Re-Arching
The following was given as a presentation to fellow luthiers at the VSA Convention in Cleveland, November 8, 2010.
HOW TO RE-ARCH A BASS TOP
All stringed instruments are prone to deformation caused by the constant pressure of string tension. I’m going to talk about how I re-arch a bass top that has deformed over time, a top that has succumbed to the stresses it has endured for decades or centuries.
My remarks will focus on the static forces present in a bass. I refer you to two excellent articles on this subject, one by Nigel Harris (click to download the full article), the other by J. E. McLennan (click to download the full article). I also recommend that you read the article on Arching Correction in the Weisshar-Shipman book. The method I have devised is designed to accomplish exactly what clamping a 2×4 on top of a hot sandbag does. I will give you a quick preview of the content of my talk and then delve into it in more detail.
I will explain WHY A PLATE DEFORMS;
HOW TO:
A. MAKE A PLASTER CAST OF THE TOP; [A] [B]
B. ANALYZE THE DEFORMATION OF THE TOP; [dL]
C. CORRECT THE CAST [C]
D. BUILD A PRESS WITH TORSION BOXES [N]
E. PRESS THE TOP WITH HEAT BLANKETS AND AIR BAGS
F. STABILIZE THE TOP WHILE EXECUTING REPAIRS
I will begin with some basic structural analysis. Arches are everywhere. Here, the downward force is transmitted through the stones of the arch out to the abutments which are anchored in the earth. At the abutments the force, traveling along the line of the stone arch, has a horizontal and a vertical component. These components are resisted by the the earth pushing up and in.
Now let’s look at a bass that’s strung up and ready to play.
The bridge supports four strings whose combined tension is about 250 pounds which results in about 150 pounds pushing down on the bridge. The top is an arch and because it is being pulled in at the ends with about 230 pounds of pressure, it wants to push up. If I push in on the ends of a strip of thin plastic it bends and buckles up. This is exactly what is happening in the bass top, which is good because, as I have said, the bridge is pushing down with about 150 pounds of pressure, 75 pounds on each foot.
The soundpost is also pushing up from the back, but it isn’t directly under the foot of the bridge, so there is also a rotation here. The bass bar supports the bass foot, but in doing so pulls down on the areas of the top to which it is glued.
Cross-section viewed from the E side
Cross-section viewed from the bottom
Here is a kind of topographic map of where the top is rising (plus signs) and where it’s sinking (minus signs).
It is these forces, acting 24/7, that cause a bass top to deform. Usually the bass side sinks and the treble side puckers up, especially in the lower bout where the soundpost is levering against the bridge. The bass side sinkage is usually worse in the lower bout because the bout is wider and thus the arching in a transverse cross-section is flatter and more likely to deflect.
Why do some basses retain their shape and others don’t? In addition to all the factors we consider when building a new instrument, there is the matter of creep. Wood under stress will change its shape over time. So if the forces are in equilibrium the bass will maintain its shape for a long time. Each piece of wood is different, so I can’t say what combination of these factors will add up to a bass that will sound great yet resist the relentless forces trying to deform it, but in general I can say that the worst repair cases have very thin tops.
Enough about the problem, now on to the solution.
Here is a bass that has a one-piece slab-sawn white pine top with 9 large knots. It is so wide, and the top had sunk so much that it couldn’t be played with the bow without hitting the C-bouts.
I start by making a plaster cast of the deformed top as it is. I lay the top on the bench and shim the edge to preserve its contour. I place shims and supports under the bass bar and in a few other places under the bass to support the weight of many pounds of wet plaster. I lay a sheet of thin plastic film large enough to cover the entire top and the surrounding area of the workbench, and then I build a wooden form around it. Usually 2 1/2″ is deep enough, but some higher arched tops require 3”. I also take into account the amount I will want to carve out of the cast to increase the height of the arch. I reinforce the cast with ½” wire hardware cloth.
