| QUESTION: A vertical dial's gnomon traces an inverted U in the summer months, and of course a U in the winter ones. They are the hyperbolic lines. BUT, in the summer it is an inverted U, yet for a shepherd's dial, the lines are always U shaped. The vertical dial nodus shadow traces are hour angle based, but do contain azimuth and altitude data. The shepherd's dial is altitude only and the gnomon ALWAYS points to the sun, not so for a vertical dial. If you consider the fact that the altitude shown on a vertical dial is skewed by the concurrent azimuth, then this begins to make sense. In fact, if you measured the altitude from the nodus of a vertical dial, you would find that the altitude actually peaks at solar noon and either side, the altitude is actually less. It only looks steeper because of the U curves, and they are skewed by azimuth. Have some fun and measure the angles yourself! QUESTION: The equatorial, the armillary, and the horizontal dial all have 6 o'clock (am or pm) at 90 degrees to the noon line (for non longitude adjusted dials). So, why does the azimuth dial not have 6 o'clock at 90 degrees to noon? The azimuth dial is horizontal and thus is a projection of the equatorial dial, and that skews the lines. On the equinox, yes 6am and 6pm are perpendicular to noon for the azimuth dial. However, the summer solstice ray from the sun to the gnomon will hit the equatorial dial at 90 degrees to noon, however if the ray continues down to the horizontal azimuth dial, it displaces south. So, for horizontal azimuth dials, 6 o'clock will be north or south of the 90 line from noon. But you say, how is it the horizontal hour angle dial has 6 o'clock at 90 degrees? the answer is because of the sloping gnomon. In fact the tip of the gnomon (nodus) on a horizontal dial is north of the 6 o'clock lines at all times of the year (for the northern hemisphere). QUESTION: Why do the print runs appear more frequently than for other books? Why did the second edition come out so soon after the first edition? The first edition lost the last two weeks of editing, those changes are available in all-updates.pdf and anyone who purchased the first edition before 4/9/05 got a free second edition. That was why the second edition came out so quickly. The print runs were kept small so that the few remaining clarifications needed, based on feedback, could get into the system more quickly. Feedback has been very good, and all feedback has been considered. The second edition has had very few "opportunities for improvement", and they are in reference-updates.pdf here. FEEDBACK is extremely welcome, and new material is posted on this web site. For example the Durer chapter, the Software chapter, the Stained Glass chapter, the Declination line chapter, etc, have all been placed on this web site, and the best place to find them is on the main web page here. Continuous feedback improves the product, and because the updates are made available, and because new material is posted here, your investment in the book is not only protected, it grows. The moral of the story is ~ please buy the book now! You can se the options to buy the book on the PayPal page. The book sells for less than you can copy it! And the book specifically allow limited copying with no charge, the sole requirement is that you notify me at "illustratingshadows at yahoo.com" and all feedback should be sent there also. All feedback is considered, and most causes an immediate change, some causes a change but not where you suggested it, and very very little results in no change. And I respond to all feedback. Thanks. QUESTION: You charged me $3.00 shipping by media mail, the stamp said $2.70 - why the difference? ANSWER: The padded envelope costs $0.70, hence the difference. And that ignores gas, and so on. S&H means shipping and handling, and handling can be many things. I eat some postage, and sales tax. QUESTION: Why isn't sunset the same as sunrise at the equinoxes? ANSWER: When the declination is 0 then sunset = sunrise provided two other things are 0 also! Namely the EOT and the locations longitude - locations reference longitude. Sunset - 12 noon + (12 noon - sunrise), then EOT is applied, then the longitude correction. If you set the EOT to 0 in the spreadsheet, if you set the longitude reference to equal the locations longitude then you will see sunset - sunrise where the declination is zero. QUESTION: On page 125 there is a winged azimuth dial. There is no way the hour points can ever be lined up with anywhere, not dial center, not the nodus base, nowhere. Since a normal hour angle dial with a right angled gnomon by definition provides azimuth by the nodus to nodus base line, is not the winged azimuth sun dial incorrect? ANSWER: Looks that way doesn't it! But no. Azimuth dials do not have hour lines, and their hour points are not fixed points, they merely form an hour line for one hour on one date. If you drew a horizontal dial with a dial center, and used the angles of lines from the nodus base to the hour point, then those lines would intersect the real single hour line. And those intersection points would be declination or calendar points. QUESTION: Why do the declination tables you have in the appendix differ from some other authors? ANSWER: Look at table A2.11 September 1. The table shows a declination of 8.4 degrees, and in the second edition it is 8.6 degrees. Waugh page 206 shows 8.5 degrees, Mayall on page 133 shows 8.3 to 8.4 degrees. Formulae such as these use approximations and series, and some use the calendar julian date, some use a true astronomical julian data. Approximations for the leap year, methods used by differing spreadsheets, and rounding due to precision all account for some variation. The question is best framed as "are the differences significant when using the method you will use when laying out a dial?" You may check online almanacs, and you may download the