Re: Accuracy of wristwatch as compass
Dan— . Here are the maximum errors, in degrees, of the three solar direction-finding methods I’ve been discussing, for Romania. . I used lat 45 as a typical latitude there. Of course a person is most likely to need a direction-finding method in a district that they don’t live in. . For the Watch method, I assumed that that method is used at the edge of a standard-size time-zone, and that EoT and longitude aren’t taken into account. . For the Altitude-Watch method, I assumed that EoT and longitude are taken into account, and that solar declination is known or well-estimated. …and that solar altitude is accurately estimated. . Shadow-Tip: 33.25 . Watch-Method: 37 . Altitude-Watch Method: 21 . (I didn’t analytically-maximize—I just looked at various whole and half-hours in the afternoon at the summer-solstice, to find which of those hours and half-hours gave the method the most error.) . Michael Ossipoff On Mon, Oct 22, 2018 at 12:20 PM Dan-George Uza wrote: > Dear John and others, > > Thank you for your insights. Although I haven't been able to track the > analysis I was looking for eventually I did find something similar. Google > "On the method of direction finding by Sun and Watch by Norman Pye". The > author makes an analysis for true azimuths and watch hour angles, dealing > with values projected onto the horizontal plane. The directional error is > due to the Sun moving in a different plane from the horizontal. From the > table I attach below it seems that the watch method works best in winter > because then the Sun stays close to the horizon and doesn't have a great > spread in azimuth. > > Hope this helps, > > Dan > > > On Mon, Oct 22, 2018 at 1:45 AM wrote: > >> Hi Dan, >> >> Sorry for the delay in replying. >> >> From a PRACTICAL point-of-view, as we all know, analogue watches >> replaced sundials, digital watches replaced analogue watches, and smart >> phones have replaced watches. Digital compasses replaced analogue >> compasses, and now smart phones have replaced compasses. I confess to >> having a mobile phone, and no longer wearing a watch. Also when I go >> bushwalking, now I carry a GPS with real-time tracking on appropriate-scale >> topographic maps. I still have a digital compass, but it was pretty fiddly >> to use, so it now sits somewhere at home. I only use a magnetic compass >> when doing serious field work, and I need to know the orientation of some >> feature I am measuring. >> >> But what has practicality to do with anything related to sundials >> >> Several years ago I was also intrigued about the accuracy of using a >> watch as a compass, and I decided to investigate it the empirical way. So I >> made up a little “tool” and every weekend when I went bushwalking, I would >> set it up and compare compass north with watch north at regular intervals. >> >> I ended up with quite a few measurements before life got in the way of >> plans, and the project petered out. I still have the results but I have >> never analysed them. In part because even then it was obvious to me that >> the question could be investigated using standard equations. But my feeling >> at the time was that the whole watch / north method was getting close to an >> urban myth. I had collected several variations on instructions, but I seem >> to have lost them in one of my several moves. But I do remember that >> depending on which you used, the error could be 30o or more. None of the >> methods said anything about the difference between true and magnetic north, >> but that may be irrelevant anyway unless you are somewhere like Antarctica >> where the difference can be 70o. More important would be DST which could be >> a major trap for the unwary. >> >> At one stage the watch / north method was called the “Boy Scout”method. >> During my travels on public transport when kids are going to school, I >> haven’t seen too many wearing analogue watches. Or watches of any form. >> They are completely welded to their smart phones, so it’s pretty obvious >> that the method has gone the way of sundials. >> >> When you find the analysis of the watch / north idea, can you post it on >> the List please? >> >> Cheers, John >> >> John Pickard >> john.pick...@bigpond.com >> >> >> *From:* Dan-George Uza >> *Sent:* Saturday, September 29, 2018 4:57 AM >> *To:* Sundial List >> *Subject:* Accuracy of wristwatch as compass >> >> Hello! >> >> I'm sure you know the method of pointing the analogue wristwach hour hand >> towards the Sun and then bisecting the angle to 12 o'clock in order to find >> south (or north, if you live down in the south). Actually I guess what you >> should be doing is bisect the angle to your noon time and not necessarily >> 12 o'clock, but anyway. A few years ago I read an interesting seasonal >> accuracy analysis of this method. I also vaguely remember the demonstration >> involved Vitruvius' analemma and I'm pretty sure it was all in a book. >> Thing is - I can't remember
Re: Accuracy of wristwatch as compass
I said, " a reasonable estimate can be gotten by substituting dec for tan dec." I meant "...dec in radians". Michael Ossipoff On Thu, Oct 25, 2018 at 12:44 PM Michael Ossipoff wrote: > > One more thing about AW: > > When dec Sun is positive, especially when it's positive and large, it > would be desirable to at least have a good estimate of when the Sun will be > due east or due west, to avoid an ambiguity that W and AW could otherwise > be subject to. > > That's because, (in afternoon) when dec Sun is positive, and the sun can > set north of due west, it isn't always certain whether, at some afternoon > or late-afternoon time, whether W or AW is giving the Sun's distance west > of south when the Sun is south of west, or giving the Sun's distance west > of north, when the Sun is north of west. > > To find out whether the sun is north or south of west, the time at which > the sun is due west can be calculated by: > > cos h = tan dec/tan lat. > > Of course, if you use AW, then you might know, or have written-down, tan > lat. And dec will always be fairly small, never more than 23.44, and, so a > reasonable estimate can be gotten by substituting dec for tan dec. > > Michael Ossipoff > > > > Michael Ossipoff > > On Thu, Oct 25, 2018 at 12:27 PM Michael Ossipoff > wrote: > >> >> Steve— >> >> . >> >> I was surprised to find that, at lat 55, the ordinary watch-method (W), >> at the summer-solstice, used at the edge of a standard-size timezone, and >> when disregarding longitude and EoT, is still a little more accurate than >> ST. (…but that isn’t entirely fair, considering that someone who knows ST’s >> max error can reduce it even by guessing.) >> >> . >> >> Of course, if the timezone were one of our more nonstandard ones, then W >> might have more max error than ST at lat 55. >> >> . >> >> But AW’s summer-solstice max error at lat 55 seems to only be about 14 >> degrees, when longitude and EoT are taken into account, and cos dec is >> known or well-estimated. >> >> . >> >> Michael Ossipoff >> >> On Thu, Oct 25, 2018 at 1:19 AM Steve Lelievre < >> steve.lelievre.can...@gmail.com> wrote: >> >>> Michael, >>> >>> >>> >>> On 2018-10-24 8:25 p.m., Michael Ossipoff wrote: >>> >>> A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if >>> you know the date, or date if you know the time. >>> >>> By writing "a Shepard's Dial marked out as a solar compass" I meant that >>> one for which the lines drawn on the cylinder are the azimuth corresponding >>> to altitude instead of the usual option of the hour corresponding to >>> altitude. So, yes, a sun compass. >>> >>> Sure, an Altitude-Dial is at its least accurate near noon, but this AW >>> method, and the TA that it’s based on, are different. The error is 0 at >>> noon, if you’re using the right EoT and longitude. The altitude (ideally >>> along with the declination) adjusts h, to get the azimuth from south. >>> >>> . >>> >>> The error is max sometime during mid-afternoon because, because it’s 0 >>> at noon, and because, when the sun is low near sunset, h is multiplied >>> by a only a factor, closer to 1, because cos dec * sec Alt is closer to 1 >>> then. >>> >>> . >>> >>> AW’s error comes from the fact that it substitutes h and Azimuth for >>> their sines. When the factor by which sin h is multiplied is closer to 1, >>> the error from that substitution is smaller. >>> >>> . >>> >>> So AW has its greatest error around mid-afternoon, between noon when >>> it’s 0, and near sunset when it’s error is low due to that multiplicative >>> factor being closer to 1. >>> >>> OK, I see what you're saying now. I was coming at it just by imagining >>> how hard it must be to get an accurate altitude measurement - perhaps a few >>> degrees out. My thinking was that around noon the azimuth changes a lot >>> from a small change in altitude so any measurement error would be >>> multiplied considerably, whereas later or earlier in the day the same small >>> change in altitude would correspond to a smaller change of azimuth. >>> >>> Cheers, >>> >>> Steve >>> >>> >>> >>> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
