Thoughts on the Sizes
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This week I got an e-mail asking "What are the appropriate dimensions for a concert ukulele bridge?" My answer was a mixture of history and technology, trying to rationalize what builders had used in the past with the physical situation of the whole range of instrument sizes. Upon more reflection, it seemed that a general discussion including gluing bridge plates might also be instructive.
I suggest that the size of the bridge should be proportional to string tension. Table 1. below gives string tensions for nylon stringed instruments in the guitar family.
|Cumulative Tension (in lbs)|
|# Strings||Soprano||Concert||Tenor||Baritone||Classical Guitar|
Classical guitars have about 6 square inches to hold against ~ 90 lbs of string tension. So this means that there is an approximate horizontal pull of (90 lbs/6in^2) 15 lbs/in^2. Under ideal conditions, Titebond glue has a shear strength of ~ 3000 psi. If we multiply bridge area by shear strength we get 18,000 lbs. Then dividing that strength value by the 90 lb string tension we get a safety factor of ~ 200. This means to me that it's no surpise that the bridge rarely fails at the glue joint, even though the average gluing job rarely approaches ideal conditions.
So what size bridges should the other instruments have, assuming that the classical guitar bridge is an appropriate analog? We simply divide the string tension for a given size instrument by the string tension for the classical guitar and then multiply the result by the area of the classical guitar bridge. For these calculations I will use the numbers listed in Table 1. Here are the approximate results: soprano bridge area: (21/86)x6 = 1.5 in2; concert bridge area: 2.3 in2; tenor 4-string: 2.7 in2; tenor 6-string: 4.5 in2; tenor 8-string: 5.8 in^2; baritone: 3.7 in2. Historically, typical soprano ukulele bridges have ~ 1.5 in2 of area. So it would seem that our simple extrapolation from the classical using string tension wasn't completely without foundation. My own tenor bridges have about 4 in2 of area and that middle range value has worked well for me for several hundred instruments.
How wide should the bridge be? Make a full scale drawing of the instrument and draw in a line representing the front edge of the bridge at its approximate scale length position. Now draw lines from the outside nut slots, parallel to the edge of the fretboard, to the bridge line. These are your outer hole center line positions. Space the other center lines equally. Vintage Hawaiian soprano ukulele bridge widths from my database average about 2.5". Classical bridges seem to have "wings" which are about equal to the tie block section in area. Soprano ukuleles have only about ***% outside the centerlines and that area is just an extension of the tie block. I suggest that there's a message here: the smallest ukuleles shouldn't have miniature classical bridge shapes because all of the area is used as a stiffener as well as glue area. "Wings" on a soprano are probably extraneous, adding excess stiffness to the top.
What depth (distance from front to back) should the bridge be? Again from my database, average depths are about 5/8", which would be appropriate for the 1.5 in2 of area. This would mean that concert size instruments should probably have widths in the 3/4" range. Tenors and baritones could be either 1" depth with small "wings" or 7/8" with slightly larger "wings".
What height should the bridge be? There are many folks who feel that half of the saddle height should be in the saddle slot and the other half above it when the instrument action is finally adjusted. Again, let's draw the instrument in full size, this time in half section. I like an approximate action of 0.10" between the top of the 12th fret and the lower edge of the strings. Using a straight edge, draw a line from the top of the 1st fret to the bridge line, using the 0.10" increment at the 12th fret as a pivot point. The height of the line above the top of the lower bout at the bridge line is the top of the saddle for this particular action. For argument's sake, divide this distance into thirds. Then two-thirds of the distance will be the height of the bridge, and two-thirds will be the height of the saddle, with one-third of the distance being overlap. Depending on the distance from the front to the back of the bridge, this saddle height could result in a high cross-over angle as the string passed over the saddle on its way to the knot slot. As shown in the page on Top Deformation, higher cross-0ver angles result in greater downward pressure on the top. Probably dividing the distance into fourths would result in a more satisfactory cross-over angle with less strain on the top but still sufficient downward pressure to make the little soprano work well. That would mean that the total saddle height would be half the vertical distance and the total bridge height would be three-quarters of the distance.
I am a firm believer in properly sized, shaped and oriented bridge plates. I have seen many dozens of older (and newer) ukuleles with cracks on the top, parallel to grain and coincident with the ends of the bridge. In nearly all cases, there was either no bridge plate or the bridge plate was the same size and shape as the bridge. What happened? In all likelihood, the instruments were made at relatively high humidities. During drier conditions, the top wood tried to shrink but was held in place by the glue joints on the edges. At this point the wood is in tension. Since the strings are under tension, the bridge is trying to rotate. The string stress is evenly distributed throughout the bridge, but unevenly distributed across the top of the instrument; there is a very strong stress change at the bridge ends, parallel to grain. This location then is the most likely location for crack formation. If bridge plates are made which extend the bridge rotational stresses to a larger area and which transition slowly (the round ends of the bridge plate) across the grain, few if any such cracks should occur.
In all my instruments, I put a bridge plate beneath the bridge, glued to the underside of the top. The bridge plate is made of graphite carbon/epoxy composite bi-axial sheet. I use 0.018" thickness for sopranos and concerts and 0.030" thickness for tenors and baritones. The width of the bridge plate extends 0.5" beyond each end of the soprano and concert bridges and 0.75" beyond the ends of the tenor and baritone bridges. In all cases, the bridge plate extends 0.25" above and below the bridge plate. The ends are rounded into semi-circles. This material is available from Composite Structures Technology as carbon shear webs and may be ordered in a variety of widths. I usually buy the 3" widths of each and cut them to size with metal cutting shears. The part numbers are: C3001 (0.018") and C3011 (0.030"). The prices seem reasonable to me and service is very good.
The bridge plate is glued on with Smith Industries 30 minute epoxy, although any of the slower curing other epoxies might suffice as well. I like the Smith Industries brand since it comes in squeeze tubes and it's easy to mix very small batches. The bridge plates are all glued with a ~ 30' radius arch. To glue the bridge plate on I've made a number of matched wooden cauls out of 2"x2"x6" Douglas fir with the radius cut the length of the block and more or less halfway between top and bottom. On the outside of the convex caul, I have labeled it "INSIDE" to remind me that it goes in the underside of the top (or the final inside of the instrument).
At the beginning of the gluing process, a piece of waxed paper the size of the cauls is cut and set aside. A piece of masking tape the depth of the bridge plate and an inch longer on either end is attached to one side. This unit is now flipped over, tape sticky side up. A sufficient amount of the resin is mixed and set aside. With a hair dryer set on high max, heat the general area of the lower bout on both sides of the plate for about 10 seconds on each side. This will dry the plate considerably. Now, having brushed the work area clean, place the top plate down, put the bridge plate in place and press on the ends of the tape. Now the bridge plate won't move when the cauls are put in place. Put the waxed paper on the bridge plate and the cauls on both sides of the top (convex INSIDE) and gently but firmly clamp. Two hours later, remove excess resin and reclamp overnight.
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