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 < [email protected]> 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
