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It appears that everyone uses 18" spacing in testing deflection but I haven't seen anyone mention a standard width that a top should be cut to. Why not?

I use 18" width as well, then adjust equations accordingly for skinnier pieces.

I cut my tops so that they are perfect rectangles 1cm longer then the length of the outline of the guitar and 1cm wider then the lower bout and then do deflection testing.

What equations do you use and are they linear or algorithmic?

It seems to me that as long as one chooses a method of measuring/documenting and sticks with it, noting what worked and what didn't, there is something of value in the testing. Consistency is the key, and my method isn't going to be the same as your method, so comparisons are pretty irrelevant. As Brian Howard noted earlier, he's not going to give out his values on deflection, just his methodology. Good approach I think. He has things worked out for himself, but they're really unlikely to provide anything more than a starting point for anyone else. Comparing your numbers to someone else's isn't really valid in my opinion. Too many uncontrolled variables.

If there was some magic number, we'd all be building these spectacular guitars, they'd all be commodities, and no one would make any money, because the results could be easily replicated. Fortunately, there isn't some easy way out, and the art of lutherie is still a major factor in the whole thing. For me, it's all in the process and the journey. End results are secondary, but hopefully good!

Dave

I don't know enough about math to answer that question, lol. You'll note that math is not my strong suit, and frankly I never really had much need of it til the G/G books. Anyhoo...

But I can tell you my approach.

Let's say my standard deflection with a 5lb weight across an 18" span for an 18" wide top was .100 for easy math.

For a 16" top that I wanted to get more or less the same stiffness...I

Divide 16 by 18 to get .8888

Then 18 by 16 for 1.125

I consider those as percentages, so 16 is .8888% of 18, so 12.2% less. 18 is 12.5% more than 16.

So about 12-12.5%, good enough.

So add 12-12.5% more deflection to account for the loss of width. So I'd want .112 deflection on a 16" top to be the same stiffness as .100 on an 18" wide top.

It seems to work out fairly well, and gets my tops in the right range. Of course that's just the initial step, and my deflections are calibrated so that the top monopole is ALWAYS higher than the final target, which is achieved in various other stages and processes during the build cycle, thinning the perimeter on closed boxes, brace shaving etc...

I've often wondered if deflection is linear or not. Is .200 twice as flexible as .100? Or is it some sort of stacked exponential thing like the cubed rule of stiffness? All I can say is that it seems to work, my tops fall into a very narrow range, all tied into density...denser tops are always thinner, thicker tops are always less dense.

As ballbanjos says, the first thing is to standardize your process, so that you can compare results easily. The only really useful tests are the ones you do, so try to keep it simple.

A lot will depend on your tooling. It's likely that using a small weight and minimal deflection is more accurate, provided you can get enough significant digits. A gauge that read to .0001" might allow you to work with a smaller weight than one that only reads to .001". Don't even try to do this sort of thing on rough sawn tops: the more uniform and smooth the pieces the more accurate your results, so do the prep work.

There are formulas for converting the numbers you get in your tests to standard units, such as Young's modulus and density. I like to put this sort of thing into a spreadsheet or program, so that I can just plug in the test numbers and it spits out the values. That way I don't mess up on stuff like getting the decimal points in the wrong place: I know you don't do that sort of thing...

Once you have the measurements, record them, and keep them handy, preferably as part of a build log. That way, when something works (or doesn't), you can repeat it (or not).

If you have standard numbers you can compare your results and processes with other folks. This does two things:
1) it tells you when you're making systematic errors, and
2) you can compare your process and results with other people, and learn from their experience.

Even simple measurements have room for error. I recall the experience of one person who was using a simple 'tap tone' test to determine the Young's moduli and damping of tops. He was getting damping numbers that were much lower than anything many of us had seen, and they kept getting better. Finally it was determined that he'd been doing his tests with the computer speakers on, so the sound was feeding back into the plates and keeping them going. It doesn't take much sometimes. This sort of thing is embarrassing, but not at all uncommon, and very easy to miss if you don't have other people checking it.

