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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