This document provides instructions and formulas for constructing an octagonal roof. It explains that the angle between crown ends and hips is always 22.5 degrees, regardless of the roof size. It then provides formulas to calculate the length of the octagonal ends based on this constant angle: half the end equals half the span multiplied by 0.414, and the full end equals half the span multiplied by 0.828. The document also addresses calculating lengths for the major and minor crown end rafters, noting they are calculated similarly to a normal hip roof.

1. Octagonal Roof

2. Draw Crown Rafters Walls are parallel Set Back ½ Rafter Thickness

3. Draw & Bisect Crown End Rafter

4. Draw Tangents to the Crown Ends

5. Draw Top Plate

6. Clean Up Drawing

7. Clean Up Drawing Angle Between Major Crown End & Centring Rafters = 90 ⁰

8. Clean Up Drawing Angle Between Crown End Rafters = 45 ⁰

9. Clean Up Drawing Angle Between Crowns Ends & Hips = 22.5 ⁰

10. Angles formed by the Roof These angles are the same no matter the size of Roof as it is a Geometric Shape

11. Length Of Octagonal Ends If the angle between the members is constant 22.5 ⁰ We can say in all cases, no matter the size of the roof ½ End = ½ Span x tan 22.5⁰ = ½ Span x 0.414 (tan 22.5⁰ is always used)

12. If the angle between the members is constant 22.5 ⁰ We can say in all cases, no matter the size of the roof ½ End = ½ Span x 0.414 Length Of Octagonal Ends

13. Length Of Octagonal Ends If the angle between the members is constant 22.5 ⁰ In all cases, we can say Full End = ½ Span x 0.414 x 2

14. Length Of Octagonal Ends If the angle between the members is constant 22.5 ⁰ Also in all cases, the full end will be Full End = ½ Span x 0.828

15. Length Of Octagonal Ends These formulas are the same no matter the size of the Roof ½ End = ½ Span x 0.414 Full End = ½ Span x 0.828

16. Major Crown End Rafter These formulas are the same no matter the size of the Roof Calculating Centring rafters and Crown End Rafter use the same method as a normal hip roof

17. Major Crown End Rafter These formulas are the same no matter the size of the Roof Calculating Centring rafters and Crown End Rafter use the same method as a normal hip roof

18. Minor Crown End Rafters These formulas are the same no matter the size of the Roof Minor Crown End Rafters join in a similar manner to a hip rafter

19. Minor Crown End Rafters These formulas are the same no matter the size of the Roof Minor Crown End Rafters join in a similar manner to a hip rafter The Plan run of the minor crown is reduced by ; ½ Centring Rafter x 1.414

20. Minor Crown End Rafters These formulas are the same no matter the size of the Roof Minor Crown End Rafters join in a similar manner to a hip rafter Minor Crown = ½ Span x ½ C.R Thickness÷

21. Edge Bevel Minor Crown End Rafters Plan Angle = 45 ⁰

22. Edge Bevel Minor Crown End Rafters Plan Angle Plan Angle = 45 ⁰ Plan Angle = 90 ⁰

23. Edge Bevel Minor Crown End Rafters Plan Angle Plan Angle = 45 ⁰ Plan Angle = 90 ⁰ Both Sides Must Be Equal

24. Edge Bevel Minor Crown End Rafters Plan Angle Plan Angle = 45 ⁰ Plan Angle = 90 ⁰ Both Sides Must Be Equal When Can You Use The Plan For the Edge Bevel ?

25. Edge Bevel Minor Crown End Rafters True Angle