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 |
Doweling |
Half Lap |
|
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.
Sound Board
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.
String Ribs
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.
Sound box
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.
Author’s Note:
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.