I am trying to create a smooth spherical depression in wood that, the depression is 1.75in in diameter and 0.5in deep. I have access to a drill press, fixed router, and some chisels but I am not sure about the best way to go about achieving this depression in the wood (I am working with cherry) any suggestions about how to achieve this? The shape I am hoping to achieve is attached in the link.
If you want to create this with the tools you mentioned you'll need a "core box" bit. This is a plunging router bit with a spherical profile.
To determine the size we'll need to determine the radius using the formula:
r = h/2 + w^2/8h
Plugging in h = 1/2 and w = 1 3/4 we get an answer of 1 1/64". Since core box bits are typically sold by diameter you'll need a 2 1/32" bit. If you're ok with something close you could probably use a 2" bit.
I'd be VERY careful with this operation, though. Plunging a 2" bit can be quite dangerous. Make sure that your workpiece is well secured and you have your router very stable. Honestly I wouldn't personally attempt this operation.
You could try using an angle grinder with the right accessories:
When it comes to carving, shaping and sanding wood there are many effective tools to consider. Only one however, can be quickly adapted to accomplish all three of these common woodworking tasks with ease. The angle grinder.
If you are a woodworker looking for a fast and easy method to quickly carve, then shape, and finally sand out large gouges and even chainsaw curfs, the angle grinder is the tool for you.
Keep in mind though, the angle grinder will remove much wood in a hurry, and like all power tools, when using your angle grinder on wood, be certain to wear safety goggles and other appropriate PPE.
And for finely detailed woodworking projects you may consider other, less aggressive alternatives.
More information in the original article: