By “auto-correction”, I refer modification of the dial, so that it will directly read Local-True-Solar-Time (LTST) at your latitude at your standard-meridian instead of where the dial is.
… Auto-correcting for longitude by rotating & tipping the dial is a “retrofit” longitude auto-correction, as opposed to initially incorporating that auto-correction in the marking of the dial. … (As I said, I have no idea why anyone would want longitude-auto-correction, to make the dial read the Local-True-Solar-Time (LTST) at your latitude at your timezone’s standard-meridian (instead of where the dial is). Because the longitude-correction could be achieved by merely adding the longitude-correction constant to each EqT entry on the correction-plaque, the auto-correction doesn’t avoid any table-consulting & correction work needed by the dial-user who wants standard-time. All it accomplishes is to make LTST determination require a correction too.) … As has already been pointed out twice, only one wedge is needed. … The longitude-correction could be achieved by, first, an initial rotation about the vertical axis, & then a rotation about some particular horizontal axis. … Three variables: … 1. The amount & direction of initial rotation, about the vertical-axis, away from the NS alignment of the gnomon. … 2. The place on the circular-dial-plate’s circumference at which the wedge is applied. … 3. The amount by which the dial-plate is tipped by that wedge. … There are three desiderata: … 1. The style is in the meridianal-plane, with its higher end poleward. … 2.The Style is tipped above the horizontal by an angle equal to the latitude. … 3. The dial has been rotated about the style so as to have the orientation of flat ground at your standard-parallel.at your latitude. (i.e. rotated in the direction of your standard meridian, by the number of degrees by which that meridian differs from yours.) … Those 3 desiderata give 3 equations in 3 unknowns. The 3 variable are the unknowns. … The equations are spherical co-ordinate-transformation formulas. The 3 equation are statements, in terms of those formulas, that the 3 desiderata are achieved. … The 3 nonlinear equations in 3 unknowns can be numerically-solved by the Newton-Raphson method, In fact according to some authors, Newton-Raphson is the only method available for a system of nonlinear equations. … You speak of rotation about 3 axes. …2 of them by wedges? (…because you’ve suggested 2 wedges.). ,,, When the 1st wedge is put in at (say) the dial-plate’s north edge, the dial plate is supported by, & stably balanced on, the wedge at the dial-plate’s north edge, & the dial edge opposite the wedge, at the south edge of the dial-plate. That means that the whole dial-plate & all of its periphery (except its south-point) are above the horizontal table-surface on which the dial was resting. … Now, when you put a 2nd wedge in at (say) the dial-plate’s east edge, & push it in till it contacts the raised dial-edge, & then & start rotating the dial-plate with it, about what axis are you rotating the dial-plate? You’re rotating it about the line drawn between the point at the dial-plate’s south edge, where the dial-plate rests on its horizontal table, & some point on the west edge of the wedge at the north end of the dial. … That isn’t a horizontal axis. … I guess you could do it that way, but it sounds like more work than the use of just one wedge. … As I said, you only need one wedge. … Your other suggestion expressed after that is unclear. On Tue, Apr 4, 2023 at 7:38 PM <kool...@dickkoolish.com> wrote: > Depending on your choice of rotation axes, only two rotations are needed, > one for the elevation of the pole and one around the gnomon for longitude > correction. These are the two that correspond to the actual changes needed. > > If you are using the three orthogonal x, y, and z axes, then three > rotations are needed. And they can tell you how to make the wedge. > > Another three rotation procedure that might be easier to understand but > may not tell you how to make the wedge is this. Rotate about a horizontal > axis until the gnomon is vertical. Now rotate around the vertical axis to > include the longitude correction. Then rotate around a horizontal axis to > put the gnomon in the correct new location. I would do this in a computer > graphics situation because it only requires the old and new position values. > --- > > > > On 2023-04-04 15:54, Steve Lelievre wrote: > > > At a new location, a dial must end up with the style parallel to the polar > axis - but how do you achieve that using a wedge? Assuming you start with > the dial at the new location on a horizontal surface with the sub-stile > line on the local meridian, the required sequence is to rotate it about the > local vertical, then about an east-west line, and then about the vertical > again. Perhaps this helps visualize it... https://youtu.be/mtEgSXJPXSw > > The wedge achieves the same thing because the twisting of the dial on the > wedge face corresponds to the first rotation about a vertical, it's tip > angle corresponds to the east-west rotation, and the turning of the wedge > corresponds to the second rotation about the vertical. > > Steve > > > On 2023-04-04 11:59 a.m., Rod Wall wrote: > > As Michael indicated in his email below: *Rotating the whole dial around > the polar axis is the correct way. *to adjust a local solar time dial to > a different longitude > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > >
--------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