I use DAP Plaster Wall Patch, which sets slowly enough so that the 3 or 4 separate batches I mix will cohere in the cast. Plaster of Paris sets too fast and generates a lot of heat when it does, which might damage the varnish. To mix, I add the dry plaster to water in a bucket and use my electric drill with a long stirring tool to work out the lumps. I pour the wet plaster into the form on top of the bass top. After 2 or 3 batches, when there is enough thickness built up, I lay in the wire mesh at a level not so deep into the cast that I will carve into it. I fill the form to the top and screed it level and as flat as possible .
As soon as the plaster has cured enough, about 6 hours, I tilt up the entire assembly on to its edge, remove the top from the cast, and peel off the plastic. I leave the cast to cure for several days to strengthen and lose some of its water. Then, while the plaster is still soft and damp, I scrape the flat side absolutely flat because I want to be able to apply pressure to it without breaking it. I use a torsion box the size of a bass top and chalk the surface, which tells me where the high spots are. I then leave it to completely dry, which takes a couple weeks or more.
When the cast is dry you can use it to support the top while you prepare the top for pressing. I want the top to be as flexible as possible for the pressing, so I remove the bass bar and large reinforcements such as breast patches and other overlays. I thin all the cleats to paper-thin. Whatever reinforcement it needs I will add after the pressing to hold the new shape.
Working in the well of the cast, I then make plywood templates of the arching. I make 5 or 6 transverse profiles and one longitudinal profile along the center seam that exactly fit the contours of the cast. I mark the outside edge of the cast where the templates fit and always refer back to these marks.
The templates give me a map of the deformation and the information I need to start correcting it. I start with the assumption that the arching was carved symmetrically, with the high point under the bridge. Most of the correcting will be made to the transverse section, but in cases where the middle of the top has sunk I’ll need to correct the longitudinal profile first.
If you picture the shape of the original arch as a wave with its high point in the middle, you can see that the high point of the wave has been moved toward the treble side. I trace the profiles onto thin cardboard.
Then I cut them out and fold them at the center line. I can now see how much the bass side has sunk compared to how much the treble side has risen. To restore the symmetry, I mark a line that splits the difference between the high of the treble side and the low of the bass side, and cut along that line. I now have half of a symmetrical profile, which I trace onto a new piece of cardboard, giving me the complete profile. I trace this new shape onto plywood and make a new template for correcting the cast. During this process I am mindful that the wood of the top is all the wood I have to work with, and it won’t stretch or compress, so if I want to push out the place that has sunk I need to push in an equal amount from somewhere else, and thus massage the wave back to symmetry.
To accomplish this push-and-pull I will need to cut-and-fill the cast. Sometimes the arching is so deformed that I will correct the cast only half way and do a preliminary pressing, but usually I go straight for the full correction. Using a small-radius scraper I make grooves in the plaster deep enough for the ends of the templates to rest on my reference marks. Then I excavate the excess plaster between the grooves. I use curved or flexible scrapers for this, cutting in different directions to even out the contours. Now when I lay the templates across the cast I have air space on the treble side. This is where I need to fill.
I prepare the surface of the cast for filling by scoring it with an old fork to give the plaster some “tooth”. Plaster hardens as result of a chemical reaction with water called hydration. If there’s not enough water present, the plaster will dry to a weak powdery crust and break off, so I brush water on the area I’ll be filling so the dry plaster doesn’t draw all the water out of the new plaster I will be adding. It’s important when adding plaster to just pour it on or maybe use a 2” paintbrush to move it into place, but do not work it with a trowel or spatula because these tools will compress the plaster and it will be very hard when it cures, much harder than the surrounding area of the original cast, and it will be difficult to carve evenly. I try to add enough new plaster so that in one operation I’ll have added enough to carve it back to the shape of the template.
