Re: "best" possible angle for insolation and visibility
Dear Fernando, I had a similar problem making a dial for 'the tropics'. It was to sit beside the pool at a hotel that we use in The Gambia, 13°N. The intention was to make it visible all day from a laying-down position. in The Gambia as in Brazil, the sun goes both to the North and to the South at various times of the year. Also the only sensible position for it was to the South of the pool. My solution was to make a horizontal dial for 45°N. At latitude 13°, this meant that it was inclined 45-13=32 degrees. It worked out quite well. The intention was to give some indication of time to people who really didn't care too much about the actual time, but they needed to know when to order the next drink! I made a cardboard prototype, but sadly the hotel management never took up the idea. Good luck with yours. The Eclipse. As you probably know it was a bit of a washout in the area of totality, but we here in Cambridge, UK, were able to stand outside and got a fairly good 90% view through broken cloud. Regards, Mike Cowham. <[EMAIL PROTECTED]>
Re: "best" possible angle for insolation and visibility
Hello Fernando The shortest answer would be to have the cylinder with the dial on its outside and few styles around it so that at least one is working. The cylinder should be inclined so that is is parallel to the Earth axis. Then you would have longest expositions. On the poles it would work half a year continuously, on the Equator half a day. For flat dials the answer is not so straightforward. If you recall equations they are combinations of trig functions and it is tricky to predict the results for different arguments. The best would be to experiment on the spots of interest :-) or use Fer's program which allows for fast calculations of dials for any latitude, orientation and inclination. For each lat you could perform few experiments for inclinations ranging from 0 (horizontal dial) to 90 (vertical) and see how the length of the exposure changes. If you made systematic research you could publish it because that would be of interest. All best Slawek At 07:54 AM 8/11/99 -0300, you wrote: >I sent this message yesterday but it was returned. >I thought the world could be over for you guys >who tried to see the eclipse. Since it seems it didn't, >here it is again: > > >Given a certain latitude, how can we find the "best" angles for >a sundial? > >For "best" I mean those that offer: > >a) the longest insolation during the day >b) the longest insolation at the various seasons >c) the best azimuth (declination) and the best reclination so the dial >can be place as high as possible and still get to be >seen confortably (based on the angle, not on the size). > >My guess is that if we are beyond 23 1/2 N or S, than >the sundial should be vertical and face South (N) or >North (S). This would give the "best" possible >angles which would allow the sundial to show every hour >from sunrise to sunset every day of the year. > >Now, if it sits in-between 0 and 23 1/2, is there are >"better" angle? > >For instance, Brasilia is 19d 45' 5" S (47 d 49' 59" W). >Of course, it the sundial is vertical and faces North, in December it >will >be useless. Now, the more I recline it, the longer it will work >towards the solstice in December. If I go as far as to have >horizontal, of course it will work all year round but will >not be seen if it is placed on the top of a column. > >If fact, I would guess I would never have to go beyond >23 1/2 degrees of reclination. > >Is this message to confusing? I think it is :-) >I am not sure I have been able to describe what I intended to >get: to place a sundial in the top of a 6-meter tall (19' 8") column >so as it can be the best possible visibility from the ground. >At the same time it should work all year round for a certain >latitude (in this case, 15 d 45' 5"S), from sunrise to sunset. > >Again, it seems clear it should face North. For visibility >from the ground, the the lesser the declination, the better. >For insolation... > >I hope this is less confusing now. > >- fernando > > > > >- fernando > > > >-- >Fernando Cabral Padrao iX Sistemas Abertos >mailto:[EMAIL PROTECTED] http://www.pix.com.br >Fone Direto: +55 61 329-0206mailto:[EMAIL PROTECTED] >PABX: +55 61 329-0206 Fax: +55 61 326-3082 >15º 45' 04.9" S 47º 49' 58.6" W >19º 37' 57.0" S 45º 17' 13.6" W > > > Slawek Grzechnik 32 57.4'N 117 08.8'W http://home.san.rr.com/slawek
RE: "best" possible angle for insolation and visibility
