riddle me this

[Rob]

 

[Herman Trivilino]

So if one fixes the angle at the very tip of the edge of both hollow and straight grinds and then compares them, the hollow grind will have more metal BECAUSE the chord will be at a different angle than the straight ground bevel.

Well, that is the way it's done when one uses the Tormek Angle Master jig to set the bevel angle.

It could be argued that that is the only accurate way to measure a bevel angle.  One is concerned with the angle that's made at the cutting edge, anything else is an approximation.

[jeffs55]

 dancing angels are about to hove into view....but this was about honour, not engineering :-)
[/quote]
Since we are arguing semantics, the angels would heave into view unless they are gone and then would have hove into view, past tense. I think!

[Rob]

LOL....thanks for the lesson in semantics Jeff :-)  And I thought I was being pedantic :-)

[Ken S]

I found this while studying the archives, and thought it was worthy of being read again.

Ken

[Jan]

For the majority of tools the hollow depth is very small. Exceptions are very thick tools. Recently I have calculated the hollow depth for my heavy duty mortise chisel with a bevel length 1 5/8" (40 mm). The hollow depth from a 10" stone should be 0.03" (0.8 mm), from a 8" stone it should be 0.04" (1 mm) and finally from a 6" stone it should be 0.05" (1.35 mm).
Nevertheless the human eye is able to recognize even a tiny hollow at first sight. The reasons for this are deeply discussed in http://forum.tormek.com/index.php?topic=2295.30

Jan

[Jan]

I have asked my brother to make a scaled drawing showing the edge of both hollow and straight grinds. In the figure below there is the situation for a grindstone with radius R = 125 mm, chisel blade thickness 4 mm and 25 degree bevel.



The dimensioned detail below shows the situation at the edge. All measures are given in mm.



The drawings support the statement from the Tormek manual that the hollow "has no practical influence on the function of the tool".
Jan

[Ken S]

Very impressive, Jan.

For those who might still be concerned, adding two or three degrees to the bevel angle will compensate. This is probably good practice with narrower chisels which concentrate the mallet force. It will also eliminate having to reduce the mallet force by 3.89% for the narrower chisels. 

Ken

[Jan]

Rob has asked the principal question: "Is there less metal behind the edge of a hollow ground edge than a straight ground edge?".
The answer from the two scaled drawings above is following: the wheel grinding process leaves more steel behind the edge than a straight grinding.
This statement is true if angle is measured at the very tip of the bevel.
Sorry for my belated remarks and thanks Ken for reviving this valuable thread.
Hats off to Rob for some brilliant posts!
Regards Jan