How do you "convex" an edge? Pros/cons?

Well arcs are inherently stronger than straight lines, and the same applies to a convex edge... there's more metal behind the edge, so it stands up to stress a lot better - it's why almost all choppers use it, whether it be a large knife or ax. The disadvantage is of course that a it has more metal behind the edge, which makes it slightly worse at slicing... the difference is hardly noticeable though and you can still easily make a convex edge capable of shaving.

As for actually doing it, you should first know how to sharpen with just a stone... after that, figure out what 18 degrees is on a flat surface, then use that angle on sandpaper atop a mousepad atop a flat surface. The slack in the mousepad gives you a nice convex edge that will stand up to hard hits a lot better than a v-edge.

Here's a video on how to do it - do the same thing, but start at 220grit sandpaper then move up to 400, 800, 1000, and 2000 then strop on a genuine leather belt (if you don't have a strop).

Here's proof (my 15" AK) that a convex edge is no worse at cutting than a v-edge:
P1010921.jpg
 
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Same basic idea as above but I just use the angle on the kuk's main edge as my guide.

I use a leather strop backed by a piece of plywood, and glue the sandpaper to the leather surface with rubber cement. If there is a fairly good edge on the kukri already then I start with 400 grit and work down to 1000 or finer if you can find it. Then I go to a strop loaded with buffing abrasive (green works well). This produces a hair pushing sharp edge. exceptionaly sharp.
 
Same basic idea as above but I just use the angle on the kuk's main edge as my guide.
By main edge, do you mean the primary bevel? I've actually done this before and found that the edge becomes too steep unless you add pressure... I personally lay it on the primary bevel then lift the angle up a degree or two (~18degrees)- it still provides a shaving sharp edge, but one that's a little bit more robust :)
 
I know just about nothing with regards to knife sharpening and I have decided I want to try the mouse and sandpaper method on my new khuk from this and other threads I have read on the HI forum. I went to my local hardware store and they had 220 and 400 grit. 600 grit was the finest they went. Where do I get 1000 or higher grit? There is a Home Depot a distance from where I am and I don't know if they carry it. Any suggestions?
 
I know just about nothing with regards to knife sharpening and I have decided I want to try the mouse and sandpaper method on my new khuk from this and other threads I have read on the HI forum. I went to my local hardware store and they had 220 and 400 grit. 600 grit was the finest they went. Where do I get 1000 or higher grit? There is a Home Depot a distance from where I am and I don't know if they carry it. Any suggestions?

Basically everything above 600grit is considered metal polishing and can best be found at auto parts/repair stores... My local Fred Meyer has 3M variety packs (220, 400, 800, 1000) for $4 in the auto section - I get 2000 and 4000 from Auto Zone :)

Be sure to practice on another knife before working on your kukris... the longer you keep sharpening the secondary bevel, the thicker it will become due to the primary bevel also being angled:
sharpen4.jpg
 
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I, too, was advised by the local hardware store to try auto-supply houses. I picked up some 800 and 1000 after that, easily, but didn't find anything higher.
 
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