Planes and Curves

I was flattening some panels by hand the other day (too wide for my machines), and that got me thinking about plane blade camber. If you search online for discussions of blade camber, you’ll find that a great many electrons have been spilled on the topic. One common thread in these discussions is frequent confusion over the fact that a bevel-up blade requires more camber (i.e., the center of the blade needs to protrude further beyond its corners) than a bevel-down blade to have the same effect.

On the one hand, everyone seems comfortable with the notion that as the blade’s bedding angle decreases, the effective radius of curvature of its edge increases. This is easy to see. First, find yourself a thin disk (e.g., a CD or DVD) and hold it up at arm’s length:

cs90
When the disc is perpendicular to your line of sight, the apparent radius of its lower edge is equal to its actual radius (2-3/8″ in the case of a CD/DVD). But start tilting it from perpendicular, and the curve flattens; its apparent radius increases:

cs45
Tilt even more, and it keeps increasing:

cs20
From the point of view of the wood fiber that’s about to have its head chopped off by an oncoming blade, the greater the tilt from vertical, the greater the apparent radius of curvature, and consequently the less the depth of cut at the center of the blade. And since the blade in a bevel-up plane is tilted further from perpendicular, its apparent radius of curvature is larger than that of the bevel-down blade unless we make its actual radius of curvature smaller (i.e., increase its camber). Easy.

On the other hand, we’ve also all seen diagrams of bevel-down vs. bevel-up planes seated on their respective frogs:

bevelupbeveldown
The resulting cutting geometries in the two cases are identical. The blade’s cutting edge comprises two intersecting planes, one formed by the back surface, and the other by the bevel. The only difference between the two configurations is that these two planar surfaces switch roles.

This is where I think some people get confused. If the two setups are equivalent, why can’t we measure the blade camber in the same way with both? In truth, we sort of can, but there’s a difference between the bevel in a cambered blade vs. a straight blade. When the camber is small, that difference is also small (and negligible), but with a strongly cambered blade, such as one we might use in a fore or scrub plane, it’s not. With a cambered blade, the bevel is not planar. In fact, the bevel is a section of the surface of a cone:

cone
That’s where the equivalence breaks down, as it’s no longer possible to directly superimpose the cutting geometry of a bevel-up blade onto that of a bevel-down blade. And so we go back to always measuring the camber with respect to the back of the blade.

Anyway, is any of this important? Only to the extent that you get a feel for how the different parameters interact, so that you’ll know how much to camber your blade to achieve a given depth of cut.

I’m avoiding the math here, because it’s been covered before (such as here and here), but I did put together a little online app that lets you plug in some numbers to see how this all works. Here’s a screenshot:

app
You can find the app here. To use it, enter your bed angle and blade width, and one of the other three values. The app will compute the other two corresponding values for you, dynamically updating the display as you modify the values. The bed angle is in degrees; the other values can be in whatever length units you choose, as long as you’re consistent (inches, millimetres, furlongs, it makes no difference).

Now, I know that someone is going to read this and then get out their micrometer and measure their blade camber to three decimal places, to which I say,

STOP!! PLEASE STEP AWAY FROM THE PLANE!!

The point of the app is intuition, not prescription. The precise value of camber that you end up with is largely irrelevant, as long as you’re in the ballpark.

Don’t worry, plane happy.

camberedblade

–Steve Schafer

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12 Responses to Planes and Curves

  1. mdhills says:

    Okay, I’ll bite — where is that CD from?

  2. abtuser says:

    Thankfully, I burned my micrometer a long time ago.

  3. Sideshow Bill says:

    I’d love to see the bloopers….

  4. Grey Guffey says:

    Can you efficiently camber bevel up blades with stones and a LV Mk2 honing guide? Seems like a ton of steel to remove. All but one of my planes are bevel up and have no camber. But I need to do them. Should I invest in a wet grinder? I have roughly 15 bevel up iros to camber.

    • steveschafer says:

      Let’s break this down into two parts:

      First, forming the initial camber – For the mild cambers that you’d typically use with a jointer or smooth plane, forming the initial curve is simple enough. A coarse diamond plate lets you get it done quickly, but it can be done using only stones as well.

      For a really deep camber, like the 11″ radius shown in the last photo above, trying to do it all by hand would definitely take a while. I use a powered grinder with a blue Norton 3X wheel, and it goes very quickly. The blade above took me less than 10 minutes, and the Norton wheel cuts so quickly that the steel barely gets warm.

      Second, honing the cambered blade – The Veritas honing guide with the optional cambered roller works very well for cambered blades. For a mild camber, you can also use the guide with a diamond plate, and that is in fact how I form the initial camber for those blades. For a deep camber, it’s tricky to reach the corners while honing, but that’s true regardless of which type of guide you use. (I compared the Lie-Nielsen guide with the Veritas, and I’d say they were equally “okay” as far as reaching the corners.)

      Bottom line: If you’re content with mild cambers, the Veritas guide will do you just fine. The addition of a diamond plate would speed up the initial formation of the camber. If you want to try to create a deep camber, some kind of powered grinder would make life a lot easier.

      • Jeff Hanna says:

        I had a question along those same lines: does it matter if the primary bevel is ground to a camber? I didn’t have a grinder when I first cambered my irons, so I just honed the camber on my secondary bevel. Not a big deal on the jointer/smoother as you’ve said, but my jack plane has an 8″ radius so it took some time. Not sure if there would be any benefit in regrinding that camber. Because of the LV MK II guide and the problem with reaching the corners as you’ve stated (you have to turn the eccentric knob to the 6 o’clock or “micro bevel” position to reach the corners), I don’t have a secondary bevel on that iron.

        Another alternative to cambering a BU plane is the Veritas custom bench planes with a 40 degree frog. This gives you the best of both worlds: a low angle attack (actually lower than a BU plane honed at 30 degrees) without requiring so much camber. I use it on my jointer plane and love it.

        • steveschafer says:

          Again, the amount of camber is the deciding factor. For a mild camber of no more than several thousandths, a straight-ground bevel followed by honing with extra pressure on the corners is the easiest way to go (but see below). As you go to stronger cambers, it gets harder, but it’s still possible.

          Eventually, you get to the point where during honing there is so much more metal to remove at the corners than in the center that you’ll tend to end up inadvertently flattening the curve a little bit every time you hone. Even with a mild camber, I find that I have to consciously put most of the effort on the corners, or else the curve begins to flatten.

          I agree that a bevel-down plane makes more sense for a fore or scrub plane.

  5. mdhills says:

    Is there value in honing the entire width of a deep camber?
    E.g., for my scrub plane, I’m typically using a very narrow portion of the blade, and not taking full-width cuts.

    • steveschafer says:

      You could certainly forego honing the corners if you’re sure you’ll never use them. Of course, the first time you set the iron too deeply, you’ll make a mess. Mostly, it won’t really matter, but I’ve certainly been in the position where an overly enthusiastic pass with the fore plane meant more passes with the jointer plane to clean it up than I would have preferred.

      Also, you can remove much more material with a traversing (across the grain) cut than you can with the grain, and I think it’s advantageous to be able to set the iron deeply for that, then back it off for later diagonal passes.

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