Thinking of making an archtop - how can I best use this wood?

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Peter Wilcox
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Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

Since I'm coming to the end of my building "career" for age and health reasons, I figured I might try an archtop before I check out. It has the potential to be a disaster, so I'm not going to spend any money on it. I have this redwood board, with a usable dimension of 13" x 47", thickness 1.3", near vertical grain variable from about 19 to 25 lines per inch (already used part of it for a flat top).

I can see 3 options for using it:

1) Resaw an appropriate size piece to 2 thin book matched pieces about 1/2" thick - this won't give an appropriate rise to the arch, but maybe I could make it flatter than usual.

2) Resaw a 13" (or 12" to fit it in the saw) wide piece of requisite length at an angle from one corner to the other, giving 2 wedges 1.3" thick on one side to zero on the opposite side, not book matched and opposite run out, but having the requisite center and edge thickness (for a 16 or 17 inch lower bout width.)

3) Cutting two 1.3" thick 20+" x 9" pieces from the whole board, giving requisite thickness but not book matched.

The board is similar enough throughout that visually not being book matched would be acceptable (to me.)

Since I expect this instrument will have many mistakes, though hopefully playable, the top wood doesn't have to be anywhere near the best. The back and sides will be maple, that I have plenty of, and the bridge and fret board probably ebony that I have if the pieces are big enough. The neck could be maple, mahogany or alder.

Any thoughts on that top wood and how best to cut it? (Or maybe just forget it?)
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Bob Ionta
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Bob Ionta »

Personally, I'd favor the desired arching over grain matching so I would not do choice #1. Between #2 and #3, #2 seems much more difficult for little advantage. The only advantage I can see is that you'd conserve wood. I used choice #3 on the cherry back of an archtop and it looks great. I never even think about the fact that it's not book matched. I might view it differently if I was building for anyone but myself but even then I'd be surprised if most players I know would mind it. Of course I can't even imagine myself selling to collectors or anyone in the high price brackets but I'd guess if you were doing that you wouldn't be asking this question.

So my choice would be #3.
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Barry Daniels »

Option #3 would be highly preferable to the other two. What you would be doing is called a slip match. I think no one would ever notice the difference since it is the same board. Just be careful to avoid the crack. They usually travel up the board further than you think.

An archtop is a daunting project but with your experience you should be able to pull it off quite well. Don't sell yourself short.
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Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

Arch height and top thickness are best scaled together on an archtop guitar. It may seem counterintuitive, but the thicker you want the top to end up the higher the arch should be. If you're not following an existing design and using 'known' wood you'll need to figure out how thick the top will need to be to withstand the bridge down load, and scale the arch from that.

As with most guitars, the most important property there is the Young's modulus of the wood along the grain (E-long), which largely determines the bending stiffness at a given thickness. This can be measured directly in a couple of different ways, and that's always the best idea if you can do it. A short cut relies on the fact that E-long tends to follow the density of the wood pretty well for most softwoods. If you can determine the density (specific gravity, compared with water as '1'), looking up the expected stiffness is easy. In this case, I'd expect the E-long value to be low relative to the density because of the prevalence of hard latewood lines, but there's always the possibility of using a 'fudge factor'...

I note that the grain lines are at an angle to the surface of the board. When making a top from a split wedge the grain lines will tend to be perpendicular to both faces of the wedge, which gets you as close as possible to 'vertical' with respect to the arch, and yields the highest cross stiffness at al points. The actual cross stiffness may not be as important as the fact the 'wedge' cutting makes it more consistent across the top. Given the choice I'd try to cut the wood so that the area in the center is the best quartered; if it goes a bit skew in the wings that makes them somewhat more flexible.

With luck, depending on how deep those end checks are, you should be able to go with option 3, which I'd think would be best. Don't discount the idea of using 'wings' on the outer edges of the lower bout, particularly if these can be kept small, so that the joint falls over the liners.

Keep in mind that redwood has a tendency to split along the grain. Make a good cradle of layers of cardboard glued to plywood to support the outside of the arches once you've shaped them, while you work on the inside graduations.

