Anselmo posted a list of equations for an arbitrarily-inclined gnomon on a horizontal dial, relating some special cases to particular dial designs. Most of the data are very well specified, but I would like clarification on two of them:
>From where is 'z' measured? Is it 0 degrees when it lies on the ground and pointed North (in the northern hemisphere)? What is the sign/direction of 'd'? Thanks! Dave 37.29N 121.97W > Let's define the following input data: > a is the East-West semiaxis of our ellipse (it's not necesarily the > major axis) > z the zenithal angle of the gnomon (ie., it's inclination: 90? if it > is vertical, 0? if it lies on the ground) > phi the latitude of the place where the dial is drawn > dec the Sun's declination for a given day > H the hour angle of the Sun for a certain moment (negative in the > mornings, positive in the evenings) > L is the length of the gnomon > > We have to derive the equations for the following variables > b the North-South semiaxis of the ellipse > x the Northern distance from a point in the ellipse to the WE axis > (passing through its center) > y the Eastern distance from a point in the ellipse to the NS axis > (passing through its center) > d distance from the foot of the gnomon to the center of the ellipse > > We can calculate them applying the following equations > > b = a * cos(phi - z) / sin(z) > d = a * sin(phi - z) * tan(dec) / sin(z) > > x = b * cos(H) > y = a * sin(H) > > [*] Here are some particular cases for the inclination (z) > > z = 90? ===> analemmatic dial > z = 90? + phi ===> Parent's dial (the ellipse is just a segment) > z = 45? + phi/2 ===> Foster-Lambert's dial (the ellipse is a > circumference). It's the same for 135? + phi/2 > > [**] Addendum: If the EW axis is 'a' then the minimal longitude of the > gnomon should be at least > > L >= a * ( cos(phi) + tan(eps) * sin(phi) ) / sin(z) > > where eps = 23.46?. > > They're easy to undersand but not so easy to include in Helmut&Roger's > spreadsheet because the spreadsheet > has got many whistles & doodles to take care of. > > Best regards, > > Anselmo Perez Serrada > > > > - > -
