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Not a math major but i play one on forums....

Nor am i a luthier, but just a guy with images in his head. So if i am wrong about this, give me one of your guitars so i don't embarass this forum by trying to build one.

Here's an illustration to support Hesh's arguments if i may be so bold. As always is the case, exaggeration is the best teacher.

The image i (hopefully) included has 5 pictures 1-5 from top left to bottom right.

Image 1...
Shows a ~2 inch sphere. If you cut the sphere in half, you have a bowl which is analogous to the radius dish.

There are two slices which equate two two braces positioned differently in the dish. The lighter colors next to the dish represent the actual brace portion of the slice.

Image 2.
if you take slice A and move it to another portion of the disk, say next to slice B, you can see how the bottom of the brace is angled differently, and if i could rotate the slice in paintbrush, you'd see that brace A glued at position B would result in the brace being tilted. Does it matter on a 25 foot radius? For you to decide.

Image 3..
imagine rotating image 1 so that slice A is between you and slice B.

Image 4...
Cut the sphere down to represent the dish and save only the outer edge of the slices to represent the braces.

Image 5...
Slide brace A to where brace B is and you can see that not only is the angle of the bottom of the brace different (from proof 2 - See theorems! visual Math!) but the actual radius is different.



Does it matter? Maybe not.

Is Hesh Correct? Absolutely!

Do i need to build my own darn guitar? probably!

[QUOTE=TonyKarol] All the braces woudl be the same, 15 foot radius .. you can sand them to that int he dish if you like, or plane them ... whatever suits you. I use a bracemaker jig first, then plane them, the bowl is only for sanding the rim and then as a clamping caul.[/QUOTE]

Tony, or someone could you post some pics of a bracemaker jig?  I'd like to find one suitable also for ukuleles whose braces are only about 8 inches wide at most. Thanks

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A higher purpose for wood.
Rich Smith
Issaquah, WA

Rob,

I think that what you have shown is a cylinder, not a sphere, you are missing the third dimension that a shpere has over a cylinder. A radius dish is best imagined by thinking of slicing a section out of a ball (if it would hold it's shape), there is no flat spot anywhere on the object. I agree 1000% with Todd Rose on all that he said and I see it completely in the body of the guitar I have put together. I have made probably 50 radius dishes now and have spent a lot of time thinking this through also. If you sand a brace at any point on the dish it is going to fit in any other place of the dish, as Todd says, move them around and see for yourself! Keeping the braces perpendicular to the plate is a good idea but at the end of the day, you are doing this part by hand and you won't be entirely accurate all of the time, but you should always be so close that you could not tell. Besides, the braces are typically shaped in such a manner that you could never measure it in any regard.

Shane

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Canada

rob, that is not a visual represention of what occurs.

Hesh, all I ask is that you do as I suggested: just take any of your radiused braces and lay them anywhere on your radius dish, and you will find that, no matter where on the dish they were sanded, they will fit the radius of the dish - any part of the dish. If they don't, then either your dish is not spherically radiused, or you didn't sand accurately. We can draw picture or debate this till we're blue in the face, but it is easy to prove - just try it and you'll see.

Where you're correct, Hesh, is about whether they will stand straight up (in relation to the table top your dish is sitting on, which is analogous to the theoretical plane the "dish" of your guitar plate "sits on") or lean one way or the other. [I don't believe this slight lean makes any structural difference, but that's a separate point that I can't prove]. My point is only that you can sand braces to stand or lean any way you want no matter where you sand them in the dish. When you take one of your braces sanded in one certain place on the dish, move it to another place and see that the radius fits the dish there, too, but the brace leans differently, then you'll see that you could have sanded it in that place as well and gotten the same result, simply by leaning it in that way as you sanded it.

I hereby drop out of this conversation.      If you try it, you'll see. I promise!

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Todd Rose
Ithaca, NY

https://www.dreamingrosesecobnb.com/todds-art-music

https://www.facebook.com/ToddRoseGuitars/

OK, here goes my professional reputation...well, sort of. I do have a masters in math, after all, although I've chosen not to work in the field.

Hesh is correct. Rob is correct. And Todd is correct.

There is going to be a section of a sphere sanded on to a brace if you sand it in a dish - so Todd is correct.

