Posted by CliffStamp

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Re: Sometimes you don't know as much as you think you know March 05, 2015 01:49AM |
Registered: 8 years ago Posts: 372 |

Ok am I way off base here?

My reply:

His argument:

QuoteTwindog

Convex edges do not have angles -- that's just geometry. The arcs are defined by a radius length of the circle of which defines the arc. When a convex edge has the same edge width and height, the only valid way to compare the general category of V edges to the general category of convex edges, the V edge is going to be more acute and the convex edge will be more robust because it has more metal behind the apex. Marcinek didn't show an example of a fair comparison, but it's easy to do. Just draw a straight line from the edge shoulder of a convex edge to the apex. The V edge will be more acute.

My reply:

Quoterazor-edge-knives

No offense man, but this is simply incorrect. Whether v, concave, or convex the apex most certainly DOES have an angle. This is the point that Marcinek was trying to make... that it all depends on the apex angle if you want to compare apples w/ apples.

You say that the V edge will be more acute and you are talking about edge "geometry"... but more acute what?... more acute ANGLES is what you are talking about

His argument:

QuoteTwindog

No offense taken, but an angle is the amount of turn between two straight lines that share a vertex. Convex edges have no straight lines. They are formed by arcs. In a pure convex edge, those arcs are defined by the radius of the arc's corresponding circle. With convex knife edges, you're mostly dealing with a hybrid of arcs.

A convex edge defined by a short radius -- say the radius of a circle the size of a BB -- is very obtuse. A convex edge defined by a long radius, say the distance of the earth to the sun, shows no difference between a V edge, if both edges have the same edge height and width.

Convex edges defined by a short radius become very obtuse near the apex. Long-radius convex edges have a relatively constant acuteness from the edge shoulder to the apex and are comparable to V edges of similar acuteness.

Re: Sometimes you don't know as much as you think you know March 05, 2015 02:06AM |
AdminRegistered: 10 years ago Posts: 12,833 |

It is rare to see someone geek out over a mathematical point.

An angle is defined usually by some reference to lines (or rays which are just a type of line) that intersect at a point. The angle is what is formed by the intersection and is a measure of basically how far the ends of the lines diverge at a given distance. As with anything, there are multiple ways of looking at it, this is really true in math.

For example if I was to just draw a straight line :

-----------------------------------

Would you say there is an angle, does that definition apply? It doesn't seem like it does as there is only one line, but I can just pick some arbitrary point and say there are two lines coming out from that point :

---------------.-------------------

The angle in this case is 180 degrees. So it is either a flat line with no angle, or it is two lines with an angle of 180 degrees. Both are equally valid.

A curve can be thought of as the limiting case of a number of angles where the number of segments goes to infinity, thus a curve doesn't have an angle, it has an infinite number of them. These angles are typically defined by tangents which can be used to map out the angles of a curve. Now you can also do the exact same thing in reverse and think of a line as a very flat curve, it is the limiting case where the number of tangents decreases from infinity to one.

If you want to really spazz out then you can define a non-linear geometry where the equations of the curve will look line the equations of a straight line. This type of thing is done in physics all the time to make the math easier so a problem is solved in a rotational space. This is often done as many things can be approximated by curves like spheres, or at least physicists like to pretend they are because it just makes the algebra easier and they leave all the complicated things to the mathematicians anyway.

An angle is defined usually by some reference to lines (or rays which are just a type of line) that intersect at a point. The angle is what is formed by the intersection and is a measure of basically how far the ends of the lines diverge at a given distance. As with anything, there are multiple ways of looking at it, this is really true in math.

For example if I was to just draw a straight line :

-----------------------------------

Would you say there is an angle, does that definition apply? It doesn't seem like it does as there is only one line, but I can just pick some arbitrary point and say there are two lines coming out from that point :

---------------.-------------------

The angle in this case is 180 degrees. So it is either a flat line with no angle, or it is two lines with an angle of 180 degrees. Both are equally valid.