One more thing about AW: When dec Sun is positive, especially when it's positive and large, it would be desirable to at least have a good estimate of when the Sun will be due east or due west, to avoid an ambiguity that W and AW could otherwise be subject to. That's because, (in afternoon) when dec Sun is positive, and the sun can set north of due west, it isn't always certain whether, at some afternoon or late-afternoon time, whether W or AW is giving the Sun's distance west of south when the Sun is south of west, or giving the Sun's distance west of north, when the Sun is north of west. To find out whether the sun is north or south of west, the time at which the sun is due west can be calculated by: cos h = tan dec/tan lat. Of course, if you use AW, then you might know, or have written-down, tan lat. And dec will always be fairly small, never more than 23.44, and, so a reasonable estimate can be gotten by substituting dec for tan dec. Michael Ossipoff Michael Ossipoff On Thu, Oct 25, 2018 at 12:27 PM Michael Ossipoff wrote: > > Steve— > > . > > I was surprised to find that, at lat 55, the ordinary watch-method (W), at > the summer-solstice, used at the edge of a standard-size timezone, and when > disregarding longitude and EoT, is still a little more accurate than ST. > (…but that isn’t entirely fair, considering that someone who knows ST’s max > error can reduce it even by guessing.) > > . > > Of course, if the timezone were one of our more nonstandard ones, then W > might have more max error than ST at lat 55. > > . > > But AW’s summer-solstice max error at lat 55 seems to only be about 14 > degrees, when longitude and EoT are taken into account, and cos dec is > known or well-estimated. > > . > > Michael Ossipoff > > On Thu, Oct 25, 2018 at 1:19 AM Steve Lelievre < > steve.lelievre.can...@gmail.com> wrote: > >> Michael, >> >> >> >> On 2018-10-24 8:25 p.m., Michael Ossipoff wrote: >> >> A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if >> you know the date, or date if you know the time. >> >> By writing "a Shepard's Dial marked out as a solar compass" I meant that >> one for which the lines drawn on the cylinder are the azimuth corresponding >> to altitude instead of the usual option of the hour corresponding to >> altitude. So, yes, a sun compass. >> >> Sure, an Altitude-Dial is at its least accurate near noon, but this AW >> method, and the TA that it’s based on, are different. The error is 0 at >> noon, if you’re using the right EoT and longitude. The altitude (ideally >> along with the declination) adjusts h, to get the azimuth from south. >> >> . >> >> The error is max sometime during mid-afternoon because, because it’s 0 at >> noon, and because, when the sun is low near sunset, h is multiplied by >> a only a factor, closer to 1, because cos dec * sec Alt is closer to 1 then. >> >> . >> >> AW’s error comes from the fact that it substitutes h and Azimuth for >> their sines. When the factor by which sin h is multiplied is closer to 1, >> the error from that substitution is smaller. >> >> . >> >> So AW has its greatest error around mid-afternoon, between noon when it’s >> 0, and near sunset when it’s error is low due to that multiplicative factor >> being closer to 1. >> >> OK, I see what you're saying now. I was coming at it just by imagining >> how hard it must be to get an accurate altitude measurement - perhaps a few >> degrees out. My thinking was that around noon the azimuth changes a lot >> from a small change in altitude so any measurement error would be >> multiplied considerably, whereas later or earlier in the day the same small >> change in altitude would correspond to a smaller change of azimuth. >> >> Cheers, >> >> Steve >> >> >> >> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
Steve— . I was surprised to find that, at lat 55, the ordinary watch-method (W), at the summer-solstice, used at the edge of a standard-size timezone, and when disregarding longitude and EoT, is still a little more accurate than ST. (…but that isn’t entirely fair, considering that someone who knows ST’s max error can reduce it even by guessing.) . Of course, if the timezone were one of our more nonstandard ones, then W might have more max error than ST at lat 55. . But AW’s summer-solstice max error at lat 55 seems to only be about 14 degrees, when longitude and EoT are taken into account, and cos dec is known or well-estimated. . Michael Ossipoff On Thu, Oct 25, 2018 at 1:19 AM Steve Lelievre < steve.lelievre.can...@gmail.com> wrote: > Michael, > > > > On 2018-10-24 8:25 p.m., Michael Ossipoff wrote: > > A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if > you know the date, or date if you know the time. > > By writing "a Shepard's Dial marked out as a solar compass" I meant that > one for which the lines drawn on the cylinder are the azimuth corresponding > to altitude instead of the usual option of the hour corresponding to > altitude. So, yes, a sun compass. > > Sure, an Altitude-Dial is at its least accurate near noon, but this AW > method, and the TA that it’s based on, are different. The error is 0 at > noon, if you’re using the right EoT and longitude. The altitude (ideally > along with the declination) adjusts h, to get the azimuth from south. > > . > > The error is max sometime during mid-afternoon because, because it’s 0 at > noon, and because, when the sun is low near sunset, h is multiplied by a > only a factor, closer to 1, because cos dec * sec Alt is closer to 1 then. > > . > > AW’s error comes from the fact that it substitutes h and Azimuth for their > sines. When the factor by which sin h is multiplied is closer to 1, the > error from that substitution is smaller. > > . > > So AW has its greatest error around mid-afternoon, between noon when it’s > 0, and near sunset when it’s error is low due to that multiplicative factor > being closer to 1. > > OK, I see what you're saying now. I was coming at it just by imagining how > hard it must be to get an accurate altitude measurement - perhaps a few > degrees out. My thinking was that around noon the azimuth changes a lot > from a small change in altitude so any measurement error would be > multiplied considerably, whereas later or earlier in the day the same small > change in altitude would correspond to a smaller change of azimuth. > > Cheers, > > Steve > > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
