The original roof on the screen room was flat and doesn't really fit with the house now that's being remodeled so the task was to put a hip roof on it. Since the roof was flat, it was pitched to allow for water to run to the down spouts that were located at the end of the structure. The first item will be to get the rafter plate as level as possible.
In the 62-3/8" across that the roof is wide it was out of level by about an 1-1/2"! With the use of some 1/2" & 3/4' plywood shim, I was able to get the plate very close to level.
This resulted in a build of 3 plates in the front and along the long side of the roof. The front was very close to level to being with so it didn't require any shimming.
The long side only required a minor amount of shimming to get the plate level. When done the plate was about 95% level which was good enough for this particular roof.
You can see from the amout of shim scrapes on the deck that it took some time to get it level.
All in all the roof plates were pretty much square also but did run out a bit along the long side of the roof. There really was no need to "fix" this because it only resulted in a difference of about 1" on a run of 6 rafters. Since the long side had shot rafters it meant a difference of 18-1/2" to ~19-3/8".
This simple point does illustrate quite one of the drawbacks of making certain assumption about the frame. My roof cuts will just cut "away" with the same measurement and then to only find that they have very bad fitting rafters. If very important to know the condition of the frame before you start cutting any section of it.
The Commons. . .
The width of the roof was 62-3/8" and its length in front was 144-1/2". The top of the ridge was to go 4" below the existing window. That left 29-3/4" from the roof deck to the top of the ridge. The H.A.P. on the 2x6's that I was using for the rafters was 4-1/2".
So to calculate the actual rise we use the variable (arz) in the formula arz = rz - rpt - H.A.P.
Where rz = 29-3/4" (this is the height of the ridge for the roof deck to the top of the ridge)
Where rpt = 3" (this is the thickness of the rafter plate, in this case there are two for 3")
and H.A.P. = 4-1/2" (this is the amount of wood remaining on the rafter after the birdsmouth is cut)
So arz = 22-1/4".
Knowing the exactly how high the top of the ridge is you can now figure where to locate it and how long the length of the common rafter will be. Since the measurement of the roof deck width is 62-3/8", starting from on corners of the plates and measuring in 62-3/8 on the 144-1/2" side will give the lines of where the ridge will end. If you measure between these lines the ridge will be 19-3/4" long.
This is were it gets a bit interesting, if you were to cut the ridge 19-3/4" and install it between the marks and 4" below the window the common against the wall would be slightly bigger then the ones that go from the front plate to the ridge. The reason for this is that the ridge's thickness of 1-1/2" will decrease the run by that amount. So instead of have 62-3/8" form front plate to wall, you have 60-7/8" (arr) to front of ridge. This is really no big deal, but it would be nice to make all commons the same length. You can do this by simply adding an 1-1/2" to each side of the ridge or just adding 3" to 19-3/4" making it now 22-3/4". Now you can use this new run of 60-7/8" (arr)as the actual run to figure the common rafter length.
So knowing the actual run and actual rise you can figure the slope( inch rise), pitch and the common rafter length. The inch rise is the value you use to set your rafter square to produce the any of your plumb cut.
Slope( inch rise) is the angle that the roof makes with a horizontal plane. It is determined by finding the quotient of the rise divided by the run. In this case 22-1/4"(22.25) / 60-7/8"(60.875) = 0.3655 or the inverse tan-1 of 0.3655 which is ~ 20°
Inch rise is the actual inches you travel up vertically for every 12 inch you travel horizontal. In this case it's (22.25*(12)) / (60.875) = 4.38" or 4-3/8". This would be what you'd set the stop on the tongue of your square at. 12 would be what you'd set the stop on the body at.
Pitch is a term that is used to define the quotient of the rise divided by 24. For insistence, a roof that has a rise of 8" is know as a 1/3 pitch roof. This is derived from 8/24 which equals 0.3333.
Unit Length is the actual length traveled in 12", to figure it we use the Pythagorean Theorem . . .(c2 = a2 + b2). in this case it would be (4.38)2 + (12)2 = (19.1406 + 144) = sqrt(163.1406) or 12.77 or 12-25/32".
Common rafter length is now quite easy to figure. Using the Pythagorean Theorem . . .(c2 = a2 + b2) it works out to be 495.06 + 3705.76 = 4200.826. The square root of (4200.826) is the length of the common rafter which is 64.8138 or 64-13/16".
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Fig 1. 