Fernando, Fellow diallists, >>> Fernando asked: Given a certain latitude, how can we find the "best" angles for a sundial? For "best" I mean those that offer: a) the longest insolation during the day b) the longest insolation at the various seasons c) the best azimuth (declination) and the best reclination so the dial can be place as high as possible and still get to be seen comfortably (based on the angle, not on the size). and with the sundial in the top of a 6-meter tall (19' 8") column so as it can be the best possible visibility from the ground. At the same time it should work all year round for a certain latitude (in this case, 15 d 45' 5"S), from sunrise to sunset. <<< in trying to find a single plane dial; At the Arctic [Antarctic] Circle the sun just does not set on the N [S] horizon at midsummer. Therefore a single dial must face generally N [S] of horizontal otherwise it will not intercept that light. However, at the Arctic [Antarctic] Circle the sun just rises on the S [N] horizon at midwinter. Therefore a single dial must face generally S [N] of horizontal otherwise it will not intercept that light. >From this we can see that only a horizontal dial will work in the polar regions to (just) satisfy both requirements. This is clearly the case at either pole where the sun travels along the whole horizon at the equinox. And, in fact, a horizontal dial will work in all regions (because while the ground is illuminated, so will be the dial) - the only problem here being that it will be out of sight on the top of the pillar, unless you either a) make it transparent and look at it from underneath or b) place a mirror above it and look at the reflection (BTW, is this a new (if rather impractical) idea of mine - can anyone cite an example?) In the Northern [Southern] hemisphere above the tropics, a direct S [N] vertical dial will not show earliest and latest hours at midsummer (or indeed at any summer date between the equinoxes). If we take a horizontal dial and tilt it towards either S or N, then the E-W line through the gnomon will be higher than that part of the dial to the S or N of the gnomon foot and will therefore shade the dial at sunrise and sunset either in summer or winter. Therefore I do not think a single dial will suffice unless it is actually horizontal. Two vertical dials will solve the problem - at 51 deg N a SW and SE pair work nicely. However as you go further towards the pole the angle between them must decrease until in the polar regions they have to be back to back e.g. N and S or E and W and sunlight arrives at one just as it leaves the other with a glancing illumination, so three (or more) become preferable if you wish at least one surface to be well lit at all times. Typically in England pillars or other structures (e.g. above a church parapet or roof) with four vertical dials (N, S, E, W) are reasonably numerous, while occasionally one finds a larger number of equally spaced ones (e.g. 6, Covent Garden, London; and 8, Douglas, Isle of Man). Omitting the N dial is often no great loss as the E and W ones can be used for more of the time anyway and there are quite a few of such E, S, W triplets (as well as some approximately SW, SE pairs). The complex multiple dials of Scotland are another subject altogether! I think that a vertical S (N) dial just works on the northern (southern) tropic. However, between the Equator and the Tropic, (and hence for Fernando's actual problem ;-) ) I'll now leave it to others to discuss the possible range of angles of a single inclining vertical dial, or between the pair of vertical dials required. Regards Andrew James
RE: 16th century navigation/surveying
I emailed my ranger and now have his reply, which I have attached to this missive. I hope it is not considered too long for this list, but I think some of you will find it as interesting and helpful as I did. There were two main issues bothering me. One was how Cabrillo could still believe the Pacific was small even after Magellan had sailed across it. There were, of course, many factors, but basically the cartographers of the day believed the North Pacific was much narrower than the South Pacific. The other issue was the conflict between the ranger's claim that the eclipse measurement in Mexico City was off by 25 degrees and Jim Morrison's claim that the error was only a single degree. It turns out there was an early, inaccurate measurement in 1541, just before Cabrillo set sail, and a later, accurate one in 1577. Thank you all for the various insights. --Art Carlson P.S. A few months ago there was an extended discussion here on the green flash. I stumbled on some good web sites explaining the phenomenon and showing some good photos: http://mintaka.sdsu.edu/GF/ From: "George Herring" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: "Terry DiMattio" <[EMAIL PROTECTED]> Subject: Re: A Question of History -- related