break angle and string tension

[HonketyHank]

Is the following approximately correct?

Downward force on mandolin top = (approx) sine of the break angle over the bridge times the string tension

As in this doctored photo:

[O. Apitius]

I'm not a mathematician but it seems to be correct.

[Tom Haywood]

I don't remember where I got this. I put it in a spreadsheet used it in the design of 2 mandolins and a bouzouki, and the results seemed to be close to the predictions. I'm not a math whiz.

F = 2Tsin(a/2)

F = Down force on top; T = String Tension; a = break over angle behind saddle in degrees.

[HonketyHank]

Tom, if my memory of the sine curve is correct, sines of small angles are very close to linear. Less than twenty degrees I think your formula and mine are pretty close, at worst to two decimal places. Under six or eight degrees to three places or better.

Here's what got me to thinking about this. I just acquired a 1905 Gibson H1 and I am exploring string choices. I am concerned a bit about overstressing the top by using medium or heavy mandola strings. Respected folks here have warned that early Gibson mandolas are susceptible to top failure. This one appears not to have had any sinkage.

Some observations:
A. My 1905 H1 has a scale length (2 times distance to 12th fret) of 16.75". Gibson mandolas went to 15.75" scale at some time before 1910. I think D'Addario uses 15.875" as a scale length when calculating string tension on mandola sets. Getting the same note from a 16.75" string and 15.875" string requires about 11% or 12% more string tension.

B. Gibson went from a very shallow neck angle to a more significant neck angle sometime between 1907 and 1909 as best I can tell from Fox's book. This allowed a greater break angle producing more downforce on the top. This change also required a taller bridge. My H1 has a break angle of 7 degrees. My F2 has a break angle of 16 degrees. My modern mandolins have break angles pretty close to the F2 (eyeballed but not measured). The down force on the top of the mando through the bridge with a break angle of 7 degrees is about 44% of the force generated at the same tension with a 16 degree break angle.

C. Fox states in his book that he could not find a Gibson mandola to measure prior to 1910, so I presume that they are relatively scarce. Thus I further presume that the observation that top failures are not uncommon in older Gibson mandolas refers mostly to post 1910 production.

D. Taking into account the different scale and break angle for the pre 1910 and the post 1910 mandola production, I figure that the same string tension produces only about 50% of the downward force on my H1 compared to a post 1910 Gibson mandola.

E. Finally, a big if, if the tops of the pre and post 1910 mandolas are carved to similar specs, I don't have to worry too much about overstressing the top of my H1. That would mean I have a lot more freedom to try different strings to try to get the sound I want.

Does this make sense?

[rcc56]

The string tension for a given note will be higher with a 16.75" scale than it is with a 15.875" scale.

I may be wrong, but I do not believe that bridge height has that much effect on top tension. An example of how this works is as follows: If an instrument that is tuned to standard pitch is set up with an adjustable bridge and you lower the bridge, the instrument will go flat and you'll have tighten the strings to get them back to standard pitch.

I still counsel avoiding the use of heavy strings on your instrument. The heavier strings may sound great, but if it caves, you'll be unhappy. The instrument might hold up fine, it may not. My crystal ball doesn't work very well these days. But it's a gamble.

I do know that I've seen quite a few old Gibson instruments that have suffered from being over-strung. A badly bowed neck can be repaired, but it can be a costly job, sometimes requiring removal or replacement of the fingerboard. Repairing a sunken top usually requires opening up the instrument and reinforcing and/or re-bracing the top. This may have a significant effect on the instrument's tone. Most of us who work on these old instruments really don't like to open them up- it's a difficult job and the risk of collateral damage is fairly high. Mandolins and guitars are not nearly as easy to take apart as violins, and violins are tricky enough.

In the past, one forum member has made a big deal over "set A is only 8% higher in tension than set B, so don't worry." The problem with that kind of thinking is that if set A is only 1% above the maximum the instrument can stand, the instrument still fails.

I hope you will treat your instrument gently. She's older than any person I know of.

[HonketyHank]

rcc56, I am glad you have responded. I agree that string tension will be higher with the 16.75" scale compared to 15.75" or 15.875", if they both have the same break angle going over the bridge. Here's a photo of my H1 just like the above photo (of a later year F2). I am kind of assuming that the teens F2 has a similar if not identical break angle as a teens H1. I don't know that, just a guess. But if it does, that higher break angle increases the down pressure quite markedly on the teens model.


compare this to the F2 photo above (note, there is a typo in the text in the photo - the sine of 7degrees is 0.122)

And I guess I need to also ask if you have seen any H1s or H2s with this very low break angle having a top failure. Everything I have been pondering centers on the possibility that maybe those low bridge models could withstand more string tension than the ones with higher fixed bridges (or adjustable bridges).

[gtani7]

I would also avoid doing science experiments on a vintage instrument. There's lots of threads in other forums about breakover angle on Gibson electric guitars (and others w/Nashville tailpiece) and banjos. On those it's easy and relatively harmless to take the tailpiece way up or down. In the reso world, people are putting higher bridge inserts into their spiders to get more break angle

https://www.stewmac.com/How-To/Onlin...eck_angle.html

[Tom Haywood]

I'd like to know what gauge strings are on it now. The top looks to be well shaped in the photo (assuming it is tuned up to pitch), with maybe a little flattening. I think down force is a useful measure in the design, but after that it is a question of how the instrument actually responds to the force over time. I would start by observing how much the current strings are depressing the top now. Then a decision about how the top might respond to heavier strings. If heavier strings are put on it, I would would watch it very closely for several weeks (starting immediately) to see if the top is depressing differently. Any greater depression than it currently has would be a serious red flag.

I don't have any experience with the H1 but, generally speaking, I suspect Gibson increased the neck angle and thus the bridge height to to get more volume and better playability. Most of the Gibson instruments I've seen are overbuilt, so I'd be kind of surprised if they increased the top thickness, but that is just a guess. Also, break angle and down force are determined largely by the distance from the saddle to the tail end of the top, having the saddle within acceptable height ranges. I suspect Gibson did not change that part of the design, again just a guess. Comparing it to a mandolin that has a much shorter after-length distance, and therefore different structural support concerns, seems to me to have limited value.

[rcc56]

I have seen a couple of very early Gibson mandolas, but I haven't had one on the workbench.

It's been many years since I studied physics, and I haven't looked up the math, but something tells me that there is another variable in the equation that is not being accounted for in your calculations.

I do know that I have worked on a lot of old Gibson mandolins, and I have seen enough bowed necks and distorted tops that I prefer to err on the side of caution.

The last victim I had on the bench was a 1912 Gibson A that had a badly warped neck. I had to remove the fingerboard, straighten the neck, re-glue and re-profile the board, and do a compression re-fret. About $600 worth of work.

If you do use the heavier strings, I would follow Tom's advice and watch the instrument very carefully.

[HonketyHank]

Well, I certainly agree that it is best to err on the side of caution. I wish I could think of a way to get an idea of the amount of top deflection under load using tools I have at hand (basic household woodwork tools). I do have a cheapo digital caliper that claims to be good +/-0.001". But my impression is that the deflection under load is "not much", but I don't know what is a lot or a little. The photo shows it with GHS PF280 strings which are "bright bronze" (which I think is 80/20), 12-24-34-48. The calculator at https://wahiduddin.net/calc/calc_gui..._from_size.htm gives a total string tension of 189 lbs at 16.75" scale for these strings.

I re-thought the geometry problem eliminating any reference to the F2 geometry (just calculated what would the break angle be on my H1 if I went from my current string height off the top to 0.70"). That came out to a break angle of 12 to 13 degrees. At a given string tension, that still has to increase the down force on the top considerably.

