COMPOUND ROOFS WORKSHOP - Introduction Complex roof geometry is a challenge most framers face eventually. These problems can be solved either mathematically or visually, but the complete carpenter will have a variety of skills to call upon, including drawing, math and traditional scribing techniques. The skill of drawing complex shapes in a form that enables the carpenter to directly measure working angles and scale dimensions has been taught for centuries by (but not limited to) the French, German and Japanese carpenter. The combination of developed drawings and basic roof math empowers the builder with a far wider variety of building shapes. The basic problem boils down to determining the lengths of the relevant pieces and predicting the angles at which they will meet, and then designing the joinery to hold it all together. The way I (and probably most carpenters) used first to figure out hip or valley rafters was to repeatedly get up on the ladder after the common rafters were set and use strings and bevel gauges to sight the angles necessary by projecting the existing roof planes to their intersecting point. I still find jack rafters can be efficiently scribed in place once the hip or valley is installed, but often we don t have the luxury of working this stuff out on-site, and we need a method we can use back in the shop. The framing square, often called a rafter square, can be most useful for finding some of the more common angles needed in compound work. Rafter squares carry tables for the angles as well as lengths of pieces, but these tables are limited to regular roofs (of equal pitch) meeting in regular plan (at 90 degrees). Drawing methods similar to those that appear in early carpentry texts in America allow you to develop full-scale views of the framing members, and just as easily with irregular as with regular roofs. Drawing roof members in their entirety at full scale is an accurate method but requires space, time and careful technique. With a little bit of simple math we can eliminate a lot of the space taken up by the stretch of timber where there is no joinery and use a technique to draw only the joinery full scale. In this workshop we will introduce two powerful tools to make complex roof joinery simpler: mathematical multipliers to locate the joinery and the kernel to draw the joinery. The multipliers are used to locate the working points along the centerline or edge of the timber that serve as a starting point for laying out the joinery, which is drawn full-scale in the kernel. There is another tool that can abbreviate the process even further. Graphical and mathematical methods have both been used to generate a series of formulae and angles used
by many timber-framing shops that do compound joinery on a regular basis. These are known in the trade as the Hawkindale angles, and are useful provided one can calculate the lengths of pieces independently, and provided one already knows how to apply the angles in their correct orientation. Together these tools the framing square, developed drawing of the kernel and joinery, using the multipliers to locate joinery, and the Hawkindale angles will make complex roofs less intimidating. GLOSSARY Most of you probably would like a secret formula, a sort of geometer's stone for converting roof timbers into hip and valley pieces. We can't offer you that; nor would we be likely to if we had it. What would be the fun of that? What we will be offering is an orderly list of tools and approaches to solving the basic two problems of compound work: what angle(s) are created at the various junctions and how do we calculate lengths? First in this list is defining of a vocabulary that will allow us to be sure we're talking about the same things. Common Rafter - any frame member that begins and ends at different elevations and runs at 90 to two parallel horizontal frames Common Rafter Roof - a typical gable truss configuration made up of opposing pairs of common rafters. Ridge - horizontal line or timber created at the peak of a common rafter roof. In a compound system, it extends to the upper reach of the hip or valley rafter. Eave - the lower horizontal line from which the common rafters ascend; it terminates at the foot of the hip or valley rafter. Plate - Timber that supports the lower ends of the rafters. Roof Plan - A typical set of plans show the roof framing as it reflects upon the floor plan, that is, the rafter lengths are not to scale but rather are shown as their run. This view basically shows the eaves, the ridge, the spacing between rafters and their orientation. It is also called the deck view, which suggests the image of the roof system being projected by a light directly above
