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The Hand Saw
This is a normal hand saw, 24" to 30" long.
This is a 'Panel Saw', a smaller hand saw (generally 20" or less).
Both have a thin, flexible saw plate (Blade) without a rigid back.
Available with a rip cut, cross cut or combination (SASH) tooth pattern.
PPI - Points Per Inch is the number of teeth. or 'points per inch' along the saw plate.
Measured from GULLET to GULLET (the inside dip between the teeth).
More teeth will give you a slow, clean and fine cut.
Fewer teeth will give you a faster, aggressive, less refined cut.
This is a 'Rip Cut Hand saw' - Used to cut along the grain (ripping cut).
Not considered a precision tool but handy for breaking down material.
They have 4 to 7 points per inch (PPI) and they're easier to sharpen than a crosscut tooth pattern. You'll see the number of teeth/points per inch stamped on the plate (Blade).
A rip tooth comes to a simple point with a sharp edge. It doesn't have a bevel cut on the FACE (front of the tooth) or FLANK (back of the tooth).
This is a 'Cross Cut Hand saw' - Used to Cut across the wood fibers rather than with them.
Teeth have a beveled face and flank to slice through wood fibers for a clean cut.
As a result, they are more complex to hand sharpen but not difficult.
Expect 7 to 12 points per inch (PPI).
Then there's a 'Sash Hand saw' - Generally considered the jack of all trades, master of none.
A Sash tooth pattern is a combination of ripping teeth and cross cutting teeth.
If you could only buy one hand saw, choose a rip saw.
It'll rip well but crosscutting won't be as refined as a crosscut tooth pattern.
Trying to rip with a crosscut handsaw isn't advisable.
The Back Saw
A back saw will have the same features but with one distinction.
It will have a rigid spine (the BACK) made of brass or steel to strengthen the thin metal saw plate (blade).
Designed for precision with fine teeth and more PPI than their larger cousins (hand saws). Available with rip or crosscut teeth patterns.