In the end, this has been an interesting thought experiment for me. I think I can say that as long as I stay somewhere in the ballpark of the PF280's in string tension, say under 200#, I should be OK. FYI, the D'Addario EJ72's calculate out to 203# and the EJ76's calculate out to 228#. I like the tone of the GHS strings except for the C string, so I might try the EJ72, C strings only, to see if that gets the tone more like I want.

And like you guys said, err on the side of caution.

[rcc56]

I just looked up the string gauges of the sets you mentioned. The PF280's will probably be OK. I use a 20 or 22 and a 32 myself. I don't think moving up to a 49 will hurt anything. But I would definitely stay away from the EJ 76 set.

[Tom Haywood]

Hank, I ran your numbers through my calculator. What it shows is the following: If you currently have a 7° break-over angle and 189 lbs. of string tension, then the down force on the top is 23 lbs.. You have a photo of the deflection that it creates. Keeping the break angle and increasing the string tension to 203 lbs. results in 24.8 lbs. down force (1.8 Lbs. increase). Going to 228 lbs. tension yields 27.8 lbs down force. Raising the break angle to 12° with your current strings results in 39.5 lbs. down force. I agree with you and Rcc56 that adding 1.8 lbs down force is probably OK. Going to 228 lbs. tension would add 4.8 lbs which is a 21% increase of force on that old top. It might be OK, but I might not want to risk it. Increasing the break angle to 8° with the current string tension yields 26.4 lbs. down force, and 9° yields 29.7 lbs. (29% increase). etc.

In reality, these calculations are only somewhat close approximations. It's hard to get completely accurate numbers for the break angle and the other geometry measurements.

[Steve Sorensen]

This seems like an extremely misguided series of questions and answers to me.

The real questions are,

1. What are the strings which most closely match those that Gibson recommended for the instrument at the time?
2. What are the strings that players used at that time to get a tone and response which generated the desired musical response?
3. How can you maximize the inherent strengths of the instrument by best matching those historic parameters?

No real questions of musical responsiveness for instruments created for a previous generation are ever answered by math.

These instruments were created when the mandolin family instruments were the most popular, wide selling, trend-setting instruments in the nation . . . trust that what generated their form and use at the time were the real forces to be considered when bringing them back to life.

Steve

[DougC]

This seems like an extremely misguided series of questions and answers to me.

The real questions are,

1. What are the strings which most closely match those that Gibson recommended for the instrument at the time?
2. What are the strings that players used at that time to get a tone and response which generated the desired musical response?
3. How can you maximize the inherent strengths of the instrument by best matching those historic parameters?

No real questions of musical responsiveness for instruments created for a previous generation are ever answered by math.

These instruments were created when the mandolin family instruments were the most popular, wide selling, trend-setting instruments in the nation . . . trust that what generated their form and use at the time were the real forces to be considered when bringing them back to life.

Steve

I could not agree more. I work on violins and see similar 'thought experiments'. And they most always result in disaster if actually applied.

[HonketyHank]

I agree. Pure math is perfect. Applied math tends to be messy.

[Tom Haywood]

Extremely misguided answers? Well, ok then, maybe you could offer some real guidance.

1. What strings did Gibson recommend for the H1 in 1905? I can't find that information anywhere. So, how would I determine which modern strings most closely match the originals?

2. I like the idea of discovering what musical response the actual players of the H1 in 1905 desired. I just don't know how to do that since most (if not all) of the players are no longer alive to ask about it, and there is no way to determine the reliability of what little may have been written down. Frankly, I've never read anything along those lines from that time period, although I've looked in relation to the mandolins.

3. How do you know the historic parameters and thus maximize the inherent strengths of an instrument without considering in some way the physics of it's geometry?

Absent this information, is physics not a legitimate tool for informing this decision? I'll agree wholeheartedly that it shouldn't be the only tool, but I fail to see the misguidance if it helps prevent overloading the top of a 114 year old instrument. I have a hard time understanding how determining the down force on the top is a "thought experiment" that will more likely cause rather than prevent a disaster.

