hollow vs flat grinding thoughts

[Jan]

So, I have now exorcised the demon.  I understand both points of view entirely but I believe the fixed chord model is a more appropriate fit to the original question than the fixed angle model.  The fixed chord model is the only truly objective test and ironically (you're going to love this) Mr Euclid would HAVE to agree because being an empiricist, he would have no other rational choice :-)

I am so happy that only the good angels have remained with us! 

I understand your point, but I do not believe that the fixed chord model is appropriate to test the original question.
Why?
Having a hollow ground bevel and looking for the position where its angle is equal to the chord angle, we will find that it is roughly in the mid point of the bevel. In the drawing below this point is marked red.



The central part of the bevel is far away from the cutting edge, this part of the bevel was hardly ever significantly involved in cutting wood. It is proven, that the tip of the chisel is dominantly important for driving the chisel into the wood.

That is my argument why the fixed chord model may not be appropriate to test your original question.

[Rob]

You mathematicians are struggling to decouple this angle symmetry issue aren't you.  I'll try one more time and then think we'll have to just leave it out there.

Jan....it doesn't matter one jot that the angle of the chord that matches the angle of the tip is in the middle.  It's completely irrelevant to satisfy the logic of the original question. The original question only asks if a hollow ground bevel is weaker or not.  It might reasonably be rephrased as what mass of metal is left behind the edge of hollow versus straight ground.

THE ONLY CONDITION BEING TESTED IS THE GRINDING METHOD.

Thus to satisfy that condition all other variables MUST REMAIN FIXED.  Can we at least agree that to be scientifically valid (objective) that that statement must be true?  We cannot hope to test the result of varying a condition unless all other conditions are fixed....correct?

So the condition we vary is the method of grinding.  Everything else must remain the same, including the position of the chisel with reference to the grinding medium.  So now our theoretical chisel is stuck in space and time (its not a real chisel being setup on a Tormek, we haven't used the angle master to set it up, its just a theoretical chisel that exists in a theoretical laboratory where two different types of grinding media are presented to it).  Next we offer the grinders to it, one straight and one a wheel.  The only means we have of testing those two grinding mediums without varying anything are if the chisel remains fixed.  Thus any theoretical setup must be against the chord because otherwise we would have to tip the edge using a theoretical angle master.  That would be varying more than the grinding medium and would invalidate the result.

Actually, a more useful metaphor might be imagining the grinding medium mounted like the blade of a chopsaw where it's cantilevered down onto a fixed chisel.  The only difference would be in test 1 the chopsaw blade would be circular (hollow ground) whereas in test 2 the chopsaw blade would be straight (like a sanding belt).  Can you see how the only way the test is a fair comparison is if the angle at which the chopsaws are brought down is the same because only if the chisels remain unmoved in any plane can the test be only varying one condition?

You need to stop making the angle at the tip of the blade the focus of the variable since its irrelevant for the purpose of the discussion.  It's not comparing apples with apples.  You either set BOTH tests up using the chord to define the angle or set BOTH tests up with the grinding tip as the angle by which they're setup.  But you cant set one up using the chord and the other using the "resultant" ground tip angle because it's an illegal test condition.

You're using the tip angle as the deciding factor when it's actually the consequence of using a hollow grind.  We're testing the effect of hollow grinding, not the effect of fixing the tip angle at 25 degrees.  Do you see the difference.  It's a funny one this and no mistake :-)

I do appreciate the mental somersaults of this, it's quite outwardly innocuous but actually its a bit of a conundrum.

I am absolutely certain of the rational conclusion to this by the way.  100% :-)  And Euclid would back me all the way.

[Jan]

Thank you for repeated detailed explanation, Rob. I believe I understand you fully.

You have formulated the original question and so you are also the person to perform the exegesis. 

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

The discussion in this thread, before you have joint us, was focused on the chisel tip cutting edge. The situation at the tip was not well understood before. Herman explained it here, I have added the drawings and Stig agreed with us. Then it was described how to use the chord of a hollow ground for micro bevel. I think it is quite fruitful and useful thread.

Jan

[Ken S]

I agree, this has been a fruitful topic. I look forward to studying it; the non math people on the forum, like me, have a slower absorption rate. Thanks for the info, guys.