Ok, I see what you mean--I misunderstood because it's a kind of dial that hadn't occurred to me. It sounded good, but then I realized that latitude is built into such a dial, so it's only usable at a certain latitude. I've sometimes used a compass or solar direction-finding when hiking in my own county, but mostly when in an unfamiliar town. When you make a sun-compass, you don't necessarily know where you'll need it. That's something that I like about the Universal Analemmatic Dial as a suncompass. ...and the fact that constructing it need consist only of printing out the markings, which, by themselves, can tell you the Sun's azimuth at any latitude, date and time. Though AW determines azimuth primarily from time, it's still true that, as you said, an altitude mis-estimate could have more effect near mid-day, because the higher the Sun is, the more greatly the altitude affects the difference between h and Az. So, what you said about that was true. I was just looking more at the error due to substituting h and Az for their sines, and assuming that the altitude estimate is good. Michael Ossipoff On Thu, Oct 25, 2018 at 1:19 AM Steve Lelievre < steve.lelievre.can...@gmail.com> wrote: > Michael, > > > > > On 2018-10-24 8:25 p.m., Michael Ossipoff wrote: > > A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if > you know the date, or date if you know the time. > > By writing "a Shepard's Dial marked out as a solar compass" I meant that > one for which the lines drawn on the cylinder are the azimuth corresponding > to altitude instead of the usual option of the hour corresponding to > altitude. So, yes, a sun compass. > > > Sure, an Altitude-Dial is at its least accurate near noon, but this AW > method, and the TA that it’s based on, are different. The error is 0 at > noon, if you’re using the right EoT and longitude. The altitude (ideally > along with the declination) adjusts h, to get the azimuth from south. > > . > > The error is max sometime during mid-afternoon because, because it’s 0 at > noon, and because, when the sun is low near sunset, h is multiplied by a > only a factor, closer to 1, because cos dec * sec Alt is closer to 1 then. > > . > > AW’s error comes from the fact that it substitutes h and Azimuth for their > sines. When the factor by which sin h is multiplied is closer to 1, the > error from that substitution is smaller. > > . > > So AW has its greatest error around mid-afternoon, between noon when it’s > 0, and near sunset when it’s error is low due to that multiplicative factor > being closer to 1. > > OK, I see what you're saying now. I was coming at it just by imagining how > hard it must be to get an accurate altitude measurement - perhaps a few > degrees out. My thinking was that around noon the azimuth changes a lot > from a small change in altitude so any measurement error would be > multiplied considerably, whereas later or earlier in the day the same small > change in altitude would correspond to a smaller change of azimuth. > > Cheers, > > Steve > > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
Michael, On 2018-10-24 8:25 p.m., Michael Ossipoff wrote: A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if you know the date, or date if you know the time. By writing "a Shepard's Dial marked out as a solar compass" I meant that one for which the lines drawn on the cylinder are the azimuth corresponding to altitude instead of the usual option of the hour corresponding to altitude. So, yes, a sun compass. Sure, an Altitude-Dial is at its least accurate near noon, but this AW method, and the TA that it’s based on, are different. The error is 0 at noon, if you’re using the right EoT and longitude. The altitude (ideally along with the declination) adjusts h, to get the azimuth from south. . The error is max sometime during mid-afternoon because, because it’s 0 at noon, and because, when the sun is low near sunset,h is multiplied by a only a factor, closer to 1, because cos dec * sec Alt is closer to 1 then. . AW’s error comes from the fact that it substitutes h and Azimuth for their sines. When the factor by which sin h is multiplied is closer to 1, the error from that substitution is smaller. . So AW has its greatest error around mid-afternoon, between noon when it’s 0, and near sunset when it’s error is low due to that multiplicative factor being closer to 1. OK, I see what you're saying now. I was coming at it just by imagining how hard it must be to get an accurate altitude measurement - perhaps a few degrees out. My thinking was that around noon the azimuth changes a lot from a small change in altitude so any measurement error would be multiplied considerably, whereas later or earlier in the day the same small change in altitude would correspond to a smaller change of azimuth. Cheers, Steve --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
When I used the standardly assumed solar altitude at Sunset (-5/6 degree for the center of the solar disk), I get 45.59 degrees for the summer maximum error. …which is almost the same as what you said. . A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time if you know the date, or date if you know the time. . Sure, an Altitude-Dial is at its least accurate near noon, but this AW method, and the TA that it’s based on, are different. The error is 0 at noon, if you’re using the right EoT and longitude. The altitude (ideally along with the declination) adjusts h, to get the azimuth from south. . The error is max sometime during mid-afternoon because, because it’s 0 at noon, and because, when the sun is low near sunset, h is multiplied by a only a factor, closer to 1, because cos dec * sec Alt is closer to 1 then. . AW’s error comes from the fact that it substitutes h and Azimuth for their sines. When the factor by which sin h is multiplied is closer to 1, the error from that substitution is smaller. . So AW has its greatest error around mid-afternoon, between noon when it’s 0, and near sunset when it’s error is low due to that multiplicative factor being closer to 1. . My favorite sun-compass is the Universal Analemmatic Dial. Fred Sawyer can send you an image of that dial’s markings. If you print it out, it serves as a sun-compass. . It tells the Sun’s azimuth at any given lat , date and time. There’s no need to look at it in direct sunlight, and of course that would be inadvisable if it’s printed on white paper. . Sun-compasses for practical purposes have been built based on it. . Tomorrow I’ll comment on the max errors of W and AW at lat 55. . Michael Ossipoff On Wed, Oct 24, 2018 at 5:25 PM Steve Lelievre < steve.lelievre.can...@gmail.com> wrote: > Hello, Michael, > > On 2018-10-24 8:42 a.m., Michael Ossipoff wrote: > > The Shadow-Tip method [has] accuracy is greater at lower latitudes. > > That's putting it mildly, I think. The method would be OK everywhere > around midday or near an equinox but I suspect it's really, really bad if > used early or late on a midsummer day at higher latitudes. I'm from 55N, > and for that latitude I reckon it could reach as much as 45 degrees off > outside of the midday period in summer. > > I've nearly always gotten very good results with [the Altitude Watch >>> method], though there are combinations of time-of-year and time-of-day when >>> it loses accuracy. Midsummer and roughly mid afternoon or morning. >>> >> Maybe I've misunderstood, the method but I don't understand why > mid-afternoon and mid-morning are the bad times of day. Why is that? I > would expect it to be around noon, when the sun's azimuth can change > significantly for relatively little change in altitude. > > Anyway, your method reminded me of another altitude method - a Shepard's > Dial marked out as a solar compass. I once made one and it worked pretty > well, with a bit of degradation around noon. A Mr. Singleton was the first > person I know of to publish the idea. > Steve > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
I’d said: . The Shadow-Tip method [has] accuracy is greater at lower latitudes. . You replied: . That's putting it mildly, I think. The method would be OK everywhere around midday or near an equinox but I suspect it's really, really bad if used early or late on a midsummer day at higher latitudes. I'm from 55N, and for that latitude I reckon it could reach as much as 45 degrees off outside of the midday period in summer. . I answer: . Yes, I get 42.7 degrees max error at that date at sunset or sunrise. But you’d know that, and so you’d know that the error will vary from 0 to 42.7, (at least on the summer side, and something very similar on the winter side) facilitating an a reasonably good estimate of how much the error will be at any time, because you know it will be less when closer to the equinox or noon.. . It’s dinner-time now, and so this is just a quick preliminary reply. After dinner, I’ll reply to the rest of your post, and will report the Watch-Method’s errors at some times at the summer solstice at lat 55. By the way, of course AW would be at its best at high latitudes. Michael Ossipoff On Wed, Oct 24, 2018 at 5:25 PM Steve Lelievre < steve.lelievre.can...@gmail.com> wrote: > Hello, Michael, > > On 2018-10-24 8:42 a.m., Michael Ossipoff wrote: > > The Shadow-Tip method [has] accuracy is greater at lower latitudes. > > That's putting it mildly, I think. The method would be OK everywhere > around midday or near an equinox but I suspect it's really, really bad if > used early or late on a midsummer day at higher latitudes. I'm from 55N, > and for that latitude I reckon it could reach as much as 45 degrees off > outside of the midday period in summer. > > I've nearly always gotten very good results with [the Altitude Watch >>> method], though there are combinations of time-of-year and time-of-day when >>> it loses accuracy. Midsummer and roughly mid afternoon or morning. >>> >> Maybe I've misunderstood, the method but I don't understand why > mid-afternoon and mid-morning are the bad times of day. Why is that? I > would expect it to be around noon, when the sun's azimuth can change > significantly for relatively little change in altitude. > > Anyway, your method reminded me of another altitude method - a Shepard's > Dial marked out as a solar compass. I once made one and it worked pretty > well, with a bit of degradation around noon. A Mr. Singleton was the first > person I know of to publish the idea. > Steve > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
