I do change the shape of the sail on my windsurfer by leaning forward, aft and/or lee or windward. The angle of attack is changed doing so therefore the wind over the sail is different each time and the board moves a certain way. My mast is always pre-bend and my sail is fully battened ensuring a certain foil shape.
Rich as a Fan Engineer I understand the principles of fluid dynamics and their effect on foil, airfoil, flat BI, cupped and other shapes. Air is a fluid although compressible compared to liquids and it's characteristics do change with temp and elevation.
If I were a rich man
I would own a brand new top of the line
sailboat with mylar or matrix titanium, etc. sails. True foil shaped rotatable mast and boom, or maybe even solid adjustable foils etc. You get the drift, for optimum trimming and performance.
I have an old cruiser that needs to be relieved of excessive weather-helm without spending any money. i.e. I don't want to pay for a rigger to trim, pre-bend the mast, I can't measure shroud and stay tensions (tight is tight) I can flatten (change old sail shape) and hope for relieve and if I can do it with the sail I will otherwise I lean the mast forward. I or anybody else doesn't know the exact trim specs for my boat anyway.
Thanks for your referals and recommendations.