It is common knowledge that skewing a plane reduces the blade’s effective angle of attack in relationship to the wood. If that’s not common knowledge for you, think about it this way, if you walk straight up a ramp, you are walking up its “pitch” angle. If you walk diagonally up the ramp, you are traveling at a shallower angle. It’s farther, walking up diagonally, but easier.
When a plane blade is pushed straight ahead into the wood, the shaving follows the pitch of the blade. When you skew the plane, the shaving follows the longer, but shallower diagonal path up the blade. This fact can come in handy if you are planing, for example, end grain and need to shear the fibers at a lower angle of attack to get the best finish. This lower angle of attack comes with the same bevel and relief angles on the blade. If you honed a low-angle plane to match the skewed angle you may need to grind the blade to a thin, fragile edge.
I recently spent too much time trying to understand the relationship between the skew angle and the resultant effective pitch angle when John Whelan came to my rescue. I found an excerpt from his book: The Wooden Plane: Its History, Form, and Function at Nichael Cramer’s website: http://homepages.sover.net/~nichael/nlc-wood/index.html. The passage is worth reading but the part I needed was this: “…the sine of the effective pitch is the product of the sine of the actual pitch and the cosine of the skew angle.” This sounded to me way more complicated than it needs to be so I cut angles off a couple of rear blocks from our plane kits and started measuring and doing the trig.
Turns out he’s right, of course. To save you some time I did a bit of Excel work and came up with a chart to show the effective angle of a the following pitches and skews:
| Skew angle –> | 10° | 15° | 20° | 25° | 30° | 35° | 40° | 45° | |
| Pitch angle | |||||||||
| 35° | 34.4 | 33.6 | 32.6 | 31.3 | 29.8 | 28.0 | 26.1 | 23.9 | |
| 40° | 39.3 | 38.4 | 37.2 | 35.6 | 33.8 | 31.8 | 29.5 | 27.0 | |
| 45° | 44.1 | 43.1 | 41.6 | 39.9 | 37.8 | 35.4 | 32.8 | 30.0 | |
| 50° | 49.0 | 47.7 | 46.0 | 44.0 | 41.6 | 41.6 | 35.9 | 32.8 | |
| 55° | 53.8 | 52.3 | 50.3 | 47.9 | 45.2 | 42.1 | 38.9 | 35.4 | |
| 60° | 58.5 | 56.8 | 54.5 | 51.7 | 48.6 | 45.2 | 41.6 | 37.8 | |
| 65° | 63.2 | 61.1 | 58.4 | 55.2 | 51.7 | 47.9 | 44.0 | 39.9 |
A common pitch plane (blade bedded bevel down at 45°, like your trusty #4, etc.), skewed 30° will attack the wood at an effective angle of 37.8°. If you skew the same plane 45°, it will cut the wood as would an edge at 30°.
I find this sort of research interesting and hope you do as well. I’m sure there are aspects of this study that I haven’t thought of and would appreciate your comments and additions.
And I think I showed some restraint in the literary application of the skew/screw pun for the title. I thought of a lot of others…
The Sharpening Blog 
This is fascinating. I’d never thought about this before, but it makes perfect sense. I guess it makes no sense to skew a plane with a high bed angle — you’d be better off using a lower angle plane without skewing it. Interesting. Thanks for doing the math. I use geometry all the time, and enjoy it, but haven’t touched trig in a lot of years.
I’m still not sure why it doesn’t make sense to have a skewed blade in a bench plane. One of these days I’m going to make a couple and see how they perform.
I think there is more to skewing than simply reducing the effective cutting angle (altho clearly that occurs). Reducing the cutting angle can lead to increased tear out which doesn’t always happen when skewing a cut, at least in my experience. There is also the shearing effect or an increase in the slicing of the wood fibres.
Also: when you skew the plane you reduce the amount of wood you remove so you cut it easily.
For exapmple on end grain a narrow chisel cut easily then a larger one.
Here you could find different values for the effective cutting angle for different skew angles using 45 degree bed angle plane.
http://members.shaw.ca/petermichaux/workshop/BevelDownOtherGeometries.html
These values are different from the ones I calculated using the formula from John Whelan’s book (and my confirming trig calcs). I wonder how they were determined.
The tangent of the effective angle is the product of the tangent of the actual bed angle and the cosine of the skew angle. Peter’s figures are right, Whelan could check his trigonometry.
Warren Mickley
I recently (independently!) derived the formula for calculating effective angle, and agree that it should involve tangents of the angles, not the sines that are used above. I wrote up an explanation here:
http://investigationsblog.wordpress.com/2010/06/07/plane-skew-angles/