Bridge torque v flexural rigidity

[garryalb]

Hi all,

I have recently acquired a set of "the book" and after a revision of math 101 and learning how to use spread sheets I am getting results from the equations related to monopole mobility, target thickness and flexural rigidity / parallel axis. I am planning some design work using string tensions other than those mentioned in the book. Bridge torque is easily calculated if you know string tension and saddle height (page 3-7). Standard classic strings give ~5 Nm and steel 12s ~10 Nm. Target ELs for the braced board are given for classical as 15 Nm^2 (page 4-40) and falcate steel string 45 - 50 Nm^2 (page 4-43). My question is how do you arrive at a target EL for a given bridge torque / string tension, I have been unable to find an equation for the relationship of these parameters. Any help anyone can offer would be greatly appreciated.

Thanks,

Garry.

P.S. Thank you so much Trevor and Gerard for putting these books together. As someone who has been building guitars for many years using the "suck it and see" method it is truly great to have the tools to engineer a structure before building. I'm sure all of us that have the books appreciate the enormous effort you have put in. Thanks again.

[Trevor Gore]

Hi Garry,

First, we're talking about EI (flexural rigidity) not EL, which is usually Young's Modulus, long grain.

On page 4-44 there is a graph showing EI for a falcate braced guitar (~45Nm^2), strung with 12s (so you know the torque), for a 2 degree bridge rotation. Keep in mind the 2 degrees rotation and you should be able to figure it from there.

[garryalb]

Hi Trevor,

Thanks for the reply.

Yes, sorry, EI (flexural rigidity) is what I am asking about. The question is, how would you relate bridge torque to EI for an instrument with significantly higher torque, say a 12 string or lower torque, say a uke to result in around 2 degree rotation? I would guess you would also have to consider how balanced the bracing layout is forward and aft of the bridge.

Thanks again for your time,

Garry.

[DarwinStrings]

G'day Gary, not Trevor here. I am just trying to nut through the EI stuff now.

It looks like Trevor has measured finished instruments that satisfy the 2 degrees and worked out the necessary EI value from them. So maybe you need to find examples of 12 strings with 2 degrees rotation or set up a dummy then work out its EI once you have carved enough brace to get to 2 degrees.

Jim

[garryalb]

Hi Jim,

Thanks for joining, great avatar mate!

The more I look at the variables required to predict an EI for different torques for the entire soundboard the more complicated it becomes. I am sure you would have to consider the balance of the structure, the length of the active part and bridge position along that length. I could measure an instrument with similar tension and correct rotation but without knowing the modulus of the parts it would only give a rough indication. A test board could be made up and may be a good option. I am not working on a 12 string, that was just an example. I am back on my long obsession with acoustic bass guitars, the first one built in 1989. One problem with designing is that different types of strings have very different tensions over the same scale. One method of compensating could be to simply change saddle height for different string tensions. The maths tells me the difference would be 4mm in height to get the same torque for the lowest to highest tension sets.

How are you going with calculating EI for an entire structure? If you have the equations set up in a spread sheet perhaps we could check each others results.

All the best,

Garry.

[DarwinStrings]

For me I will only be looking at that section 50mm forward of the bridge rather than the whole structure. I have started my fourth falcate and the method described suits that form of bracing plus I am happy to continue that bracing pattern. No spread sheets so far but I am getting there, will get back here when I do.

Jim

[DarwinStrings]

So I have been scribbling on paper, but still not sure if I have a grip.

I decided to try the maths without a thought to the CF tow and see if I got a answer that looked reasonable, still not sure if the answer looks reasonable cause if I increase the answer I got of EI = 23.28 by 26% (from the table on page 4-47) it doesn't get near Trevor's figure of 45-50. With that sized braces, top and E I get about 1.3 degrees of rotation. So am a bit confused still but not finished.

Here is a look at what I did (after a few attempts) and I am not sure if I have worked the formulae properly, I'm doing quite a bit of head scratching so will do a nit comb this evening just in case.

