I'm new to hand tools woodworking, and started working with a ryoba saw. I wanted to know - to what extent does the straightness of the saw affect the straightness of my cuts?
How should I test the straightness of the saw and what is the tolerance? I mean, I suppose that a saw isn't required to be as flat as the sole of a hand plane, is it?
Hand saws do have to be straight for them to work right.
While you can use a saw which has a bend at a certain point, or a slight bow along most or all of its length (both flaws not uncommonly seen in old saws you might buy secondhand), it's far from ideal.
A saw plate with a bow can tend to bind in the cut and will tend to impart that curvature to cuts. While this sounds very bad it actually isn't an absolute dealbreaker1 because you can do your best to compensate for it while cutting, and, almost all sawn surfaces will be refined further in the next step anyway.
This applies to long edges (a rip cut) as well as faces (created when resawing) and the typically much shorter ends that have been crosscut. See Ripping vs Resawing - is there a reason for the difference? if you need more info. Edges will be jointed flat/straight (and generally square) and ends will be 'shot' dead straight and square in some setup, but most often in a shooting board of some kind. See What is a shooting board? if you're unfamiliar.
In hand-tool woodworking it's extremely rare to use a surface "straight from the saw" and it tends to be an expert-only thing. (Excluding rough carpentry and coarse 'rustic' work.)
How should I test the straightness of the saw and what is the tolerance?
In general sighting along the saw when the plate is oriented vertically is sufficient to tell whether a saw is straight or not. You can go further if there is a flaw and you need to localise it but basically just looking along the plate and asking yourself "Does this look straight?" is enough.
And in your case, with this saw specifically, as it's a ryoba notice how flexible the plate is. You might even call it floppy! If you hold it in the air horizontally the plate will just naturally sag. If you hold it up vertically it'll be much, much straighter and should have no bends in it 2.
1 I should probably mention that both bends/kinks and bows along the length can be fixable, or at least can be lessened, with some careful handwork by the buyer. Because of the interest in secondhand tools there exist various online guides to doing this, some very good. Using one or more of these guides even a first-timer can do this kind of thing successfully if the problem is not severe...... it might be argued that a beginner should probably pass on such a saw, however, purchasing only for the handle or even just the brass nuts and medallion can be viable strategies if the price is right.
2 Do note this also applies to Western panel saws, both rip and crosscut; even though they have much thicker and stiffer plates than most Japanese-style saws they are long enough to bend down from the handle end under their own weight.