A curve can be thought of as the limiting case of a number of angles where the number of segments goes to infinity, thus a curve doesn't have an angle, it has an infinite number of them. These angles are typically defined by tangents which can be used to map out the angles of a curve. Now you can also do the exact same thing in reverse and think of a line as a very flat curve, it is the limiting case where the number of tangents decreases from infinity to one.

If you want to really spazz out then you can define a non-linear geometry where the equations of the curve will look line the equations of a straight line. This type of thing is done in physics all the time to make the math easier so a problem is solved in a rotational space. This is often done as many things can be approximated by curves like spheres, or at least physicists like to pretend they are because it just makes the algebra easier and they leave all the complicated things to the mathematicians anyway.

Re: Sometimes you don't know as much as you think you know March 05, 2015 01:55PM |
Registered: 8 years ago Posts: 372 |

QuoteCliffStamp

It is rare to see someone geek out over a mathematical point.

An angle is defined usually by some reference to lines (or rays which are just a type of line) that intersect at a point. The angle is what is formed by the intersection and is a measure of basically how far the ends of the lines diverge at a given distance. As with anything, there are multiple ways of looking at it, this is really true in math.

For example if I was to just draw a straight line :

-----------------------------------

Would you say there is an angle, does that definition apply? It doesn't seem like it does as there is only one line, but I can just pick some arbitrary point and say there are two lines coming out from that point :

---------------.-------------------

The angle in this case is 180 degrees. So it is either a flat line with no angle, or it is two lines with an angle of 180 degrees. Both are equally valid.

A curve can be thought of as the limiting case of a number of angles where the number of segments goes to infinity, thus a curve doesn't have an angle, it has an infinite number of them. These angles are typically defined by tangents which can be used to map out the angles of a curve. Now you can also do the exact same thing in reverse and think of a line as a very flat curve, it is the limiting case where the number of tangents decreases from infinity to one.

If you want to really spazz out then you can define a non-linear geometry where the equations of the curve will look line the equations of a straight line. This type of thing is done in physics all the time to make the math easier so a problem is solved in a rotational space. This is often done as many things can be approximated by curves like spheres, or at least physicists like to pretend they are because it just makes the algebra easier and they leave all the complicated things to the mathematicians anyway.

Thanks for the explanation Cliff!

Re: Sometimes you don't know as much as you think you know March 11, 2015 08:35AM |
AdminRegistered: 10 years ago Posts: 3,334 |

hehe.. Razor.. that is a bizzare explanation provided.

I did videos on this before, but I probably deleted them now.

the following in no way bears much relation to an educated reply. you have to put my words through google translate selecting cKc -> Cliff as the option.

its also typically incorrect to mention radius in relation to convex knives, because the convex is never going to be a arc defined as part of a circle. its generally a continuous amount of vectors running in different directions. The apex will always have an angle as determined by the direction of the first vector in relation to the center of the spine of the knife.

its also impossible to state that a V edge is more acute than a convex for the same edge angle. this is something that would relate to using a spine thickness and knife width in relation to such things. the reality is that a single plane flat ground knife with only 1 bevel cannot have the same spine thickness as a convex knife that starts at the same apex angle. this is dealt with using multiple bevels.. the convex would always have a thinner spine.. even if by only thousands of an inch.

a convex edge as measured with the apex as the starting point can only get thinner as the angle gets less behind the apex. a convex edge starting at 20dps must have less metal than a flat edge apex starting at 20dps. the reason is that the curvature is continuously lowering the angle which reduces the volume.

