding the formulas. No doubt, I got exactly what I was looking for and more! Thank-you, good buddy, I feel like you've extended a hand to help me up.

Here's a drawing using a sheet of plywood with the examples I gave.Joe Carola

You can use the framing square to mark the sheathing cut by using the 13 and 12 for the 6/12 pitch.

Joe Carola

Last one I did we just ran them long, snapped a line, and used a cordless skill saw to cut it. Not as glamorous I know, but the one before that was taking way to much time.

Edit: they were new dormer roofs.......found a website you might like http://www.blocklayer.com/Roof/RoofEng.aspx its getting late, my hands are working faster than my brain

Edited 10/27/2008 9:56 pm ET by

arcflashEdited 10/27/2008 10:08 pm ET by

arcflashEdited 10/27/2008 10:13 pm ET by

arcflashI hear you! Great web-site! Embolden'd and beholding...........CubeSquare

CS,When I gave you the first link, I thought you'd browse a bit. . . ;_)Here's a link that has just what you whated/needed/: http://www.josephfusco.org/Articles/Roof_Cutting/Basic_Roof_Framing/Documents/Glossary_Definitions_1/Calculating%20the%20Plwood%20Cut%20Angle.htmlAnd here is one to my roof calcultor as well: http://www.josephfusco.org/Calculators/Simple%20Roof%20Calculator.htmlhttp://www.josephfusco.org

http://joes-stuff1960.blogspot.com/

Thanks Joe! I have a feeling I'll be spending time on those sites! For now, I bookmarked 'em. Time is tight! Gotta run.......rise...........

ArcFlash, every time I go to Blocklayer I like it more than the last time. I watched a video on trigonometry which began with the Indian Princess Soh Cah Toa. Great stuff! Just another quick Thank-You!

No sweat, bro. I found it while working out the details of a screened porch. Haven't built the porch yet, and I think it will be a shed roof anyways, but I saved that site thinking it would come in handy later. I didn't see the trig movie, so I'm heading that way now. Good luck with the roof. I cut my teeth on a hip roof, and I'm still learning.