Dr.Al
Old Oak
First of all I'll get a quick disclaimer out of the way. I know this is getting very, very close to the banned topic of sharpening. I'm not trying to comment on whether or not one should use a honing guide or what angles one should sharpen one's tools at, just a bit of a point of interest on the maths behind honing guides. Hopefully that's within the limits of what's acceptable :lol:
With that out the way...
Something had never quite sat right with me with the projections written on the side of my (Eclipse 36) honing guide:
I couldn't quite get in my head how the plane projections are fixed when it's the top surface of the plane iron that defines the angle (thinking about it now, it's probably because when the guide was designed most plane irons were the same thickness). Anyway, that got me going down a rabbit hole and I decided to work out the maths involved:
In that image, r is the radius of the wheel (r = 9.5 mm in the case of the Eclipse guide I have), w is half the body length (w = 20 mm in the case of my guide), p is the projection and d is the distance from the centre of the wheel to the top surface of the tool.
For my guide, d is about 17.5 mm for chisels and 20.5 mm plus the thickness of the iron for plane irons. Chisels are referenced to the top surface whereas plane irons are referenced to the bottoms, hence the difference:
What that means is that the correct projection for a given angle is decidedly different for the (say) 2.1 mm plane iron in my Stanley #4 to what it is on the 3.4 mm iron on my Axminster #5 or the 5 mm iron on my Veritas BU smoothing plane. Now of course (oops, straying into banned territory here) bevel angles don't matter much on BD planes, but on the BU smoothing plane I'm almost certainly getting a different angle to what I would expect as the honing guide projections assume a 2.1 mm iron.
Does it matter? Well that's a banned topic, so I won't answer that :lol:
Anyway, to prove the point (and because I quite enjoy CAD), I thought I'd model it. Here's a model of the honing guide:
This is what it looks like with both a chisel and a 2 mm plane iron fitted simultaneously (because anything's possible in CAD
) and with the angle set to 25°:
The projections don't quite match the writing on the side, but they're close enough for me given that my model of the guide was based on somewhat haphazard measurements.
Now look what happens when I stick a 5 mm plane iron in:
Similarly with 30° and a 2 mm iron:
and 5 mm:
As I said, I'm not sure how much it matters, but I found it interesting to delve into the (relatively simple) trigonometry and I thought others might be vaguely interested too.
It's worth noting that the Veritas Mk2 honing guides always reference off the top surface, regardless of the tool, so none of the above applies to them.
With that out the way...
Something had never quite sat right with me with the projections written on the side of my (Eclipse 36) honing guide:
I couldn't quite get in my head how the plane projections are fixed when it's the top surface of the plane iron that defines the angle (thinking about it now, it's probably because when the guide was designed most plane irons were the same thickness). Anyway, that got me going down a rabbit hole and I decided to work out the maths involved:
In that image, r is the radius of the wheel (r = 9.5 mm in the case of the Eclipse guide I have), w is half the body length (w = 20 mm in the case of my guide), p is the projection and d is the distance from the centre of the wheel to the top surface of the tool.
For my guide, d is about 17.5 mm for chisels and 20.5 mm plus the thickness of the iron for plane irons. Chisels are referenced to the top surface whereas plane irons are referenced to the bottoms, hence the difference:
What that means is that the correct projection for a given angle is decidedly different for the (say) 2.1 mm plane iron in my Stanley #4 to what it is on the 3.4 mm iron on my Axminster #5 or the 5 mm iron on my Veritas BU smoothing plane. Now of course (oops, straying into banned territory here) bevel angles don't matter much on BD planes, but on the BU smoothing plane I'm almost certainly getting a different angle to what I would expect as the honing guide projections assume a 2.1 mm iron.
Does it matter? Well that's a banned topic, so I won't answer that :lol:
Anyway, to prove the point (and because I quite enjoy CAD), I thought I'd model it. Here's a model of the honing guide:
This is what it looks like with both a chisel and a 2 mm plane iron fitted simultaneously (because anything's possible in CAD
) and with the angle set to 25°:The projections don't quite match the writing on the side, but they're close enough for me given that my model of the guide was based on somewhat haphazard measurements.
Now look what happens when I stick a 5 mm plane iron in:
Similarly with 30° and a 2 mm iron:
and 5 mm:
As I said, I'm not sure how much it matters, but I found it interesting to delve into the (relatively simple) trigonometry and I thought others might be vaguely interested too.
It's worth noting that the Veritas Mk2 honing guides always reference off the top surface, regardless of the tool, so none of the above applies to them.
