NOON CURVE

The noon sight in principle allows you to determine the position and indeed the latitude can be measured to a good accuracy. However, in practice the inferred longitude is often inaccurate due to the difficulty of marking the precise moment of LAN. The sun hangs at its maximum altitude for a couple of minutes and every four seconds of uncertainty in the time of LAN introduce an error of 1 arc minute of longitude.

In order to mitigate this problem with the noon sight it is recommended to make several observations around the time of LAN, fit the measurements with a “noon curve” and infer the Ho and UT from this fit. The spreadsheet noon_curve.xls does precisely that. It is an extended version of the noon_sight.xls spreadsheet with the difference that the Ho (H1) and UT (H13) at LAN are computed from the noon curve instead of being entered by the user.

The noon curve is constructed via the following steps:

• Enter the UT’s of your sights in column A and the corresponding Ho’s in column B. You will need at least three observations for the noon curve (which is a quadratic fit) to be defined.

• Insert a Chart (XY scatter type) with column B as the Y axis (“Data range” tab) and column A for X-values (“Series” tab).

• Right-click on the plotted curve and select “Add Trendline” from the context menu. In the “Type” tab select “polynomial” of order 2; in the “Options” tab check “Display equation on chart.”

• Find the noon curve fitting equation of the type y = ax2 + bx + c on the plot, retrieve the a, b, c coefficients (complete with signs) and enter them into cells F1, F2, and F3.

• The entries for Hemisphere (H4), Sun bearing (H5), and Equation of time (H14 or H15, plus the optional interpolation data in cells F14, F15) are entered as in the noon_sight.xls spreadsheet.

• The position is displayed in cells H9, H10, H11 (latitude) and in cells H16, H17, H18 (longitude).

Alternatively, you may also use the spreadsheet noon_motion.xls (see below), which produces the same results without the need for plotting a chart. That spreadsheet computes the coefficients a, b, and c of the quadratic fit automatically. Extra pieces of information on input include the number of observations in cell F4. Also, in this context set F1 cell value to zero and enter a solstice day (June or December 21) in cells F6 and F7.