Mtn Hawk said:
It seems to me that the optimum edge would depend on the material being cut, sliced, chopped, or whatever, rather than a specific edge geometry or angle.
Generally yes, the basic consideration is wedging forces, examine soft and hardwood axes, one has a very thick convex profile and the other a thin hollow ground profile. Both do the exact same thing, chop woods, however the type of wood changes the optimal grind significantly. This same basic difference in property of soft vs hard wood and how it effects optimal geometry is the same basic consideration for any profile. On some materials you want enough metal to wedge the material apart (convex grinds), other times you want to reduce wedging and side friction to a minimum (hollow grinds), a flat grind just goes inbetween and isn't optimal at either, but also isn't horrible at either as well.
However, I believe it was Cliff Stamp who mentioned in another thread that the convex edge is superior for chopping soft wood.
Not as much the edge, but the primary profile, the actual way the blade itself is shaped :
That blade has dual convex primary grinds, it sweeps down and up in arcs from the 3/4" point on the blade. The actual edge (the part that does the cutting) on any knife is v-ground regardless of how it is sharpened because the abrasives themselves lack curvature.
The profile of a convex edge clearly shows that it is thicker above the edge than a V-edge.
For a given thickness, a convex edge will retain more metal than a v-ground edge, however in general, people who run convex edges tend to alter the profile dramatically so this presupposition no longer holds. Generally someone takes a stock profile, say 0.035" thick by 20 degrees per side, then puts it on a belt sander and applies a a bevel which sweeps from 8/10 degrees. This is then used as "proof" that a convex edge is superior.
Of course what it actually shows is that a 8/10 degree edge cuts better than a 20 degree edge (assuming the durability isn't overloaded). The same thing would be seen if a straight relief grind was applied as recommended by J.J. of Razor's Edge. You would in general see better performance if the primary profile was adjusted to reduce the edge thickness to a minimum instead of adjusting the edge angle to a minimum because that makes the edge very wide and sharpening efficiency is vastly reduced.
There are some durability issues as well, at the same level of cutting ability a thinner edge with a more obtuse angle is more durable for cutting than a thicker edge with a more acute angle, however in extremes of chopping and really heavy dynamic cutting, the thicker edge with the more acute angle will reduce gross damage.
-Cliff