Re: Highest Altitude Sundial
Hi Roger I visited those sundials just few weeks ago. The island is Tenerife where there is the highest mountain of Spain, El Teide, 3700 m. At 2400 m there is the Observatorio del Teide, with telescopies and other instruments, managed by IAC, Instituto de Astrofisica de Canarias (other observatories are in the island of La Palma at the same altitude). One of the observatories is a pyramid with instruments to study Sun sysmology, the pyramid has 3 faces and 2 of them have a sundial. The sundials, inclined and declined, were projected by an italian scientist, Mario Salomone Morrone, in 1988. The dials have the declination curves every 5° of declination and the analemma for every hour. To enter in the area you need a permit by IAC, their offices are in the University of La Laguna, Instituto de Astrofisica, La Laguna, Tenerife. I met a diallist of Canaria, Luis Ramirez Castro, he was very kind and helpful, he asked the permit and drived me to the Teide. (I have his email if someone is interested). I registered the sundials on Sundial Atlas (ES115, ES116 www.sundialatlas.eu/atlas.php?so=ES115) where you can found photos, link to IAC, pdf documents, ecc. I don't know if these sundials are the heighest, on the Alps (Italy, France, Switzerland) there are many sundials and it may be there are sundials in the refuges over 2400 m (the highest refuge in Italy is at 4500 m, Capanna Margherita, Monte Rosa, about 80 beds, no sundials). Some years ago I found sundials in other islands: in Madeira (1) and in the island of Terceira (2) in Azores. They all are on Sundial Atlas. ciao Fabio Fabio Savian fabio.sav...@nonvedolora.it Paderno Dugnano, Milan, Italy 45° 34' 10'' N 9° 10' 9'' E GMT +1 (DST +2) - Original Message - From: Roger Bailey rtbai...@telus.net To: Sundial List sundial@uni-koeln.de Sent: Tuesday, September 06, 2011 5:55 AM Subject: Highest Altitude Sundial Remember way back when this great list was just getting started. There was a thread on finding the highest altitude sundial. I remember posting suggestions from Canada, Battle Abbey 7000 ft, US, Lowell Observatory 7000 ft and a proposal for Mauna Loa Hawaii. I remember the winner was a sundial at an observatory in the Canary Islands. But where? There are seven Canary Islands and many excellent observatories but where is this highest altitude sundial. It does not seem to be listed in the usual sources. Does anyone on the list have better recall of this thread and more recent information? I am continuing to search for sundials on interesting islands. So many islands, so many sundials, so little time. Sundials show slow time. There are no seconds or minutes, just the inevitable progress of time. Life's but a Walking Shadow. Regards, Roger Bailey Walking Shadow Designs --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Sundials and map projections
Will, This is exactly how I study sundials. Here are a few of the recent classic books (the first is a must-have): Map Projections – A Working Manual; John Synder Map Projection Transformation – Principles and Applications; Qihe Yang, Jphn Snyder, Waldo Tobler Flattening the Earth – Two Thousand Years of Map Projecctions; John Snyder Map Projections – A Reference Manual; Lev Bugayevskiy, John Synder …Tom Kreyche From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Will Vaughan Sent: Tuesday, September 06, 2011 8:43 AM To: sundial@uni-koeln.de Subject: Sundials and map projections I recently read James Morrison's interesting book The Astrolabe which put me in the mindset of thinking of astrolabes as maps. It occurred to me that sundials can also be thought of as maps: specifically, sundials are self-projecting, automatically updated maps of the Sun's position in the celestial sphere. The Sun's hour angle and declination (and therefore the time and date) can be read off a network of hour and date curves, the projected graticule of the celestial sphere. All common sundials are gnomonic, stereographic, or pseudo-orthographic map projections of spherical sundials. I have made a webpage using this approach to investigate the common sundials: http://wvaughan.org/sundials.html In my opinion, understanding sundials through map projections has several advantages over the brute-force spherical trigonometric approach in books like Rene Rohr's Sundials: History, Theory, and Practice: it simplifies the derivation of sundial equations, clarifies the important distinction between a gnomon and a nodus, and suggests many other possible (unexplored?) sundials on the surface of a cone or cylinder. I'd be interested to hear previous thoughts along these lines and any comments or corrections for http://wvaughan.org/sundials.html. Thank you very much, Will Vaughan 41° 50' N, 71° 24' W P.S. I've attached the dial plate of a sundial + terrestrial map I designed for my location in the mapping software ArcGIS; the shadow of the nodus of this sundial falls on the ground point of the Sun. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
R: RE: Sundials and map projections
John Synder's book is available on line at the address
http://pubs.er.usgs.gov/publication/pp1395
Ciao.
