Hello Mac,
Building/plans etc not actually my thing, but like many folks have had to get to grips with it.
Semi-retired engineer here and the Frau and I are into heavy DIY as we are renovating our "tin chapel" retirement place whilst living in it.
We won't mention other tasks like the mighty "Bagheera". A Jaguar V12 saloon currently hiding under cover waiting for me to get back to work on her, once the million and other jobs are done. I will have to build her a garage eventually, hence my interest in all things lean-to and raftery!
Also thus my membership of this club, having purchased a Rover 75 tourer as temporary wheels pending restoration of Baggie.
Now back to the plot.
2nd part:
1) His building calculator wouldn’t win any prizes.
If the rafter rises 7” for every 12” of horizontal travel (horizontal travel here = his adjusted run of 35”) then we have:
total rise = 35 x 7/12 = 245/12 = 20” 5/12 and NOT the 20” 7/16 as produced by his calculator.!
You don’t need a specialised calculator. Any simple one that can do + - x / and squares and square roots is fine.
O.K. with our first plumb cut marked (and cut?) at the top end of the rafter we need to know how far down to cut the bird’s mouth.
Note in pic1 we are interested in distance GH.
Now we come to the Pythagoras bit he was avoiding
with apologies if I’m teaching my granny to suck eggs)
In a right angle triangle of sides a, b, and c, where c= the hypotenuse (longest side) we have:
c x c = (a x a) + (b x b)
e.g. for a 3, 4, 5 triangle:
5 x 5 = (3 x3) + (4x4)
viz 25 = 25
so c = square root of 25 = 5 (as we expected here).
For our rafter distance GH x GH = (rise x rise) + (adjusted run x adjusted run)
Now 20”5/12 = 20.42 to 2 dec places so using the other figures in his example we have
= (20.42 x 20.42) + (35 x 35)
= (416.98) + (1225)
= (1642) approx
So GH = square root of 1642 = 40.52”
So if we mark off 40.52” down the top edge of the rafter from pt G to get point H (pic2) we will be in a position to begin marking out the bird’s mouth.
With H marked, take the card template and positioning edge CD as per pic 3 mark out this edge across the rafter as per pic 4. Call this new line HI. Mark on the line HI ptX which is up 1/3rd the length of HI from I.
As 1/3rd = 0.333 in decimal then calculating IX distance is easy = HI x 0.333
More to come in next bit