Mathematical quiz, in the form of a consistent shade roof design...

Sorry if this is posted in the wrong forum, "green building" seemed the most generic place in which to post.

At the time of writing, I am currently sitting outside under a lanai/patio and the weather here in south florida is absolutely perfect, it's soo good that you don't even notice it... I'd say air temp is 72°, a breeze makes it feel 70° and the radient heat from the sun warms it up to 74°, just perfect.

I'm just one step away from having total bliss, see the issue is that I have to move my chair every couple of minutes to balance having sun on my body, but not in my eyes. We're dealing with a first world problem here.

Without digressing further about the weather, what shape would one need to build a pergola/roof so that the shadow was completely static throughout the day?

I can only imagine 2 variables, the location [equator would simply be a half ring shape, if I'm not mistaken] and the time of year, or in other words the angle at which the earth moves upon the sun.

For the sake of simple math let's assume we need to shade a 10'x10' area, this should make it fairly easy to scale other sizes.

I assume that every design would be slightly different due to location, and that every design would need some type of seasonal adjustment.

But my puny pea brain just can't wrap itslelf around the exact shape it would need to be, I would literally have to make miniature clay molds and do time lapse photography and do it simply by trial and error.

My hunch is it would be shaped somewhat like the St. Louis arch, with a narrow bridge and wide bases, but the whole thing would be tilted towards the sun.

Does any of this make sense, or have I just been getting too much sun?

Life is a killer down there huh Nick!

It's a hard knock life, lemme tell ya!

I had to wake up at 9am to get our farmers market to buy affordable, local, organic, free range, raw dairy products before everybody else that got up at 10am bought it all up. Takes a lot of work to stay alive around here!

I sometimes wonder if bored people with tireless minds such as myself were the kind of people who invented internal combustion engines and cellular phones... Or did we invent trivial things such as Snuggies and Corndogs.

Well either way, I invented the constant shade patio dammit.