down onto the deck, or floor, of the house. This view is where most roof calculations and drawings begin. Run - the distance a rafter travels measured horizontally, or level. Rise - the distance a rafter or roof travels measured vertically, or plumb. Rafter length - the actual measurement of the rafter as it travels the diagonal distance to reach its rise and run. Plan Angle or Deck Angle - Within the roof plan, your first hint that you have a compound system comes when you notice a diagonal line between a ridge and an eave. This line tracks the run of the hip or valley and defines the compound plan rectangle and triangles. Two of the sides of the plan rectangle are the runs of the two common rafters immediately outside the diagonal; the other two sides are the eaves (for a hip roof) or the ridges (for a valley). The plan angle is defined by the diagonal and is the measured angle between the hip and eave or the valley and ridge. Compound Roof - Any roof system that includes a turn in the roof systems while maintaining constant transition in plane. Valley roof - A compound roof that folds in. It can represent the transition of roof when the exterior walls meet in an interior corner or it can be the resolution of a gabled dormer rising from a common roof. Hip Roof - A compound roof that folds out. Its most usual circumstance is around the exterior of a floor plan, but it is often seen in eyebrow dormers and cupolas. Roof Plane Angle - the angle created at the vertex of a compound roof. Specifically, it refers to the measured angle between the valley or hip line and an abutting common rafter or jack rafter. Valley Line - The absolute terminus of the two opposing roof planes in a valley system. Valley Rafter - the framing member used to enclose the valley line and provide structural resolution between the opposing pitches. Hip Line - the absolute terminus of the two opposing roof planes in a hip system. Hip Rafter - the framing member used to enclose the hip line and provide structural resolution between the opposing pitches. Jack Rafter - A roof framing member that runs in common pitch and terminates at the hip or valley rafter. In a valley system the jack runs from the ridge down to the valley and in a hip system it runs from the eave up to the hip rafter.
Purlin - A rectangular roof framing member running 90 to a common rafter and whose top surface lies naturally in the roof plane. Principle Purlin - An enlarged common purlin used to receive the peak of a valley rafter of a dormer. Header - A roof framing member running at 90 to a common rafter and whose sides are in a vertical plane. Typically a header is used to resolve a compound system, such as a dormer, that does not rise all the way to the main ridge. Irregular Roof - a roof system which includes the intersection of two roofs of different pitches or which meet at an angle other than 90, or both. Pythagorean Theorem - The basis of roof geometry. It states that in any right triangle (one which contains a 90 angle), the square of the hypotenuse (the longest side) is equal to the sum of the square of the other two sides (the two shorter sides which form the 90 angle). It is usually formulated as a 2 +b 2 = c 2. Acute angle - an angle which is less than 90 Obtuse angle - an angle which is more than 90 Backing angle - the measured angle of the sloped surface cut into the top of a hip or valley rafter to match the planes of the intersecting roof surfaces. Complementary angles - in a right triangle the angles at either end of the hypotenuse are said to be "complementary", meaning they add up to 90. Hence the complementary angle of 25 is 90-25, or 65. Trigonometry - branch of mathematics which studies the relationships between angles and the sides of triangles, specifically based on the properties of right triangles. The central proposition is that the legs and hypotenuse of any right triangle of a given set of acute complementary angles maintain fixed ratios between them no matter how large or small it becomes. Similar triangles - For any right triangle, if a line is struck within that triangle perpendicular to any side, it will form a similar triangle that shares the same proportions as the original. Sine - The ratio between the side opposite a given acute angle of a right triangle and the hypotenuse. Cosine - The ratio between the side adjacent a given acute angle of a right triangle and the hypotenuse. Tangent - The ratio b, tween the side opposite a given acute angle of a right triangle and the side adjacent.
Reading Materials: Here is a list of relevant articles from Timber Framing and Fine Homebuilding. I ll provide you with electronic copies of these on a flash drive at the workshop for your future reference, but if you have access to them in your home shop/library, it would be good to look them over before the course so that you can get the most out the experience. Hip and Valley Framing: I, II, III by Ed Levin. Three articles in the Guild book Timber Frame Joinery & Design Workbook, Vol. 1 (also known as the Red Book ). These articles also appeared in Timber Framing Nos. 17, 19 & 21, respectively. When Roofs Collide: I, II, III, IV, & V by Will Beemer. Five articles from Timber Framing Nos. 70, 71, 73, 90 & 92, respectively. Framing a Hip Roof by Larry Haun. Fine Homebuilding, Oct/Nov 1995 Framing a Roof Valley by Rick Arnold. Fine Homebuilding, Feb/Mar 2004 Roof Framing Revisited by Scott McBride. Fine Homebuilding, Aug/Sept 1985