The use of the words ‘tension’ and ‘tensioning’ in the area of custom handsaw manufacture is surrounded by a cloud of mystery and misperception. As it pertains to backsaws, tension, refers to the grip of the folded saw back on the plate or blade of the saw. If the tension of the saw back causes the plate to be
stretched or compressed longitudinally the tooth line of the saw plate will be deflected and will look as if it is bent. Correcting a problem of this nature is really very easy. On the other hand, tensioning as it is used in reference to hand or panel saws which lack backs refers to the selective application of hammer
blows to the metal of the saw plate to induce internal stress features that are used to straighten and stiffen the plate. In my experience making saws I have come to find that saw plate tensioning, for want of a better term, is vital to producing a saw with a straight tooth line. I only make backsaws using folded backs because I like the traditional looks as well as the serviceability afforded because they can easily be removed and replaced without resort to heat-guns and/or solvents to remove the plates of saws made
with slotted backs. I make my backs by driving the back down the length of the saw plate, some call
this the 'side-entry' technique. My backs have zero-clearance between the lips of the back when I'm done folding them which prevents driving the plate down on to the plate perpendicular to the long axis of the back.
Here's an illustration:
As the back is driven from left to right down the saw plate the friction between the lips of the back and the top of the saw plate tends to stretch the plate ever so slightly. The tooth line however is not stretched and the differential stresses applied to the saw plate tend to cause the toot line side of the plate to wrinkle. This is a problem when using thinner saw plates and it is particularly acute when I put backs on my taper-ground 0.015" saw plates. These saw plates generally taper between 0.002" and 0.003" from the tooth line to the bottom of the back and unless properly tensioned they are impossible to get straight.
In the process of changing the position of the back on a saw I thought to document the process of tensioning on a saw build I have described on another thread in this section (http://www.woodworkforums.com/showth...=181862&page=2).
First here's the saw.

It's my interpretation of a Disston #4, the saw plate is 0.0155" tapering to 0.0135" measured just below the back. When I was setting up this saw I originally fitted a stainless back but found that it was too light for my liking and switched to one of my 0.125" thick heavy brass backs. I got the saw back together and found that the projection of the back above it's mortise in the stock was higher than I like.
This is how the tooth line looked before I started.

So I need to move it down and deepen the mortise to suit. First I took the plate/back assembly out of the stock and clamped the toe end of the plate gently but firmly in the vise.

You want the vise tight enough to hold the plate without slipping but not so tight as to dent the plate with the vise jaw serrations.
Now to induce some flex to the plate I use my patent-pending saw-back remover to lever the back up.

Now that's not very pretty is it?

So how to fix it? First clamp the plate up in the vise and then, with a soft faced hammer tap the back back down onto the plate VERY GENTLY.

As you tap you will notice two effects. First the tooth-line will visibly straighten and second the ringing sound of the plate will decrease in frequency until it reaches a minimum.
Better!

And finally we're straight again.

And the back is down where I want it to be.
P.S.,
If the back is already stuffed all the way down on the saw plate you won't get anywhere tapping it down, you must first pry it up a bit using the patent-pending saw back remover.