......When you say tap the spine up and down, trying to work out which way is up- Hitting the spine down towards the teeth, or towards the handle, or tapping the sides?
By "up" I mean away from the tooth line - as deema said, it's often knocked down so the blade is deeper in the spine at the front. This is so common on old saws you may think it's meant to be that way, but I think it's just the result of knocks & bumps. Tapping or re-fitting the spine will frequently cure a curved blade, but certainly not always. Saws get mistreated in their long lives & blades & spines do get buckled & bent - tapping the back won't fix this.
There have been discussions amongst the saw-making/restoring fraternity about how far a back should be tapped down, but little consensus. It obviously depends on the depth of the slot, for starters. Folded backs have a "full" slot, and new or newish saws with folded backs that I've handled typically have the blade 2/3rds to 3/4 of the way in. Slotted backs (i.e. those made by cutting a slot in a solid bar) vary according to who made them - some makers cut quite shallow slots and glue the blade in with a metal glue like "Loctite", or in the case of one boutique maker, he rivets them in. Traditionalists frown on such measures because they say it robs them of the "adjustment" potential, but the adherents of "fixed" spines say you won't need to adjust anything because the blade can't get out of whack. Choose your own side...
Claims are also made that folded backs are superior to those made by slotting a solid bar. I've yet to see any convincing arguments let alone empirical data that would back up this claim. In my view, a well-folded back & a well-made slotted back should work identically. As long as the blade is gripped fairly evenly or at least in the 'right' places it should do what it's supposed to do. A bit tighter over the first couple of inches & the last couple can work well (see below).
Now, about this "tensioning" business. I fail to see how tapping the back vertically onto the blade introduces any useful tension in the blade. I follow the example of an American maker when assembling a saw. I apply the back so it is sitting about 10mm forward of where it should be, & tap it down as far as required. Then I carefully tap the spine back until it snugs up to the back of the recess in the handle. This is where the tighter grip at back & front serve a purpose, it
will introduce some tension along the blade, though not much, & it is all along the top of the blade but this
may assist in holding it straight.
I've been experimenting with this "tensioning" method for a couple of years; it took a bit of fiddling to get it right on the first couple I tried, but I think I have it reasonably sorted now. Does it make a noticeable difference to the action of the saw? At first I thought so, but have decided it's as much wishful thinking as a real effect; it's certainly not a night & day thing.
There are several factors that influence how a user perceives a given saw, such as grip or "hang" angle, which affects effort & control. Size, weight & length of blade are also major factors. These are all somewhat arbitrary & subject to personal preference, but what makes the biggest difference of all & universally appreciated, is having well sharpened & set teeth of an appropriate pitch for the job in hand....
cheers,