All of this stuff is worlds easier than it was forty years ago. There's really no excuse not to do it.

I think if you standardize a process then you can share it with others and that information is useful. Like I said I cut tops to just outside the border of the shape of any guitar then I mark out the bracing and use a brick (Thanks B. Howard) placed on the location of the bridge and the measurement is taken right over the X. The brick of course has a specific weight but most bricks probably weigh close to the same or a noobie could at least find one that is close enough to mine. So if they repeat the same exact experiment then I would expect them to get similar results.

This is what I use.
As Mr McKenna said, "standardize a process then you can share it with others and that information is useful"
450 mm spacing, Modulus of Elasticity (E long) worked out in SI units (pascals)
Weights are magnetic tool bars. One is used for pre-load, add another 2 for measurement of deflection.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

I am happy to share my semi-neanderathal technique

I made a frame with movable dowels for support copying something someone showed here years ago. Different dowel positions for different sized tops.
I check deflection with the sound hole cut out and rosette installed and use it as a gauge for final thicknessing.

Always the same position of the top in the frame and same point for measurement and weight application. Pre-weight with one pound, zero, and then add an additional one pound. Do several checks and look at the average.

I have found that for me a deflection of around 0.045 - 0.053 seems to work best with my traditional Martin style bracing pattern. Brace scalloping and final voicing with the box closed is done by tap tones so pretty primitive compared to some of the very sophisticated techniques posted.

I had the luxury of access to some professional ears at the store where I sold and would try to correlate everything with both my impression and the impression of some players I respected after the instrument was finished. Over a period of several years the numbers I currently use seemed to give consistent results.

Just another approach. I think it does take a while to correlate numbers with outcomes and additional ears are good.

IMG_1780 by Terence Kennedy, on Flickr

IMG_1779 by Terence Kennedy, on Flickr

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It's not what you don't know that hurts you, it's what you do know that's wrong.

I use a different method, but I'm told that it's helpful to have the weight go across the top, as Colin's do, rather than being a 'point load'. The top can bend in the crosswise direction with a point load, depending on a number of factors, and that will essentially mean that you're not measuring the whole top, or simply the long-grain Young's modulus, as you think you are. Most of the time this sort of thing won't be a problem, but it can be a big issue when it matters. I use the image of 007 tied in a chair, with the water in the room rising: the depth doesn't matter until it gets to his nose....

By the same token, and for many of the same reasons, it's useful to measure the deflection both ways. It can be different.

I use a vibration test, and the analogous thing to watch for is curvature in the stationary 'node' lines. For 'pure' bending they should be straight, and go across the plate parallel to the ends for a rectangular top half bending along the grain. Often enough they have some curve, or run at a bit of an angle, and then you're looking at a combination of lengthwise and crosswise bending. You have to decide if the deviation is enough to matter, and if so, how to get the 'real' number. In one case a few years back the node lines ran at enough of an angle that they went off the plate at the corners on opposite sides at the two ends. Just plugging in those numbers to the equation for long-grain stiffness gave a very low value for the Young's modulus; less than half of what you'd expect on the basis of the density, but the top didn't feel that floppy. I trimmed the width of the plate down (iirc) and re-tested it. The pattern was fine, and the long grain E value came out just about where it would be expected. That top made a very nice guitar when thicknessed based on the second test. I'll note that if I'd been relying on a tap tone, and could not see the node lines, I might not have picked that up. It was probably a couple between a low-order twisting mode and that bending mode that may not have been strong enough to show up in the spectrum as another peak. Reducing the width would raise the pitch of a twisting mode, but not the bending mode, so the relationship changed and the node lines shifted.

All of this points to the fact that there is no 'perfect' test you can do that will give you 100% accurate values for the things you'd like to know. You need to understand how the test works, how it can generate false, or misleading readings, and where the limits of accuracy are.