Lesson 7 of 13
Hips and Valleys
This is the lesson where framers separate. Everything from lesson six still applies, but the rafter no longer runs straight in. It runs on the diagonal, and that one fact changes every number.
Step one
Read the material
Three ideas. The second one is the famous number, and almost nobody is taught where it comes from.
Concept one
The hip travels the diagonal
Look down on a hip roof from above. The common rafters run straight in from the plate to the ridge. The hip runs from the corner, diagonally, across the square that the two commons make.
So while a common rafter travels its run, the hip travels the diagonal of that same square. And you already know the diagonal of a square from lesson four: it is the side times the square root of two, which is 1.4142. A twelve foot common run means a hip run of 16 feet 11 5/8 inches, not twelve feet.
A valley is the same geometry turned inside out, where two roofs meet in a trough instead of a peak. Same numbers, opposite fold.
Concept two
Seventeen, and where it really comes from
A common rafter is laid out on a square using twelve on the body. A hip is laid out using seventeen. Every framer learns that, and most are never told why.
Here is why. While a common travels twelve inches of run, the hip travels the diagonal of a twelve by twelve square, which is 16.97 inches. Seventeen is 16.97 rounded to something you can actually find on a framing square.
The rounding costs you about three hundredths of an inch per foot of run. Over a twelve foot run that is roughly a third of an inch of hip, which matters on finish work and does not matter on a shed. Use 17 when you are scribing with a square. Use 16.97 when you are computing a length you intend to cut once.
Concept three
The hip length, from the common run
The hip is still a hypotenuse. Its flat leg is the diagonal run and its upright leg is the same rise as the commons, because the hip meets the ridge at exactly the same height.
That gives a per-foot number just like lesson six, only built on 16.97 instead of 12. For every foot of common run, the hip gains the square root of 288 plus the pitch squared, in inches. At six in twelve that is exactly 18.000 inches per foot of common run, which is one of the tidiest numbers in framing.
So: take the common run in feet, multiply by that per-foot number, divide by twelve. Notice you use the common run, not the diagonal run. The diagonal is already baked into the 288.
Step two
Work it with your hands on it
The drawing is the plan view looking down: the common run, and the hip crossing the diagonal. The panel gives you both rafters side by side.
Hands on it, off the screen. Lay a framing square on a scrap and scribe a line using 12 and your pitch. Then scribe a second line using 17 and the same pitch. Those are your common and hip plumb cuts, and you can see the difference between them with your eye.
If you can get on a hip roof, sight down a hip rafter and a common and notice that they land on the ridge at the same height while covering very different ground.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can find a hip run, explain the 17, and compute a hip rafter from the common run. Lesson eight is stairs.
Trades Geometry
Lesson seven of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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