I've had a lot of luck using 'curtate cycloid' cross arches on archtops. I've made the low point of the arch over the inner edge of the liners all the way around, which seems to help keep them from 'sinking'. The recurve around the edge is part of the whole system; you don't go around later and thin it out after the box is assembled. Again, I'm using Cladni tuning on this, so that should not be necessary. To each his own. The scaling of the arch height to the thickness comes from this; a high arched thin top tends to 'buckle' when you're driving some of the 'free' plate modes, producing odd results, and the guitars don't sound the way I want in any case.
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Mike Conner »

One alternative not mentioned here (so far) is to relocate offcuts from the waist area to fill out the width of the lower bout. I have done this very successfully on my builds. The archtops and dreadnought size I have built are 16" wide at the lower bout. I have used some curly maple and walnut for back plates that were resawn from approx 7" wide boards. I carefully joint both edges of the board - one edge is then glued for the center of the plate. There is enough material at the waist to relocate to the outer edge and fill out the width, and since it is from the same board I've had excellent success matching the grain/figure.
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Mike Conner »

Oh, and I start with 0.75" thick plates for the front and back arches, so you would be resawing and surfacing down to that before jointing, etc.
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

Thanks for your comments/suggestions - really appreciated. It's a lot to think about, especially never having carved a plate before, and still unclear to me how to design the curves for the arch and recurve areas. I have Benedetto's book with the templates in the back, and have watched some youtube videos, and read part of your pdf so far, Mike - very helpful.

Unfortunately I have a new bug in my brain, to make this a bass instead of a guitar, so at least it will be something I can play adequately. There is very little info I've found on this, though it looks like for optimal volume and frequency response the box will have to be larger and thicker. Any suggestions along those line would also be helpful. I know one suggestion will be to make a guitar first, but I don't know if I have two of these instruments left in me. :)
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Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

There's a reason why upright basses are the size they are. The wave lengths for the lowest notes are so long that the top doesn't even start to become efficient at making those sounds until it's four feet long or more. If you're thinking of an electro-acoustic that's another matter, since you can rely on the amp the fill in the low tones.

Designing arches using the 'curtate cycloid' method is really easy. In fact, if you download Mike Mahar's free 'Luthier Lab' Android app it's got a utility for that. You can work up an outline (also in LL), specify the lengthwise arch, and it will print out a full sized contour map for you. I've always done it the old fashioned way, but that's not too hard either. First; about 'curtate cycloids'.

If you mark a spot on the rim of a wheel, and trace out the path of that spot as the wheel rolls along a straight line, you get a 'cycloid' curve. Cycloids were sexy math a generation or so before Strad worked, since they were the basis of the Ptolemaic system of astronomy, and the math was all worked out then. By Strads' day it was being used in crafts. The full cycloid curve is a series of humps up from the points along the plane where the rim touches the surface. If you mark a spot partway in from the rim toward the axis of the wheel you get a 'curtate cycloid'. Several years ago somebody got the idea that this may have been the system the old boys used to draw arches, and checked it out. Given the distortions of age and normal uncertainties, it's about as close as any other system, and it's much simpler than many.

Basically, you start by specifying the lengthwise arch along the outline of the instrument. The high point will be at the bridge, and I usually make the low points around the edge at the inside edge of the liners. You thus specify the height of the arch at any line across the body, and the length between the low points.

What you need now is a disc that will roll once along that line from one end to the other. If you remember that pi~22/7 (as any good craftsman would) it's not too hard to make one from some card stock. If you punch a hole in the disc that's 1/2 of the arch height out from the pivot point you can stick a pencil in the hole and use it to draw out the cross arch by rolling the disc along a straightedge. I find it helps a lot to rosin the straight edge, so the disc doesn't slip so much. draw that on some card stock and cut it out to use as a template. Remember that you're drawing the outside of the arch, from the lowest point around the edge to the top, and subtract the thickness of the plate at the edge from the arch height off the surface. That is, if the arch as measured over the top is 18 mm, and the edge will be, say, 3.5 mm, you punch the hole in the disc (18-3.5)/2 mm from the pivot, or 7.25 mm.

You can lay out as many cross arches as you like on an outline of the top. Find all the places along the cross arches that are 2 mm above the low point at the edges, and connect those with a nice smooth line. Repeat at 2 mm intervals until you've got all of the contour lines. Label these clearly with the height above the bench, adding in the thickness of of the edge at the low point. If that's 3.5 mm than the lines are at 3.5, 5.5, and so one. Here's a shot of a couple of different contour plots for the same size of guitar but different long arches.
patterns.jpg
These patterns can be placed over the wood to trace the outlines of the contours. I remove most of the wood with a drill press planer, starting with establishing the high point at the top and working down by positioning the half pattern on the center line using the high point, and flipping it. This produces the stepped blank.
contours.jpg
I note that I don't cut down to the lowest (3.5 mm) contour this way, to allow for extra thickness at the edge for the binding. I've used the Dremel setup for cutting violin purfling slots, and a 1/8" bit, to make a channel in from the edge almost down to that level for guidance here. It's a (relatively) easy matter to smooth out the arch from there.
contoured.jpg
Hope this helps.
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

