Hip Rafter Trace Angles

Last spring Joe Bartok and I studied intersecting hip rafters, rotated 45° from plumb. While studying the intersecting hip rafters, When Hips Collide,  we drew out the geometric development for the Hip Rafter Trace Angles. I didn't realize it at the time, but the geometry for the Hip Rafter Trace Angles can be used for the Witches cut or hip rafter purlin housing angle. The other day when I was drawing out the geometry for the witches cut on a canted hip rafter I needed to check my geometry with a 3D model. Than I begin to think about the Hip Rafter Trace Angles for the When Hips Collide study and sure enough the same geometry can be used for just about any trace angle on a plumb hip rafter or canted hip rafter.

All rafters have a DP- Shadow Line. When the rafter is plumb, the DP- Shadow Line is the same as the rafter run line. The Hip Rafter Trace Angle is developed from the intersection of the DP- Shadow Line of the two rafters and a line that is perpendicular to the DP- Shadow Line of the hip rafter, that intersects the rafter run line at the hip rafter. In the drawing below the hip rafter is canted. The Hip Rafter Trace Angle on the canted hip rafter is the same angle that can be used on the Witches cut. The purlin rafter in the drawing  is rotated into the roof surface at the same angle that is used for the rectangle rafter tails of the Witches cut.

In this drawing I tested the theory on a plumb hip rafter and yes it works correctly on plumb hip rafters.

In the drawing below the roof  slope is unequal and the hip rafter is plumb. Using this drawing technique it makes it pretty easy to draw out the Hip Rafter Trace Angles for the Witches cut or hip rafter purlin housing angle.