----------------------------------------------------------------------

It's not Cliff, its Dr Stamp

#kebabstickcut, it's a thing - make it happen

I did videos on this before, but I probably deleted them now.

the following in no way bears much relation to an educated reply. you have to put my words through google translate selecting cKc -> Cliff as the option.

its also typically incorrect to mention radius in relation to convex knives, because the convex is never going to be a arc defined as part of a circle. its generally a continuous amount of vectors running in different directions. The apex will always have an angle as determined by the direction of the first vector in relation to the center of the spine of the knife.

its also impossible to state that a V edge is more acute than a convex for the same edge angle. this is something that would relate to using a spine thickness and knife width in relation to such things. the reality is that a single plane flat ground knife with only 1 bevel cannot have the same spine thickness as a convex knife that starts at the same apex angle. this is dealt with using multiple bevels.. the convex would always have a thinner spine.. even if by only thousands of an inch.

a convex edge as measured with the apex as the starting point can only get thinner as the angle gets less behind the apex. a convex edge starting at 20dps must have less metal than a flat edge apex starting at 20dps. the reason is that the curvature is continuously lowering the angle which reduces the volume.

----------------------------------------------------------------------

It's not Cliff, its Dr Stamp

#kebabstickcut, it's a thing - make it happen

Re: Sometimes you don't know as much as you think you know March 11, 2015 05:38PM |
Registered: 9 years ago Posts: 905 |

Weirdly this is hard to understand but I agree (a convex edge starting at 20dps must have less metal than a flat edge apex starting at 20dps. the reason is that the curvature is continuously lowering the angle which reduces the volume)

This proves the convex is weaker

Back to the issue of angles in convex edges, for practical purposes, aren't we talking about the angle at which the edge starts to grab? Of course there are variables here like pressure and material (grab soft plastic or grab steel)

...and in non-practical terms if we could sharpen 1 atom wide then even on a convex edge we could find the angle at which we took that final apex pass, though I am unable to visualize that.

This proves the convex is weaker

Back to the issue of angles in convex edges, for practical purposes, aren't we talking about the angle at which the edge starts to grab? Of course there are variables here like pressure and material (grab soft plastic or grab steel)

...and in non-practical terms if we could sharpen 1 atom wide then even on a convex edge we could find the angle at which we took that final apex pass, though I am unable to visualize that.

Re: Sometimes you don't know as much as you think you know March 11, 2015 06:58PM |
AdminRegistered: 10 years ago Posts: 12,833 |

If you want to be really particular, on a quantum level events are always discreet even though they may appear to be continuous. Any curve, if viewed under sufficient magnification will be faceted, at some level it is faceted on the crystal structure. Normally when people say something is curved/smooth/arc they mean either that it visually appears to be that way or that it feels that way.

The issue with convex vs flat is one of those things where the discussion has gone horribly off track and has never been able to regain its footing. Jerry Hossom was one of the makers who completely confused the issue and much of the nonsense he wrote is still being repeated and people will swear that if you "convex" a machete it cuts better / stays sharp longer. This is nothing more than a case of correlation being used to infer causation. Here is the same thing, only obviously silly :

You speak to a friend and notice he has a cold, you observe he is carrying tissues. The next person you see with a cold you see again they have tissues. Two times seems to be a bit of a coincidence and so you decide to check into it. You then find a staggering link that that people who have colds tend to be very likely to carry tissues and people who don't have tissues rarely have colds. The data is staggering, 95% of people with colds have tissues, almost no one without a cold carries them! You then deduce that tissues cause colds.

Now this is silly, but we only know it is silly because we know that the causation link is the other way. But that same extremely flawed reasoning is what leads many people to infer if you "convex" a machete/knife/axe/tween then they work better. What is actually happening is very simple but as Fox Mulder has said "the stories are out there" and once they are they always grow in the telling.

When a maker typically "convexes" an edge and the tool cuts better they typically will grind off a lot of material from behind the edge and they typically sharpen it better than it has ever been sharpened, the latter is really true for machetes which often are barely sharpened at all from the factory. Thus if you take a Cold Steel raw machete as-supplied and have it "convexed" which brings it to a high polish and a greatly thinned out profile then of course it cuts much better.

However you can also do what Chris does which is apply a primary grind, then adjust the bevel thickness/angle to meet the minimum durability requirements and that will cut better and sharpen far easier than one wide convex bevel. But the inertia is there on convex grinds just like it is on single bevels. Watching it is like watching the forging comments or the material science comments in the 90's, the goggles they do nothing.