article Date: Mon, 9 Aug 1999 16:55:30 -0700 Message-ID: <[EMAIL PROTECTED]> MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook 8.5, Build 4.71.2173.0 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Importance: Normal Content-Transfer-Encoding: 8bit Mr. Carlson Below is the draft-article I refer to and promised in my response to your e-mail. Again, if you would like to see the maps mentioned please send a mailing address and I'll see that a copy of the newsletter containing the article is sent to you. George _ Not Far To The West Christopher Columbus was lost to his dying day. In fact, between 1492 and 1542, all Europeans in the New World, in a sense, were lost. Why? Because most Renaissance mapmakers accepted the classical belief that China existed approximately 180 longitudinal degrees east of Europe1.. It's actually 120 degrees east. In this article I hope to convince you with early 16th century maps why Columbus, Juan Rodriguez Cabrillo, and others thought Asia lay just beyond the western horizon. Let's begin with this 1503 woodcut-map, drawn by Gregor Reisch, is based on the work of Claudius Ptolemy, a Roman-Egyptian geographer of the 2nd century AD2.. Ptolemy collected the geographic work of other scholars and the tales of travelers to fill in the details of this map. A 1478 version of the exact same map is known to have been in an Atlas owned by Christopher Columbus. The important feature of this map to note relative to our story is the extent of it's eastern extreme. Asia is depicted as extending more than 180 degrees to the east of Spain! Why does the map depict Asia extending so far to the east? Because Ptolemy said so, that's why. Renaissance scholars had no means with which to measure longitude and only crude estimates of distance covered by ships. They had no reason, or evidence, to refute the knowledge of Ptolemy. Columbus, like most explorers after him for 100 years, accepted Ptolemy's estimate3.. And, like many amateur scientists, he manipulated his data. Columbus interpreted the writings of Marco Polo to indicate that the mainland of Asia extended east 253 degrees, and he cited Polo's accounts of a large island named Zipango (Japan)4. said to lay an additional 30 degrees east of China. This left, in his estimates, about 77 degrees of ocean to cross from the Canaries to Japan5.. When Columbus bumbled into the West Indies he had traveled about 60 degrees, but he estimated he'd traveled about 75 degrees. Far enough, he thought, to have reached the eastern fringes of the Indies. Since the people he encountered appeared to be "Indian," it was natural for him to conclude he was in the "Indies". He maintained that Cuba and the other islands of the Caribbean were the East Indies until his death in 1506. Scholars and explorers throughout the early 16th century argued about just what Columbus had found and how it fit with the writings of Ptolemy and the beliefs of the Church. Consistently they persisted in the belief that China lay less than 180 degrees west of Spain (60 degrees or less west of Mexico.) Furthermore, according to the Bible the apostles had spread the gospel to all the peoples of the world. For this to be feasible it was necessary for mapmakers to depict the America's as accessible from Asia. Virtually all maps from the 16th century, therefore, depicted Asia and the Amer
"best" possible angle for insolation and visibility
I sent this message yesterday but it was returned. I thought the world could be over for you guys who tried to see the eclipse. Since it seems it didn't, here it is again: Given a certain latitude, how can we find the "best" angles for a sundial? For "best" I mean those that offer: a) the longest insolation during the day b) the longest insolation at the various seasons c) the best azimuth (declination) and the best reclination so the dial can be place as high as possible and still get to be seen confortably (based on the angle, not on the size). My guess is that if we are beyond 23 1/2 N or S, than the sundial should be vertical and face South (N) or North (S). This would give the "best" possible angles which would allow the sundial to show every hour from sunrise to sunset every day of the year. Now, if it sits in-between 0 and 23 1/2, is there are "better" angle? For instance, Brasilia is 19d 45' 5" S (47 d 49' 59" W). Of course, it the sundial is vertical and faces North, in December it will be useless. Now, the more I recline it, the longer it will work towards the solstice in December. If I go as far as to have horizontal, of course it will work all year round but will not be seen if it is placed on the top of a column. If fact, I would guess I would never have to go beyond 23 1/2 