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 <email9648...@gmail.com> 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 <email9648...@gmail.com> > 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 >>> >>> >>> >>>
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