Instruments- discuss specific features, luthiers, instrument problems & questions
As magical as the dulcimer is, it is still bound by the laws of physics and basic engineering principals. The engineer in me is compelled to try to explain why all parts of a dulcimer between the string attachment points are under a bending moment, regardless of where the strings are attached. Let me first define a few terms so that we can communicate.
Neutral axis- all bodies (dulcimers included) have a neutral axis that runs the length to the body. When deflected, parts of the body on one side of the neutral axis go into tension while parts on the other side go into compression. If you have a board supported at each end and you load the middle with a weight, the top of the board will be in compression and the bottom in tension.
Force- a force has both magnitude and direction. For the string of a dulcimer, the force is defined by the tension in the string and the location of the string in space.
Moment- the moment (or torque) on a body is the force on the body times the distance from the neutral axis to the line of action of the force.
If we reduce the dulcimer to a simple block of wood, say 2” x 5” x 30” to examine the loading from the strings, we will be able to see why the block is under both a force and a moment from the string tension. Before we get to the actual loading case for the dulcimer, let’s examine the hypothetical case of the strings running right down the middle of the block of wood (1” from either edge and right on the neutral axis). The body of the dulcimer will be under pure compression loading. So if the string tension is 80 pounds and the cross sectional area of the block is 10 square inches, the stress on the block is 80/10 or 8 pounds per square inch. But the string doesn’t run through the middle of the dulcimer, it runs above the body. For this example, let’s say it is 0.25” above the block. The block is still seeing the same compressive loading as before, but now there is an additional moment added to block because the string is not running through the neutral axis. The moment is the tension (80 pounds) times the distance from the neutral axis (1.25”) or 100 inch pounds. This bending moment acts on all elements of the dulcimer body and is the enemy when trying to keep the dulcimer from taking a permanent deflection over time. Exactly how and where the strings attach has no impact on the fact that entire body of the dulcimer between the attach points is under this bending moment.
In an actual dulcimer, the analysis can be quite complex because of the large number of components, many of which have shapes that change as you move from the head to the foot, but the loading is there nonetheless. So as a designer, the challenge is to make sure the structure of the body is adequate to resist the inevitable bowing that will occur. The phenomenon of creep in wood is well documented and is generally thought to have no lower limit of loading for it to occur. If the loading is low enough, the creep may not be apparent over a few decades or even a few lifetimes, which is probably good enough for an instrument. Without dropping over the cliff of engineering analysis, we can try to reduce potential “weak spots” in our dulcimer body. A prime culprit in many designs is the strum hollow. You can greatly reduce the likelihood of a bowed dulcimer by reducing or eliminating it. Most players do not restrict themselves to just strumming over the hollow anyway.
It is this insidious creep that has prompted me to use carbon fiber in my instruments. It has many admirable properties including resistance to creep, extremely high strength to weight ratio and amazing stiffness. These properties come with serious health hazards that demand precautions that are expensive and time consuming to implement. Over time I would love to get to the point where I can eliminate it from my designs and be confident that they can survive for a century or two. The great part about lutherie is that there is always more to learn.