Good question - similar to how long is a piece of string? Obviously an engineer can calculate this out specifically -taking into account numerous factors - the sail size, shape, configeration , number of corners ,exposure/location of other buildings and the wind zone to name a few !
But to give you some indication we took a medium sized webbing edge 4.7m x 6m rectangle Hypar Shade Space sail and tensioned it up to the recommended tautness. which what we call "drum tight" throughout and nil sag in the middle. The139mm Steel poles were just begining to flex inwards a few mm at the top which is normal . We had attached an inline digital scale between the sail and the pole and you can see the reading in the photo.
With a force of just over 200 kg ( 440 lb ) on a calm day with no wind you can see why the recommended steel sizes for shade sails are most likely a little higher than you may have thought.
Remember in a storm or big wind this pressure will increase greatly so thats why a 100mm x 100mm (4x4) timber fence post is not a good idea to rely on . also remember that every 500mm (20 inches) taller a post is causes signifigant more leverage at ground level.
see our pole size recommendations here
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Best Outdoor Shade Sail Shape for Your Space in Australia