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 >
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