I now check the longitudinal and transverse profiles and cut and fill where necessary. A piece of 80 or 100 grit sandpaper stuck to a slightly convex piece of Formica makes a good tool for the final smoothing of the plaster surface. At this stage my hands “see” better than my eyes, and I work it until it’s right. Now I check the fit of the top in the cast and I carve away about 1/8” from the entire perimeter of the cast to make sure that the edge of the top doesn’t get hung up on the edge of the plaster when I press it.
I want a temperature reading on both sides of the top to know when I’ve added enough heat. The temperature sensor I use on the varnish side is a ½” square of thin metal with two wires attached to it. I set it flush with the plaster by carving a small depression into the plaster to accommodate the sensor and its wire, and I use tape to hold it in place. I have chosen a location where the top will be in contact with the plaster from the very beginning, assuring that the heat will be conducted through the wood to the sensor. I’m now ready to press the top.
My press is made of two torsion boxes held apart by spacers at the four corners and bolted together with eight ½” diameter threaded rods. A torsion box is a “stressed skin panel”. It is a 3-dimensional I-beam. It’s very strong, rigid, and light, and, when made accurately, it’s very flat. It consists of a core which is about 5” deep, and two skins of ½” plywood.
To make a torsion box I use ¾” plywood for the ribs of the core, arranged in a 6” or 8” grid. The core pieces can be screwed together without glue. I reinforce the corners and the attachment points on the sides by adding web pieces to support the skins where the bolts will attach. This job is made easier if you have a large, flat table to work on. But even if your work surface isn’t perfectly flat, if the core pieces are cut accurately, it will make itself flat. The accuracy is obtained by having your table saw adjusted so that everything is square, parallel, and perpendicular. In this diagram I have darkened one of the four sub-assemblies which are screwed together before adding the rim pieces. Now I glue and screw the skins on. I use plenty of yellow glue. This is where the torsion box gets its strength.
I place the cast on the lower half of my torsion box sandwich. Next, I line the cast with two layers of very thin plastic sheeting. This is to provide a slippery surface where the varnish meets the cast. Now I place the top into the cast.
I sponge the inner surface with water to replace what moisture will be forced out when the heat is applied. Approx. 7% of the weight of the wood is water to begin with, so I don’t need to add much.
Often there are so many cracks in a top that it is tattered into parallel strips glued together, and often these strips are cupped, making a scalloped transverse section. Since the pressure of the air bags is a modest 12 – 13 psi, the ridges that these strips form along their edges are sometimes resistant to flattening. To overcome this I place a layer of 1/8” masonite strips about 2 ½” wide running across the grain, covering the entire top.
Next, I lay in the heat blankets, covering the entire area of the top, being careful they don’t overlap. One of my heat blankets has a temperature sensor attached to it, so I place the sensor where it will be in contact with the wood.
A heat blanket is basically a woven mat of glass fibers and wire heating elements bonded together with silicone rubber. Two wires are soldered near the edge, and, once you’ve attached a standard wall plug to them, you can plug it into an outlet. At full current, a heat blanket will achieve 450F, so for most uses they must be plugged into a controlled power source. Heat blankets draw 5 watts per square inch. The combined area of the nine blankets I use to cover a bass top adds up to almost 6,000 watts. This requires a heavy-duty controller. Mine is a single-phase distributive zero-cross silicon controlled rectifier controlled by a potentiometer. This control feeds into an array of duplex outlets, and this is where I plug in the blankets. I purchased all of this equipment from Antech Sales in Medina, NY.
I cover the heat blankets with a cloth on top of which I add a layer of sand, level with the edge, to fill in the well. This prevents the air bags from bulging and distorting at the edges where they meet and possibly opening up an area where there is no pressure. I isolate the sand with a layer of cloth over it.
Next is a layer of ½” cork as insulation between the heat blankets and the air bags.
