The sole of a hand plane needs to be flat. There are three reasons for this.
To be able to create a flat wooden surface, the sole needs to be flat. The skill of the user plays a part in this too of course, but it is difficult to create a straight edge with a concave jointer for example.
To be able to set the plane to a fine shaving, the sole needs to be flat too. This is particularly obvious in a wooden plane, which tends to develop a bump in the sole behind the mouth. This lifts the edge up from the wood and you need to adjust the blade deeper to get a cut. When the plane only wants to take thick shavings or nothing at all, this is something to look at.
The third reason is reducing tearout. The front of the mouth pushes down the shaving before it gets cut, so it can't lever out a splinter ahead of the cutting edge.
How flat does the sole need to be? According to Clifton, the premier British plane maker, the sole needs to be flat within 0.075 mm. Here is how they check this: Clifton sole flatness. For the first two reasons mentioned above this is plenty flat enough. Wooden surfaces rarely need to be flat to machine room specs. But it stands to reason that the third reason asks for more precision. How can the plane sole prevent tearout if it isn't pressing down on the shaving? And 0.075 mm is about three times as much as a thin smooter shaving.
When I first did my tests as mentioned in the previous blog, the mouth size test was very disapointing. There was almost no difference between an open and a very tight mouth of only 0.05 mm. The measured results are in this diagram. The diagram shows shaving thickness versus surface quality. The surface quality is scored from 1 to 3: smooth, rough feeling spots, real tear out.
On close inspection with my straightedges, I finally found a gap between straightedge and plane sole, in front of the mouth. I really had to look just right, have a light behind the straightedge. My straightedge is manufactured according to ISO 874/2, acurate to at least 0.02 mm over 50 cm. Not quite good enough for Clifton, but I double checked the measurement with a beveled edge straight edge which should be more precise. Mine is Russian though, so I can't verify the standard it was made too. Anyway, my measuring equipement exceeds what is generally available in a woodworking shop.
This is the gap I was looking at. Clicking on the image will enlarge it. I couldn't measure it with any of my feeler gauges, it certainly passed the 0.075 mm test easilly. A piece of aluminium foil is about 0.015 mm thick and barely squeezed through the gap between straight edge and plane sole. For the American readers, one thousands of an inch is 0.025 mm.
After filing away the bump behind the mouth and a few swipes on sanding paper on a surface plate, the plane sole was repaired and no light gap could be seen anymore. I repeated the tests.
As can be seen (click on the images to enlarge them) the results are a bit better now, but certainly no where near as good as could be produced with a close set capiron. A mouth size of 0.3 mm is ineffective. In the curly wallnut only the 0.05 mouth improved the performance, and 0.05 is really tight! Maybe you can get better results with the Japanese plane sole configuration, where all pressure on the plane is concentrated just in front of the mouth, but my first efforts in this direction didn't improve anything, so I abandoned further attempts.
Conclusion of this experiment? A plane sole needs to be pretty flat, but to be able to control tearout with the size of the mouth of the plane, the sole needs to be absolutely flat with the front of the mouth pressing down on the wood. And even then the results aren't great. But a tight mouth can still be helpfull in combination with a higher cutting angle or a close set capiron.