How to make a Radius Dish

Dave Higham

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Radius dishes are fairly expensive to buy and very messy to make if you make them, as most do, from MDF using a router or sander and dedicated jigs. Here is another method of making a dish which is cheap, clean and easy and you don’t even need a router so you don’t need to make jigs. The only disadvantage I can think of is that it involves a little math, although if you have a CAD programme you can even avoid that. I should mention that this is not my idea. I saw something similar a long time ago on another forum but I can’t remember where or who posted it, otherwise I’d give him credit.

What this method involves is forcing a thin sheet of MDF into a spherical dish by screwing it down to a heavier rigid base with a series of spacers between the two. Here’s a drawing of a section through the dish showing what I mean.
Radiusdishcalculation.jpg


Using the formulae you can decide how many spacers you think you need and at what radii (r) and calculate the thickness they need to be using the second formula. If you have some strips of wood that are close to the required thicknesses, you can use the first formula to calculate at what radius to place them.
If you have a CAD programme you just draw it out and the programme will tell you how thick to make the spacers or where to place them.

So having done the math, I prepared the materials and this is what they looked like.
A piece of 1¼” particle board (offcut from a kitchen worktop). 16” diameter seems to me to be big enough for any size of ukulele.
A piece of ¼” MDF
Strips of wood for spacers
Woodscrews
Dish1.jpg


I taped the strips together and marked them at 1” intervals, then drilled clearance holes for the screws in the centre of each section.
Dish2.jpg


I then sawed the strips down the middle (the brass rod was to line them up, I didn’t saw through that!).
Dish3.jpg
 
The strips were then sawn into separate pieces.
Dish4.jpg


The base board was then marked out for the positions of the spacers (12 on each circle seemed to be enough) and pilot holes drilled for the screws.
Dish5.jpg


I stuck the spacers down using thin CA (Zap)
Dish6.jpg


Here they are all glued in place. Note that the inside edge of the spacer is placed on the circle where the MDF disc will make contact when it is screwed down.
Dish7.jpg
 
Clearance holes for the screws are drilled and countersunk in the MDF disc. Make sure the screw heads are below the surface. I then put a blob of glue on each spacer, positioned the disc and screwed it down, starting from the centre. Here it is, finished with a piece of wood placed on it to shown the curve.
Dish8.jpg


If you were worried about the dish flexing under pressure from go-bars, for instance, a few blobs of strategically placed ‘Bondo’ (car body filler) before screwing the disc down should make the whole thing solid. Just make sure you get it screwed down before the Bondo hardens!

Some people have made a similar dish by using one spacer in the form of a ring around the outside edge and one screw in the centre of the disc, but this doesn’t give you a spherical form. This drawing shows the difference. The red shape is circular. The green shape is a spline curve which is tightest in the middle and flattens out towards the ends.
Radiusorsplinedish.jpg


This shape can be used if you want to make tops or backs that are only curved in one direction and instead of a dish you make a ‘trough thingy’. In fact it’s the logical shape to make for that sort of top or back, as it’s the shape the wood takes naturally if you flex it. I made this one for an acoustic bass guitar with a deep curve on one side, for the back, and a shallower one on the other for the front. The intermediate spacers were just pushed into place and glued to make the whole thing more rigid.
Acbass004.jpg
 
Nice photo documentation indeed. And the CAD images are great too. A little more time consuming than other methods but much cleaner and healthier than having all that mdf dust in the shop. Thanks for sharing.
 
Very nice tutorial and great photos and drawings. Concerning whether you get a spherical shape when you use a ring, would you get a parabola instead? I presume the purpose is to focus the sound, so a parabola may actually work better ( more likely about the same) if you build it with the focal point in the right place. I have no idea where the right place is for a ukulele's sound to be focused. I am planing on a flat bottom for my first build, but think your method will be the one I use for my first disc. Thanks.
 
My pleasure. Sharing is what makes great forums.

I'm not sure myself what the difference is between a spline curve and a parabola, except that I seem to remember that a parabola is what you get when you take an off-centre vertical slice through a cone. I wouldn't worry too much about 'focussing the sound'. I dont think that's what domed or arched fronts and backs are all about. The problem with a circular dish made with an annular spacer around the edge and one screw in the middle is that the shape changes at different positions on the dish. So, if you stick sandpaper to it and rub your braces on the surface to profile them you're not going to get the shape you want.

Difficult to describe but in this drawing, the brace is the same shape as the dish.
Splinedishproblem1.jpg


But if you move the brace, it doesn't fit the dish any more.
Splinedishproblem2.jpg


So if you're making a domed front or back, rather than an arched one, a spherical dish is better as the shape is the same wherever you are on the dish.

One of the problems with making arched tops or backs is that, for the braces to fit the arch properly, they have to be sanded by holding them in the position they will be in once installed, and rubbing longitudinally in the trough (if you see what I mean).
Braces.jpg
 
Been said before david... however: the whole purpose of an arch is to strengthen and avoid sinking. It's why many Asian ukes have sinking fronts - no arch. The fix - fan bracing on Kiwaya sopranos which of course, kills some of the sound!

Although I cannot undertsand why Martin fronts, flat built, stand up.
 
Thanks for explaining Pete. It's true that it's been said before but that's the nature of forums. There's always someone new coming along (good thing) and asking a question for the umpteenth time (less good). Some forums like the MIMF have extensive libraries or archives of past discussions and newcomers are invited read the FAQ page and search the library and if they don't find the answer, come back and ask again. I've tried searching for info on this forum without much success.

For guitar makers there are several good books available now and a lot of the information in them can be applied to ukulele but as you keep telling us, ukulele aren't guitars. You really should write the book Pete.;)
 
It's like a keystone effect... physically... kinda... right? I'd have to agree on fan bracing being a bad idea on sopranos... maybe even larger instruments... makes me think about ribs in nature... the human body's ribs don't fan out... flexibility and strenth. Hmmm

And the ribcage is the pumping station...
 
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Good explanation Dave and Pete. I hadn't thought much about the arch adding strength, although arches on structures are certainly known for that, or the difficulties of sanding the braces on a non-spherical surface, but both make sense. I guess I will be making a sanding disc sooner than I thought. I think the cheap asian ukes get away without arches because they make the tops pretty thick, which is also why many of them sound dead.
 
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Maybe. I did a survey a while back just measuring top thickness of my existing ukes.
Ohana and Mainland come in around .083" - .089" near the sound hole.
My Kanilea and Koaloha come in around .072" - .078".
So, solid wood low priced Asian made are a little thicker.
What's interesting is my Anuenue (mid priced Asian) is at ~.068". A real light weight but none the louder for it.
 
Maybe. I did a survey a while back just measuring top thickness of my existing ukes.
Ohana and Mainland come in around .083" - .089" near the sound hole.
My Kanilea and Koaloha come in around .072" - .078".
So, solid wood low priced Asian made are a little thicker.
What's interesting is my Anuenue (mid priced Asian) is at ~.068". A real light weight but none the louder for it.

The size of the ukulele matters as well...
 
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