"Since we're sharpening the saws ourselves I think the ultimate crosscut saw would have its teeth alternate (or some other ratio) between crosscut teeth and rip teeth. Like a dado plane. Crosscut to cut the sides, rip to clean out the kerf. "When ripping there is no need to cut the sides so rip teeth work fine. What makes a crosscut saw cut? I can see pretty well what happens on the sides of the cut, the teeth are shaped like a bunch of tiny side-rabbets (even cut in both directions !) "
Hmm, actually, there's no "!" about cutting both directions. I stared at crosscut teeth long enough and came to the same conclusion, that crosscut teeth are capable of cutting both directions, too. So now me and you are the only two people in the world who see that. One direction may cut better, but each direction can cut. (After all, the pull stroke is how we start our cuts, isn't it?) Easy way to see this is to imagine peg teeth, where the up and down (i.e., front and back) angles of each tooth are equal, both at 45 degrees. Handed just a segment of saw blade filed this way, you'd have no idea which way was "front". As the angle moves away from 45, one direction becomes the "cutting direction", but the other direction still works to a smaller degree. (I don't think that's worth anything in practicality, though. I still lift the saw a bit on the backstroke. But many two-man lumbering saws were filed as peg-teeth, for the very reason of cutting in both directions.)
Anyway, I couldn't resist commenting on that, since I always thought it was only me who noticed that, and that if I mentioned it they'd all call me crazy. This notion of cutting both ways goes very much against conventional wisdom, or at least against the way it's commonly stated. But that's not the question at hand, anyway, so onward we go ... "...but for the life of me I don't see anyone cutting the part of the wood in the middle. The 'bump' between the two cutting edges of a tooth does extend all the way to the other side of the saw but it is not a cutting edge itself being far too big an angle. Does this part just sort of wear down the middle part ? This would explain why a crosscut saw (in my insignificant experience) doesn't sail through wood the way a ripsaw does."
Paul, I think I can explain it. Can you "morph" in your mind's eye? First picture a riptooth configuration, filed straight across, and at a pure 90 degrees rake. Imagine going against the grain -- literally! -- and using it to crosscut. (Or maybe you've actually done this? I have. It cuts, but raggedy as hell. Hey, maybe that's where the name "rip" came from?) Anyway, the tooth hits the fibers broadside like a snowplow straight on into ropes tied to telephone poles across a street, and the force will break them, but not necessarily right in front of the tooth. Hence, the raggedyness of the cut, since the fibers are breaking randomly left and right of the saw teeth, too.
Now in your imagination "morph" that riptooth into a crosscut configuration. You'll see the cutting edges form on alternate sides of the teeth. These edges are what cut the fibers, kind of like the spurs on a dado plane, making two very close-together slices across the fibers. (In fact, that's probably a good analogy, a dado plane, only this would be a *very narrow* dado plane blade.) What was a "chisel" edge on the ripsaw is now leaning over side to side, alternating on subsequent teeth, and contrary to intuition, yes, this still serves to clear out the area between the parallel slices. Now here's where I think you might be getting lost, and it's because, once again, of common terminology usage. Everyone calls the leading edge of a rip tooth a "chisel edge". Well, unless you lean the teeth *forward*, *into* the direction of cut, it's not really analogous to a chisel. (And woe to you if you *do* lean the teeth forward, for then you have 500 little hand plane blades going forth into the wood, and you'd have to saw with a consideration given toward grain rising or diving, just as in handplaning. But no, regardless of what everyone says, a ripsaw doesn't have teeth like chisels (or by extension, like handplanes). Ripsaws actually have teeth that work more like scrapers. Or like a handplane blade only if, instead of bedding the plane iron at 40 or 50 degrees, you stood it straight up and "bedded" the iron at 90 degrees, fully perpendicular to the workpiece. Or even *beyond* perpendicular, since many rip teeth are filed leaning back from the cut direction a bit, usually by about 10 degrees or so. So in a ripsaw, the teeth function as a series of many tiny *scrapers*, and not chisels.
Once you see it this way, now all you have to do in order to see what a crosscut's doing is to imagine that "scraper edge" just a bit taller on one side than on the other, so it's scraping out the path between the parallel slices with a scrape that's first deeper on one side, then as the next tooth passes by, deeper on the other side, and back and forth like that.
The dado plane analogy works well, I think. When plowing a groove -- i.e., down the line of the grain, not across it -- your plane does not need nickers, or spurs. Neither does the ripsaw, then. But go across the grain, and your plane needs spurs to make the location of separation of the fibers occur consistently in the same two lines (i.e, the left and right edges of the kerf), and then bring along something to pop those fibers out (which in the case of the plane is the iron, and in the case of the saw is the edge of the tooth crossing across the thickness of the sawblade.
Paul, I don't know how familiar with the geometry you are, but in case you're not too intimate with it and the geometry's getting away from you, here's another way to picture the two teeth configurations (rip vs. crosscut) in your mind.
