fer de vries
Tue, 31 Aug 2010 03:26:24 -0700
Frank, At our website http://www.de-zonnewijzerkring.nl you may read the procedure I use in my program ZW2000 to calculate sundials.
Follow: calculate and construct flat sundials - extensive version main procedure I start with the sun's position relative to the equatorial plane, given by decl and t. (sun's declination and hourangle) translate into x0, y0, z0 rotate with angle 90 - phi (phi = latitude) to x1, y1, z1 in the horizontal plane. rotate with angle d = declination of the plane to x2, y2, z2 rotate with angle i = inclination of the plane to x3, y3, z3 This is the sun's position relative to the sundial plane. calculate the shadowpoint as x, y. Have a look at the "definitions" page for the used definitions. This is my favorite method to calculate all kind of lines on sundials. Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring http://www.de-zonnewijzerkring.nl Molens http://www.collsemolen.dse.nl Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: "Frank King" <frank.k...@cl.cam.ac.uk> To: <sundial@uni-koeln.de> Sent: Tuesday, August 31, 2010 8:37 AM Subject: Declination and Inclination > Dear All, > > An intriguing question has been raised on the > Italian Sundial list by Fabio Savian. Slightly > re-expressed he is asking... > > When specifying the orientation of a plane > dial, is your order: > > A) Declination then Inclination > > B) Inclination then Declination ? > > This is important because rotations are not > commutative: R1.R2 does not equal R2.R1. > > My own answer is firmly (A) and (slightly > simplified and avoiding using either word) > I think as follows: > > 1. Start with a vertical plane facing > due north (sic). > > 2. Rotate about a vertical axis until > it has the correct azimuth. > > 3. Rotate about a horizontal axis until > the tilt is right. > > I use this order because both rotations are > about axes IN THE PLANE being used. This > keeps rotation matrices simple and so on. > > An alternative is: > > 1. Start with a vertical plane facing > due north. > > 2. Rotate about a horizontal axis until > the tilt is right. > > 3. Rotate about a vertical axis until > the azimuth is right. > > This is fine but the second rotation is not > about an axis in the plane being used. > > Here I quote a delightful observation by > John Davis in the BSS Glossary referring > to a definition of inclination: > > Beware: this convention is not followed > by all authors. > > He could be referring to a host of other > definitions :-) > > OK. Which way do you all do things: > > Dec then Inc or Inc then Dec ? > > There is no right answer but it would be > interesting to hear who does what! > > Frank King > Cambridge, U.K. > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial