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I don't know exactly how the Clarke drill sharpener works but be aware that you need a clearance behind the cutting edge.
Merely rotating the drill will not provide this .. it needs to be advanced slightly as the drill is turned past each cutting edge.
Then, when you hold the drill vertically and look at the line where the new grind surface meets the outside diameter, it should taper down slightly behind the leading edge .. if that makes any sense.
Failure to provide this clearance means that the drill just rubs on the work.
Tbh, in my opinion, having the optimum angle for the "point" is not of huge importance.
More important by far is having clearance behind the cutting edges and equal angles on each side/flute.
Also a good chisel edge at the apex, which should be as near as possible to 90deg to the tapered cutting edges.
Actually, when drilling from scratch without a pilot hole, it is the chisel edge which does most of the cutting .. or at least initiates it.
In fact some specialised, deep-hole drills (sometimes called gun-barrel drills) only have the chisel edge and no tapered cutting edges or flutes at all.
On a cautionary note, I have seen budget drill sets where 80% of the drills were incorrectly ground and would not cut properly, if at all.
But then again, after I reground them they were fine, so if you're prepared to do this then budget drills are probably a reasonably sound option for occasional use.
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