Hello folks,
I've been kicking this idea around for ages but I've mostly been defeated by finding a suitable site. I wanted to say, 'here's the idea and I've tried it' but I haven't. So here's the idea. I was walking into work one morning, the sun streaming down, and I thought, 'Wouldn't it be cool to have an analemmatic dial marked out in the car-park using the corner of the building as a gnomon?' I spent a little while pondering the logistics of moving the office building two or three times a month when it occurred to me that you don't move the gnomon, you change the relative positions of gnomon and dial. So you can move the dial instead. Repainting the hour points two or three times a month is certainly less trouble than moving the building but I couldn't see it flying. But you could always mark out a selection of dials at different positions, that is mark the month positions at every hour point. I visualised explaining this to someone while looking out of the office window and it looked messy, even in imagination. Then I thought, 'but if the hour points were marked on the _window_, so long as you looked through from the right position the _projection_ of the window marks onto the carpark would have the right relationship with the shadow of the building.' Hence the 'Virtual Analemmatic Dial' or the 'Projective Analemmatic Dial' or 'The Office Workers' Dial'. I've had some modest success with thinking up names if nothing else. The extra maths involved is not great. You need to calculate the postions of the hourpoints in X-Y coordinates (you're doing that anyway) and then rotate them through an angle determined by the window's orientation and translate them into a set of coordinates with an origin at the window's position. The rest is just similar triangles. The tricky bit, of course, is 'so long as you looked through from the right position'. A stick of the right height on which the observer rests his/her chin? Who would do it even assuming it was possible. So I came up with ground marks. Choose two suitably located ground marks and mark their projection on the window with the rest of the dial. When the observer looks through the window from the position from which the ground marks match up with their images on the window, the shadow of the gnomomn will have the right relationship with the hourpoints on the window. And the beauty of it is: to change the realitive position of the gnomon and the _projection_ of the hourpoints, you just move your head. I'd pictured this being done by printing the dial image on OHP acetate and sticking it to the window; you could print a dozen to cover different times of the year instead of having date marks. This way, using the standard tools, you could print an actual picture of the two ground marks on the acetate to facilitate the lining up. Or print the image of the traditional date marks, translated to the two ground mark positions on the acetate for a permanent installation. Or make it a stained-glass window project. Once the basic idea is grasped it's clear you're not limited to the corner of your building as a gnomon. Any object casting a more-or-less vertical shadow on a more-or-less horizontal surface that you can see out of the window will do. Indeed, so long as the shadow is pointy at the top it would probably work. An Egyptian obelisk, perhaps. There's quite a bit of surveying involved in this. You have to know the true compass bearing looking out of the window, the window's X-Y-Z coordinates in the system centered on the gnomon (which is oriented N-S), and the X-Y position of the ground marks in the same system. But it's doable. I think. What do you think? Richard -
