what is head cut for this shed rafer?
Hello all
Maybe I’m having a brain fart here, but is there a way to mathematically find the head cut for a shed rafter that ties into an existing pitched roof without using degrees? I have done it converting my 7/12 pitch(shed rafter) to 30 degrees and my main roof 12/12 to 45 degrees and just did the math with supplement angles. But lets say for fun I don’t have a speed square with degrees printed on or a protractor. Can I find the “pitch” for my head cut by just knowing the 7/12 and 12/12 rise over run for each roof?
I also remember a guy told me about the “double the angle and minus 90” but by my math that only works with the same pitched roof. A 7/12 coming in to a 7/12.
Any thoughts are great
Replies
Put your framing square on the bottom of a 2x at 12 and 12. On the left side of the square make a mark at 7. Pivot the left side of the square down to the mark and continue the line to the top of 2x. Hope that makes sense.
The one is this drawing I made is a 5/12 and 10/12 combination. You just do the same thing using a 7 and 12.
sweetI wish I didn't know now, what I didn't know then
Paulewog: You can solve directly from the pitches, multiply by 12 and the result is all ready for use on a framing square:
Formula for Difference of Pitches.
Supplementary: Formula for Sum of Pitches.
The equations are easy to remember and you can often do the math without a calculator.
For your roof specifically:
(12/12 – 7/12) ÷ (1 + 12/12 × 7/12) = .416667/1.58333 = .26316
Framing Square: 12 × .26316 = 3.15789, about 3 3/16 over 12
Joe Bartok
Edited 12/2/2006 10:26 am ET by JoeBartok
Edited 12/2/2006 10:32 am ET by JoeBartok
thanks Joe C,and Joe B, and rpm inc. Makes total sense.
I hope you guys know how valuable of a tool this forum is and you alls knowledge is, to us greenhorns.
again thanks
Pauly
Paul,Another way to do it by math is subtract the lower pitch from the higher pitch in degrees and subtract that from 90° and that's what you hold a speedsquare on.45° - 30.26° = 14.74° 90 - 14.74 = 75.26°
Pivot speedsquare at the top until it hits 75° and that's your angle.Framing Square.14.74° Pitch is 3.157097" or 3-3/16"Hold the framing square at 3-3/16/12 and scribe the 12" side and that's your angle.Joe Carola
Edited 12/2/2006 12:25 pm ET by Framer
For those who wish to do more research, the formulas in those links to the pdf documents I posted were actually modified "textbook" formulas.
Analytic Geometry: Angle between Intersecting Lines, where m1 and m2 are the slopes of the lines.
Trigonometry: Sum and Difference of Tangents, where tan a and tan b are the tangents of the angles.
Since pitch = slope = tangent of an angle = rise/run, I took the standard formulas and substituted the pitch.
Joe Bartok
Edited 12/2/2006 12:26 pm ET by JoeBartok
Edited 12/2/2006 12:27 pm ET by JoeBartok
Paul,Here's a link to a thread about this a couple years ago. I showed how you can also do this with a speedsquare. That was with a 5/12 and 12/12 pitch.http://forums.taunton.com/tp-breaktime/messages?msg=49588.51Joe Carola
Against the wind . . .
Forrest