Just a little more information about centre drills.
There are a few other types that you may come across in your travels, and maybe don't know about.
The first is a 'protected centre' centre drill. These are usually used in shafts that go through bearings, where to disassemble, the ends of the shafts are beaten with hard things like hammers etc. So when the end of the shaft gets damaged, the centre drilling should remain untouched, so allowing easy mounting again between centres on the lathe, to get rid of the end damage to the shaft.
I don't have a picture of one available, but I have shown what they are like on the C-o-C at the bottom, the top sketch.
The next, and more important one for what we do is a radiused centre drill. This is a piccy of what they look like.
These are used mainly when turning between centres when the tailstock is set over for taper turning. If you can imagine, the centre can't sit correctly in a straight sided V centre, purely because the shaft is at an angle to the centre in the tailstock, but can sit correctly if the sides of the V are curved. I have tried to show what I mean in the C-o-C. On the bottom half of the sketch, the top picture is a normally drilled centre and the bottom one is done with a curved centre.
I have had a couple of these in my collection for many years, and use them whenever I am doing offset taper turning. I also have a few protected centres, but because they are too large for my tailstock, I have never used them. I suppose I should buy some smaller ones rather than relying on freebie donations.
I hope this helps
John