12 February 2011

Hollow and round planes - 2

Still nothing about my 6 missing hollow and round planes.  This more or less ends my current perspectives to experiment with profile planes.  Let's go virtual.
I finally did what I intended,  trying Sketchup out as a way to look at problems when sharpening a blade on sandpaper on a profile set with the plane.

- I drew an arc 10 wide with radius 10.  I discovered I could do that by entering 10 and 10R to set the arc.  I already downloaded a arc: center and 2 points plugin to emulate compass work.  That's the frustrating part of Sketchup,  it is good but far away of descriptive geometry techniques. Where is my Sketchup divider compass?
- Made a surface of it and extruded it to volume and made it again a surface by deleting the bottom surface.
- Intersected it with two planes at 45° and 30°.  Checking literature I found that a relief angle must be between 10 (11) and 15°.  Seeing that the edge of the blade shows depressions and cracks in the corner for hollows,  a low relief angle is better for the edge.  But with an extreme relief of say 0°, the blade would not dig into the wood and shavings caught between blade and workpiece could slide along unharmed.
- By selecting the two surfaces I could let Sketchup create the intersection line. After that I grabbed the two intersected planes and flipped them on top of each other.
The result are two different ellipses. Ellipses? I should have remembered my trigonometry and put, at last, my sin() and cos() functions to good use.

The result shows there is a difference,  and for hollows it is a problem as the sides of the plane will dig in. A first solution is to sharpen on a bigger profile, a 10 on a 12 profile etc.  The next idea that comes to my mind is the ruler trick.  Applying the ruler trick to a hollow would thin out the sides and make them less deep.  So it would weaken the sides of the blade (that's bad), but also make the curve shallower (that's good if you already messed up the depth).

I need to model the ruler trick with a profiled blade.  Another aspect I need to look at is sandpaper thickness. Certainly for smaller planes  the thickness of the sandpaper influences the geometry.