That section, though, can be at an angle relative to the flat sides of the brace. Hence, if one were to set a brace in a sphere it might not stand perpendicular to the tangent of the sphere unless it was sanded that way. Thus, if held vertical relative to gravity, a brace will stand up at a different angle relative to the tangent of a sphere if placed in one depending on where it was sanded - so Hesh is correct.

And, in fact, if one sands a brace in different parts of the dish then, taking the front projection (looking at the brace flat-on to one of the flat faces) the apparent 2D radius of the bottom of a vertically-held-when-sanded brace can be anywhere between the dish radius and zero depending on the size of the dish relative to the sphere it is a section of and where the brace was held when sanded - so Rob is correct.

There you have it, my grand unified theory of brace radiusing. You're all looking at the exact same phenomenon from different angles. Maybe I should have gone into physics where unified theories matter :)

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Bob Garrish
Former Canonized Purveyor of Fine CNC Luthier Services

[QUOTE=Dominic] A sphere is a called a sphere because of its symmetry which means anywhere you sand as long as it is at 90 degrees to the tangent it will be the exact same shape.

The only reason to use a different part of the form is to get to fresh sandpaper . [/QUOTE]

That is unless you want the braces to glue up "TRULEY" perpendicular to the tangent intersection of the sphere. Then the angle that the brace is held while sand must be held True-perpendicular to that tangent plane on the sphere. But that is an unneeded practice in 99.9 case out of 100 cases. As someone else said the only case that reall would require this is a very tall brace. Now if wer were talking much smaller radii of sphere then the more critical this would be. but we deal with 15'(180") and 20' (300") radii. That way closer to flat in 20 inches of chord length than it is is to hemispherical.

ups.. i'm sorry.. it seems i started a hot conversation.. but i'm sure these are not lost words. everyone can learn something from others idea. it doesn't mean that you would change your idea but you would consider another point of wiew.

this is how the luthery can grow and be better! thanks to all...

we just have to try and find the personal way!!

i've tried to sand the braces where they will be glued.. with a "strange" result!..

when i took off the clamping bars the back doesn't stay "flat" on the radius dish.. it lift up on the middle...

is this normal??????

thank you

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everything you know is wrong

Yes this is normal because you only have the arc in the lateral direction (side to side) not the longitudinal direction (top to bottom). When you glue the back onto the sides it will all work out just fine.

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[QUOTE=MichaelP] [QUOTE=Dominic] A sphere is a called a sphere because of its symmetry which means anywhere you sand as long as it is at 90 degrees to the tangent it will be the exact same shape.

The only reason to use a different part of the form is to get to fresh sandpaper . [/QUOTE]

That is unless you want the braces to glue up "TRULEY" perpendicular to the tangent intersection of the sphere. Then the angle that the brace is held while sand must be held True-perpendicular to that tangent plane on the sphere. But that is an unneeded practice in 99.9 case out of 100 cases. As someone else said the only case that reall would require this is a very tall brace. Now if wer were talking much smaller radii of sphere then the more critical this would be. but we deal with 15'(180") and 20' (300") radii. That way closer to flat in 20 inches of chord length than it is is to hemispherical. [/QUOTE]

no edit ergggg!!! oops!!!! That should have been 15'(180") and 25'(300")

There has to be a better way to radius the back of a ukulele than trying to manoeuver a 20 2' radius dish over the body of a uke some 8 inches wide and 12 inches long.  Suggestions?

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A higher purpose for wood.
Rich Smith
Issaquah, WA

[QUOTE=ToddStock] The great thing about milling MDF is that if you do it on a hot, humid summer day, you'll look like a 6'2" granola bar when done [/QUOTE]

ROTFLMBO for 10 min. now

been there

[QUOTE=ToddStock]Move the uke rather than the dish. I profile the sides and linings by clamping the ribs in a mold, insert the spreaders at waist, lower, and upper bouts, and use a couple deep reach Bessey Tradesman clamps at the end blocks as handles.[/QUOTE]

Thanks Todd, good suggestion!

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A higher purpose for wood.
Rich Smith
Issaquah, WA

[QUOTE=Ricardo] There has to be a better way to radius the back of a ukulele than trying to manoeuver a 20 2' radius dish over the body of a uke some 8 inches wide and 12 inches long.  Suggestions?
[/QUOTE]

Just make a smaller dish, I have made smaller dishes with tighter radii for mandolin makers who had the same concerns as this.

Shane

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Canada

You guys are cracking me up! Todd, I think you used to be a comedian in a former life. Like Michael, I almost fell out of my chair laughing. Thanks for the laughs, and very good thread.