[Marty Jacobson]

rcc56, I am glad you have responded. I agree that string tension will be higher with the 16.75" scale compared to 15.75" or 15.875", if they both have the same break angle going over the bridge.

That's two different things. Break angle has no effect on string tension, it affects downforce only. So you can have high string tension and little or no downforce, or low string tension and a lot of downforce (like bowlback mandolins).

Also, downforce on the bridge is a small part of the equation. Glue joints at other places may fail, or you may end up with unplayable neck deflection, before the downforce on the top becomes an issue.

[j. condino]

17 posts and not a single mention of the string afterlength between the bridge and taipiece.....

[HonketyHank]

That's two different things. Break angle has no effect on string tension ...

I agree. Don't know what I was thinking when added that if-clause.

[HonketyHank]

17 posts and not a single mention of the string afterlength between the bridge and taipiece.....

Will measure it tomorrow.

[O. Apitius]

I assume that the "afterlength" tension would increase as break angle increases. That extra downward force has to come from somewhere.

E. Finally, a big if, if the tops of the pre and post 1910 mandolas are carved to similar specs, I don't have to worry too much about overstressing the top of my H1. That would mean I have a lot more freedom to try different strings to try to get the sound I want.

Does this make sense?

Yes, that's a big if but your logic seems sound. (no pun intended) If it were me, I would put the strings on it that I liked, within reason, (It's probably best to avoid modern strings designated as "heavy" or any set that will result in a downward force in excess of say, 45 lbs..) keeping a very close eye on any deformation of the top. I would check very often the first day and then less so as time goes by, removing the strings at the first sign of any trouble. Granted there is still some risk in this approach but the option is playing a set of strings that you're not satisfied with. It would also be a good idea to monitor neck bow/relief whenever increasing the string gauges. The ultimate decision is yours of course.

Modern mandolins and mandolas are built with an expected downward force of about 35 - 45 lbs. You could do the math to determine if your desired string set falls within that range. Of course, this assumes that your 1905 H1 is built to the same graduation specs as later mandolas with steeper break angles, which is not necessarily the case.

[O. Apitius]

That's two different things. Break angle has no effect on string tension, it affects downforce only.

Technically, break angle will increase the total string tension. The vibrating length tension will remain the same of course but the "afterlength" tension will increase with a steeper break angle.

[rcc56]

When I first got my Gibson mandola, I bought an off the shelf set that had a .014 first string and a .024 second string. I don't remember what the third and fourth were. After a short period of time, the top started to sink and I pulled them off immediately. I have used 12-20 or 22-32-49 ever since and the instrument sounds good and has remained stable ever since.

A good set for Gibson oval mandolins is 10 1/2-14-24-40. I've never seen an old Gibson develop problems with either of these sets as long as the top brace was not loose.

I haven't crunched the numbers on these sets. I prefer to rely on observation and practical experience.

These old-timers tend to be a bit more delicate than a well made modern instrument. They seem to hold together better if they are treated gently.

[ProfChris]

If you want to monitor changes in top deflection then you could take a piece of board and cut away enough of it so your mandola fits in the opening. Glue on a couple of sticks to touch the top either side of the strings just in front of (or just after the bridge). When those sticks are resting on the top, mark with a pencil where the rims of the mandola come to on your board.

Something like this, but used the other way up: |__________|___|____________|
I guess you could just glue 5 strips of wood together rather than cutting a board.

Now you can just place this device on top of the instrument and see where the pencil marks are. If level with the rims, the top hasn't moved. If lower, your top has sunk.

[HonketyHank]

17 posts and not a single mention of the string afterlength between the bridge and taipiece.....

4.38" from back of bridge to first contact with tailpiece. Actual lengths will of course be different for the different strings due to compensation cuts on the bridge and differing angles from centerline.