Draw two right triangles on cardboard. (Or just imagine it.) Cut out the triangles. Lay one flat upon the other. Now stand them up on the desktop on either side that's not the hypotenuse, so that one of the sides that borders the right angle is standing straight up and the other side bordering the right angle is on the desktop. Move one cardboard away from the other just a skosh, so that you now have a cardboard-air-cardboard sandwich. Imagine there's a tightrope stretched between the two apices ("mountaintops"). This geometry, this line figure you're imagining, is exactly what a ripsaw tooth looks like. (Well, take the line geometry into solid geometry, okay, okay... :-)
To get from this to a crosscut is easy. Cut the base of one of the triangles off, by some small amount, say equal to the gap between them, so that one of the triangles is now a bit shorter than the other one. See in your mind how that tightrope between their apices now slopes downward a bit, from the higher triangle to the lower one? This geometry, made solid, is exactly what a crosscut tooth looks like. In a sawblade, of course, there's more than one tooth; in a ripsaw, each tooth's identical to the one in front of it, but in a crosscut, each tooth's a mirror image of the one in front of it, or put another way, odd-numbered teeth (if indeed they have numbers, eh?) lean one way and even-numbered teeth lean the other way.
And here's maybe why your notion of alternating rip/crosscut teeth may not be, in theory, as insane as it at first sounds. (Although putting the notion into *practice* is another thing, as always.)
On a crosscut saw, the part of the tooth that removes the waste between the parallel slices -- the "tilted scraper", if you will -- is sloped not for any intentional reason; that slope is merely an unintentional result of getting the slicing points onto the teeth, those slicing edges being the very essence of a crosscutting saw. You could achieve much the same effect as a crosscut saw, in theory, by rigging something that consists of two X-acto blades tied in close parallel followed by a thin something, say a small file tang, that scrapes along between the two slices, popping the fibers out. They pop out easily enough since the fibers between the slices are no longer connected to anything other than the lignin glue below them, making them easily "poppoutable". (Sometimes, though, I wonder if they don't perhaps "roll out" at first as the "tilted scraper" portion of the sawtooth passes over them, like rollers in a conveyor belt. I don't imagine we'll ever know for sure, unless some enterprising soul does a microscopic stop-action study on sawteeth function, something not too in demand by industry these days, I'm afraid. But whether they pop out, or roll out, isn't really as important, I think, as is the simple fact that they do come on out of there, one way or another.) (BTW, my pet "crosscut saw mystery" is how the sawdust freed by the sawteeth manages to stay in the gullets all the way to the end of the cut, rather than sliding along the tooth bevel over to the side of the saw and wedging in between the sides of the kerf and the sides of the saw, effectively locking the saw in the kerf. Hey, don't get me started on *that* one... ;-)
"I'm getting interested in trying a mixed tooth sharpening but haven't figured out how to drop all the rip teeth (rakers) down a bit after jointing so that the crosscut teeth hit the wood first."
By hand, what else? (Heh heh.) No, seriously. But the regular 60-degree file won't work, or you'll be filing the tooth adjacent, too. So try one of those feather files, the ones made for Japanese saws. A few strokes on the sloped side of a rip tooth should bring it lower by a smidgen.
BTW, Paul, I haven't really, up to this point, speculated why you're wanting to customize a tooth configuration anyway? (Especially one that flouts convention so blatantly.) I imagine you're looking for a crosscut that cuts faster? Thinking about this some more, I don't know if you'll get there with your configuration. I think the hardest part (i.e., the limiting factor) of a crosscut saw's job is making the parallel slices, not freeing the waste; just a hunch only, though. The crosscut saw is really two tools in one, a parallel slice maker and a waste remover. The sawtooth design as it exists almost by necessity combines both functions in every individual tooth. You're trying to specialize those teeth, giving some teeth one function and some teeth another. On your rip teeth, yes, you can remove the slicing function and retain the waste-removal function, but on your crosscut teeth, the ones that will do the slicing, realize that they will retain their "tilted scraper" edges, so you're not going to be able to make those into single-purpose bodies.
Then again, there is always a tension between the two functions, I think. If the teeth slice deeper than the teeth can remove waste, that's wasted effort. And if the teeth don't slice deep enough for their removal capability, that produces wasted effort, as well. It's up to the sharpener to find the balance. (Yeah, like we, simple galoots, could really do that. Right. In truth, we just follow conventional angles, more or less, and assume they're optimum. But sometimes I wonder. (As you seem to be doing.) In my earlier attempts at saw sharpening, on one junker saw I put too much of a bevel into the teeth, and I could have swore it was bogging down because it was slicing way deeper than it could keep up with in removing the waste. (Looking up the kerf, in cross-section from the edge of the board at the end of the kerf, it sure did look like pretty deep slices on either side of a mass of wood in the center of the kerf.) So maybe here's something you might try, a deep-deep-slicing saw with every third tooth a rip shape, say, to kind of "reach down in there" and clear out to the kerf slices' bottom.
Oh well, I'm just brainfloating here.
Well, Paul, I hope at least some of this was coherent enough. Hey, you ask some pretty stimulating questions. Keep it up. My fingers are dead tired from typing, but my galoot mind's a-smiling away. And it's good to talk with you again. :-)
-- Steve
P.S. Please don't forget to consider the theoretical possibility that I'm totally wrong on everything I said, too. It could happen. ;-)

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