I always tell people that buy my brace maker jig that they should sand it in the radius dish after cutting it on a table saw, or jointer if they want a sphere on the bottom of the brace. Using a any type of radius shaping jig will not produce a sphere on the bottom of a brace. Todd is correct, the radius is the same anywhere in the dish, and Hesh is correct that if you don't sand in the correct location it will look like it is leaning on you. This leaning can make gluing in a go-bar deck a little more difficult and therefore another good reason for sanding in the correct location in the dish.
Tracy

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Tracy
http://www.luthiersuppliers.com

when i was at benning it was hot enough that i ddn't need any added outside moisture to look look like a vanilla lamington!

[QUOTE=Hesh1956] This is a topic that I have gotten in trouble before when discussing.....but that never stopped me any way....



There are other builders who do this as well and I learned it from someone but can't remember who. It might have been Frank Finichio since I have his very fine DVD set.

AND..... Bolix welcome to the OLF!!! [/QUOTE]

Hesh - That's a good idea and I think I'll try it next time.

Actually, I'm not sure what's on Frank's DVD, but in his class the build is done without dishes at all - braces are glued to plates with cam clamps, after pre-radiusing on a router jig and radiused sanding block.

Welcome Bolix!

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Jim Kirby
kirby@udel.edu

Structurally the only thing you will achieve by tilting your braces away from the centre of the sphere is to change your perfectly quarter sawn brace wood into not quite so perfectly quarter sawn brace wood.

That is, the most mechanically efficient way to get your braces as light and strong as possible is to place the brace with its stiffest grain direction perpendiular to the load it is supporting which in this case is the radius it is forcing the back into. If you tilt your braces you are moving away from this most efficient relationship which means you need to make the braces heavier to achieve your desired stiffness.
Dom

very apt analysis dom.

   These are a few figures that give an exagerated conceptual difference to sanding braces at different angles to the center line(green CL) of the sphere. This is to keep the brace CL(red CL) perpendicular to the top and not to the CL of the spherical form.

    The first figure shows, though the spherical radius is the same, the spherical segment(purple) generated on the brace is not, again to keep the CL of the brace pointing "straight up" in relationship to the finished guitar.



   This figure shows that one can, in fact, as Rod said sand in any place in the spherical sanding dish and generate the same form simply by angling(blue line) the brace CL{red} to the spherical CL(green).



   One can do the opposite by sanding offcenter to the perpendicular CL of the spherical radius and still obtain the proper spherical segment formed on the brace.



   By not sanding as Hesh does what one really gets is a toroidal segment(the outside portion of a donut shape) not conical. This causes the braces CL's to be lined up at angles to the horizontal plane of the guitar, the top facing up.



    Yes the spherical radius is the same, the spherical segment, again, is not! Considering the size of the radius in real terms does it make a difference.... depends on how much you want to put into the guitar. I can do the math in numbers but getting into spherical radius points gets hairy if you don't do it often and I'd have to pull out length and width measurements of the braces themselves.

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Billy Dean Thomas
Covina, CA

"Multi famam, conscientiam, pauci verentur."
(Many fear their reputation, few their conscience)

Billy - Very helpful drawings here, but one correction. As also pointed out by Rob in his also very helpful drawing, the radii of the braces done off of the low spot are indeed smaller. Think of a globe with latitude lines above and below the equator. The braces away from the low spot above are being oriented in the direction of constant latitude, and each circle representing a constant latitude gets smaller (i.e., lower radius) as you move away from the equator. So, these braces, which are oriented along latitude rather than great circle lines, do get a tighter radius as indicated in Rob's drawing.

I'll see if I can crank up matlab and do a table of results for a range of dish sizes. It would be good to have a table available.

Jim

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Jim Kirby
kirby@udel.edu

I was involved in this same discussion a fair while back . Like Hesh ,I radius the braces at their respective areas on the dish .
I was shot down in flames by the other guys so much ,I wish I hadn't mentioned it    

I have given the subject a great deal of thought ,and the only difference is that Hesh's ( and mine) have braces that stand upright ,rather than lean into the centre of the sphere . That is the only difference I can come up with . I wouldn't think that would make them appreciably stronger , but I feel better about it , having them this way .
I'll continue the same method too, but won't mention it again. ,,,,,unless I'm talking to Hesh of course

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CRAIG LAWRENCE of AUSTRALIA
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