Thanks Alan - that's very helpful. One question: how do you determine the lengthwise arch, since it's asymmetrical.
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Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

I usually use a bent stick to generate the the upper and lower curves, above and below the bridge, separately . Clamp a block down to the drawing with it's bottom surface at the level of the top at the bridge, and parallel to the plane of the upper edge of the side (I hope that makes sense!). If you like you can clamp down another with the corner pointing down at the low point of the lower edge. Get a flexible rule or a thin stick of uniform grained wood and push it up against the blocks, so that the stick is flat up against the block at the bridge. Depending on how the stick stick flexes, and where and it what direction you push on it, you can get a range of curves. When you get something you like pencil it onto the drawing.

The bridge location is always the highest point on the top. There are a few different schools of thought as to what the arch should look like. Orville Gibson followed a use that was common at the time, at least in the US, making the arch quite flat in the middle, with most of the curvature downward to the edge nearer the ends. This is often called a 'high' arch in the trade, possibly because it comes up so fast at the ends. It's at least plausible that the old master violin makers used something like this, but probably not as extreme as we sometimes see on fiddles and archtops around 1900. The down pressure of the bridge tends to flatten the center over time, and the distortion tends to push up on the ends in the center of the bouts. A few generations of copying extant old instruments with sunken tops will exaggerate the effect. The bottom pattern in the pics was a version of this, based on a long arch taken off an older Gibson and provided by a student. I 'corrected' it to have more curve in the center. The upper pattern, the one that's already cut out, is for a so-called 'flatter' arch, with a more uniform curve along the center line. I'll note that both of them have the same height at the bridge: 21 mm. The assembled box in the picture has the 'Gibson' style arch; it was an 'homage' of you will based on a Loar L-5 that one on my customers really liked the sound of.

I checked out the arches in Benedetto's book, and iirc, the cross arches don't fit the long arch. Maybe I measured wrong...
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

Thanks again, Alan. It looks like the arches are somewhat open to interpretation, particularly the long arch. I've had bad weather here which is extending into the near future, which is depressing besides needing keeping up on maintenance, so won't get to this for awhile. I'll post when I get something going.
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Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

" It looks like the arches are somewhat open to interpretation, particularly the long arch. "

Indeed. I think of the arching and graduation of the plates on an archtop as being analogous to the bracing layout and profiling on a flat top. In both cases you're working to get the mass and stiffness distribution 'right', whatever that is. There are various ways to produce a top that works structurally, but they sound different.
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

Thanks to all who responded, and I appreciate all the comments and advice, especially Alan's. It's made me take another look at why I try to make instruments, and it seems it's for the enjoyment of "designing" and making them, and not for the final result. So in that vein, I've decided to make an archtop bass, and resaw the wood using method #2 above.
redwood-resaw2.jpg
redwood-resaw1.jpg
top1.jpg
top2.jpg
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

I calculated the x and y coordinates of the various arches using Liutaio Mattola's curtate cycloid calculator:
https://www.liutaiomottola.com/formulae/curtate.htm

I changed the long arch from the bridge to the neck to raise it a little higher in the midsection. I made a template to redraw the locations of each level after each pass with the safety planer had erased some of them. After the levels were established I sanded them smoother with an angle grinder sander - very gingerly as it cuts fast. Then with a random orbital sander and hand sanding to smooth it out.

The lower bout is 17" and the body length 21", and I think I'll make the sides about 4" wide to give more air volume inside which may help the bass frequencies, but still playable slung over the neck and shoulder.

Again, thanks for the suggestions, and I'll soldier on.
top3.jpg
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top5.jpg
top6.jpg
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Karl Wicklund »

Reassessment of motives is always eye opening. Keep us posted!
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Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

Off to a good start!
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Peter Wilcox
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Peter Wilcox »

This guitar continues and finishes here: https://www.mimf.com/phpbb/viewtopic.php?f=5&t=6654
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Allyson Brown
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Allyson Brown »

Alan Carruth wrote: Sun Dec 19, 2021 12:53 pm There's a reason why upright basses are the size they are. The wave lengths for the lowest notes are so long that the top doesn't even start to become efficient at making those sounds until it's four feet long or more. If you're thinking of an electro-acoustic that's another matter, since you can rely on the amp the fill in the low tones.