Hello, Michael, On 2018-10-24 8:42 a.m., Michael Ossipoff wrote: The Shadow-Tip method [has] accuracy is greater at lower latitudes. That's putting it mildly, I think. The method would be OK everywhere around midday or near an equinox but I suspect it's really, really bad if used early or late on a midsummer day at higher latitudes. I'm from 55N, and for that latitude I reckon it could reach as much as 45 degrees off outside of the midday period in summer. I've nearly always gotten very good results with [the Altitude Watch method], though there are combinations of time-of-year and time-of-day when it loses accuracy. Midsummer and roughly mid afternoon or morning. Maybe I've misunderstood, the method but I don't understand why mid-afternoon and mid-morning are the bad times of day. Why is that? I would expect it to be around noon, when the sun's azimuth can change significantly for relatively little change in altitude. Anyway, your method reminded me of another altitude method - a Shepard's Dial marked out as a solar compass. I once made one and it worked pretty well, with a bit of degradation around noon. A Mr. Singleton was the first person I know of to publish the idea. Steve --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
I meant: Multiply h * sec Alt Sun by cos dec In my example, sec Alt Sun was 1.25, and cos dec is somewhere between 1 and 1 - 1/12 (as it always is). Michael Ossipoff On Wed, Oct 24, 2018 at 10:55 AM Michael Ossipoff wrote: > > I mis-stated what the secant is. I said: > > 'The secant of the Sun's altitude is the *direct* distance from the tip > of the object to the tip of its shadow, divided by the height of the > object. Of course you probably don't have time to measure with > measuring-tape, and you just estimate that ratio." > > ii meant: Divide the direct distance between the tip of the object and the > tip of its shadow, by the horizontal distance between the base of the > object and the tip of the shadow. > > But, as a practical matter, instead of measuring and calculating, you just > estimate by what percentage the direct tip-to-tip distance is greater than > the base-to-shadow-tip distance. > > For example, say it looks as if the object tip to shadow tip is 25% > greater than the base-to-shadow-tip distance. > > That sec Alt Sun. So multiply h by 1.25 > > And, as I said, optionally multiply a rough estimate of cos dec, which > will always be somewhere between 1 and 1 - 1/12. > > ...1 at equinox, and 1 - 1/12 at either solstice. > > Michael Ossipoff > > > On Wed, Oct 24, 2018 at 10:30 AM Michael Ossipoff > wrote: > >> Dan-- >> >> It's as you said. The Watch Method works best (and is only really any >> good) when the Sun is low. So, it's really only any good in winter, or very >> late or early in the day. >> >> ...and a lot of people do most of their hiking in the summer. >> >> Its accuracy increases with latitude. >> >> But, as Favio pointed out, there's error due to EoT and longitude, if you >> don't take those things into account. ...and, by definition, if you're >> using the ordinary watch method, you aren' taking those things into account >> >> For a long time, the Watch method was the only solar direction-finding >> method ever mentioned in outdoor books and articles. >> >> But, in 1962, a kid in this country suggested something simple, and >> everyone wondered why it hadn't occurred to them: >> >> The Shadow-Tip method: >> >> 1. At the tip of the shadow of a twig, place a pebble, or make a mark in >> the dirt. Of course you could place a stick vertically in the ground and >> use its shadow. The stick needn't be straight. >> >> 2. After 5 or 10 minutes, again place a pebble or make a mark at the >> shadow-tip's new position. >> >> 3. A line between those two marks will be roughly east-west. >> >> The Shadow-Tip method is both easier, and more accurate than the >> Watch-Method. It's accuracy is greater at lower latitudes. Of course, an >> additional advantage of Shadow-Tip is that it doesn't require any equipment >> at all. ...and doesn't reqiuire EoT or longitude. >> >> But neither of those is the method that I use. For many years, I've been >> routinely using an approximation to the Time-Altitude (TA) method. >> >> TA calculates the Sun's azimuth from the time and the Sun's altitude. Of >> course you need EoT and longitude. You don't need latitude. It has been >> used some by navigators and surveyors, but it isn't usually favorite. But >> its formula is brief, and it lends itself to the practical and convenient >> approximation that I use. >> >> The approximation of TA that I use, I call "the Altitude Watch Method >> (AW). >> >> Instead of making it look complicated by first posting the TA formula, >> let me first just describe AW: >> >> 1. Say you know the longitude, and the EoT for the current day. Adjust >> the time accordingly. For longitude, that amounts to adding 4 minutes for >> each longitude degree east of your timezone's central meridian, or >> subtracting 4 minutes for each degree west of that meridian. >> >> 2.. Of course each hour moves the solar hour-angle 15 degrees, and each >> additional 4 minutes moves it another degree. That's the Solar hour-angle, >> from the meridian. >> >> 3. Multiply that h value by the secant of the Sun's altitude. That can >> be estimated by observing the shadow of a post, tree, building, etc. >> ...or of a pen held vertical against your forearm or the palm of your >> hand. >> >> The secant of the Sun's altitude is the *direct* distance from the tip >> of the object to the tip of its shadow, divided by the height of the >> object. Of course you probably don't have time to measure with >> measuring-tape, and you just estimate that ratio. >> >> Multiplying h by sec Alt of the Sun greatly improves accuracy, and that >> sec Alt is probably all you need to take into account to correct your h >> estimate, for practical purposes. >> >> 4. If you don't know and take into account the Sun's declination, that's >> ok, because it doesn't have much effect. But, on the other hand, we usually >> have a rough idea of the Sun's declination. For example, right now, toward >> the end of October, it's going to be somewhere between 0 and -23.44 degrees. >>
Re: Accuracy of wristwatch as compass