--

Now on a fundamental level, sharp lines and transitions are not going to improve cutting ability so once you take a knife and you adjust the blade, edge and apex bevel so the minimum durability is there, and then you smooth out all the transition points the knife will cut better, smoother, bind less, stick less, etc. . But that improvement is a refinement which only works if the base cross section was right in the first place. A splitting maul and a felling axe both have convex bevels, but they are not at all similar in performance because the cross section difference is large.

The issue with convex vs flat is one of those things where the discussion has gone horribly off track and has never been able to regain its footing. Jerry Hossom was one of the makers who completely confused the issue and much of the nonsense he wrote is still being repeated and people will swear that if you "convex" a machete it cuts better / stays sharp longer. This is nothing more than a case of correlation being used to infer causation. Here is the same thing, only obviously silly :

You speak to a friend and notice he has a cold, you observe he is carrying tissues. The next person you see with a cold you see again they have tissues. Two times seems to be a bit of a coincidence and so you decide to check into it. You then find a staggering link that that people who have colds tend to be very likely to carry tissues and people who don't have tissues rarely have colds. The data is staggering, 95% of people with colds have tissues, almost no one without a cold carries them! You then deduce that tissues cause colds.

Now this is silly, but we only know it is silly because we know that the causation link is the other way. But that same extremely flawed reasoning is what leads many people to infer if you "convex" a machete/knife/axe/tween then they work better. What is actually happening is very simple but as Fox Mulder has said "the stories are out there" and once they are they always grow in the telling.

When a maker typically "convexes" an edge and the tool cuts better they typically will grind off a lot of material from behind the edge and they typically sharpen it better than it has ever been sharpened, the latter is really true for machetes which often are barely sharpened at all from the factory. Thus if you take a Cold Steel raw machete as-supplied and have it "convexed" which brings it to a high polish and a greatly thinned out profile then of course it cuts much better.

However you can also do what Chris does which is apply a primary grind, then adjust the bevel thickness/angle to meet the minimum durability requirements and that will cut better and sharpen far easier than one wide convex bevel. But the inertia is there on convex grinds just like it is on single bevels. Watching it is like watching the forging comments or the material science comments in the 90's, the goggles they do nothing.

--

Now on a fundamental level, sharp lines and transitions are not going to improve cutting ability so once you take a knife and you adjust the blade, edge and apex bevel so the minimum durability is there, and then you smooth out all the transition points the knife will cut better, smoother, bind less, stick less, etc. . But that improvement is a refinement which only works if the base cross section was right in the first place. A splitting maul and a felling axe both have convex bevels, but they are not at all similar in performance because the cross section difference is large.

Re: Sometimes you don't know as much as you think you know March 12, 2015 01:21AM |
AdminRegistered: 10 years ago Posts: 3,334 |

Quotewnease

Weirdly this is hard to understand but I agree (a convex edge starting at 20dps must have less metal than a flat edge apex starting at 20dps. the reason is that the curvature is continuously lowering the angle which reduces the volume)

This proves the convex is weaker

Physically weaker for the same apex angle is correct, but also where it gets interesting.. In part it comes down to the fact that for the same apex angle the convex will have less resistance going in and so less force, and therefore potentially less damage etc. This would also be true for faceted flats.

I firmly believe that the Truth behind why convex appears more "durable" is not that it physically is, but that all the other factors involved result in less stresses to the edge. There is also the fact that for the same spine thickness, targeting say a 15dps edge on a flat, the convex has to have more volume to attain the same spine thickness, but the reality is that it will be more than 15dps maybe 15.0001dps or 15.1 to make it simple.. small enough the deceive people into thinking that they have a convex of 15 with the same spine thickness, but thicker and stronger (which is now true at the apex)

Cliff is always referring to a thick edge on a thin primary placing the point of damage in the wrong location. The convex basically helps this by providing the thicker edge, but quickly reducing so that you get the edge holding of the stronger V, with the lesser resistance of a lower edge angle..