Last is the air bags. These come from Aero Tec Laboratories in Ramsey, NJ. They are made of the same materials used to make puncture-proof bladders for inside the gas tanks of race cars and Presidential limousines. I have three bags, one for each bout of a large bass: 18 x 26; 12 x 20; and 16 x 22. Usually the two larger ones are sufficient for an average sized bass. They are outfitted with a ¼” nipple and a length of ¼” tubing. I fabricated a manifold from barbed plastic fittings, air-tight disconnects, a pressure gauge, and a shut-off valve, all of which I obtained from MSC. I inflate the bags with my bicycle pump.
Now I complete the sandwich with the upper torsion box. I space the torsion boxes apart so I’m left with about ¾” for the bags to inflate. Eight ½” threaded rods hold the sandwich together. 13 psi doesn’t sound like much pressure, but multiplied by the square inches on the top of a bass it adds up to about 8,000 pounds!
I’ve prepared for this moment for at least a month. I’m ready to press the top. It all happens very quickly. I turn up the heat slowly, and watch the readouts. I’m aiming for a maximum of 120F on the varnish side and 150F on the inside. When it’s hot enough, after maybe five or ten minutes of heating, I pump air into the bags up to 13 psi. I find that this is enough pressure, and besides, my torsion boxes start to creak at this pressure. It’s done! I close off the air valve and let it cool overnight.
In the morning I let the air out of the bags, disassemble the press, and see how I’ve done. Usually there is some spring-back So I evaluate the results by looking and by placing the top in the cast and feeling where there is air space. If the springback is significant I will over-correct the cast by cutting and filling and press it again.
If the top requires major reinforcements, it might be advisable to glue the top into the cast to stabilize it, for instance while fitting a large breast patch. It’s impossible to chalk a patch to a moving target. So now I need to reverse the over-correction by cutting and filling again. Alternatively, you could make a new cast of your newly re-arched top.
If there are cracks or other areas that can be repaired before being glued into the cast, this is the time to repair them. The cast can support areas where wood needs to be removed or it can help to align cracks while they are being glued. I use plaster casts for a variety of repairs. Plaster of Paris in a plastic bag provides support when carving out a soundpost patch or a long inlay. The mass of the plaster is small enough that heat build-up isn’t a danger.
It’s easy to glue the top into the cast. I use the bags and the press with no heat. My first priority is to protect the varnish. To provide a moisture barrier for the varnish I give it two coats of Solu-Var, a mineral spirits based reversible varnish that is used by art restorers and is available from art supply houses. I am careful not to get Solu-Var into cracks that will require gluing later. I fill these areas with glue which can be removed later if necessary. Next, to provide some structural integrity to this fragile shell, I adhere silk to the varnish side using Solu-Var as an ahdesive.
Before gluing I make 1/4″ by 1/4″ grooves in the surface of the cast, about 1 1/2″ on center. These are channels for the water which will soften the glue when I’m ready to release the top from the cast. Now I size the plaster cast with Liquid Hide Glue, on the surface only, not in the grooves. Then I apply glue to the silk and the cast and clamp them together in the torsion box with air bags. When this is dry the top is completely immobilized and ready to receive all manner of inlays or a breast patch.
To release the top I squirt water into the grooves and after about a half hour or more the glue is ready to give. I then remove the silk and Solu-Var, wash the glue from the cast, and when everything is dry, use the cast to support the work while I graduate the breast patch. An alternative method of releasing the glue is to soak the entire cast in water by making a small pond in a plastic-lined box and warming the water to hasten the softening of the glue. The downside of this approach is that the cast is destroyed in the process of removing the top because it becomes so heavy and weak.
Antech Sales, Inc.
105 Elwood Ave. PO Box 110
Medina, NY 14103
Phone (800) 836-0754 (585) 798-4300
Attn.: Carl
www.antechsales.com
Aero Tec Laboratories, Inc.
Spear Road
Ramsey, NJ 07446
Phone (201) 825-1400
MSC (account required)
Phone (800) 645-7270
www.msc.com