I mis-stated what the secant is. I said: 'The secant of the Sun's altitude is the *direct* distance from the tip of the object to the tip of its shadow, divided by the height of the object. Of course you probably don't have time to measure with measuring-tape, and you just estimate that ratio." ii meant: Divide the direct distance between the tip of the object and the tip of its shadow, by the horizontal distance between the base of the object and the tip of the shadow. But, as a practical matter, instead of measuring and calculating, you just estimate by what percentage the direct tip-to-tip distance is greater than the base-to-shadow-tip distance. For example, say it looks as if the object tip to shadow tip is 25% greater than the base-to-shadow-tip distance. That sec Alt Sun. So multiply h by 1.25 And, as I said, optionally multiply a rough estimate of cos dec, which will always be somewhere between 1 and 1 - 1/12. ...1 at equinox, and 1 - 1/12 at either solstice. Michael Ossipoff On Wed, Oct 24, 2018 at 10:30 AM Michael Ossipoff wrote: > Dan-- > > It's as you said. The Watch Method works best (and is only really any > good) when the Sun is low. So, it's really only any good in winter, or very > late or early in the day. > > ...and a lot of people do most of their hiking in the summer. > > Its accuracy increases with latitude. > > But, as Favio pointed out, there's error due to EoT and longitude, if you > don't take those things into account. ...and, by definition, if you're > using the ordinary watch method, you aren' taking those things into account > > For a long time, the Watch method was the only solar direction-finding > method ever mentioned in outdoor books and articles. > > But, in 1962, a kid in this country suggested something simple, and > everyone wondered why it hadn't occurred to them: > > The Shadow-Tip method: > > 1. At the tip of the shadow of a twig, place a pebble, or make a mark in > the dirt. Of course you could place a stick vertically in the ground and > use its shadow. The stick needn't be straight. > > 2. After 5 or 10 minutes, again place a pebble or make a mark at the > shadow-tip's new position. > > 3. A line between those two marks will be roughly east-west. > > The Shadow-Tip method is both easier, and more accurate than the > Watch-Method. It's accuracy is greater at lower latitudes. Of course, an > additional advantage of Shadow-Tip is that it doesn't require any equipment > at all. ...and doesn't reqiuire EoT or longitude. > > But neither of those is the method that I use. For many years, I've been > routinely using an approximation to the Time-Altitude (TA) method. > > TA calculates the Sun's azimuth from the time and the Sun's altitude. Of > course you need EoT and longitude. You don't need latitude. It has been > used some by navigators and surveyors, but it isn't usually favorite. But > its formula is brief, and it lends itself to the practical and convenient > approximation that I use. > > The approximation of TA that I use, I call "the Altitude Watch Method > (AW). > > Instead of making it look complicated by first posting the TA formula, let > me first just describe AW: > > 1. Say you know the longitude, and the EoT for the current day. Adjust the > time accordingly. For longitude, that amounts to adding 4 minutes for each > longitude degree east of your timezone's central meridian, or subtracting 4 > minutes for each degree west of that meridian. > > 2.. Of course each hour moves the solar hour-angle 15 degrees, and each > additional 4 minutes moves it another degree. That's the Solar hour-angle, > from the meridian. > > 3. Multiply that h value by the secant of the Sun's altitude. That can be > estimated by observing the shadow of a post, tree, building, etc. > ...or of a pen held vertical against your forearm or the palm of your hand. > > The secant of the Sun's altitude is the *direct* distance from the tip of > the object to the tip of its shadow, divided by the height of the object. > Of course you probably don't have time to measure with measuring-tape, and > you just estimate that ratio. > > Multiplying h by sec Alt of the Sun greatly improves accuracy, and that > sec Alt is probably all you need to take into account to correct your h > estimate, for practical purposes. > > 4. If you don't know and take into account the Sun's declination, that's > ok, because it doesn't have much effect. But, on the other hand, we usually > have a rough idea of the Sun's declination. For example, right now, toward > the end of October, it's going to be somewhere between 0 and -23.44 degrees. > > So, optionally, mutltiply h * sec Alt Sun by the cos dec, the cosine of > the declination. Roughly estimating that is much easier than it sounds: > > The cosine varies between 1 and 0. For 0 degrees, the cosine is just 1. > For plus or minus 23.44, the cosine is about 1 minus 1/12. > > So, if it were the winter solstice, you'd subtract, from sec Alt Sun, 1/12
Re: Accuracy of wristwatch as compass
Dan-- It's as you said. The Watch Method works best (and is only really any good) when the Sun is low. So, it's really only any good in winter, or very late or early in the day. ...and a lot of people do most of their hiking in the summer. Its accuracy increases with latitude. But, as Favio pointed out, there's error due to EoT and longitude, if you don't take those things into account. ...and, by definition, if you're using the ordinary watch method, you aren' taking those things into account For a long time, the Watch method was the only solar direction-finding method ever mentioned in outdoor books and articles. But, in 1962, a kid in this country suggested something simple, and everyone wondered why it hadn't occurred to them: The Shadow-Tip method: 1. At the tip of the shadow of a twig, place a pebble, or make a mark in the dirt. Of course you could place a stick vertically in the ground and use its shadow. The stick needn't be straight. 2. After 5 or 10 minutes, again place a pebble or make a mark at the shadow-tip's new position. 3. A line between those two marks will be roughly east-west. The Shadow-Tip method is both easier, and more accurate than the Watch-Method. It's accuracy is greater at lower latitudes. Of course, an additional advantage of Shadow-Tip is that it doesn't require any equipment at all. ...and doesn't reqiuire EoT or longitude. But neither of those is the method that I use. For many years, I've been routinely using an approximation to the Time-Altitude (TA) method. TA calculates the Sun's azimuth from the time and the Sun's altitude. Of course you need EoT and longitude. You don't need latitude. It has been used some by navigators and surveyors, but it isn't usually favorite. But its formula is brief, and it lends itself to the practical and convenient approximation that I use. The approximation of TA that I use, I call "the Altitude Watch Method (AW). Instead of making it look complicated by first posting the TA formula, let me first just describe AW: 1. Say you know the longitude, and the EoT for the current day. Adjust the time accordingly. For longitude, that amounts to adding 4 minutes for each longitude degree east of your timezone's central meridian, or subtracting 4 minutes for each degree west of that meridian. 2.. Of course each hour moves the solar hour-angle 15 degrees, and each additional 4 minutes moves it another degree. That's the Solar hour-angle, from the meridian. 3. Multiply that h value by the secant of the Sun's altitude. That can be estimated by observing the shadow of a post, tree, building, etc. ...or of a pen held vertical against your forearm or the palm of your hand. The secant of the Sun's altitude is the *direct* distance from the tip of the object to the tip of its shadow, divided by the height of the object. Of course you probably don't have time to measure with measuring-tape, and you just estimate that ratio. Multiplying h by sec Alt of the Sun greatly improves accuracy, and that sec Alt is probably all you need to take into account to correct your h estimate, for practical purposes. 4. If you don't know and take into account the Sun's declination, that's ok, because it doesn't have much effect. But, on the other hand, we usually have a rough idea of the Sun's declination. For example, right now, toward the end of October, it's going to be somewhere between 0 and -23.44 degrees. So, optionally, mutltiply h * sec Alt Sun by the cos dec, the cosine of the declination. Roughly estimating that is much easier than it sounds: The cosine varies between 1 and 0. For 0 degrees, the cosine is just 1. For plus or minus 23.44, the cosine is about 1 minus 1/12. So, if it were the winter solstice, you'd subtract, from sec Alt Sun, 1/12 of whatever sec Alt Sun is. Right now, we're between the equinox, when dec Sun is zero, and the solstice, when dec sun is -23.44. So, the estimate for the solar azimuth (measured from south) would be gotten by reducing sec Alt Sun by something less than 1/12 of itself. Say half of 1/12? You can guess about that, or just disregard it. I've nearly always gotten very good results with AW, though there are combinations of time-of-year and time-of-day when it loses accuracy. Midsummer and roughly mid afternoon or morning. The great advantage of AW of the Watch method (W) is that AW is much more accurate. The main advantage of AW of the Shadow-Tip method (ST) is that AW doesn't require you to stop walking. AW can be used in a car (where a magnetic compass isn't accurate due to nearby steel. (...except for an installed compensated compass). ST is what I recommend to people, because it's by far the easiest method, and much more accurate than W. But I use AW, because it combines good accuracy with great convenience. On Mon, Oct 22, 2018 at 12:20 PM Dan-George Uza wrote: > Dear John and others, > > Thank you for your insights. Although I haven't been able to track the >
