Calculating Neck Height, Neck Angle and Break AngleIn a factory, the top, neck angle, break angle, etc. are all identical. Machines carve the top, inside and out, it cuts the neck mortise, tenon and neck angle. The factory instrument cares not about the differing stiffness and weight from top to top.
It is time to separate the factory instrument from the luthier built. You have already had the opportunity to choose specific woods for the project. Either you wanted specific grain or beautiful figure or both. Here is your first opportunity to fine tune the down pressure of the bridge to the top of the instrument.
Graham suggests in his book and through correspondence concerning Celtic style mandolins, a break angle of 17 - 19 degrees. Some correspondence to Roger Siminoff revealed that 16 degrees is a maximum to shoot for in F5's.
I found that I had been measuring the break angle incorrectly recently but here is a diagram showing the break angle.
Attachment:
break-angle-dia.jpg
You can see that the break angle is a function of the neck angle, neck height, thickness of the top and the height of the bridge. Since we have now carved the top and can measure the height, we only have the neck angle, neck height and bridge height left to calculate. Bridge style will greatly change your angles here. If you go with a carved bridge you can make it shorter than if using an adjustable bridge. In this case I will be carving my own bridges but will also make the adjustable bridge available as an option.
The Loar style adjustable bridge is 3/4". So now we have data points to calculate our break angle. The only variables left to decide on are the neck angle and neck height from the top. I am following Graham's suggestions in most cases and modifying as needed or to show alternate ways of completing the task. In this case, the 3/16" top edge height will be used in the calculation.
The only variable left is the neck angle. The suggested neck angle is 6 degrees to allow room for the adjustable bridge. Try not to increase your neck angle too much or you may have trouble finding a case to fit (thanks Graham).
Below I have diagrammed the instrument with .583 thickness, 3/16" top edge, 3/4" bridge. I have given 1/4" from the neck to allow for a 3/16" fretboard, fret wire height and strings. I hope the diagram allows you to visualize the system.
Attachment:
InfinityLuthiers-break-angle-dia1.jpg
You can see that I have a greater break angle(21.2) than recommended. There are two additional factors that can change the break angle. The first is the tailpiece height. I typically use James tailpieces. Here is one on an A model mandolin. You can see that the hinge pin is just over 3/16" from the top of the top edge. The hinge pin is in line with the base plate of the tailpiece, so, the strings are just above the hinge pin.
Attachment:
Sitka-tops-Celtic-o.jpg
NOTE: Something to consider when raising your tailpiece to reduce the break angle is the added torque placed on the tail block. Raising the tailpiece acts as a great lever that tries to pull the top of the tail block forward and down. If too much pressure is place on the top this could implode. Roger Siminoff has done some research on break angle and top pressure
here.
With this information I can now change my diagram to incorporate the change. Now I have a break angle of 19 degrees.
Attachment:
InfinityLuthiers-break-angle-dia2.jpg
One issue I still have is that the neck angle is at 6.8 degrees. The only way I can lower the neck angle while keeping the 19 degree break angle is to raise the neck.
Here I have raised where the neck meets the body from 3/16" to just over 1/4". This will cause more work when binding the top. But, my binding is 1/4" tall so it will not be a great problem. Also notice that this lowered the break angle to 18.1 degrees. This is right in the middle of the recommend range.
Attachment:
InfinityLuthiers-break-angle-dia3.jpg
Another method to consider when needing to reduce the break angle; you can sand the feet of your adjustable bridge.
Based on this information I now know what angle to plane my neck ramp, how high on the body and neck meet and have a good feeling about getting the most out of the mandolin top. Of course there are other factors that will play a part in the overall performance but not many are as important as the bridge height, neck and break angle.