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Why is the back plate arched?

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I tried to find answers on the web, but zero. For the belly I don't have doubts, the arching makes sense because it copes better with the bridge pressure. But for the back, I still don't understand why it is not flat. Is it a matter of sound projection?

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I think this is a great question! There are certainly successful flat-backed basses, and at least one Strad cello which used to have a flat back.

I think the flat backed basses have internal horizontal bracing, like a guitar. It seems this would achieve a similar function of stiffness, to an arch, but I don't know.

M

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Structural integrity of the entire structure, a small but crucial increase in air volume and other stuff related to non static dynamic interactions that create pumping action.

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I used to think that the back's shape should be parallel to the top--it should be concave rather than convex as viewed from the outside.  I thought this would make the back withstand the force from the sound post better--the wood be mostly in a compression stress state across the grain where it is strong rather than in tension where it is weak.  Sort of like a concrete river dam where the water pressure puts the concrete into compression.

 

I made some violas this way but I failed to increase the rib height to maintain the same internal volume necessary to keep the same A0 frequency which players were used to.  I also received insulting comments from fellow makers like --Oh wow you dumb shit.  You glued the plate on backwards!

 

Rather than explaining this idea over and over again I just gave up and just started making the back plates perfectly flat so it didn't make any difference which side was glued to the ribs.  This has a whole flock of advantages--it saves a lot of wood (much cheaper) and the all the labor time to hollow it out and so on.  A flat plate is less stiff than an arched plate so its  resonance modal density is higher which in turn I believe makes all the notes more even in loudness and character.

 

However the most important advantage is that when you set the instrument down on its back it's quite steady.

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Interesting to note that there are a lot of almost flat backed mandolins out there. Many of them have good tone and plenty of volume, not to mention twice as much string tension. But since most mandolins have what amounts to two fairly thick bass bars, I agree that structural integrity is the answer. 

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An observation, at least, suggests building in flexibility.  The combination of outline with cross and longitudinal arching makes for more complexity than I can keep in one mental image.

 

Long arch: Neck block and end block have couples rotating towards bridge.  Post is pushing down.  Stiffest back would be flat sections from post to each end block.  Putting in curve gives flexibility.  

 

Cross arch:  Same thing, if ribs trying to move apart, then S bend gives flexibility.

 

I can draw pictures and arm wave.  Probably a great deal more plays into it, but the flexibility of the shell in various directions seems intuitively important.

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An observation, at least, suggests building in flexibility.  The combination of outline with cross and longitudinal arching makes for more complexity than I can keep in one mental image.

 

Long arch: Neck block and end block have couples rotating towards bridge.  Post is pushing down.  Stiffest back would be flat sections from post to each end block.  Putting in curve gives flexibility.  

 

Cross arch:  Same thing, if ribs trying to move apart, then S bend gives flexibility.

 

I can draw pictures and arm wave.  Probably a great deal more plays into it, but the flexibility of the shell in various directions seems intuitively important.

That's what I thought too.  The string tension puts the back into longitudinal tension.  The stiffest back shape in that direction would be a straight section with no longitudinal arching.

But its not clear to me if we're supposed to be designing for flexibility or stiffness.

 

If you add a cross arch to the back you end up with a wavy edge sort of like a potato chip which makes fitting it to the rib an interesting challenge.

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This might be naive but I thought in part the curves might have to do with focusing the sound toward the f-holes for better projection.

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This might be naive but I thought in part the curves might have to do with focusing the sound toward the f-holes for better projection.

That's what I thought, and also, maybe the sound post is more stable if the back is arched?

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That's probably not how it works but I'd love to hear a soundclip of Marty's flat back violin, just out of curiosity.

All my flat plate instruments have been violas. 

 

I'll start making my first flat top and back violin next month.  It will probably take several more tries to work out the plate thicknesses and shape before they're better than a typical Strad or DG.

 

Unfortunately it will feel quite different so it will not be possible to do a unbiased blind playing test with it.

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 The internal space needs to be a certain shape in order to create the right quality of sound.

 

... and how have you determined this?

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Why are turds tapered?

Not all turds are tapered.  So the question should be why some are tapered and why some aren't.  I always wondered why horses make horse balls and cows make cow pies even though both eat the same grass.

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