Structural Analysis of Folk Harps:
-Copyright, Rick Kemper 2005
The folk harp is a deceivingly simple instrument. The earliest carvings and drawings of a recognizable three sided harp date to 8th century Europe. Given that their ancient pedigree and simple form, just how complex can they be? Turns out, from a structural standpoint, they are pretty sophisticated.
In this article, I am not going to try to delve deeply into the acoustics behind what makes a harp’s tone somber and dark, or light and clear. This was written to give the new builder or designer an understanding of the materials, mechanics and forces at work in a common folk harp.
There are several basic components of the folk harp. For purposes of this discussion, I will use a basic 36 string Celtic Model – one of the most widely produced and played instruments in the folk harp world.
The Strings: Besides generating initial vibrations that drive the harp’s sound, strings generate tension. That tension must be resisted by the frame of the harp. Most harps have string tensions that range form 15 – 60 lbs on each string. Twenty five pounds of tension is a good average for a medium tension folk harp, So the entire harp would have about 900 pounds of tension.
The Pins: Folk harps have bridge pins and tuning pins. Tuning pins rotate to change string tension. Most harps use traditional tapered pins. I have used both piano or Zither type pins, and they seem to work as well in necks built of harder woods like maple and cherry. Bridge pins are used to level the strings. As the strings stretch over time, the additional wraps over the tuning pin usually move the string towards the neck. The bridge pins ensure that the harpists fingers don’t trip over a high or low string.
Positioning of the bridge pin relative to the tuning pin:
Most builders try to make the string deflect 15 to 25 degrees as it passes over the bridge pin. If the angle is too small, the harpist may pluck it right off of the pin. If it is too large, several bad things can happen: The string will not slide readily over the pin making tuning difficult. At acute angles the pin can crush the wood fibers in the neck. They can become lose and may shift up or down. Finally, on wound strings, thin outer windings can crush and break under the load, ruining an expensive string.
It is important to place the bridge pin far enough away from the tuning pin so that the string does not push the bridge pin in our out. Some builder’s use as little as 5/8”. I try to use at least an 1-1/4 on my designs.
From the Grossly simplified Statics page we found that the neck of the harp can be idealized a simple truss with a 900lb distributed load. This load is counteracted at by the pillar and sound box as shown in the diagram below:
Figure #3 Harp Neck and torquing action
The calculations indicated that we should expect a wooden neck with a two inch by 4 inch cross section to deflect about 3/8ths of an inch downward at its center.
Remember, these are idealized equations. In the real world, the neck of a harp is not as flat as a bridge. Acoustic or aesthetic considerations require that it have a sharp curve for mid-range strings. When I think about wood’s isotropic frailties I begin to understand why special consideration needs to be given to the neck which is notoriously prone to cracking and failure.
There are three approaches to preventing the neck from cracking. The most common is to laminate two or more layers of wood together. Another approach is to overbuild the neck using a big chunk of wood. Other builders will actually build the sound box with a curve so that the neck can be built fairly straight. Others use a power saw to cut a kerf (slot) in the bottom of the neck and inlay a strip of wood to eliminate splitting. Dusty Strings harps often leave a “bridge” of wood on the upper side of the midrange curve to reinforce this part of the neck.
It is interesting to note how quickly the stresses rapidly increase with a Harp’s size. Those extra three or four strings not only add an additional hundred weight of tension (they are usually heavy bass wire strings on large harps), they add 2 or more inches to the span between the top of the pillar and the sound box.
On Celtic Harps, the tension is carried off to one side of the neck. Structurally, the builder has to anticipate these loads and brace the neck in a way that will counteract the torquing effect.
This torquing effect can be calculated in foot lbs, i.e. 900 ft-lbs located ½” away from the surface of the neck:
900 lbs x .5” /12 in/foot = 75 foot lbs
75 foot-pounds may not seem like a lot, but remember the lesson from frailties - wood tries to “run away” from it loads over time. The strain of the torquing effect is counteracted by its attachment to the pillar and the top of the sound box. At the top of the sound box, most harps have an extra block of wood glued onto the side of the neck with the strings on it. This shoulder block is a design elements which helps keep the neck from tipping over. Many harp builders and plans specify doweling to keep the shoulder block from shearing off the neck under the sustained load.
The other design element that counteracts the offset torquing effect of the strings is neck’s attachment to the pillar. Traditionally, this joint was a mortise and tennon joint. More modern approaches use ½” to ¾” dowels or a simple half lap joint. Each has its own advantages and drawbacks:
Different Neck/Pillar Joints
Mortise and Tennon
Can be left dry, allowing easing later disassembly and repairs.
Easier to do than a mortise and tennon, usually glued
Simplest to build especially if neck and pillar are laminated from 4/4 stock
Requires more skill to make a good tight fit
If glued, may eventually fail in tension on side opposite strings
Large area of Cross grain glue surface and deflection in neck can lead to glue failures
Pillar: The Pillar is a column in compression. The compression load is over half of the total string load, or about 500 lbs in this case. The pillar of a Celtic harp is usually built with a graceful curve in it, giving the instrument a look distinct from the concert pedal harp. Like the curve in the neck, a severe curve can be weak, failing at ends where the grain cuts sharply across the pillar. A straight post would be the most efficient structure, but the curve is necessary to ample clearance for the harpists fingers and the bass strings while vibrating.