613.JPG (67.32 KiB) Viewed 20985 times

612.JPG (85.29 KiB) Viewed 20985 times

Jim

[garryalb]

Hi Jim,

Wow you're keen, all that by hand! I have never used spread sheets but it didn't take long to learn (though I'm not sure if the equations are working correctly), you can download open office free. The great advantage is being able to plug in different variables and see the result immediately. I ran your number and came up with similar results to yours, but I really don't know if that means anything. If you change the variables to a soundboard @ 330 X 2.8 (the width of Trevor's design 50mm in front of the bridge) and 4 braces @ 5 x 7 all with a modulus of 11.9 GPa the result comes in at 45 Nm^2. Not sure if this is how Trevor is calculating this but perhaps someone else will give us a clue and run the numbers to confirm.

How have your falcate guitar come out? Are you using the target thickness equations, Trevor's design and cf braces?

Garry.

[garryalb]

Sorry Jim,

I actually had 7.2mm height for braces in the spread sheet for a total result of ~ 46.6 Nm^2 (too late to edit)

[DarwinStrings]

I have Excel Gary and use it for top thickness etc but like the top thickness stuff I like to try to get a grip on the maths by hand before I go to the spread sheets.

When I look at my design the secondary falcates don't really get to the 50mm mark (well maybe there is 0.5 - 1mm of them max at that point) so I just used the two main falcates in my equations.

I am very happy with the results of the two finished guitars so far but they still have room for improvement and I didn't use the flexural rigidity stuff for them so am working the brace size down on each guitar, the last one had 7mm mains and the one I am building now I have gone down to 6.4mm and hope that will get me closer to 2 degrees. The reason I attacked the flexural rigidity stuff is cause I want to make the same guitar in nylon strings and would like to get closer to what I want on the first try.

I use my own design that is a "parlour" (pic and sound clip in the Gallery of the first one) with a 320mm lower bout and 460mm long body and I do use CF tow as removing creep is a objective for me living in high heat and humidity cycling.

I am still a bit unsure of the CF in the equations other than to increase EI by 26% which is Trevor's closest match in that table (for 1 strand of 3K tow)

Jim

[garryalb]

Hi Jim,

Just had a look and listen to your lounge guitar in the gallery, great job, sounds fantastic. I'd be interested in your thoughts on the tornavos and design of the tilt neck, is there any other info available?

Garry.

[DarwinStrings]

PM sent Gary.

Jim

[Trevor Gore]

Sorry to take so long in getting to this, but I think you have sorted it out amongst yourselves. Well done!

For a falcate braced guitar, I do the EI calc. using the soundboard and 4 braces (primaries and secondaries) as the torque resisting structure. The idea of measuring 50mm in front of the bridge is so as to make the calculation tractable without the complexity and expense of using FEA. The method seems to produce meaningful and comparable numbers. For example, the koa guitar I built recently used this method and came out exactly as planned.

The EI calc is about getting in the right structural ballpark so that you avoid a roller-coaster soundboard. Some people people argue that roller-coaster soundboards sound better. For example, this was the motivation behind the Redgate "wave" top, but that, of course, is just someone's preference. There is no doubt that fine sounding guitars can be made without highly distorted tops.

The important things from an acoustical point of view are getting the monopole mobility in the right ball park, as this relates to loudness and responsiveness, and getting the modal resonances in the right places for the type of guitar you are building. The EI numbers I recommend are compatible with that, of course, but the 2 degrees of bridge rotation is just a number for guidance (you don't hear it), whereas you do hear changes in monopole mobility and modal resonances.

[DarwinStrings]

Cheers big ears.

Jim

[DarwinStrings]

Hi Trevor, am still on this one. What thickness do you assume for the CF tow please.

Jim

[Trevor Gore]

I measured... ...

0.1mm.

[Nick]

An Engineer never assumes Jim, that's why they invented measuring equipment

[DarwinStrings]

I couldn't work out how to get my rule between the brace and the top, also the bloody thing only goes down to half a mm.

Jim

[charangohabsburg]

An Engineer never assumes Jim, that's why they invented measuring equipment

Well, that's only half the truth. The other half is that for an engineer 3x3 = Pi² = 10