h a l f b a k e r yRenovating the wheel
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As the day progresses, the sun's position appears to move in an arc. The shape of the arc depends on latitude and the time of year. Note that for any given position of the sun in the sky, at a fixed latitude, one can calculate the exact time and the number of days since the solstice.
Sundials typically
use one coordinate to describe the time, usually the angle of a shadow, or sometimes the length of a shadow. There exists a super-accurate sundial which uses both [link]. It projects a shadow onto a wavy grid, calculated from the equation of time and the local latitude. From the tip of the shadow, you follow the line to the edge of the grid and read off the current time, accurate reportedly to within 30 seconds.
The Sophisticated Sundial is made up of three parts. The first is a big fisheye lens, pointed directly up. The image projected onto the surface below will have the sun moving in an arc.
The image is formed onto a bundle of optical fibres. The other ends of the fibres are arranged in a ring around the clock face, such that each 'arc' of fibres on the focal plane maps to two 'loops' on the clock face, hence, a blob of light should form at the exact expected position of the hour hand.
The ring can be rotated slightly to correct for local longitude and a 15 degree offset for daylight saving time if needed.
Now for the clever/halfbaked part. By tilt-shifting the lens, it may be possible to dynamically correct for local latitude.
This should work anywhere far away from the equator, but between the tropics of Cancer and Capricorn, the arcs will appear to bend in different directions depending on the time of year. Outside of this region the image is merely 'stretched' and is easy(ish) to correct.
While it would be possible to have a cassette of fibreoptics to correct the image that you slot in to the sundial depending on your location (lame) I can't help but think there must be a simple, lens-based solution. The expense of accurate sundials is because of the need to tailor-make them to the latitude they're designed to operate at. An adjustable, generic, super-accurate sundial like this would justify the effort of precisely threading thousands of optical fibres into a clock.
Precision sundials
http://www.precisionsundials.eu/
[mitxela, Feb 02 2012]
Slow Light
http://www.pinholep...org/SSGB%20Page.htm
Vaguely relevant art project [pocmloc, Feb 03 2012]
[link]
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One problem, which precision sundials apparently fixes by having two plates, is that the curves are different summer soltice to winter solstice than they are winter solstice to summer solstice. |
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// The image projected onto the surface below will have the sun moving in an arc. // |
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The image projected onto the surface below will have the apperance of the sun moving in an arc relative to an observer in a fixed position to the sundial; In fact, it is the planetary surface below both the observer and sundial that allegedly moves, but relativistically, this cannot be proven. |
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[MechE], that will be because of the misalignment of the solstices and perihelion/aphelion (line of apsides). So perhaps the visual size of the sun needs to be taken into account as well, to provide a measure of the earth-sun distance. |
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An elegant way to account for longitude is to tilt the entire apparatus to the appropriate angle. |
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Wouldn't you want a small lens, set into a large opaque shade? You're not trying to melt anything! |
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A friend once pointed out that his sundial was not very useful, as there was nowhere in his yard that was not shaded by trees. I suggested he put the sundial on the roof, and point a webcam at it. Thus, with the simple expedient of a computer, some long cabling or a pair of wireless stations, and appropriate correction tables, it would be possible to calculate the time! This idea, while interesting, suffers from the same problem of over-egging the pudding. |
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To me, the point of a sundial is no longer to find out what time it is in the sense of standardised time-zone time (a problem that has been throbbingly solved using electronics) but to indicate raw, local solar time in a very direct way. How that differs from standard time is half the fun. |
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//a simple, lens-based solution.// |
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Not lens-based. It works like this: put the sundial
on the equator, and run the fiber-optic bundle to
your own latitude. |
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Perhaps we could integrate some kind of repeater or light-
storage mechanism for use in the RRCLs*, where the sun
goes to bed early and sleeps late. |
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* Really Really Cold Latitudes |
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Just put a sundial at each of the geographic poles, and run the fibres to your house. At least one of them will be in sunlight at any given time. |
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"put the sundial on the equator, and run the fiber-optic bundle to your own latitude" |
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Among others, it's incidents like this that make me miss [UnaBubba], although his temperment appears to have led to his undoing. |
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//put the sundial on the equator, and run the fiber-optic bundle to your own latitude// |
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I feel ashamed for not thinking of this myself. |
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It might be simpler to rig a spotlight running on a curved
track, shining down at the sundial to display the time
during the long winter nights. I can probably come up with
twelve feet of aluminium gear-trak more easily than
12,000 miles of fiberoptic cable. |
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Pah! An iPad and sundial app. would also work on a cloudy day. |
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You could mount a traditional sundial on a geared base, which is continually adjusted to cancel out the difference between time zone and solar time. |
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Yeah, probably. I'm a pretty resourceful Heathen. I gots
contacts. |
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With 12,000 miles of cable I'd think you'd need
connections more than contacts. |
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My father-in-law is a (regional) corner-office man with a
telecom company. Maybe he can hook me up. Anyway, I'm
not the one who suggested running fiberoptics all the way
from the Earth's poles--I'm just hypothetically facilitating
it. |
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//Pah! An iPad and sundial app. would also work on a cloudy day// |
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I think it's getting the pointy bit to stick on the ee-pad screen correctly that's the problem. |
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Currently waiting on the copyright of a pointy bit that sticks on the ee-pad which can fold down to reduce flesh wounds in the user... |
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