Thread: The Secret to The Secret to Cambering Bevel Up Plane Blades

I was interested ... and I think I ended up reproducing the original calculation.

d = the depth of camber
w = half the width of the blade
alpha = bevel angle.

The real, curved bevel is approximated with prisms and straight lines.

End result: the amount removed is proportional to the width; to the square of the depth of camber; and to the tan of the bevel angle.

I remember looking up the formula for getting the radius from a chord of a circle for another post ... it was simple, and made sense after I had thought about it a bit ... I'll look again.

Practically though, surely you can get a single bevel by marking the curve on the blade, grinding it vertically on the line, and using a jig (or not) to do the bevel at the radius you want. If you can hone a hollow grind by hand, then you can do a curved bevel by progressively rotating the iron across.

Cheers,
Paul

img001.jpg img002.jpg

That curve I see in the drawings is for a scrub plane, you can use that blade in a low angle jack plane and have it effectly become a scrub plane but you will not have such an extreme camber on a no.7 jointer or a smoother. The camber must be very small.

It isn't to scale ... my artistic skills are non-existent.

The approximation depends on the camber depth being much smaller than the width of the plane.

Cheers,
Paul

Thanks for clearing that up it is important that you did as others might of of mistaken it and replicated that on their blades.

Regarding the radius/chord relationship ...

if you fiddle around with the diagram at (Chord - Math word definition - Math Open Reference)2. Given the radius and distance to center



You can easily get from r^2 = d^2 + c^2 (c = half the chord)

to r = (c^2 + a^2) / (2a) (a = the offset back from the circle)

- - -
There's a calculator here: Chord/Radius Math

and if you give it 1" (end to centre) and 1/16" or 0.0625 (you can enter it either way)

it gives you r = 8 1/32"

Cheers,
Paul

I don't know where this distance has come from but if we start over complicating what should be a simple camber that's done by eye nothing will get done. Keep it simple press down on the corner of the blade and alternate to the other till you get a camber. Wasting your time calculating and measuring magic numbers that don't exist is time wasteful.

I think that's what was said to Socrates, Pythagoras, Isaac Newton etc

Paul I appreciate the explanation. My original question was because I wasted to know the math for the opposite side of the curve if you like.
I don't see the connection section1 between understanding mathematical principles and wasting time. If I want to know and someone else wants to participate in the discussion that's great. If you don't that's fine also.Having this discussion in one thread of a large forum is like this to a couple of blokes discussing a pov in the corner of a pub over a beer.
I have free handed a curve on a blade before for a bevel down plane. I have also used a template. I started this dialogue to see if I could use a measurement to repeat the same curve for any given diameter.

That's fine brother understanding the mathetical process isn't important to me as it serves no purpose it neither hinders my work no does it benefit it, I once upon a time used to over analyise everything, over complicate everything and try my hardest to replicate machine work but as my friend Tony Konovaloff said "We are not machines" but look maybe I've misread the first question. To my understanding your making a template to create a camber this is what I understood and my answer I feel is appropriate to the question. None of the old school craftsman Tony, Chris, Frank, Paul, my grandfather just to name a few have used a template to create a camber. It is done free hand or with the aid of a jig and to approx by the eye, same is applied to dovetail you can do it freehand and those mentioned above do it freehand or you can use a jig it is upto you it makes no difference in the structural strength whether what ratio it is how far apart it is just pure and simple visual appreance.

If you want cambers to match apply the same pressure to one corner of the blade as you did the other and apply the same amount of strokes on each side and after a while it will be the same on both sides. To get 1/16 approximate with the eye if you want precision use a ruler if you a go little over it won't matter if it's microscopic then keep going at it. This is my work method that I have been taught by the old guys which is the same that has been passed down to them and I'm still learning.

I sincerely hope I have helped and not hindered in anyway to your learning of this great art.

Originally Posted by Pac man

I am wondering if any one has done the math to cambering bevel up plane blades in Dereks article here

What i understand from reading this paper is that when constructing a template for grinding the camber i get a block of wood the same width of the blade and mark of 1/16" of each end, then draw an arc across this. Is it my assumption from what is written that this measurement always produce a 5 1/2 inch camber.

If this assumption is correct what distance do i measure from the end of the timber to create other bevels particularly an 8 1/2 inch template. Apart from getting the pencil and string out to draw the arcs is there another way to do the math?

look, i could be wrong, most likely are as i only work these things out in my head and my head doesnt work as well as it used to..but it looks to me as though derek has made an error or a typo, or i'm just missing something atm <shrugs>... Derek will probably think i'm having a go at him again, however, as far as i can tell coming in 1/16 or approx 1.5mm will give you an 8-1/2 inch radius not 5-1/2", coming in approx twice that will give you a 5-1/2 inch radius , he mentions coming in 1/16 on the ends for a 5-1/2 radius but the photo shows he has overshot that by about twice that measurement which would be the correct measurement (for 5-1/2" radius on a 2-1/4" blade), there is also some room for confusion as the article mentions using a 2" wide blade but the photo shows he is using a 2-1/4" wide blade, the discrepancy is small but can alter the calcs a fair bit.

