Hello Anselmo, Glad your computer is working again and that you are back on the list.
Thanks for pointing us to the formulas for analemmatic sundials with a gnomon in any direction. They work well, however, as they are written, they are restricted to horizontal sundials. But they can be changed for use for any inclined/declined plane. For any plane, calculate the equivalent horizontal plane and note the style height, the hourangle of the substyle and the angle between the substyle and the line of greatest slope. In the formulas you mentioned use for lat the value of the calculated style height and for hour angle the value (hour angle - hourangle of substyle). For the gnomon's inclination and declination don't use the values relative to the horizontal plane, but values relative to the dial's plane and its substyle. With this procedure yo may calculate any analemmatic sundial with arbitrary gnomon. The pattern you get must be rotated with the angle the substyle has to the line of greatest slope. The principle is that the dial is calculated as an horizontal dial for the equivalent latitude, including the necessary longitude correction. Have in mind that this general procedure doesn't work for the Lambert's circles or for the new develloped sunset/sunrise marks as proposed by Roger Baily and Helmut Sonderegger. For these options on an analemmatic dial other restrictions have to be taken into account. Because of calculating angles also have in mind to make necessary tests to find the right quadrant for the calculated angle. Another point to concider is the definition for the inclination of the gnomon used in your message. This differs from the definition in some other programs distributed on the list but works well also. Best wishes, Fer. Fer J. de Vries mailto:[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/ Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: "Anselmo Pérez Serrada" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Sunday, May 26, 2002 6:17 PM Subject: Back from the shadows > Hi all! > > Well, here am I again, after three successive virus attacks, a > hardware failure ("carpets and CD units are incompatible" told me the > guy at the shop!) > and a lot of work kept me isolated from the outer world. I'm trying to > recover my e-mail folders from a post-mortem backup, so I do not know what > has been going on in the list, but as far as I remember, some of you > asked me for the formulae for an analemmatic sundial having its > (moveable) gnomon > inclined. There they go (copied from Savoie 's book): > > Let's consider a set of ortogonal axis centered in the foot of the > gnomon and pointing towards the East (x), North (y) and Zenith (z). Let > be as well > i the angle from the vertical line to the gnomon (i = 0 means a vertical > gnomon, and i=90 an horizontal one), and D its gnomonical declination > (D=0 means > a gnomon pointing to the South, D=90 is pointing to the West and so on). > The coordinates of the ellipse of hours are: > > x = -r*(tan(i)*sin(D)*cos(Lat)*cos(HourAng) - sin(HourAng)) > y = -r*cos(HourAng)*(tan(i)*cos(D)*cos(Lat)-sin(Lat)) > > where r is a free parameter (it stands for the radius of the equatorial > circle from which the dial derives). > And the scale of dates is still a straight segment whose coordinates are: > > X = r*tan(i)*sin(D)*sin(Lat)*tan(SunDecl) > Y = r*tan(SunDecl)*(tan(i)*cos(D)*sin(Lat)+cos(Lat)) > > From them you can derive all the projection sundials like > Foster-Lambert's, Parent,'s, and a lot of curious new ones. > > Sorry about the delay! > > > - > -
