I realize that there is a lot of info on determining the angle in a compound miter. However, whilst reading some comments on this topic I was taken aback as to how many readers felt that 3D CAD was the only way of determining that angle.
That is simply not true. This angle can be determined, with the use of a pencil and paper and mild drafting skills.
2D CAD can replace the drafting table and improve the computational accuracy of the joint.
The method relies on creating several auxiliary views from the standard orthographic views.
Step one, is to create a true view of one of the sides (or faces). This will show the true angle to set the taper jig to. It will also show the joint in true length. To do this, a view is created that is perpendicular to the face in question.
Step two, is to create a view showing the joint as a line. This is the view that will show the true angle of the joint, the angle that the saw blade is set to. To do this, a view is taken perpendicular to the joint that is shown in true length. This view will now show the true angle of the joint for the view will be looking right down the joint.
As I stated earlier, accuracy of the manual method utilizing a drafting table is poor. Especially for small angles. To improve the accuracy the joint can be drawn, say, 10 times the original size. 10 is chosen to simplify calculations. The measurements are simply a factor of ten larger than the actual.
I have submitted screen dumps of a drawing project that has four sides that are angled out at 10 degrees.
The first shows the overall project. The second view shows the joint enlarged to improve clarity.
For reference only, I have dimensioned the opposing joint, WHICH IS NOT CORRECT for it is NOT in true view. I hope this isn’t confusing.
This article is THE way in which any joint angle is determined. ANY tables or calculations, even solid modeling, are only derived from the procedure that I have presented here.
I only present this procedure to show that without ANY modern systems (confusers) the the problem can be solved.
I hope this hasn’t been too confusing, for auxiliary views are created THE SAME WAY that the “standard orthographic views are created. Its just that many do not realize this and consequently have an aversion to auxiliary view creation.