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 <email9648...@gmail.com> 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 <email9648...@gmail.com> > 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 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 <cerculdest...@gmail.com> >> 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 <john.pick...@bigpond.com> 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 <cerculdest...@gmail.com> >>>> *Sent:* Saturday, September 29, 2018 4:57 AM >>>> *To:* Sundial List <sundial@uni-koeln.de> >>>> *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 >>>> >>>> --------------------------------------------------- >>> https://lists.uni-koeln.de/mailman/listinfo/sundial >>> >>>
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