Designing arches using the 'curtate cycloid' method is really easy. In fact, if you download Mike Mahar's free 'Luthier Lab' Android app it's got a utility for that. You can work up an outline (also in LL), specify the lengthwise arch, and it will print out a full sized contour map for you. I've always done it the old fashioned way, but that's not too hard either. First; about 'curtate cycloids'.

If you mark a spot on the rim of a wheel, and trace out the path of that spot as the wheel rolls along a straight line, you get a 'cycloid' curve. Cycloids were sexy math a generation or so before Strad worked, since they were the basis of the Ptolemaic system of astronomy, and the math was all worked out then. By Strads' day it was being used in crafts. The full cycloid curve is a series of humps up from the points along the plane where the rim touches the surface. If you mark a spot partway in from the rim toward the axis of the wheel you get a 'curtate cycloid'. Several years ago somebody got the idea that this may have been the system the old boys used to draw arches, and checked it out. Given the distortions of age and normal uncertainties, it's about as close as any other system, and it's much simpler than many.

Basically, you start by specifying the lengthwise arch along the outline of the instrument. The high point will be at the bridge, and I usually make the low points around the edge at the inside edge of the liners. You thus specify the height of the arch at any line across the body, and the length between the low points.

What you need now is a disc that will roll once along that line from one end to the other. If you remember that pi~22/7 (as any good craftsman would) it's not too hard to make one from some card stock. If you punch a hole in the disc that's 1/2 of the arch height out from the pivot point you can stick a pencil in the hole and use it to draw out the cross arch by rolling the disc along a straightedge. I find it helps a lot to rosin the straight edge, so the disc doesn't slip so much. draw that on some card stock and cut it out to use as a template. Remember that you're drawing the outside of the arch, from the lowest point around the edge to the top, and subtract the thickness of the plate at the edge from the arch height off the surface. That is, if the arch as measured over the top is 18 mm, and the edge will be, say, 3.5 mm, you punch the hole in the disc (18-3.5)/2 mm from the pivot, or 7.25 mm.

You can lay out as many cross arches as you like on an outline of the top. Find all the places along the cross arches that are 2 mm above the low point at the edges, and connect those with a nice smooth line. Repeat at 2 mm intervals until you've got all of the contour lines. Label these clearly with the height above the bench, adding in the thickness of of the edge at the low point. If that's 3.5 mm than the lines are at 3.5, 5.5, and so one. Here's a shot of a couple of different contour plots for the same size of guitar but different long arches.
patterns.jpg

These patterns can be placed over the wood to trace the outlines of the contours. I remove most of the wood with a drill press planer, starting with establishing the high point at the top and working down by positioning the half pattern on the center line using the high point, and flipping it. This produces the stepped blank.
contours.jpg

I note that I don't cut down to the lowest (3.5 mm) contour this way, to allow for extra thickness at the edge for the binding. I've used the Dremel setup for cutting violin purfling slots, and a 1/8" bit, to make a channel in from the edge almost down to that level for guidance here. It's a (relatively) easy matter to smooth out the arch from there.
contoured.jpg

Hope this helps.
Can you share the final work.
Alan Carruth
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Alan Carruth »

There are a number of ways to proceed once you have the arch roughed in; it depends on what tooling you have, and are used to. I mostly go at it with violin maker's planes, and hard scrapers. Some folks prefer gouges, and others like to use a disk sander. I make up a set of contour gauges and check often as I go. Once you've got the main lines right it's a matter of chasing down bumps to get everything nice and smooth and flowing. Direct sunlight, that casts a good shadow, is really helpful for this, but I often end up using a small LED spot light too.
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Re: Thinking of making an archtop - how can I best use this wood?

Post by Allyson Brown »

Alan Carruth wrote: Fri Oct 06, 2023 2:30 pm There are a number of ways to proceed once you have the arch roughed in; it depends on what tooling you have, and are used to. I mostly go at it with violin maker's planes, and hard scrapers. Some folks prefer gouges, and others like to use a disk sander. I make up a set of contour gauges and check often as I go. Once you've got the main lines right it's a matter of chasing down bumps to get everything nice and smooth and flowing. Direct sunlight, that casts a good shadow, is really helpful for this, but I often end up using a small LED spot light too.
I think that is a good method of making an archtop.
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