Thursday, September 26, 2013

Reciprocal Roof

Billy Dillon thought it would be fun to build a reciprocal roof .  I agreed, and I said I would build a pentagonal reciprocal roof. He wants to build an hexagonal reciprocal roof , because he likes the geometry of an hexagonal roof better and I wanted fewer rafters to cut.

Billy Dillon's Hexagonal reciprocal roof model.

German Schiftzirkel  (Reciprocal ) roofs.

Shift = Shiften
Zirkel = Circle or Compass

Here's a drawing of the geometry for the  typical Mandala Reciprocal Roof with 8 sides(Octagonal).

Here's my Pentagonal Reciprocal Roof  drawing. 

 need to see if there's a theory on the radius's of the two circles that the rafters are tangent to.  In the octagonal reciprocal roof   their 45 cm and 8 cm. 8÷ 45 = 0.1777 ratio. I don't know if the 0.1777 is a standard ratio for the two radius's. I tried a 45° rafter slope angle for the pentagonal roof, but the seat lines wouldn't connect properly. I readjusted the slope angle to 30° and the seat lines work. I wonder if there's a theory on the roof slope as well.

Use the same geometry for Jack Rafters Plumb To Earth
for the Seat-Claw Angle. This not in any book. This is geometry I developed.  I would also classify the reciprocal roof rafters as Jack Rafters Plumb To The Earth offset/skewed from the plate line. Using the same geometry of Jack Rafters Plumb To Earth draw a line tangent-perpendicular to the reciprocal roof rafter that intersects the extended run line of the opposing  reciprocal roof rafter. Then draw a line to the rise line of the reciprocal roof rafter. The intersection of theses two lines will give you the seat angle of the reciprocal roof rafters.

I drew the back bevel angles the wrong direction on the 2x4 rafter, but reversed the back bevel angle before I cut the rafters.


  1. This roof is so interesting! It's however in need of professional contractors to ensure that the structure is finished properly. I've seen different roofing patterns that you've done and I'm certainly amazed by your various ideas. I hope you'll post more roofing designs. Thanks!

    Town & Country Roofing

  2. This roof is really cool! It may need professional contractors to ensure that its executed well. If you need roofing in Kamloops there is a company that can do it for you! Thanks for the post.

  3. Is there any video showing how it was cut?

  4. Great roofing ideas for a small gazebo