Hollow / Flat / Convex

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Nov 9, 2005
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A while back I made a simple picture to show the differences between the three grinds. I just improved the picture and explained the differences a little bit on another forum and thought it would be helpful to post here as well. I know I am not the first to do this, nor the best at it, and I know this information is available elsewhere, but I think my picture makes visualizing the cutting dynamics very easy and might help some people.



Notice how the hollow grind is the thinnest in the shallow cut, and the angle it meets the material is the most acute. The flat ground blade is slightly thicker in the shallow cut, and the angle is slightly more obtuse. The convex ground blade is thicker still, and the angle is even more obtuse.

But for the deeper cut, the hollow ground blade has more thickness to make up, so not only is it just as thick as the other two (given that the blades are equally thick), but now the angle it meets the material being cut is *MORE* obtuse. The flat grind slightly less so. And the convex grind (which achieved most of its thickness early in the grind) has the most acute angle.

So for shallow cuts, the hollow grind is the best. The convex grind is the worst, and the flat grind is in the middle. As the cut deepens, the order switches.

The hollow grind has the least material behind the edge, so it will cut like a thinner knife in more shallow cuts. It is also the weakest grind. The convex grind is the beefiest, but for shallow cuts it will cut like a thick knife.

So it depends on what type of cutting you do. I have found that I do "shallow cuts" most often (by far) so hollow grinds tend to be best for me.

While the flat and convex grinds are stronger and better at deeper cuts, those two advantages are not as important as the single advantage of the hollow grind. Most of the things I cut at work are cut with just the edge and don't require a thick blade: tape on boxes, plastic strap, plastic flex wrap... If you do a lot of "deep cutting" or more heavy duty work, a flat or convex grind might be better. I also use and like flat and convex grinds. When I have to cut down a box, I like flat grinds as the whole blade has to go through the box. For most uses, you can't tell the difference.

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Feel free to expand on this explanation, or to correct anything you feel is inaccurate.
 
Thanks! I've known about these grinding methods forever, but haddn't thought of it in this manner.
 
Nice comparison, but the 'wedging' comparisons of these blade-profile grinds become moot for some cutting applications.

For example, cutting rope-under-tension, all will perform similarly - since binding pressure of the material is nil. Same for slicing paper. Performance will be dominated by edge-quality - not blade-profile.

When cutting something like a 3" diameter raw parsnip or rhutebaga, the hollow-ground blade profile will penetrate nicely for the first 1/2" or so, but will then wedge at least as badly as the other blade profiles, due to high binding pressure of the inelastic material.
 
I have to agree with Gud4u. for shallow cutting like paper the blade grind isn't going to make a difference. I do like your pictures though . :)All the grinds can be ajusted to a degree to improve cutting or strenth. Depending on what you want or need. I find the convex grind is the easiest for me to do this to. Here is my method. http://www.bladeforums.com/forums/showthread.php?t=425415
 
When cutting something like a 3" diameter raw parsnip or rhutebaga, the hollow-ground blade profile will penetrate nicely for the first 1/2" or so, but will then wedge at least as badly as the other blade profiles, due to high binding pressure of the inelastic material.

Yes, but it should be noted that is only for that particular type of hollow grind, it should not be implied that this is a property inherent to that grind. Japanese kitchen knives for example use hollow grinds to improve deep cutting ability. A western example :

aj_utility.jpg


This is a hollow ground blade which has the same type of hollow grind as a hardwood felling axe. That knife also shows one of the main benefits of the grind which is the ability to sharpen the edge at the minimal functional angle. This is extremely time consuming on a flat/convex bevel because you basically have to rework the primary with each sharpening.

But for the deeper cut, the hollow ground blade has more thickness to make up, so not only is it just as thick as the other two (given that the blades are equally thick), but now the angle it meets the material being cut is *MORE* obtuse. The flat grind slightly less so. And the convex grind (which achieved most of its thickness early in the grind) has the most acute angle.

I think this is an interesting viewpoint but consider that a machete has a very acute angle at high up on the blade (its basically zero) but is very poor for deep cutting on woods but works well for deep cutting on leafy vegetation, though isn't optimal. You have to consider the nature of the material, specifically the force responce, which is why felling axes for soft woods have convex primary grinds and felling axes for hardwoods have hollow primary grinds though both are intended for deep cutting. Your diagrams also have an artifical constraint (same thickness/width) so while most of the conclusions are true, they are not actually general properties of the grind.

For example most stock removal blades have full tangs and slab handles while most forged blades have distal tapers, taped tangs and enclosed handles. However is this actually a constraints of stock vs forged or just a choice of the maker. If you were looking at issues of balance would you consider stock/forged or just which knife used the correct tapers? It is similar with the curvature. Much of the performance comes from how it is applied and you can end up in odd places if you place artifical constraints on the comparison.

Consider instead how would the grinds compare if they were each applied so as to closest match the minimal necessary cross section for blade stability. This can show for example that the hollow grind actually makes the strongest blade for a given cutting ability and the convex blade the weakest. This is a more complex comparison but it will show the actual purpose of the grinds. As well, how do the blades will react to being turned in the cut - this is one of the main wood working considerations for flat vs convex.

In general a flat ground blade is simply a compromize between the ability of the hollow/convex grinds. There are reasons for the different grinds, just like there are a need for different steels, but unfortunately the grinds are often used for blade types for which they are not well suited (just like the steels) which makes it very confusing to figure out what they do well. I discussed the force responce viewpoint towards the end of the following thread :

http://www.bladeforums.com/forums/showthread.php?t=421313

-Cliff
 
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