Offset Jack Rafter Plumb To The Earth

Drawing the Offset Jack Rafter Plumb To The Earth on the Rabattement Surface does not work correctly, using the base Profile of the Common Rafter Slope Angle. The seat lines of the Common Rafter Slope Angle make it impossible to establish the correct miter angles at the ends of the jack rafter.

Some of the books written in the past have errors in their geometric drawings. The method's they used for drawing an Stereotomic view of the rafter is not always correct and this is just one example. It's easy to make this type of mistake, without the use of a 3D Cad program or using trigonometry to check the angles. The error in the bevel angles is small enough that a carpenter could have easily cut and installed the  timber without ever knowing the geometric drawing method was not correct.

The correct bevel angle at the foot of the rafter in this drawing is 41.56420°, using the Rabattement Surface incorrectly results in a bevel angle of 41.75758°. The difference in these bevels angles is small enough not to be concerned about. However, the difference at the peak of the rafter would cause the rafter not to fix correctly. 48.43580° --> 52.33260°

The best way to layout a stereotomic view of the offset jack rafter plumb to the earth is to use Orthographic projection in plan view using the  offset jack rafter run line and slope line developed from the slope of the profile. The offset jack rafter plumb to the earth and the offset common rafter plumb to the earth (Prow Rafter) should be developed using the same method used for drawing out the stereotomic view of a hip rafters.