Re: Accuracy of wristwatch as compass
Dan, Using a watch seems too imprecise to give more than a general idea of the direction of North. However, the basic concept has been developed to provide precision solar compass instruments. In most cases these come with tables to correct latitude, date and local solar time. If you don't know it, you might enjoy a glance at Malcolm Barnfield's article *The Sundial goes to War * http://www.sundials.co.za/THE%20SUNDIAL%20GOES%20TO%20WAR%20web.pdf Best wishes, Patrick Vyvyan On Mon, 22 Oct 2018 at 14:09, fabio.sav...@nonvedolora.it < fabio.sav...@nonvedolora.it> wrote: > dear Dan > > the wristwatch as compass has 3 problems: > a) it shows the time of a different longitude, the one of the time-zone > (GMT or DST). > You should correct it for the local time but it is possible only if you > know your longitude. > > b) you should correct the time also for eot, it means you should start > with the local Sun time for the longitude where you'll use it. > > You can admit a little bit of imprecision avoiding a) and b), if your > longitude is not so far from the one of the time-zone. > > c) you have to rotate the watch around the 3-9 axes of the colatitude > angle, so you have to evaulate also your latitude. > > Overall it isn't a reliable way to find the north, it is useful to have > a rough estimate if you haven't other instruments. > > I have some 3D drawings for a book I'm writing, I attach 2 images, if > you wish I can send you, or anyone who request them, a more defined jpg. > > ciao Fabio > > -- > > Fabio Savian > fabio.sav...@nonvedolora.it > www.nonvedolora.eu > Paderno Dugnano, Milano, Italy > 45° 34' 9'' N, 9° 9' 54'' E, UTC +1 (DST +2) > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
dear Dan the wristwatch as compass has 3 problems: a) it shows the time of a different longitude, the one of the time-zone (GMT or DST). You should correct it for the local time but it is possible only if you know your longitude. b) you should correct the time also for eot, it means you should start with the local Sun time for the longitude where you'll use it. You can admit a little bit of imprecision avoiding a) and b), if your longitude is not so far from the one of the time-zone. c) you have to rotate the watch around the 3-9 axes of the colatitude angle, so you have to evaulate also your latitude. Overall it isn't a reliable way to find the north, it is useful to have a rough estimate if you haven't other instruments. I have some 3D drawings for a book I'm writing, I attach 2 images, if you wish I can send you, or anyone who request them, a more defined jpg. ciao Fabio -- Fabio Savian fabio.sav...@nonvedolora.it www.nonvedolora.eu Paderno Dugnano, Milano, Italy 45° 34' 9'' N, 9° 9' 54'' E, UTC +1 (DST +2) --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Accuracy of wristwatch as compass
Hi Dan, Sorry for the delay in replying. >From a PRACTICAL point-of-view, as we all know, analogue watches replaced >sundials, digital watches replaced analogue watches, and smart phones have >replaced watches. Digital compasses replaced analogue compasses, and now smart >phones have replaced compasses. I confess to having a mobile phone, and no >longer wearing a watch. Also when I go bushwalking, now I carry a GPS with >real-time tracking on appropriate-scale topographic maps. I still have a >digital compass, but it was pretty fiddly to use, so it now sits somewhere at >home. I only use a magnetic compass when doing serious field work, and I need >to know the orientation of some feature I am measuring. But what has practicality to do with anything related to sundials Several years ago I was also intrigued about the accuracy of using a watch as a compass, and I decided to investigate it the empirical way. So I made up a little “tool” and every weekend when I went bushwalking, I would set it up and compare compass north with watch north at regular intervals. I ended up with quite a few measurements before life got in the way of plans, and the project petered out. I still have the results but I have never analysed them. In part because even then it was obvious to me that the question could be investigated using standard equations. But my feeling at the time was that the whole watch / north method was getting close to an urban myth. I had collected several variations on instructions, but I seem to have lost them in one of my several moves. But I do remember that depending on which you used, the error could be 30o or more. None of the methods said anything about the difference between true and magnetic north, but that may be irrelevant anyway unless you are somewhere like Antarctica where the difference can be 70o. More important would be DST which could be a major trap for the unwary. At one stage the watch / north method was called the “Boy Scout”method. During my travels on public transport when kids are going to school, I haven’t seen too many wearing analogue watches. Or watches of any form. They are completely welded to their smart phones, so it’s pretty obvious that the method has gone the way of sundials. When you find the analysis of the watch / north idea, can you post it on the List please? Cheers, John John Pickard john.pick...@bigpond.com From: Dan-George Uza Sent: Saturday, September 29, 2018 4:57 AM To: Sundial List Subject: Accuracy of wristwatch as compass Hello! I'm sure you know the method of pointing the analogue wristwach hour hand towards the Sun and then bisecting the angle to 12 o'clock in order to find south (or north, if you live down in the south). Actually I guess what you should be doing is bisect the angle to your noon time and not necessarily 12 o'clock, but anyway. A few years ago I read an interesting seasonal accuracy analysis of this method. I also vaguely remember the demonstration involved Vitruvius' analemma and I'm pretty sure it was all in a book. Thing is - I can't remember where! Can you help? Dan Uza --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: accuracy attachments
Hi Walter, I too thought some small pictures were nice, but, as I have a few websites I can post items to, I'll do that in the future, so that those that want to see the pics can, those that don't, wont. I'm hoping the adobe Acrobat pdf format I've chosen will work for everyone, since readers are free for most platforms. On the accuracy thing I have a few comments. For me, time as characterized by the orbiting and rotating of the earth as complicated by height, refraction, elliptical orbits, perturbations and lovely earthly wobbles is the real time. I mean, we live with it every day and the sun being up makes it day. Again, this beloved time is actually a set of observations of a number of interacting processes which are not forever repetitive to the finest structure. Anyhow, at an observatory I once visited they commonly reflected and enlarged the image of the sun to about 6 feet (2 meters) in diameter on a large, long blank white wall with a fine grid and took timed photos of it as it as it moved rapidly across the wall. They said they could resolve time to hundredths of seconds with this method. Using a sextant and accurate tables, fixing on just an upper or lower limb of the sun, accuracies of better than a second in time are often made if the position in space is very accurately known. The key to accuracy appears to be in enlarging the image and using either a predetermined elliptical shape to measure it's position, or some fixed point on the edge of the image, or a grid and photos. An idea to make smaller time intervals more meaningful is to know that light travels about a foot (11.8 inches) in a nanosecond. So the difference in time between the path of light at dawn and noon, being different by about 