It depends where you live (e.g. climate) and the type of soil (clay, coral,
heavy organic, sand, etc). 42 inches is generally the deepest needed to
stay straight barring a hurricane, earthquake, tornado or high straight-line
winds. You can rent a power or hand auger. Make sure you know where the
underground utility and sewer lines are. Most areas have a service that
mark these for free and your city should be able to tell you where the sewer
line is in your yard.
Also, ask locally about any codes regarding decks. This is a good
reference for depth of a weight bearing arbor.

"Dica" wrote in message
...
i want to put up a 3 post triangular arbor and sling a hammock between the
outer posts. i'm looking for a 2 person hammock, so the posts should be
able
to support up to about 350 pounds. how deep should i sink the posts? i'll
be
using 2X8 pressure treated wood to form the triangle at the top of the
arbor, so there will be additional support where the two outer posts would
want to sag in to the middle.