How is the shape of the blades of an air fan determined? Trial and error, or is there a theory behind it? What are they trying to maximize, volume of air dislocated per rotation?

-
I guess a follow up question is how do you measure the amount of air that is dislocated. – archgoon May 9 '11 at 19:24
More on fans: physics.stackexchange.com/q/9030/2451 – Qmechanic May 9 '11 at 19:35
+1 for using the Engineering tag. Got to support my kind :-) – ja72 May 10 '11 at 2:16
'Dyson' make a blade-less fan. No idea how it works though :P – qftme May 10 '11 at 8:03
@qftme - there is a fan in base and then a series of angled holes in the ring shaped part that blow the air toward you. The clever part is that this high speed air drags more room air through the loop in the middle so gives you much more flow than the small hidden fan alone – Martin Beckett May 10 '11 at 15:34

Mostly trial and error - but in a computer.

A combination of Computational Fluid Dynamics (modelling how the air flows over the blade) and Finite Element Modelling (how the stresses in the metal behave)

Both of these are complex areas - and when they come to together you need a lot of expensive computers and some even more expensive engineers.

-
Maybe you also want to add en.wikipedia.org/wiki/Blade_element_theory , which is basically a subset of the computational methods you are referring to, but still often used. – Bernhard Aug 27 '12 at 8:01

I would guess the Lift/Drag ratio of the blades is important. Lift = wind thrust (and speed), and Drag = friction and power loss.

Since the part of the blade moves slower the closer to the center, the angle of attack needs to increase to provide the same wind speed. Keeping an even velocity profile is probably important in order to minimize losses due to turbulence.

There is probably a lot to be done with the wing-tips that is not done due to aesthetic reasons. pffft.

-