----- Original Message ----- From: "Dave Bell" <[EMAIL PROTECTED]> To: "Anselmo Pérez Serrada" <[EMAIL PROTECTED]> Cc: <[email protected]> Sent: Saturday, June 07, 2003 7:04 PM Subject: Re: Dial calculation mystery
> On Sat, 7 Jun 2003, [ISO-8859-1] Anselmo Pérez Serrada wrote: > > > I think I can help you on this. They use a very elegant method to draw a > > sundial based on geometrical > > affinity that traces back to our High School days: > > > > 1. Draw two concentrical circles : one of radius r and the other one of > > radius r*sin(Lat) > > 2. Now draw a sheaf of 24 equispaced lines from its center as if it > > were an equatorial dial. > > 3. These lines intersect the circles at points I' and I'', II' and > > II'', and so on up to XXIV' and XXIV''. > > 4. Now trace horizontal lines from the inner points and vertical lines > > from the outer points. Let's call > > I the point where the lines from I' and I'' intersect, II the point for > > II' and II'', and so on. > > 5. If we connect these points we just have the analemmatic ellipse, > > right? Well, but if we trace lines > > from the center to these points we get a horizontal dial for that > > latitude. Isn't that nice? > > Very well described, Anselmo! > > Everything agrees perfectly with the original article, except you have one > circle of radius 1 and the other of 1*sin(lat). Now, if I am looking at > this correctly, that would make the second circle smaller than the first > (and also avoid the singularityat 0 degrees!) However, is the ratio of the > two circles' size the same in both constructions? I'll have to draw them > up, and scale one to match the other... > > Dave > 37.28N 121.97W Yes, the ratio is the same. The ratio of 1 to sin(lat) is the same as the ratio of 1/sin(lat) to 1. But I think Anselmo makes one small error. Yes, the points at step 4 are the hour marks of an analemmatic dial if, by 'horizontal lines' he means east-west lines, but to draw a Horizontal Sundial you want to draw north-south lines from the inner points and east-west ones from the outer points. This is because an analemmatic dial's major (longer) axis is east-west, whereas for a horizontal dial constructed this way the major axis is north-south. Chris Lusby Taylor 51.4N 1.3W -