radius squared, subtract half the cord (1/2 width of blade) squared, the answer (value) is square rooted (!) which gives you a number you then subtract from the radius, which gives you the final amount you need to come in on the edge of the blade

i see where section1 is coming from as well, i use a roofing square to find any angle in a roof, young guys now rarely know how to use one they use a calculator, which is quick and simple but loses something in the process


i sure wouldn't use calculations to determine the radius, i go by look and feel but i can see how some people understand it coming at it backwards, besides thats how a book might describe it


cheers
chippy

Originally Posted by Pac man

If this assumption is correct what distance do i measure from the end of the timber to create other bevels particularly an 8 1/2 inch template. Apart from getting the pencil and string out to draw the arcs is there another way to do the math?

The website I mentioned will give you that Packy

Give it the width of the blade as the "End-to-end" measurement and the depth of camber as the "Offset" amount, and it will tell you the radius of an arc that fits that scenario.

And yes - the numbers are different. I get ...
2" by 1/16" = 8 1/32" radius.
2" by 1/10" = 5 1/16" radius.


But practically speaking 1/16" = 0.0625", 1/10" = 0.1000"
The difference between them is 0.0375" ... just under a millimetre (40 thou)
Pretty close if I was marking it out.


Re practicalities, I am all for it. Admittedly I don't know squat about real woodwork, but I can't yet imagine any situation where a 25^o bevel is fantastic but 23^o or 27^o only so-so.
I implied in my post that I'm sure this is one of those situations where it can be done for real in 5 minutes or written about in 30 pages.

I think everyone should probably try sharpening by hand ... then once you have the right grind you can hone by moving the iron perpendicular to the edge at each section along the edge.
And it carries over to carving chisels and moulding plane irons ... you just start to need slip-stones.


But finally, to me it was an interesting .. and fun ... mental exercise. I wasn't getting it from the written description, so I started trying to sketch it. What I at first thought was going on wasn't the correct idea - and that eventually dropped out from considering the sketches. It wouldn't matter if it was sailing, shooting or morris-dancing ... fun and engaging for some people ranges from irrelevant to sickening to others.
Other people like crosswords - or planning out a kitchen install.
Hey - there are pen-turners here.

You might consider it a bit interesting that the expressions fall out so neatly - unexpectedly even - from the diagram.
Personally I like that Derek came to the non-obvious conclusion that it might be more efficient to grind a normal straight 25^o bevel and then impose a higher degree secondary camber upon that.

Cheers,
Paul

Originally Posted by ch!ppy

i see where section1 is coming from as well, i use a roofing square to find any angle in a roof, young guys now rarely know how to use one they use a calculator, which is quick and simple but loses something in the process

I had wandered across a big entire book ... books ... on this online and had a search to try to find them again.

I have often thought - wrt woodwork articles - that instead of trying to mark out (eg) a 12.5^o angle it could more accurately be done by measuring along 'x' cms and up 'y' cm. You can make it as accurate as you like by making the x and y larger.

The books I had seen gave me the impression of a carpenter and his framing square like a samurai with his sword - inseparable.

I found this first: The Power of a Carpenter’s Square » LarryEiss.com



He links to amazon, but they are free here: The Evenfall Studios Woodworks Library

Look at all the titles by Fred T Hodgson ... it was searching his name that lead me there in the first place, but I can't remember why I was chasing after him

Cheers,
Paul

I'm with ch!ppy and section 1. So much has been written by so many that just over complicates a simple craft. It's a highly skilled craft but skills anyone can learn.

A perfect example of just getting on with it. The right size and a top job in 3 days.
https://www.woodworkforums.com/f11/ci...louvre-162867/

Originally Posted by Ball Peen

A perfect example of just getting on with it. The right size and a top job in 3 days.
https://www.woodworkforums.com/f11/ci...louvre-162867/

I like it a lot! I also like the thicknesser in the background

Many ways to skin a cat (seems like a strange expression now-a-days) ...
but if there were 7 windows to do in different sizes then ...
you might come up with ...
(a) a different non-calculating way/jig that could be applied to them all,
or equally ...
(b) a calculated approach that derives a set-out method that applies to any size of window.

One point to make is that while this thought process might be being addressed to bevels and cambers here, it also applies to other situations - in carpentry for example.

In Modern Carpentry A Practical Manual by Fred T. Hodgson, 1902 He's pretty emphatic that "Geometry" is a positive skill for the tradesman ...

modern_carpentry_1902_a.PNG modern_carpentry_1902_b.PNG modern_carpentry_1902_c.PNG modern_carpentry_1902_d.PNG

We had a big fire here last year - 64 homes damaged or gone - so there has been a lot of rebuilding.
Just recently I have been driving past several newly framed roofs - and thinking about the serious number of angles that occur in roof-framing, and how it all has to come out square (uniform at least) and level.

Cheers,
Paul

Geometry is here to stay and is an important part of most trade training. The cambre of a plane iron or changing the leading edge of a gouge for many is intuitive, direct, and fast .