How the hips meet the ridge, and why the hip is shortened

The crown rafter arrangement CutRoof uses at each end of the ridge, and the two numbers it changes.

The top of a hipped roof is where the schedule stops being obvious. Four hips, two ridge ends and a crown rafter all arrive within a few hundred millimetres of each other, and how they are arranged decides the ridge board length and every hip's cut length.

CutRoof uses one arrangement, and prints it on the schedule in words so nobody has to reverse engineer it from the numbers.

The arrangement

The ridge board is cut to the theoretical line and stops short of the ends of the building. At each end, a crown rafter stands in line with the ridge, plumb cut against the end face of the ridge board. The two hips at that end land on the sides of the crown rafter, one either side.

So the hips do not meet the ridge board at all. They meet the crown rafter, and the crown rafter meets the ridge.

The ridge board length

The ridge runs from the first crown rafter to the last, which is the plate length less the span:

L − S = 9000 − 4800 = 4200 mm

On a 9000 by 4800 roof the ridge board is 4200 long, which is under half the length of the building and always looks short when it is written down on its own.

The crown rafter

A crown rafter is a common rafter with one difference. It butts the end face of the ridge rather than a side face, so nothing is in its way and there is no half-ridge deduction to take.

Its run is the full half span, 2400, and its true length is 2930. Every other common on the same roof runs 2384 and measures 2910. Two commons, twenty millimetres apart, both correct, which is why the schedule lists the crown rafters as their own member with their own working rather than burying them in the common count.

Why the hip is shortened

A hip's length to the apex, 3787 on this roof, is a length to a theoretical point in mid-air. The crown rafter's side face is in the way before it gets there.

The hip's centreline meets that face 33mm short of the apex on plan:

(b ÷ 2) × √2 = (47 ÷ 2) × √2 = 33 mm

Along the hip, at its own pitch of 26.3 degrees, that is 37mm. So the cut length is 3787 less 37, which is 3750.

Then the hip has a width of its own. Its double cheek cut sets the short point back 26mm behind the long point, giving 3724 at the short point. The schedule prints both, because you mark to one and the saw finishes at the other.

Cutting it

Set the crown rafters first and get them plumb and in line with the ridge, because everything at that end of the roof is measured from their side faces. Offer the first hip up before cutting the other three. If the cheeks bear evenly on the crown rafter and the birdsmouth sits down on the corner, the whole set will.

Every figure above is worked out by the same engine that produces CutRoof's cut schedules, and is checked against it on every build.