Gian
Messaggio originale
Da: tkrey...@well.com
Data: 06/09/2011 19.24
A: Will Vaughanwilliam.m.vaug...@gmail.com, sundial@uni-koeln.de
Ogg: RE: Sundials and map projections
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--
Will,
This is exactly how I study sundials. Here are a few of the recent classic
books (the first is a must-have):
Map Projections – A Working Manual; John Synder
Map Projection Transformation – Principles and Applications; Qihe Yang, Jphn
Snyder, Waldo Tobler
Flattening the Earth – Two Thousand Years of Map Projecctions; John Snyder
Map Projections – A Reference Manual; Lev Bugayevskiy, John Synder
…Tom Kreyche
From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On
Behalf Of Will Vaughan
Sent: Tuesday, September 06, 2011 8:43 AM
To: sundial@uni-koeln.de
Subject: Sundials and map projections
I recently read James Morrison's interesting book The Astrolabe which put me
in the mindset of thinking of astrolabes as maps. It occurred to me that
sundials can also be thought of as maps: specifically, sundials are
self-projecting, automatically updated maps of the Sun's position in the
celestial sphere. The Sun's hour angle and declination (and therefore the time
and date) can be read off a network of hour and date curves, the projected
graticule of the celestial sphere. All common sundials are gnomonic,
stereographic, or pseudo-orthographic map projections of spherical sundials. I
have made a webpage using this approach to investigate the common sundials:
http://wvaughan.org/sundials.html
In my opinion, understanding sundials through map projections has several
advantages over the brute-force spherical trigonometric approach in books like
Rene Rohr's Sundials: History, Theory, and Practice: it simplifies the
derivation of sundial equations, clarifies the important distinction between a
gnomon and a nodus, and suggests many other possible (unexplored?) sundials on
the surface of a cone or cylinder.
I'd be interested to hear previous thoughts along these lines and any comments
or corrections for http://wvaughan.org/sundials.html.
Thank you very much,
Will Vaughan
41° 50' N, 71° 24' W
P.S. I've attached the dial plate of a sundial + terrestrial map I designed for
my location in the mapping software ArcGIS; the shadow of the nodus of this
sundial falls on the ground point of the Sun.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
Walking Shadow Riddle
A Riddle: I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I'm sure this relates to sundials and mapping, but the answer eludes me. One of the characters was told by the wise man to: walk towards your shadow all day, starting at sunrise and stopping at sunset at which point the walker would discover the location of a treasure. So I asked myself, what would the path of the trek look like on a map? But I can't figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He'll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he'll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he's at the North Pole? John C. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Walking Shadow Riddle
My guess is he ends up where he started, i.e., the wise man is telling him, in the usual pseudo-wise ways of pseudo-wise movies, that he already has the treasure but just doesn't realize it. On Tue, Sep 6, 2011 at 2:08 PM, John Carmichael jlcarmich...@comcast.netwrote: A Riddle: ** ** I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I’m sure this relates to sundials and mapping, but the answer eludes me. ** ** One of the characters was told by the wise man to: “walk towards your shadow all day, starting at sunrise and stopping at sunset” at which point the walker would discover the location of a treasure. ** ** So I asked myself, *what would the path of the trek look like on a map?*But I can’t figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He’ll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he’ll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he’s at the North Pole? ** ** John C. ** ** ** ** --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Walking Shadow Riddle
Here's my guess: If, as you suggest, you start at dawn on the equinox and on the equator you will walk east for six hours before noon and west for six hours before sunset, finishing at the point where you started. If you start at the north pole at the equinox you will move in a spiral, crossing each longitude once every 24 hours. John Lynes From: John Carmichael jlcarmich...@comcast.net To: 'Sundial List' sundial@uni-koeln.de Sent: Tuesday, 6 September 2011, 19:08 Subject: Walking Shadow Riddle A Riddle: I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I’m sure this relates to sundials and mapping, but the answer eludes me. One of the characters was told by the wise man to: “walk towards your shadow all day, starting at sunrise and stopping at sunset” at which point the walker would discover the location of a treasure. So I asked myself, what would the path of the trek look like on a map? But I can’t figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He’ll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he’ll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he’s at the North Pole? John C. --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Walking Shadow Riddle
Interesting question!! I couldn't get my head around it, either, so tried plotting it in Excel. Grabbing a table of Solar Azimuth for Tucson on today's date, I estimated a 5 mph rate. Since the Sun rises just barely South of East, the path starts out heading North and mostly West. By noon, our trekker has reached 25 miles West and 12 miles North of his starting point. By sunset, he has walked back East to a point 25 miles North of his start. The path looks like half of an ellipse with an East-West major axis of roughly 50 miles, and a North-South minor axis of slightly over 25 miles. December 21st looks a lot different, and I'm having trouble buying it! Dave _ From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of John Carmichael Sent: Tuesday, September 06, 2011 11:08 AM To: 'Sundial List' Subject: Walking Shadow Riddle A Riddle: I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I'm sure this relates to sundials and mapping, but the answer eludes me. One of the characters was told by the wise man to: walk towards your shadow all day, starting at sunrise and stopping at sunset at which point the walker would discover the location of a treasure. So I asked myself, what would the path of the trek look like on a map? But I can't figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He'll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he'll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he's at the North Pole? John C. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Walking Shadow Riddle
