You can see on those photos how a lot of the flame is wasted heating the stand and just going up the sides.
A very much maligned (but it works...) way of determining the optimal burner to pot distance is simply to bring some water to a boil
(just use your stove...) then hold the pot over the flame and move it slowly up and down .
At some point you will see a more vigorous boil and that is the right distance for your burner/fuel combination.
Start at about two inches away.