Ken

[Herman Trivilino]

Ok, Rob. First you told us that having identical angles didn't matter:

The original issue was an attempt to resolve the assertion that "a hollow ground bevel has a weaker edge than a straight ground bevel"  There was no mention of the tip angles being identical. 

Then you told us that it does matter ...

In my mind the only test that meets the ciriteria "conditions are identical" is the one where the two triangles are overlapping and identical ie all angles are equal with 25 degrees at the bevel. 

... but apparently only under the conditions that you specify. You are saying we should be measuring the angle of the chord (the angle of the secant line) and I am saying that we should be measuring the angle at the tip (the angle of the tangent line).

For the mathematically inclined, the larger the radius of the grindstone, the closer we get to the two lines being the same.

So, if we all agree to do it Rob's way and measure the angle of the secant line the hollow ground chisel may be weaker because it contains less steel.

If instead we retain the freedom to measure the angle of the tangent line then the hollow ground chisel may be stronger because it contains more steel.

My choice is to retain the freedom to measure the angle of the tangent line for two reasons:

1. That's the angle at which the two steel surfaces meet when they form the edge on the tool.

2. That's the angle we measure with the Tormek Angle Master.

I would argue that the Tormek Angle Master method is the better way to do it because it measures the angle at which the two steel surfaces meet when they form the edge. If you were dealing with a small enough radius that it made a difference, you find that two tools sharpened this way, one flat and the other hollow, would perform more like each other if you matched the edge angle at the place where the two surfaces meet rather than some other angle such as the one that Rob tells us we must use.

[jeffs55]

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

How many times did I say that?

Jan
[/quote]

[jeffs55]

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

How many times did I say that?

Jan

[/quote]

[Rob]

It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

Eureka :-)
It's been obvious to me from the start (& Jeffs55)...but I've never been able to tear you guys away from the belief that the resultant tip angle is where all the action is.  I'll say for the last time chaps that we all need to recall this was a theoretical question only, in a vacuum if you like.  It wasn't ever related to the Tormek or how one might achieve the necessary angles on the Tormek with the anglemaster.  Somewhere along the journey, I guess because I posted it on the Tormek forum, it picked up an energy all of its own and became related to how it might get done with Tormek actual accessories (the angle master in particular).  It was originally a teasing type statement that came out of chatroom internet ether, what I call urban myth that stated simply "a hollow ground bevel has a weaker edge than a straight ground one"  There were no qualifying statements really.  We invented everything else, like, the tip angles must be the same or the chord angles must be etc etc.....all our own assumptions after the fact. 

So what I think this thread has ended up doing is shine some very thoughtfully considered light, with some excellent technical drawing and maths to prove the discussion about the tip angles.  It's also evolved the dialogue about the angle masters capabilities and has possibly set peoples minds at rest about whether or not they need be concerned about whether an edge is hollow or otherwise ground.  I have really enjoyed everybody's superb input so I thank you for that.

One final point from me. Despite the assertion that the chord angle is the only fair and true method by which I believe you can compare straight versus hollow, I actually agree the tip angle discussion is by far the more useful one for a practical application, with a real Tormek in the real world :-)

[Jan]

Thanks Rob for your kind summarizing words. I really appreciate it! 

Jan

P.S.: Today I hear dancing angels too. May be they had been waiting for the outcome of our discussion and they are now happy we have found consensus. As spiritual beings, messengers and guardians, they may have some access to our forum. More likely through our minds then through an IP address, I guess. Having said that, do knife sharpeners have some special patron saint? It may be Saint Catherine of Alexandria, also known as Saint Catherine of the Wheel.

[Jan]

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.
Jan

How many times did I say that?

Sorry, Jeff(55) for not responded sooner to the reservations expressed in your posts. 

For me it is quite challenging to express my thoughts and fully understand some posts here because English is foreign language for me. I am doing my best, but you know, you can not teach an old dog new tricks. So, mea culpa!

You are resonating with Rob's way, Herman and I prefer to measure the tangent line angle at the tip. The most comfortable attitude is to understand both ways and in specific situation to use the more appropriate approach. 

In my thinking, Rob's way is more a thought experiment, while Herman's way is better linked to everyday sharpeners practice and sheds light on topic, which had not yet been understood well.