To accommodate the tension load, some designs laminate a relatively thin board to the outside of the pillar. This creates a neck that has T shaped cross section, with the top of the T taking the bulk of the tension load (like the lower web of an I-beam). This board also resists the significant torquing loads which can cause pillars to bend significantly over time.
A single string vibrating alone is too quiet to be useful instrumentally. All string instruments (except the electric guitar) use some kind of big light resonator to change the mechanical energy of a vibrating string to sound waves in the air. A good resonator is light and has a large surface area. In most instruments, this is done with a wooden sound board that is made of a thin piece of clear-grained softwood.
The harp is unique in that the tension of the strings is taken directly by the sound board. Almost all the other string instruments are built with strings that pass over a bridge. The bridge presses down on the sound board with a small portion of the strung tension. In guitars and violins it is the sound boxes and necks take the principal strain of the strings. Pianos use a steel frame to take the thousands of pounds of tension that the strings generate.
Acoustics demand that the sound board be large and light. Structural considerations beg for a sound board that is heavy narrow and thick. There are a number of approaches that have been used to meet these demands. Most builders spend a lot of effort on their sound boards, claiming it is the most critical element to good sound.
Grossly simplified Statics gives the dimensions and predicts deflections of the deflections at the top, middle and bottom of the sound board I use in this harp.
A few observations:
If you are making a sound board out of solid wood, orient the grain across the face of the sound box. Don’t be fooled by harps that appear to have the grain oriented along the length of the sound box– they are almost always thin laminations over a solid core. Traditionally built wire harps are an exception to this rule. Their sound box/board is typically carved from a large, single piece of wood.
Ounce for ounce, plywood is one of the strongest lightest panel materials made by man. Purists may turn up their noses at a plywood sound board. It sure eases the mind of the first time builder who may not be ready to plane a $60 piece of Sitka spruce down to two and three millimeter thicknesses.
The builder must ensure that the board is solidly attached to the sound box. Think carefully about the forces at work on the sound box and string band. If you are uncertain about board thicknesses, or the adhesives that you are using, Be certain that your glue or fastening system can withstand the sustained strain. After a few failures, many builders resort to screwing the board to the liners (using a wooden battens or corner molding) or to using high strength, gap filling epoxy resins.
In addition to pulling out on the sound board, the strings create shear and tension near the bottom of the harp where the post is attached.
Because of these heavy loads, String Ribs are usually made out of a hardwood like maple. Traditionally there is an outer and an inner rib, and they vary in cross section along the length of the sound board. At the top they may be as small as ½” wide and a sixteenth of an inch thick to a robust one inch thick and two inches wide at the base (and bass) end. String ribs have several functions:
· Keep the string knots and grommets from pulling through soft wood of the sound board.
· Transfer the vibrations of the string to a larger area of the sound board
· Reinforce a solid sound board from splitting.
· The String ribs carry a major portion of the string tension to the foot of the pillar
· And finally the string ribs help transfer the vibrations from the string that is plucked to other strings – contributing to the harp’s distinctive sound that is rich in sympathetic harmonics.
Many builders have began to omit the outer string rib, and substituting a thicker inner string rib. This appears to work well on as long as efforts are made to keep the grommets from splitting and /or crushing the soft wood of the sound board.
The sound box supports the compression load of the neck at its shoulder (about 400 pounds in our example). The sound box will also bear a substantial portion of the string tension load (525 lbs or so) on the upper portion of its face. Depending on the stiffness of the sound board and string ribs, the sound box also takes a compressive load of 125 lbs or so on the lower portion of its face.
Unlike a bridge, the top of the sound board is in tension, and the back is in compression.
The sound box contributes to the resonance of the harp’s sound. It traps a chamber of air behind the vibrating sound board. Most of the energy in sound waves in the harp escapes through the sound holes. This is another trick of amplification that the harp shares with the Guitar and violin family.
Sound holes are placed in a variety of places, dictated by largely by tradition and aesthetics. Make sure that the sound holes are placed so that the builder and the player can easily install/replace strings. I have found that 25-35 square inches spread across two or three sound holes works well for a 36 string nylon harp. It is important to not cut sound holes in a pattern that can structurally weaken the sound box-i.e. use rounded corners and avoid long slits that run the entire width or length of the back or sides of the sound box.
Stave back and round back sound boxes generally have thin walls, and are built with liners that run along the edges where the sound board is attached. These liners provide a larger gluing surface for the sound board, and help the sound box withstand the tension loads (top to bottom) and compressive loads (side to side) imposed by the strings. On many designs, the sound box is reinforced with several braces withstand the compressive load.
I am a Mechanical Engineer by training, Telecom/Internet geek by vocation, and a wood butcher in the evenings and on weekends. I built my first Celtic harp in March of 1999 with invaluable assistance from Glenn Hill, Lee Gayman, Dan Cady, a set of plans from Robinson’s and the archives of the Harp Makers list. Six years later I find myself building harp #46 and logging a list of hopeful clients.
I hope that this article has demonstrated in some way the deep respect I have developed for the craftsmen who have labored through the centuries to refine and advance the quiet elegance of these delightful instruments.