4 thousand miles is about 0.02 seconds. I like the spirit and message of your comments! Edley McKnight [43.126N 123.327W] Hello again, thank you for all for the reactions, but what is wrong with my feeling about a second, when I say you can feel it , I mean of course you can count in seconds not in milli- or nano- seconds. I had thought about the sharpness of the shadow, but forgotten to mention it. Considering the center of a shadow of a thick gnomon I do not like, it is to subjective - your eyesight angle of view may be different as to another person. But what about the reverse, instead of a shadow use the light. This was used by clockmakers of the past for adjustment of their watches. They used a horizontal dial the gnomon was a small disc with a pierced small hole positioned according the local latitude looked only at noon to the spot thrown on the dial. (as you maybe discovered my interest in sundials is in relation with mechanical clocks or watches). So, why not with the aid of modern optics, obtain this needelpoint of light, the sun is needed in either case, shadow or light;Again, very interested in your comments. ( and also, as said, a university for this study would be nice, no?) Now on attachments, I am a bit surprised by the comments I read, what is prohibitive about pictures ? If it is the price of the connection-time, my opinion is, forget your PC use the conventional method offered by the postal services, you will spend money in either case as you know, the speed is uncompatible between the two. I started with a 56K modem, after that idsn, now I have ADSL, fast indifferent to your connection time which may be 24/on 24, the price remains the same, in my country all providers are constantly lowering their prices. As to the danger of a virus enclosed in an attachment, you have to live with it trust the anti-virus programs, which you have to update often. I personally like pictures in a mail as insertions, use the insertion facility often for drawings taken by my digital camera. So long, Walter 50.42.1 north4.33.46 east
Re: Accuracy again
I think I have to disagree here, Edley: A small mirror does indeed mimic a pinhole aperture, and the resulting image would also move quickly along the tangent surface. However, neither a plane mirror nor a pinhole actually focusses the Sun's image! A pinhole lens works by limiting the rays passed to a very small aperture angle; this results in rays from each point on the Sun's surface falling on a distinct point on the image plane. You end up with a large, dim image of the Sun, subtending 1/2 a degree referenced to the lens to image distance. While the spot would move 2.2 cm/sec (I'll use your numbers, untried!), the spot would be 262 cm in diameter! Additionally, diffraction effects would introduce a fuzziness to the edges of the solar image. I don't remember the formulae offhand, but I suspect the edge would be spread over considerably more than 2.2 cm. Dave 37.29N 121.97W On Sat, 22 Dec 2001, Edley McKnight wrote: Dear Walter and Membership, Accuracy again. Increasing the surface movement of the shadow or spot of light by the means of optical levers allows very fine time measurements. In our mind's eye we can fix a small mirror so that it reflects a small part of the sun's image far out into space. In seconds the reflected image can move from star to star. At that vast distance the surface rate of movement of the reflection is thousands of lightyears per second! In general when we magnify the sun's image size on a surface we increase the rate of movement of the image on that surface. If we choose to only reflect a very small portion of that image, it still moves very fast, being a sensitive indicator of the angle of the sun's rays. Thus, if the mirror were about 300 meters away from the surface, the spot reflection would move about 2.2 centimeters per second if the path of the refection were in the equatorial plane. Of course that distance could be folded by reflecting from optically flat first surface mirrors so that a smaller device could measure small increments of time. The larger sundials use an optical lever with it's fulcrum at the tip of the gnomon, thus increasing the rate of surface movement of the shadow. A small opening, acting as a pinhole lens, can focus a spot of light and sharpen the image. Enjoy the Light! Edley McKnight [43.126N 123.357W]
Re: Accuracy , Prenumba and Gnomon shape
Interesting question. I too would be interested in an answer (other than the spot shadow sharpener which has been discussed at length in the past). -Bill Gottesman In a message dated 12/22/2001 8:46:59 PM Eastern Standard Time, [EMAIL PROTECTED] writes: Accurate Diaists , Maybe this is off subject... but, is it possible to build a dithered gnomon so that it could minimize the prenumba (- spelling?). Or some other shape that produces a more finite edge. Best regards, Mike
RE: accuracy
Hello Shadow Watchers(?), This dial that came to the list as spam, but also seems to give resolution of a time down to 1 minute. I do not know how accurate it is but gennerally Pilkington Gibbs dials seem pretty professional. http://cgi.ebay.com/aw-cgi/eBayISAPI.dll?MfcISAPICommand=ViewItemitem=1498358081 It also uses light instead of shadows for time. Mike 36.9151 : 121.3539 --- David Pratten [EMAIL PROTECTED] wrote: Dear Walter, Greetings. There is another factor which limits sundial accuracy to about +/-22 seconds. This is the variation in the value of Equation of Time from year to year within a leap cycle. See www.sunlitdesign.com/infosearch/sundialaccuracy.htm David www.sunlitdesign.com -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of walter.jonckheere Sent: Thursday, 20 December 2001 8:47 PM To: sundial@rrz.uni-koeln.de Subject: accuracy Greetings to all We all know that the atomic clock has the highest possible resolution, while for sundials 2 to 1 minute seems to be the best achievement. I have a feeling 1 second could be obtained considering what follows. ( I consider a second ideal as one can feel it, I mean it is a timespan well related to the human body, one second you live, the next you may be dead; it is also somewhat related to the heartbeat) Consider a horizontal sundial whith the 15 degrees hour lines; it is impossible to trace minute lines when keeping usual dimensions for the dial. However, if we go far away from the base point of the gnomon, the portion of the arc between 2 hours, becomes larger; so imagine we go to where 60 lines can be drawn between two adjacent minute lines and we keep only the top part of the line 11h59m59s and try to draw it on the ground related to a very accurate positioning of the local meridian. These data allow also to calculate the height of the gnomon tip. If both dimensions are feasable to realise, we would have the desired accuracy of one second; of course the positioning of the meridian is of paramount importance and probably the most difficult to materialise. ( is this a nice subject for a university ?) Of some important influence is the width of the gnomon. The indication of noon time is never accurate because of this width, while the shadow cast for the earlier hours, may be considered as a hairline and is thus more accurate, which means that the morning part of the dial is more accurate if the shadow hairline is taken into account for determination of the meridian. So in fact, sundials should have a gap at noon corresponding to the width of the gnomon, and the afternoon part should be calculated in function of the right hairline shadow related to a second parallel meridian. Very interested to read your comments Walter = Mike DeAmicis-Roberts phone: 831-636-0454 email: [EMAIL PROTECTED] __ Do You Yahoo!? Send your FREE holiday greetings online! http://greetings.yahoo.com
Re: accuracy
