Pensacola 2026-02 Predictions

SThurston2 (not a flerf)

Map = North pole AE map. Geometry = On a flat Earth the Sun (A), the Observer (B), and the North pole (C), are three points which make a triangle. The capital letters are used for both points and angles. 
The distances will be measured in units of the distance you have to travel due South to change your latitude by 1 degree and will be called degrees.
The Sun's latitude will be the predicted declination at Noon UTC as provided by SunCalc. Good enough for an approximation.
The distance A to C is named b = (90 - the Sun's latitude).
The distance B to C is named a = (90 - the Observer's latitude).
The distance A to B is named c = the distance required to change the elevation of the Sun by 90 degrees. That is the same as 90 degrees of latitude change using the rule 60NM per degree of elevation change and 1 NM = 1 arcminute of latitude change.
Using the known 3 sides of the triangle, use the Law of Cosines (Cos(C) = (a^2 + b^2 - c^2)/2ab) to get the angles.
The UTC time is given by (12 + 24 * (angle C + Mod(360 - Obs Longitude, 360)) / 360).
The heading is (360 - angle B).

The flat Earth predictions are

Feb 23 at 22:00:01 heading 279.2;

Feb 24 at 22:01:01 heading 279.6;

Feb 25 at 22:02:01 heading 280;

Feb 26 at 22:04:00 heading 280.4;

Feb 27 at 22:05:00 heading 280.8

Ion

A prediction for the line-of-sight distance between two GPS coordinates.

Flat earth prediction

1. Calculating the Euclidean coordinates from the GPS coordinates

We model the Earth as a flat plane where the equator is a circle, the distance from the North Pole to the equator is 10,002 km, and all verticals are perpendicular to the plane.

Let $r_{\text{equator}}=10002\text{ km}$.

The distance from the North Pole to a given latitude:

$r_{\text{lat}}=r_{\text{equator}}(1-\frac{\text{lat}}{90^{\circ }})$

The coordinates:

$x=r_{\text{lat}}\cos (\text{lon})$

$y=r_{\text{lat}}\sin (\text{lon})$

$z=\text{altitude}$

2. Calculating the straight-line distance between two Euclidean coordinates

We use the Pythagorean theorem.

$l=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$

Globe prediction

1. Calculating the Euclidean coordinates from the GPS coordinates

We approximate the Earth as a sphere with a radius of 6,371 km.

Let $r_{\text{point}}=6371\text{ km}+\text{altitude}$.

$z=r_{\text{point}}\sin (\text{lat})$

The x and y coordinates lie on a small circle scaled by the cosine of the latitude.

$x=r_{\text{point}}\cos (\text{lat})\cos (\text{lon})$

$y=r_{\text{point}}\cos (\text{lat})\sin (\text{lon})$

2. Calculating the straight-line distance between two Euclidean coordinates

Again, we use the Pythagorean theorem.

$l=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$