Why does lowering string action (without buzzing) cause decreased volume?

I think we are talking about exactly the same thing(y)(y)(y)
I consider it ever so slightly different. The angle the string makes with the bridge is independent and different than the lever effect that is totally dependent on the width/length/distance of the bridge. Lowering at the nut also changes the break angle, but not the lever length.
 
There has been published empirical research by Alan Carruth into break angle and string height.

His experiments find that break angle makes no measurable difference in volume or wave form within a broad range (from memory, 11 degrees seems to be the minimum required), though a higher break angle increases the tilting force on the saddle and thus increases the risk of breaking out the front of the bridge.

By contrast, changing the height of the saddle peak above the soundboard does change volume measurably.

The physics of all this is complicated and somewhat counter-intuitive - for example, the back and forward movement of the saddle doesn't contribute appreciably to the fundamental note but does modify the harmonics of the string, and the soundhole does not 'let the sound out'.

The standard dimensions and angles traditionally used for stringed instruments seem to fall pretty much at the optimum values. This shouldn't be surprising (though it is for those of us who are used to scientific advances) because traditional instrument design is the product of centuries of trial and error, and ought to have been expected to converge on the best solutions. This doesn't mean that new ideas aren't worth trying, but I suspect that changing just one aspect of design (eg a new kind of bridge) while keeping the rest of the instrument the same is likely to produce an instrument which works less well. Radical redesign of the whole (eg resonator instruments, electric guitars) is a different matter of course.
 
when the saddle height is lowered the break angle changes, the break angle determines the downward force on the nut and amount of energy tranmitted to the top, the lower the break angle the less force is applied to the nut, the less energy transmitted to the uke top. Depending on how your strings are attached (through the top) the break angle may be able to be adjusted. Slots are cut in the bridge to allow the string to exit through the top at more of an angle. here is a photo from Beau Hannams Insta gram site showing the slots I mean. https://hazeguitars.com/blog/acoustic-guitar-tone-and-string-break-angle a better explaination.
THANK YOU!!! Makes total sense. The normal force ofc goes as sine of break angle and the tangent forces don't get you much sound
 
I believed it was all break angle but it appears not, I found this reply to break angle question on Australian/New Zealand Luthiers Forum. Scroll down to the reply by Trevor Gore ((10th or 11th reply) those that dont know of Trevor, he wrote a/the book on thisstuff) and its all pretty much there (and more) and mentions Alan Carruths findings.
http://www.anzlf.com/viewtopic.php?t=7647
 
I have an Island Style soprano Ukulele from the 1930s with a bridge only 1/4 inch high no seperate saddle, no fret board , and it sounds as loud as any other ukulele .
 
I have an Island Style soprano Ukulele from the 1930s with a bridge only 1/4 inch high no seperate saddle, no fret board , and it sounds as loud as any other ukulele .
My Kumalae of the same vintage has a taller bridge, and is louder even than my Timms - those Island ukes of the time are built scary light!
 
In short, less force is exerted on the saddle by the strings the lower the action is which compromises how much
"power" from the strings is driving the top... and by that I really mean the break angle of the strings behind the saddle.
Note
1- You can have a high action and low saddle (with no string break angle behind the saddle)
2- You can have a low action and low saddle (with no string break angle behind the saddle)
3- You can have Perfect action and low saddle (with no string break angle behind the saddle)
4- You can have high/low/perfect action with High saddle, which gives more power to the top due to better break angle over the saddle but this can cause the front of the bridge to break due to to much stress.
Hence- get the neck angle correct so you have Perfect action with perfect saddle height all which gives perfect string break angle behind the saddle which gives the best comprimise of "power" to teh top and the front of the bridge not cracking.
 
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