And the position of the sun relative to the building is also a simple formula based on time of year. Given that this is the country that gave us freakin' Stone Henge you have to expect that someone remembered that there is a formula to predict exactly where the sun will be relative to a spot in England every day of the year. The clever ones actually used that to tell them what day it was since they couldn't be bothered to invent the wrist watch.
Or you could use a simple rule of thumb. Something like, "Let's not build skyscrapers that are giant parabolic reflectors aimed at things of value (people, cars, other buildings, etc.)"
This seems like a really stupid mistake to make. TWICE.
No way, it would be near instantaneous. Position of the sun in the sky is really trivial stuff. Hell, don't even bother, just use this: http://aa.usno.navy.mil/data/docs/AltAz.php
Wikipedia apparently has a pretty nice page on calculating the position of the Sun if anybody is interested: http://en.wikipedia.org/wiki/Position_of_the_Sun It's basically a lot of trig and a bunch of constants; pretty neat. Interestingly the information given on that page is only valid for a shorter timeframe than the information given on the USNO page.
> Well except you have to model the position of the sun for every hour and day of the year
That sounds exactly like some things xkcd has done in the "what if?" series. He's done all sorts of variations on similar calculations.
And while xkcd is smart, he's not superhumanly so (his fame is due to the unique combination of creative thinking, humour, geekery and smarts).
In other words, this is possible and a good engineer should be able to calculate this. Especially when you know that any concave reflective surface is going to focus the light somewhere. In addition you know that due to the movements of the sun during the day and the year, this focal point will in 3D to different positions. So yes, odds are that it's going to hit some spot, somewhere, where it's going to be able to do damage, at some point during the year. Then you get to make a simple risk calculation about expected strength of sunlight that time of the year.
And then you will remember to realize that over the course of the lifetime of this building, climate always has a non-zero probability of powerful outliers[0], and the conclusion is:
Simply don't build gigantic concave mirrors in residential areas.
[0] I'm not 100% sure if this is the case for strength of sunlight, since it's mainly dependent on what angle the sunlight arrives, which is not really up to chance. Still, even in the winter when the sun is quite low, as long as the sky is clear, I can easily light an incense stick with an A4-size fresnel lens. And I guess a whole building-side has a "slightly" bigger margin of how narrow the point of focus needs to be.
To work out where an object will fall, you have to model the path of various objects of all shapes, masses and densities with wind of all strengths and directions (including shifting and gusting winds), and considering the original orientation of the object, and any spin placed on it at point of release (in three axes).
Just working out the angles at which light from a distant ball of fire will hit a surface should be a piece of cake. You could probably do it pretty easily for every point (assuming a certain size of point) at that distance at which it isn't completely hidden, just in case the planet suddenly changes its orientation.
So what? People have been doing that for centuries using almanacs. And with computers that sort of thing becomes stupidly simple. IIRC that functionality is even built in to Google Sketchup.
