Dad?
Well what you’ve got to do is re-saw and plane three rough planks of mahogany, then bend them on a jig, slowly, over several months so they don’t snap.
Then you layer those curved planks, staggered with six tail extensions, all re-sawn and planed to identical thickness (according to your caliper-micrometer). 
Then you glue everything together over several days with more clamps and jigs. And once it's dry and you've shaped and sanded it all down, you place the entire U-shaped arc into a cylinder with a irregular and variable pivot and hope the whole thing fits.

And it did. Perfectly. Cause we’re really good.
And it did. Perfectly. Cause we’re really good.