I learned a few things making my first scarf joint, I hope what I learned helps you.
I started by using the above diagram as my guide. I can do this I thought. Just decide which method I want, measure, cut and glue (very precisely) and I'm done. Except, as I started to measure and make some calculations, I discovered there were questions the diagram did not answer. After building a few CBGs, I do know how long a board I need if i'm not using a scarf joint. But the diagrams above did not answer some basic questions - is the board necessarily longer (or shorter?) and by how much? And would Type 1 be longer or shorter than Type 2? Does the headstock have to be longer for Type 2? and if not, again, what measurements do I use? Should I leave it to trial and error? No, wood is a precious thing to waste. So I got me a pen and a paper (and I made up my own little sign... sorry, I couldn't resist) and did some math.
The answer is - the board is the same length for all three, no scarf joint,Type 1 or Type 2.
First, make your calculations as if you were building without a scarf joint to determine the board length (this takes into account your box size, the length of your headstock, etc.). Then, use the following steps to help you measure and cut so the headstock will be exactly as long as what you want, for either Type 1 or Type 2.
Let's say we want the headstock to be 130 mm (about 5 inches). The following templates represent a 3/4 inch thick neck, about 20 mm.
Type 1 - Measure as shown from the tip of the board. Draw the 15 degree angle as shown, Cut and position the headstock as shown. This will give you the 5 in. / 130 mm you want for the head stock. The fingerboard in this method will cover the glue joint.
Notice the joint is visible on the upper surface of the neck - may want to use this type if you are going to add a fingerboard to cover the glue joint.
Type 2 is a little different but just as simple. Measure as before from the tip of the board but on the opposite surface. Draw the 15 degree angle as shown. Cut and position the headstock as shown. This will give you a 5 in. / 130 mm head stock.
The upper surface shows no glue joint, so visually it's clean. If the glue joint on the headstock offends you, you can glue a veneer over it.
For my first test, I actually cut up some rigid styrofoam insulation to confirm these measurements. The results don't look very pretty so I made the above templates to more clearly demonstrate what to do. Hope this helps!
Also, here's a diagram of my scarf joint jig. It is a rectangular box, made of poplar scraps, bolted (but easily removable) to the mitre guide of the table saw. My sincere thanks to the person who posted the photo of this guide in Google images, I was not able to relocate the original photo to thank the author for providing such a simple solution. The bonus of this jig is I can use the saw's mitre gauge to measure any angle I wish to cut.
Comments and feedback welcome!
And here's a photo of the glue up of my first scarf joint