Jan

[Ken S]

I must confess that when I was doing comparison chisel grinding between the T4 and T7, I used different width chisels. If I examine the two chisels very carefully with a straightedge and good light, I believe I may be able to perceive a slight difference. I do not doubt that there is a difference. I have misplaced my angel measuring tool.

I also believe the weakness aspect to the edge, however I also believe that how an individual chisel is heat treated is a more noticeable factor. With some specialized tools, such as Jan's grandfather's large mortising chisel, I might opt for a flat grind with water stones. However, I would certainly do the hard grinding with the Tormek and do only the final flattening of the hollow grind by hand.

Ken

[Rob]

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.
Jan

How many times did I say that?

Sorry, Jeff(55) for not responded sooner to the reservations expressed in your posts. 

For me it is quite challenging to express my thoughts and fully understand some posts here because English is foreign language for me. I am doing my best, but you know, you can not teach an old dog new tricks. So, mea culpa!

You are resonating with Rob's way, Herman and I prefer to measure the tangent line angle at the tip. The most comfortable attitude is to understand both ways and in specific situation to use the more appropriate approach. 

In my thinking, Rob's way is more a thought experiment, while Herman's way is better linked to everyday sharpeners practice and sheds light on topic, which had not yet been understood well.

Jan

I think given English isn't your first language Jan you put us all to shame my friend :-)  Your command of English is doubtless a lot better than my command of your native language :-)

I also agree that my scenario was entirely "thought" only and that Herman's is much more real world and practical.  I appreciated all the points of view and perspectives, a most interesting debate :-)

[Elden]

Ok theory set aside, let's assume someone brings me a chisel that is flat ground at a 25° bevel. After it is sharpened they want it to be just as "strong" as it is now. I plan to use the Tormek to form a hollow grind that covers the whole face of the chisel. It is also desired that no more pressure will be required to make the resharpened chisel to cut than when it it was fully sharp with the flat bevel. Without trial and error methods and minimal steel removal, where should the Tormek wheel first come into contact with the flat ground bevel assuming the flat bevel is truly and squarely flat?

[Herman Trivilino]

Ok theory set aside, let's assume someone brings me a chisel that is flat ground at a 25° bevel. After it is sharpened they want it to be just as "strong" as it is now. I plan to use the Tormek to form a hollow grind that covers the whole face of the chisel. Without trial and error methods and minimal steel removal, where should the Tormek wheel first come into contact with the flat ground bevel assuming the flat bevel is truly and squarely flat?

If you set the Angle Master to 25^o you will end up with a chisel that has more steel on the heel relative to the tip than it had when it was flat ground at 25^o. The angle at the tip will be 25^o when you're done. The angle at the tip was 25^o when it was flat ground. Theoretically that extra steel will make the chisel stronger and it should perform the same at the tip. It will not perform the same at the heel, though, as that extra steel on the hollow ground chisel may be a bother when paring.

But, to answer your question, you would have to set the Tormek Angle Master at a smaller angle. How much smaller? It depends on the thickness of the chisel. See the chart Jan posted earlier in this thread.

[Ken S]

We really should be debating this in Latin wearing our Oxford Don attire.

Two images come to mind:

The first image is a skate board park, with concave ramps to build up speed. That seems to fit one idea of hollow grinding, where there is not much steel behind the blade.

The second image is the truck emergency ramps on very hilly highways. I seem to recall seeing these on the West Virginia Turnpike as part of very long and steep downgrades. The theory is that if a big truck looses its brakes on a downgrade, the driver can pull onto the ramp. the ramp goes up gradually and causes gravity to stop the truck (assisted by softer paving). This images better fits my idea of a hollow grind starting with the designated angle. It is more substantial.

I think we should consider grinds in three categories. The first is flat grinding. The second is the traditional hollow grinding of the home and small workshop equipped with a six inch dry grinder. This is the obvious hollow grind.

I would suggest a third category. This is the mild hollow grind of a larger grinding wheel. The spiritual ancestor of this group is the large, hand turned wet grinding wheel. By definition and Mr. Euclid of Alexandria, this kind of grinder also produces a hollow grind. For lack of a more scientific term, I would call this a "barely hollow grind". I would classify both Tormek models in this category, the T7 being further in the category.

Ken