half dovetail timber joint layout

I recently looked at some pictures of horizontal log timber structures with half dovetail joints.  This joint is very nice because the surfaces are angled to lock the timbers together and also direct water down and out which will prevent rot. 

When making these joints one needs to know the following:
1) timber dimensions, width and height
2) desired spacing between the timbers, this gap will normally be chinked
3) timber extension at joint (the distance that the end of a timber will extend beyond the joint)

I did not find any nice description of the layout online so I came up with the following which will hopefully prove helpful.

Example:  timber size is 8" high and 6" wide.  Desired gap spacing between timbers in a wall is 2".  Timber ends will extend 1-1/2" beyond the joint.

I started with a picture which will be used to solve this example and explain the process.  Two 6" x 8" timbers are stacked vertically in a South wall with a 2" space in between these two timbers.  One 6" x 8" timber is placed in a West wall, perpendicular to the South wall timbers.  The horizontal center line of the West wall timber is in the center of the 2" gap in the South wall. 

Look at the end of the West wall timber where it intersects the upper timber in the South wall, it makes a rectangle that is 6" wide and 3" high.  In this rectangle the center is found by drawing diagonal lines, the center point is labeled point "A" in the picture. 

The layout line for the joint will be found by drawing a line through point A.  Since we want an extension of 1-1/2" we will draw a line through point A that intersects the bottom of the South wall timber 1-1/2" past the West wall timber.  The picture actually shows several lines through point A, one with no extension, one with a 1-1/2" extension, and one with a 4" extension. 

We want a 1-1/2" extension so we see that this line goes through point A and intersects the 3" x 6" rectangle 1/2" below the top on the East side of the rectangle and also necessarily 1/2" from the bottom on the West side of the rectangle. 

This is the solution, the angled dovetail cut will be across the end of the 6" wide timber as follows, 1/2" down on one side and 2-1/2" down on the other side.  The angle of this cut works out to be the ArcTangent of (2.5 / (1.5 + 6)) =  18.4 degrees. 

The other cut will be on the bottom of the timber, it will be 2.5" high and 7.5" long.

The second picture shows a small section of half dovetail timbers created for this example.  Drawings were created using google sketchup.