String-break-angle loads

Addendum….

Questions have arisen from readers of both The Luthier’s Handbook and The Ultimate Bluegrass Mandolin Construction about the kind of loads that occur with string break angles (the angle the strings make over the bridge) that exceed 16°. In a few cases, luthiers have asked about the best way to construct an extra-tall mandolin bridge to solve the problem created by an improperly prepared dovetail joint with a neck pitch higher than 6.5°. In one case, the neck pitch was such that resultant string break angle reached 21°.

Although a tall bridge will solve an action problem, the excessive down pressure loads generated by string break angles in excess of 19° could cause the soundboard to implode, and this must be considered before attempting to build an extra-tall bridge.

In a search for hard data, I ran a series of tests with a set of D’Addario J-73 mandolin strings, comprised of .010″, .014″, .024″w, and .038″w string gauges. The total longitudinal (lengthwise) string load generated by this set (with strings at pitch) was 157 pounds.

Force Guage Tests were run in one degree increments from 1° to 22° and the down pressure was measured with a Dillon® Certified Force Gauge at each angle. The strings were re-tuned to concert pitch for each test to ensure consistency of the tests.

Findings:

1) With this set of strings, the down pressure at 16° was 45.5 pounds. As the break angle increased two degrees to 18°, the down pressure increases almost 10 pounds. At 20° the load increased almost 50% to 62 pounds!

2) Small changes in neck pitch radically affect the string break angle. A change of one degree (1°) in neck pitch will change the bridge height by .210″ and the string break angle by 4°.* As a result, the change from a 6° to 7° neck pitch angle could increase the down pressure of the bridge on a mandolin soundboard by as much as 17 pounds!

3) In a separate recent experiment, a test Adirondack Red Spruce F5 soundboard with a thickness of .110″ in the mininum area (center of the “recurve”) with conventionally sized and tuned tone bars, ruptured at a string break angle of 22°. At this point, the down pressure was approximately 78 pounds. The rupture occurred in an area beneath the tailpiece – the region that also receives a severe compressive load from the strings pulling at the tailpiece. This compressive force causes a twisting moment at the tailblock and exerts an inward and downward force at the edge of soundboard, both of which contributed to the soundboard’s implosion.

4) On mandolins, care should be given to using cast tailpieces that are not aligned to allow the strings to have a straight line of pull to the corner of the soundboard and rim. A higher-than-necessary cast tailpiece will pull down at the top of the rim and tailblock and exacerbate the compressive, bending load stated in #3 above.

5) The following charts display the results of the string break angle tests:

String Break Test Results String Break Angle

*Notes:

1) The slight irregularities in the table and chart are caused by: friction points in the text fixture’s “saddle,” the inability to read degrees to greater precision than one degree (1°), and the inability to read the Dillon® Force gauge to a greater precision than 1/2 pound.

2) Consistent neck pitch settings can be achieved by using the V-Joint neck connection method. The surrogate bridge used in setting the V-joint neck ensures repeatably accurate neck sets by controlling the attitude of the neck’s fretboard plane to the crown regardless of any anomolies in the headblock or rim.

3) An F5 mandolin body with a 6° neck pitch, a soundboard that measures .640″ high (above its baseline) at the crown, and normal “action”, will deliver a 16.5° string break angle.

3) The maximum load limit for mandolin soundboards is about 80 pounds (78 pounds in the test stated in paragraph #3 above chart). This suggests that a 16° string break angle presents a download that is 50% of the soundboard’s maximum load limit. By a comparison, a violin soundboard (with soundpost in place) will rupture at about 100 pounds. A 16° string break angle on this instrument presents a 25 pound download which equates to 25% of the violin soundboard’s maximum load limit.