Something like that is my thought.

----------------------------------------------------------------------

It's not Cliff, its Dr Stamp

#kebabstickcut, it's a thing - make it happen

Re: Sometimes you don't know as much as you think you know April 22, 2015 12:04AM |
Registered: 9 years ago Posts: 3,261 |

Started off with a great evening of sharpening did all the kitchen knives, attempted plateau sharpening with decent results on a few of them and then I thought about my Aranyik Gigantic cleaver. It is about that point my night took a turn for the worse. I had used it to prepair a curry the other night long and short the tip was damaged from crab shells and the heel of the blade from opening a tin of coconut milk.

Cut into the stone to remove the damage

Shape the primary and check for light reflecting. Yep still shiny

Shape some more still reflecting

Shape some more still reflecting only now it looks like more than before

Look closer realize it is a huge burr that is reflecting light.

D'oh!!! Repeat

D'oh! Did it again

This time I just try to deburr with a high angle pass >45 deg the burr flops back and forth, back and forth. It was like watching a tennis match.

Maybe the third time is the charm....

The knife is on a shelf I am on the couch it was almost stuck in the wall thank goodness my daughter called for me when she did. I am giving up for the night.

www.theflatearthsociety.org

BIGFOOT FINDS YOU, YOU DON'T FIND BIGFOOT!

IT IS THE E-NEP THROWING BROTHERHOOD

Cut into the stone to remove the damage

Shape the primary and check for light reflecting. Yep still shiny

Shape some more still reflecting

Shape some more still reflecting only now it looks like more than before

Look closer realize it is a huge burr that is reflecting light.

D'oh!!! Repeat

D'oh! Did it again

This time I just try to deburr with a high angle pass >45 deg the burr flops back and forth, back and forth. It was like watching a tennis match.

Maybe the third time is the charm....

The knife is on a shelf I am on the couch it was almost stuck in the wall thank goodness my daughter called for me when she did. I am giving up for the night.

www.theflatearthsociety.org

BIGFOOT FINDS YOU, YOU DON'T FIND BIGFOOT!

IT IS THE E-NEP THROWING BROTHERHOOD

Re: Sometimes you don't know as much as you think you know April 26, 2015 06:18PM |
AdminRegistered: 8 years ago Posts: 7,183 |

Re: Sometimes you don't know as much as you think you know October 09, 2015 08:53AM |
Registered: 7 years ago Posts: 104 |

The way I would put it is that for any given edge shoulder thickness (and on convex edges there is no defined shoulder, so you have to pick that first), then the V-edge will always be thinner below that. To argue otherwise is to argue the shortest line between two points is not a straight line...

What convexing does do is allow edges to be stronger than similarly thin V-edges, but they still do this by being thicker below the chosen reference point...

Today I discovered for the second time, argueing online on the big forum, that even claimed "knifemakers" think a 20° edge means a 20° angle is what is the actual cutting apex... No wonder 20° degree edges are seen as adequate!

I think it would have been a huge help is all those in-box sharpening vignettes, instead of using a line neatly dividing the blade, used another line referenced to the other side of the edge bevel, so the true figure of 40° would be the only figure referred to as the "Edge Angle"...

I am starting to think maybe everyone's knives would now be twice as sharp...

Gaston

What convexing does do is allow edges to be stronger than similarly thin V-edges, but they still do this by being thicker below the chosen reference point...

Today I discovered for the second time, argueing online on the big forum, that even claimed "knifemakers" think a 20° edge means a 20° angle is what is the actual cutting apex... No wonder 20° degree edges are seen as adequate!

I think it would have been a huge help is all those in-box sharpening vignettes, instead of using a line neatly dividing the blade, used another line referenced to the other side of the edge bevel, so the true figure of 40° would be the only figure referred to as the "Edge Angle"...

I am starting to think maybe everyone's knives would now be twice as sharp...

Gaston