Epiphany-Geometry-Retention

[tomhosang]

Given you push and you cut (sawing motion), there are two things:

A thinner angle will create less resistance (more cutting force / red above). Plus, geometrically, the worn thinner edge will stay thinner (dark blue line), at least for the initial abrasive wear.

I think you're on the correct path here. I don't think it has much to do at all with pressure. As long as you aren't hitting anything hard, the pressure and speed of a cut don't really matter much. It comes down to apex width. Thinner apex = sharper edge. A thinner edge will maintain a thinner apex for longer (right side dark blue line is obviously thinner than the left) resulting in better edge retention from abrasive wear. Talked about at the 10:00 mark in the video below.

 

[FortyTwoBlades]

Yeah, I have been thinking about this and I believe you are right because the key concept here is actually distribution of force.

Picture someone laying on a bed of nails. They're safe as long as their weight is being distributed between all the nails. If you were to concentrate the same downward pressure on just one nail, it would pierce their flesh instantly.

A thicker edge distributes the downward force of the cut over a larger area. A thinner edge concentrates the same force into a smaller area.

It is also geometry to some extent as well. Picture a needle vs a sledge hammer for an extreme example. The sledge hammer has no chance to pierce a sheet of fabric no matter how hard you swing it, while the needle slips in between the fibers easily.

Rather, for equal sharpness--and therefore thickness AT the edge itself--the thicker blade is a steeper ramp that turns the energy into a much more abrupt stop as it slams to a halt. If you have too thin of a backing geometry this is what can lead to ripples or buckles in a blade. A thinner angle is a more gradual incline and can spread out the force more during impact providing that the backing geometry is sufficiently resilient. Also, a sledge hammer CAN pierce a sheet of fabric if the force is sufficient. It just requires a heck of a lot of force. All cutting is, at a certain scale, ripping/tearing/shearing of the target material.

 

[rhino]

I believe that I just understood, for the first time, why a thinner edge geometry will maintain a sharper edge while cutting most materials.

I’d like to apologize to anyone/everyone here that has already made this point dozens of times - for some reason I didn’t quite understand.

Ok here goes: Everything else being equal, it seems to be a commonly accepted fact that a blade with thinner geometry (the shape of a blade in cross-section), will retain an edge longer through most commonly encountered materials that folks expect knives to cut (plant/wood fibers, meat, plastics, and compounds like cardboard).

This never really made sense, but I believe I just finally understood that this is because a thinner geometry takes less pressure to push through the material, and less pressure = less edge damage.

That’s it right? Is there anything else going on or simply that a thin edge doesn’t need to get pushed so hard to make the cut?

Small point of order: the amount of pressure required to make a cut does not vary. What changes is that less force is needed for a thinner edge to apply the same amount of pressure.

Pressure = Force / Area

Thinner edge = smaller area = higher pressure for a given force -or- less force for a given pressure

 

[Guy McVer]

Small point of order: the amount of pressure required to make a cut does not vary. What changes is that less force is needed for a thinner edge to apply the same amount of pressure.

Pressure = Force / Area

Thinner edge = smaller area = higher pressure for a given force -or- less force for a given pressure

Stop.

Stop the internet.

Everybody stop the internet.

Someone is splitting hairs in a discussion about knife edges.

Everybody get out. We have to shut it all down now. No more memes, no more block chains. It's all over.

 

[catspa]

I don’t have the main breaker for the Internet, but I think he makes a valid point.

Parker

 

[scdub]

Small point of order: the amount of pressure required to make a cut does not vary. What changes is that less force is needed for a thinner edge to apply the same amount of pressure.

Pressure = Force / Area

Thinner edge = smaller area = higher pressure for a given force -or- less force for a given pressure

Yeah that sounds right - I should have used the word force instead of pressure.

It’s interesting to me how complicated and deep sharpness/sharpening/edge physics is - like a fractal - and possibly an actual fractal in some ways of thinking about it or at high enough magnification.

 

[rhino]

Yeah that sounds right - I should have used the word force instead of pressure.

It’s interesting to me how complicated and deep sharpness/sharpening/edge physics is - like a fractal - and possibly an actual fractal in some ways of thinking about it or at high enough magnification.

Try not to think about it too much!

Speakingv of fractals, in grad school I wrote a paper about using fractals to model flames. And that is all I remember!