spreadsheet for A2.11, or any other spreadsheet here if you wish, and then refine them. Similarly, I have three different formulae for the equation of time that use the normal yearly leap cycle, and two that use the astronomical julian day that accounts for an annual drifting. Not one produces a result that always matches other tabulations. The most accurate would consider the astronomical method, and that changes by the year, which explains other discrepancies. In the times of Chaucer, their EOT was different measurable from ours in the 21st century! QUESTION: Why is your book's polar dial formula different from somt other authors? ANSWER: This book uses noon as the basis for the polar dial and 6am or 6pm as the basis for meridian (east or west) facing dials. Those points exist on the dial, so it made sense. It also means that references in the formula are from the sub-style in all cases, and not from the sub-style in one case, and infinity in the other. Not inconsistent, merely different. The end result is that this book's hour lines match those of all other authors. |
| How the sun makes hour lines (pdf) |
| FAQs |
| QUESTION: Equatorial, equinoctial or armillary, meridian or vertical? What is what, different people use the same terms for different things. Armillary often refers to the full armillary spheres, actually bracelets, as worn on an arm, hence the word. Equatorial dials are ones whose plane is parallel to the equator. Many people say that the armillary plane is parallel to the equator. Others, like me, say that the armillary dial plate is perpendicular to the equator, since that is where the numbers on the dial plate lie, thus an armillary has arm bands that parallel the ppolar axis. The equatorial dial truly has a dial plate with numbers on it paralleling the equatorial plane. The equatorial dial is sometimes called an equinoctial since it bifurcates at the equinoxes, summer shadows are on the sky side, winter shadows on the earth side. Meridian dials are dials whose plate lies in the meridian, namely parallel to the polar axis, like the true east and true west facing vertical dials. Some people call vertical north or south dials meridian dials since their style lies in the meridian. All styles lie in the meridian for hour angle dials. The real point is to know what you are looking at. Gnomonics is filled with ambiguous terms, declination can mean (1) wall declination from true north or south, (2) the suns declination or angle of rays north or south of the equator, or (3) magnetic variation whereby that variation acuses true and magnetic north not to coincide. |
| QUESTION: Why does the sunrise/set time in the PDA XLS (Docs To Go) disagree with the standalone almanac PRC for the PDA? The spreadsheet corrects for longitude and EOT, the standalone program shows the net correction and leaves it to you to do the math. It does this because it also shows altitude and azimuths which are not corrected either. |
| WHAT IS THE BOTTOM LINE FOR CALENDAR CURVES? January 4, 2008 Declination lines or curves are always symmetrical about the SD (style distance line). They only look non symmetrical on dials such as the east and west decliners because about half of the dial is always missing. IE an east dial has no afternoon hours, a west dial has no morning hours. Thus a declination set of curves for lat 32 is the same as lat -32. In other words, the sign can be ignored on SH, since SH is always above the dial plate, and SH (style height) is the latitude for declination or calendar curves. Not true for SD, style distance, because it may be either side of the vertical. The use of SH for the apparent latitude for the calendar curves is important because... 1. A dial plate is merely a presentation device for shadows, and thus is a geometrical mapping of the sun's circular movement to a plate that displays it. 2. This shows further an important point, namely that with correct alignment, altitude and azimuth are portable, an issue I discuss towards the end of book 2. There is argument that this is not the case, however, clearly it is portable provided certain constraints exist. 3. That is why I have a calendar curve generator in DeltaCAD that is separate from the dials, it further emphasises the relationship of calendar or declination lines or curves and SH. |
| How the sun makes hour lines (pdf) |
| QUESTION: Italian hour lines are clearly local apparent time. So why make a longitude correction on a dial with Italian hour lines? If the dial plate is not longitude corrected then the winter and summer solstice indicated times on the dial plate are used for the anchor points of the Italian hour lines. But, if the dial plate is longitude adjusted then that would no longer be true because the displayed or indicated times would no longer be LAT (local apparent time). So, if the dial plate has been longitude corrected then the Italian hour line anchor points should also be longitude adjusted so that the end result is that the Italian hour lines are where they would be on the dial plate were no longitude correction applied at all. See the case study of the polar dial for an example. |
| QUESTION: Why is the noon line not vertical on my vertical dial. May 3, 2008 The noon line is vertical for vertical dials that are at the longitude of the legal meridian. As you move off the legal meridian, the hour line will no longer be vertical but offset. The offset makes a noon line that is actually before or after noon by an amount of minutes equal to the difference between your longitude and the legal meridian times 4. I am at about long 108, the legal meridian is at 105, so the is about a 3 degree difference or a 12 minute difference. So my dials have a vertical line to the west, showing noon (or any other hour for that matter), 12 minutes early. Ditto for vertical decliners. The books have "rules of thumb" in the indices which have such things pointed out. |