-----Original Message----- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 10:07 AM To: 'Tony Moss' Subject: Shadow Tapering
Dear Tony (I'm ccing The List on your letter because it is a great new observation that The List has never discussed before. Your observation concerning the decreased shadow width at the Noon Gap of thick polar axis gnomons on giant sundials will surely be interesting to everybody. I'd be most interested in hearing other dialists' opinions about this interesting shadow phenomenon and possible solutions to combat it. Everybody should read Tony's letter below.) How interesting! Yes, now that you mention this effect seems inevitable knowning what we know about umbras, penumbras and fuzz zones.! I had not thought of this phenomenon and have never personally observed it because I have never seen a dial like this at Noon. To minimize the shadow tapering on giant polar axis thick gnomon sundials, your idea of using the equinox's taper as a design guide seems reasonable. The amount of shadow tapering would be greater with gnomons that have a steep slope (gnomons at high latitudes). Since this one is at 28 degrees, the shadow taper would be less. According to your theory, one might be able to decrease the effect of shadow tapering by constructing the thick polar axis gnomon so that it get slightly wider towards the top. Of course this would violate all the gnomonic laws we hold so dear! The two shadow casting edges of the angled gnomon would not be precisely parallel and would not face precisely north! I don't think I'm ready to make this unorthodox design change without doing some rigorous experiments first. But I could maybe try an alternative less radical solution to the shadow tapering problem. But this would also require experiments, because it also violates traditional sundial design rules. One might make the gnomon slightly wider than is called for by traditional gnomonics, so that the shadow completely fills the Noon Gap on the Equinox. How does this solution sound to you and everybody else? It's a radical idea that makes me cringe a little but it just might work. I wonder how one could mathematically calculate how much wider to make the gnomon to counter the thinning of the observed shadow. It'd probably be easier and more correct to conduct an experiment using a full-size model. John p.s. the dial we are discussing is horizontal, but the tapered shadow effect would also be visible on any large sundial with a thick polar axis gnomon. -----Original Message----- From: Tony Moss [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 9:04 AM To: John Carmichael Subject: Re: Sundial for an odd timezone Hi John, > You got that right! Frank's comment about the locals changing the Time Zone > system is just as scary because it would ruin the dial. > > This is a typical horizontal dial with a thick polar axis gnomon with two > shadow casting edges. > > My Silverlink dial was/is 20 metres in diameter with a polar axis gnomon 6 metres high and 12" wide with two parallel style edges. Up to that point I had only made small-ish dials so my habit had been to set a pair of *parallel* noon lines from the dial origins and then set of the calculated angles from the noon lines. When I did this with the big dial I first set out a parallel noon gap near the plate edge expecting the shadow to fill this at noon!! It was only when I came to observe this in sunlight that I found the apparent shadow was less than 10" wide because of the umbra/penumbra effect. The shadow was *tapered* of course and so should the noon gap lines be too. Once you have the noon line correctly placed you can then set out the hour lines at their calculated angles. At that point I resolved that big sundials can only be set out initially by actual marking of the shadow at solar noon. Exactly the same problem occurs with small dials of course but the amount of shadow taper is insignificant. The problem doesn't end there because at the solstices the shadows are longer or shorter with different amounts of taper. Perhaps the best compromise is to mark out the noon gap at an equinox. On the BSS tour of Italy I saw two large and VERY expensive horizontal dials with parallel noon gaps. Obviously set out at the CALCULATED angles so I wonder how accurate the a.m. and p.m. hourlines are?? Hope this makes sense. Tony --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
