Scrubbed Coves
#5
A few weeks ago I mentioned making a notched log.  https://forums.woodnet.net/showthread.php?tid=7328788   
When I worked the notch with a scrub plane, I got a surprisingly smooth, uniformly curved surface.  The chisel marks disappeared.  So did scallops from the highly curved blade of the scrub plane.   Here’s how it looked:

[Image: IMG_2799_zpsmsmpsleg.jpg]

The explanation I offered at the time is that curvature starts because the scrub plane can't get all the way into the corners of the notch.  Once started, curvature will increase as long as center of the blade can reach the wood.  But bridging across the sole of the plane will eventually leave the blade “high and dry,” unable to cut unless it is extended deeper.

To test this hunch, I scrubbed a series of with-grain coves in 2x12 KD-WRC scrap.  I screwed parallel rails to the workpiece to act as a 3-3/8” starter notch and then scrubbed a 3”-wide cove to a succession of curvatures.  

I began at 1/16” vertical blade projection and scrubbed the cove until cutting stopped, then measured the radius of curvature.  Then I increased the projection by 1/64” and repeated the process until the curvature of the cove exceeded the effective curvature of the blade.  Beyond that point the cut moves to the corners of the blade, and the surface of the cove becomes stepped and ragged.

LN says they supplied the blade with a 3” radius, bedded at 45º.  Projected perpendicular to the sole, the cutting edge profile should follow an arc with radius-of-curvature at the center of 3”√2 or 4.24”.

The measured cove curvatures are consistent with those predicted from the geometry of bridging.  Developing the relationship between blade projection and cove curvature was a fun little trip down the Halls of Euclid.  I’m happy to share the math if anyone expresses an interest.  Here are the results. 

[Image: scrubbed%20curvature%20experiment%20tabl...kmwzej.jpg]

Photo 2 shows the cove surface still mostly silky-smooth after planing at 7/64” projection. 
[Image: IMG_2846_zpstdpkt7hk.jpg]

 Photo 3 shows significant deterioration of the surface starting when the projection is increased to 1/8”.  The top step appears to be intrinsic to the process, but beyond 1/8” more steps appear.  

[Image: IMG_2850_zpsdjym8ror.jpg]
 
Photos 4, 5 & 6 show successive initial cuts at 7/64”, 1/8”, and 9/64” vertical projection.   Note how the cut widens as the projection increases.  

[Image: IMG_2844_zps1yak1eww.jpg]

[Image: IMG_2847_zpsxynlih8k.jpg]
[Image: IMG_2849%201_zpsteblr8kh.jpg]

In Photo 5, the cove radius from the previous cycle almost exactly matches the effective cutting radius.  The corner cuts in Photo 6 show that the previous cycle @1/8” has taken the cove radius below the effective radius of the blade.  The blade is now less curved than the cove it is shaping.

I expected the changeover from center-cuts to corner-cuts to occur at 7/64” projection, when the limiting radius went below 4.24”, the nominal effective cutting radius.  Instead, the changeover occurs at ~1/64” greater projection and correspondingly lower cove radius.   

This was puzzling until I examined the cutting edge.  After a few years of sharpening, it seems I’ve ground the corners preferentially, making the blade radius closer to 2-5/8” than 3” [Photo 7].  2-5/8” blade radius gives an effective cutting radius of 3.7”, consistent with the observations.

[Image: IMG_2860_zpsdx81reti.jpg]

So, I seem to have a self-limiting, convergent process that can make refined large-radius coves under some circumstances using a hand tool deigned for coarse work.  There’s something very pleasing about that incongruousness.  “Such order from confusion sprung….” 

Is it possible to actually do anything useful with this?  I’m not sure yet.  I think I could make nice cove in this soft, straight-grain cedar at any radius greater than the effective blade curvature, if I wanted some.  Apart from the ironwood notch, I have not tried it on harder woods or complicated grain.  I have some possibilities on the back burner.
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#6
Core box planes are designed to do this. Interesting topic.


John
"When I nod my head, hit it." - M. Howard.


"I think you should learn how to use hand tools before you even touch a power tool." - Sam Maloof
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#7
I have, once or twice, used a scrub for scalloped finish work with the grain, with very good results - surprised me.
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#8
John,
Thanks for pointing that out.  
http://www.woodmagazine.com/woodworking-...-box-plane
There are no new things under the sun.
Wink

Paul
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