I believe that Brad had it right in terms of the philosophical intent of the question poser. But we must plunge ahead into the actual mechanical outcome. Dave, I believe you have approximately the right shape path for a walker with an apparent sun path that crosses his meridian south of his zenith. Continuing with that setup and the walker being on the equator to begin his walk at sunrise, I question whether the walker ever makes it back to the same line of longitude from whence he started. By walking away from the sun he has ended up extending the time from 6 hours between sunrise and solar noon to 6 hours plus. After solar noon, he is retreating from the sun and shortening the time to sunset to less than 6 hours. Hence, he winds up at a location north of his starting point, but longitudinally west of his starting longitude. In John's first setup with the walker on the equator on the equinox, the sun passes through the zenith so the walker would only be treading on the equator, but using the same argument above, heading west until solar noon would take 6 plus hours and the time spent heading back east would be under 6 hours so a constant speed walker would fall short of returning to his starting point. Larry Bohlayer From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Dave Bell Sent: Tuesday, September 06, 2011 9:43 PM To: 'John Carmichael'; 'Sundial List' Subject: RE: Walking Shadow Riddle Interesting question!! I couldn't get my head around it, either, so tried plotting it in Excel. Grabbing a table of Solar Azimuth for Tucson on today's date, I estimated a 5 mph rate. Since the Sun rises just barely South of East, the path starts out heading North and mostly West. By noon, our trekker has reached 25 miles West and 12 miles North of his starting point. By sunset, he has walked back East to a point 25 miles North of his start. The path looks like half of an ellipse with an East-West major axis of roughly 50 miles, and a North-South minor axis of slightly over 25 miles. December 21st looks a lot different, and I'm having trouble buying it! Dave _ From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of John Carmichael Sent: Tuesday, September 06, 2011 11:08 AM To: 'Sundial List' Subject: Walking Shadow Riddle A Riddle: I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I'm sure this relates to sundials and mapping, but the answer eludes me. One of the characters was told by the wise man to: walk towards your shadow all day, starting at sunrise and stopping at sunset at which point the walker would discover the location of a treasure. So I asked myself, what would the path of the trek look like on a map? But I can't figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He'll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he'll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he's at the North Pole? John C. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Walking Shadow Riddle
My intuitive solution was similar. You end up south of your original position as there is no north going component to bring you back to the start during daylight. The curve varies with latitude and declination but the results is the same. In spite of what Dorothy said in the Wizard of Oz, There is no place like home, go south to discovery the treasure. John, I guess you can say Been there, done that. Regards, Roger Bailey Walking Shadow Designs Life's but a Walking Shadow Been there, done that. From: Dave Bell Sent: Tuesday, September 06, 2011 6:42 PM To: 'John Carmichael' ; 'Sundial List' Subject: RE: Walking Shadow Riddle Interesting question!! I couldn't get my head around it, either, so tried plotting it in Excel. Grabbing a table of Solar Azimuth for Tucson on today's date, I estimated a 5 mph rate. Since the Sun rises just barely South of East, the path starts out heading North and mostly West. By noon, our trekker has reached 25 miles West and 12 miles North of his starting point. By sunset, he has walked back East to a point 25 miles North of his start. The path looks like half of an ellipse with an East-West major axis of roughly 50 miles, and a North-South minor axis of slightly over 25 miles. December 21st looks a lot different, and I'm having trouble buying it! Dave From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of John Carmichael Sent: Tuesday, September 06, 2011 11:08 AM To: 'Sundial List' Subject: Walking Shadow Riddle A Riddle: I was watching a dumb movie last weekend and there was a bit of dialogue that caught my attention. I'm sure this relates to sundials and mapping, but the answer eludes me. One of the characters was told by the wise man to: walk towards your shadow all day, starting at sunrise and stopping at sunset at which point the walker would discover the location of a treasure. So I asked myself, what would the path of the trek look like on a map? But I can't figure it out. This is as far as I get in my thinking: I started considering an example with these conditions.- The walk begins at dawn on the equinox, and the man is on the equator. And the walk ends at sunset. So we know that the walk will last twelve hours. If the average speed of a walking man is 5 km/hr. , it is 12 hours from sunrise to sunset; then we know that he will walk 60 km. He'll start walking towards the west at dawn and his path will turn towards the north in the morning as the sun heads south. After Solar Noon, his path will turn towards the east he'll end up facing due east at sunset. And we know that the path will be a curve since his shadow will always be changing direction. But what would the curve look like on a map? Would it be a hyperbola? How would the curve change if he walks on the summer solstice instead? What if he's at the North Pole? John C. --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