Patrick powers is correct in noting that the 0.5 degree width of the sun (corresponding to 2 minutes of time) creates a shadow penumbra that is virtually impossible to read to the second. But, a sharp edge can be achieved by a focusing dial, which creates an crisply defined image of the sun, 2 minutes of time wide, with no penumbra. If the leading, or trailing edge of this image is chosen as the indicator, then it would be possible to read it to a few seconds, and perhaps to 1 second, on a large dial scale. Alignment becomes the limiting factor for such a dial. A focusing dial that is accurate within 60 seconds all day long (and oftern within 30 seconds) can be seen at www.precisionsundials.com/renaissance.htm Bill Gottesman Burlington, VT In a message dated 12/20/2001 5:03:43 AM Eastern Standard Time, [EMAIL PROTECTED] writes: Subj: accuracy Date:12/20/2001 5:03:43 AM Eastern Standard Time Greetings to all We all know that the atomic clock has the highest possible resolution, while for sundials 2 to 1 minute seems to be the best achievement. I have a feeling 1 second could be obtained considering what follows. ( I consider a second ideal as one can feel it, I mean it is a timespan well related to the human body, one second you live, the next you may be dead; it is also somewhat related to the heartbeat) Consider a horizontal sundial whith the 15 degrees hour lines; it is impossible to trace minute lines when keeping usual dimensions for the dial. However, if we go far away from the base point of the gnomon, the portion of the arc between 2 hours, becomes larger; so imagine we go to where 60 lines can be drawn between two adjacent minute lines and we keep only the top part of the line 11h59m59s and try to draw it on the ground related to a very accurate positioning of the local meridian. These data allow also to calculate the height of the gnomon tip. If both dimensions are feasable to realise, we would have the desired accuracy of one second; of course the positioning of the meridian is of paramount importance and probably the most difficult to materialise. ( is this a nice subject for a university ?) Of some important influence is the width of the gnomon. The indication of noon time is never accurate because of this width, while the shadow cast for the earlier hours, may be considered as a hairline and is thus more accurate, which means that the morning part of the dial is more accurate if the shadow hairline is taken into account for determination of the meridian. So in fact, sundials should have a gap at noon corresponding to the width of the gnomon, and the afternoon part should be calculated in function of the right hairline shadow related to a second parallel meridian. Very interested to read your comments Walter
Re: accuracy
I consider a second ideal as one can feel it, I mean it is a timespan well related to the human body, one second you live, the next you may be dead; Walter, This is very strange statement. True that you live one second and are dead the next, but by the time that happens it's a bit late to start measuring and assessing the time span! Moreover you only get one chance, which isn't much good to get a feeling for it. Nonetheless I understand what you mean... Regards peter Tandy
RE: accuracy
Dear Walter, Greetings. There is another factor which limits sundial accuracy to about +/-22 seconds. This is the variation in the value of Equation of Time from year to year within a leap cycle. See www.sunlitdesign.com/infosearch/sundialaccuracy.htm David www.sunlitdesign.com -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of walter.jonckheere Sent: Thursday, 20 December 2001 8:47 PM To: sundial@rrz.uni-koeln.de Subject: accuracy Greetings to all We all know that the atomic clock has the highest possible resolution, while for sundials 2 to 1 minute seems to be the best achievement. I have a feeling 1 second could be obtained considering what follows. ( I consider a second ideal as one can feel it, I mean it is a timespan well related to the human body, one second you live, the next you may be dead; it is also somewhat related to the heartbeat) Consider a horizontal sundial whith the 15 degrees hour lines; it is impossible to trace minute lines when keeping usual dimensions for the dial. However, if we go far away from the base point of the gnomon, the portion of the arc between 2 hours, becomes larger; so imagine we go to where 60 lines can be drawn between two adjacent minute lines and we keep only the top part of the line 11h59m59s and try to draw it on the ground related to a very accurate positioning of the local meridian. These data allow also to calculate the height of the gnomon tip. If both dimensions are feasable to realise, we would have the desired accuracy of one second; of course the positioning of the meridian is of paramount importance and probably the most difficult to materialise. ( is this a nice subject for a university ?) Of some important influence is the width of the gnomon. The indication of noon time is never accurate because of this width, while the shadow cast for the earlier hours, may be considered as a hairline and is thus more accurate, which means that the morning part of the dial is more accurate if the shadow hairline is taken into account for determination of the meridian. So in fact, sundials should have a gap at noon corresponding to the width of the gnomon, and the afternoon part should be calculated in function of the right hairline shadow related to a second parallel meridian. Very interested to read your comments Walter
RE: accuracy
At 08:25 AM 12/21/01 +1100, David Pratten wrote: Dear Walter, Greetings. There is another factor which limits sundial accuracy to about +/-22 seconds. This is the variation in the value of Equation of Time from year to year within a leap cycle. See www.sunlitdesign.com/infosearch/sundialaccuracy.htm David and others, This might be true if the equation-of-time correction is obtained from a look-up table by date. But if the sundial includes the EoT correction in the shapes of its curves, or in the shape of the gnomon, the declination of the Sun is what controls the value of the correction being applied. In that case, I think the error would be *much* smaller than +/- 22 seconds. -- Roger
Re: Re accuracy of GPS clock
John Pickard wrote: Fernando, Good to hear that you decided to ignore Ruby! Oxygen thief! Thank you. I have a rather old (i.e. 5 years!) Garmin GPS45 which I have used all over Australia, Argentina, Chile and Antarctica. Out of curiosity I have checked the clock against the time beerps on our national radio. Spot on to the second. Of course, in modern terms, only nano seconds seems to be acceptable, but for sundial work, my Garmin would not cause any noticeable errors. I'll be 100% satisfied with one second. I just want to find when thesun norths so I can find my meridian. Since I am not a superman (yet!), I would not be able to process any higher accuracy, would I? :-) I am interested in the GPS pages, but don't worry. I am sure I can find them using Altavista, NortherLight or any other Internet portal. By the way haven't you ever travelled in Brazil? Travelling in the woods, deserts, rain forests, swamps is the kind of think I would like to have done when I was younger. Since I never did it when I was in better shape, I think I'll have to do it sometime now or in the future. I am quite interested in hearing about your trips, excursions, expeditions... - fernando -- Fernando Cabral Padrao iX Sistemas Abertos mailto:[EMAIL PROTECTED] http://www.pix.com.br mailto:[EMAIL PROTECTED] Fone: +55 61 321-2433 Fax: +55 61 225-3082 15º 45' 04.9 S 47º 49' 58.6 W 19º 37' 57.0 S 45º 17' 13.6 W
Re accuracy of GPS clock
Fernando, Good to hear that you decided to ignore Ruby! Oxygen thief! I have a rather old (i.e. 5 years!) Garmin GPS45 which I have used all over Australia, Argentina, Chile and Antarctica. Out of curiosity I have checked the clock against the time beerps on our national radio. Spot on to the second. Of course, in modern terms, only nano seconds seems to be acceptable, but for sundial work, my Garmin would not cause any noticeable errors. There is a couple of web GPS pages, and I am sure that you could find out more there. Unfortunately I can't give you the URLs at the moment, they are on my notebook, that I managed to kill. BTW, these GPS web sites also have information on the Y2K problem and GPSs. Seems that most of the good brands have no problem. If anyone is interested in these URLs, post a message and I will see if I can recover them from my notebook. Cheers from cloudy Sydney John Dr John Pickard Senior Lecturer, Environmental Planning Graduate School of the Environment Macquarie University, NSW 2109 Australia Phone + 61 2 9850 7981 (work) + 61 2 9482 8647 (home) Fax + 61 2 9850 7972 (work)