degrees of reclination. Is this message to confusing? I think it is :-) I am not sure I have been able to describe what I intended to get: to place a sundial in the top of a 6-meter tall (19' 8") column so as it can be the best possible visibility from the ground. At the same time it should work all year round for a certain latitude (in this case, 15 d 45' 5"S), from sunrise to sunset. Again, it seems clear it should face North. For visibility from the ground, the the lesser the declination, the better. For insolation... I hope this is less confusing now. - fernando - fernando -- Fernando Cabral Padrao iX Sistemas Abertos mailto:[EMAIL PROTECTED] http://www.pix.com.br Fone Direto: +55 61 329-0206mailto:[EMAIL PROTECTED] PABX: +55 61 329-0206 Fax: +55 61 326-3082 15º 45' 04.9" S 47º 49' 58.6" W 19º 37' 57.0" S 45º 17' 13.6" W
Re: "best" possible angle for insolation and visibility
"Slawomir K. Grzechnik" wrote: > Hello Fernando > > The shortest answer would be to have the cylinder with the dial on its > outside and few styles around it so that at least one is working. The > cylinder should be inclined so that is is parallel to the Earth axis. Then > you would have longest expositions. On the poles it would work half a year > continuously, on the Equator half a day. In fact I have always wanted to put some styles in a cylindric water tank I have im my small farm. I have lacked the time (and certainly the expertise) to do so. But it is vertical, not inclined. > The best would be to experiment on the spots of interest :-) > This is good but hard to do. - fernando > or use Fer's program which allows for fast calculations of dials for any > latitude, orientation and inclination. For each lat you could perform few > experiments for inclinations ranging from 0 (horizontal dial) to 90 > (vertical) and see how the length of the exposure changes. If you made > systematic research you could publish it because that would be of interest. > > > All best > > Slawek > > At 07:54 AM 8/11/99 -0300, you wrote: > >I sent this message yesterday but it was returned. > >I thought the world could be over for you guys > >who tried to see the eclipse. Since it seems it didn't, > >here it is again: > > > > > >Given a certain latitude, how can we find the "best" angles for > >a sundial? > > > >For "best" I mean those that offer: > > > >a) the longest insolation during the day > >b) the longest insolation at the various seasons > >c) the best azimuth (declination) and the best reclination so the dial > >can be place as high as possible and still get to be > >seen confortably (based on the angle, not on the size). > > > >My guess is that if we are beyond 23 1/2 N or S, than > >the sundial should be vertical and face South (N) or > >North (S). This would give the "best" possible > >angles which would allow the sundial to show every hour > >from sunrise to sunset every day of the year. > > > >Now, if it sits in-between 0 and 23 1/2, is there are > >"better" angle? > > > >For instance, Brasilia is 19d 45' 5" S (47 d 49' 59" W). > >Of course, it the sundial is vertical and faces North, in December it > >will > >be useless. Now, the more I recline it, the longer it will work > >towards the solstice in December. If I go as far as to have > >horizontal, of course it will work all year round but will > >not be seen if it is placed on the top of a column. > > > >If fact, I would guess I would never have to go beyond > >23 1/2 degrees of reclination. > > > >Is this message to confusing? I think it is :-) > >I am not sure I have been able to describe what I intended to > >get: to place a sundial in the top of a 6-meter tall (19' 8") column > >so as it can be the best possible visibility from the ground. > >At the same time it should work all year round for a certain > >latitude (in this case, 15 d 45' 5"S), from sunrise to sunset. > > > >Again, it seems clear it should face North. For visibility > >from the ground, the the lesser the declination, the better. > >For insolation... > > > >I hope this is less confusing now. > > > >- fernando > > > > > > > > > >- fernando > > > > > > > >-- > >Fernando Cabral Padrao iX Sistemas Abertos > >mailto:[EMAIL PROTECTED] http://www.pix.com.br > >Fone Direto: +55 61 329-0206mailto:[EMAIL PROTECTED] > >PABX: +55 61 329-0206 Fax: +55 61 326-3082 > >15º 45' 04.9" S 47º 49' 58.6" W > >19º 37' 57.0" S 45º 17' 13.6" W > > > > > > > Slawek Grzechnik > 32 57.4'N 117 08.8'W > http://home.san.rr.com/slawek -- Fernando Cabral Padrao iX Sistemas Abertos mailto:[EMAIL PROTECTED] http://www.pix.com.br Fone Direto: +55 61 329-0206mailto:[EMAIL PROTECTED] PABX: +55 61 329-0206 Fax: +55 61 326-3082 15º 45' 04.9" S 47º 49' 58.6" W 19º 37' 57.0" S 45º 17' 13.6" W
