Scale length vs String tension vs Bridge rotation vs Brace height

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AKEric
Myrtle
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Joined: Fri Sep 28, 2018 1:29 pm

Scale length vs String tension vs Bridge rotation vs Brace height

Post by AKEric » Fri Oct 29, 2021 4:24 am

Hello to all,

I have a friend who wants a smallish guitar with a short scale length. The body size straddles the line between how Trevor defines small and medium. It’s on the large side of small and small side of medium. The scale will be 24.9” (632.46 mm).

My three falcate/live back guitars so far have been solidly in the middle of medium size with a 650 mm scale. All landed within the target frequency ranges, and I think they sound exceptional (thank you again, Trevor, for sharing your path to a successful guitar). In all three, the bridge rotation came up short of the 2 degrees recommended (1 to 1.35), but as Trevor has said in this forum, the rotation won’t make or break a good guitar. I laminate braces out of Sitka, and I experimented a bit with the max brace height. (6.1, 6.5 & 7.1 mm) to see how this might affect the finished frequencies.

With this smaller guitar, I should be able to brace it a bit lighter because the string tension will be some degree smaller due to the shorter scale length. Lower brace height, however, could bring the top’s (T(1,1)2) target frequency down too much. Using a similar brace height from above would most likely deliver even less bridge rotation. It seems like a catch-22 to me.

Is the difference in string tension between 650 and ~632 mm scales enough for me to be concerned with this? Something I'm not seeing?

If anyone has some insight on this, much appreciated.

Eric

seeaxe
Blackwood
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Location: Auckland NZ

Re: Scale length vs String tension vs Bridge rotation vs Brace height

Post by seeaxe » Sat Oct 30, 2021 12:09 pm

From the interweb
https://www.vedantu.com/question-answer ... 705c7c9db5

The formula for frequency of the string is v=(k/L)*(sqrt of (T/m)), where k is a constant. m is mass per unit length of the string, so assuming you are using the same strings, solving for the tension at a scale length of 632mm.,
T632 = T650* 632 squared over 650 squared or
T632 = 0.945*T650.

So its about 5% less tension.

Are these steel strings? 650 scale length is normal for a nylon string classical. I'm interested in your brace height as I used 10mm high for my classical (which has about half the tension of a steel string) Predictably I got very little bridge rotation but the monopole mobility number was pretty good. Nevertheless I ended up with a very dull top E string. (Not sure thats down to the bracing, yet) Was going to reduce the braces a bit on the next falcate
Richard

AKEric
Myrtle
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Joined: Fri Sep 28, 2018 1:29 pm

Re: Scale length vs String tension vs Bridge rotation vs Brace height

Post by AKEric » Tue Nov 02, 2021 4:15 am

Thanks for the reply Richard. I guess I'll keep things about the same as my other builds. These are steel sting guitars, and the 6 to 7 mm brace height has worked well for me using Sitka spruce.

Eric

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