Pensacola 2026-02 Predictions - Revision history

Ion: /* Ion */ Typo fix: Euclidean → Cartesian

2026-03-18T09:09:12Z

Ion: Typo fix: Euclidean → Cartesian

← Older revision		Revision as of 05:09, 18 March 2026
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	==== Flat earth prediction ====		==== Flat earth prediction ====

	===== 1. Calculating the ~~Euclidean~~ coordinates from the GPS coordinates =====		===== 1. Calculating the Cartesian coordinates from the GPS coordinates =====

	We model the Earth as a flat plane where:		We model the Earth as a flat plane where:
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	</math>		</math>

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

	[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Flat_2.png\|frameless]]		[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Flat_2.png\|frameless]]
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	==== Spherical earth prediction ====		==== Spherical earth prediction ====

	===== 1. Calculating the ~~Euclidean~~ coordinates from the GPS coordinates =====		===== 1. Calculating the Cartesian coordinates from the GPS coordinates =====

	We model the Earth as a sphere with a radius of 6,371 km.		We model the Earth as a sphere with a radius of 6,371 km.
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	</math>		</math>

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

	[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Globe_2.png\|frameless]]		[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Globe_2.png\|frameless]]
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	==== Ellipsoidal earth prediction ====		==== Ellipsoidal earth prediction ====

	===== Calculating the ~~Euclidean~~ coordinates from the GPS coordinates =====		===== Calculating the Cartesian coordinates from the GPS coordinates =====

	We model the Earth as an ellipsoid with the parameters as per WGS-84.		We model the Earth as an ellipsoid with the parameters as per WGS-84.
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	function predictDistance(point1GPS, point2GPS) {		function predictDistance(point1GPS, point2GPS) {
	const distanceFlatEarth = euclideanDistance(		const distanceFlatEarth = euclideanDistance(
	elementwiseAverage(point1GPS.map(~~euclideanFlatEarth~~)),		elementwiseAverage(point1GPS.map(cartesianFlatEarth)),
	elementwiseAverage(point2GPS.map(~~euclideanFlatEarth~~)),		elementwiseAverage(point2GPS.map(cartesianFlatEarth)),
	);		);
	const distanceSphere = euclideanDistance(		const distanceSphere = euclideanDistance(
	elementwiseAverage(point1GPS.map(~~euclideanSphere~~)),		elementwiseAverage(point1GPS.map(cartesianSphere)),
	elementwiseAverage(point2GPS.map(~~euclideanSphere~~)),		elementwiseAverage(point2GPS.map(cartesianSphere)),
	);		);
	const distanceEllipsoid = euclideanDistance(		const distanceEllipsoid = euclideanDistance(
	elementwiseAverage(point1GPS.map(~~euclideanEllipsoid~~)),		elementwiseAverage(point1GPS.map(cartesianEllipsoid)),
	elementwiseAverage(point2GPS.map(~~euclideanEllipsoid~~)),		elementwiseAverage(point2GPS.map(cartesianEllipsoid)),
	);		);

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	/**		/**
	* Compute the ~~Euclidean~~ coordinates for the given GPS coordinates on a flat		* Compute the Cartesian coordinates for the given GPS coordinates on a flat
	* earth.		* earth.
	*		*
	* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).		* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).
	* @returns {[number, number, number]} A ~~Euclidean~~ coordinate.		* @returns {[number, number, number]} A Cartesian coordinate.
	*/		*/
	function ~~euclideanFlatEarth~~([latitudeDeg, longitudeDeg, altitudeMeters]) {		function cartesianFlatEarth([latitudeDeg, longitudeDeg, altitudeMeters]) {
	const RADIUS_EQUATOR = 10002 * 1000;		const RADIUS_EQUATOR = 10002 * 1000;

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	/**		/**
	* Compute the ~~Euclidean~~ coordinates for the given GPS coordinates on a		* Compute the Cartesian coordinates for the given GPS coordinates on a
	* spherical earth.		* spherical earth.
	*		*
	* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).		* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).
	* @returns {[number, number, number]} A ~~Euclidean~~ coordinate.		* @returns {[number, number, number]} A Cartesian coordinate.
	*/		*/
	function ~~euclideanSphere~~([latitudeDeg, longitudeDeg, altitudeMeters]) {		function cartesianSphere([latitudeDeg, longitudeDeg, altitudeMeters]) {
	const RADIUS_SPHERE = 6371 * 1000;		const RADIUS_SPHERE = 6371 * 1000;

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	/**		/**
	* Compute the ~~Euclidean~~ coordinates for the given GPS coordinates on an		* Compute the Cartesian coordinates for the given GPS coordinates on an
	* ellipsoidal earth.		* ellipsoidal earth.
	*		*
	* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).		* @param {[number, number, number]} pointGPS A GPS coordinate (latitude in degrees, longitude in degrees, altitude in meters).
	* @returns {[number, number, number]} A ~~Euclidean~~ coordinate.		* @returns {[number, number, number]} A Cartesian coordinate.
	*/		*/
	function ~~euclideanEllipsoid~~([latitudeDeg, longitudeDeg, altitudeMeters]) {		function cartesianEllipsoid([latitudeDeg, longitudeDeg, altitudeMeters]) {
	const SEMI_MAJOR_AXIS = 6378137;		const SEMI_MAJOR_AXIS = 6378137;
	const FLATTENING_FACTOR = 1 / 298.257223563;		const FLATTENING_FACTOR = 1 / 298.257223563;
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	/**		/**
	* Compute the distance between two ~~Euclidean~~ coordinates.		* Compute the Euclidean distance between two Cartesian coordinates.
	*		*
	* @param {[number, number, number]} ~~point1Euclidean~~ First ~~Euclidean~~ coordinate.		* @param {[number, number, number]} point1Cartesian First Cartesian coordinate.
	* @param {[number, number, number]} ~~point2Euclidean~~ Second ~~Euclidean~~ coordinate.		* @param {[number, number, number]} point2Cartesian Second Cartesian coordinate.
	* @returns {number} The Euclidean distance between the coordinates.		* @returns {number} The Euclidean distance between the coordinates.
	*/		*/

Ion: /* Code */ Remove redundant function

2026-03-18T05:25:51Z

Code: Remove redundant function

← Older revision		Revision as of 01:25, 18 March 2026
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	return result;		return result;
	}

	/**
	* Format a distance as a string.
	*
	* @param {number} distanceMeters A distance in meters.
	* @returns {string} A string representation of the distance in yards.
	*/
	~~function formatDistance(distanceMeters) {~~
	~~const METERS_PER_YARD = 0.9144;~~

	~~const distanceYards = distanceMeters / METERS_PER_YARD;~~

	~~return `${distanceYards.toFixed(0)} yards`;~~
	}		}

Ion: /* Ion */ Output the predictions in meters, feet and yards

2026-03-18T05:12:10Z

Ion: Output the predictions in meters, feet and yards

← Older revision		Revision as of 01:12, 18 March 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|+ Line-of-sight distance		\|+ Line-of-sight distance prediction
	\|-		\|-
	! Earth model !! ~~Prediction~~		! Earth model !! meters !! yards !! feet
	\|-		\|-
	\| Flat earth \|\| 675 ~~yards~~		\| Flat earth \|\| 617 \|\| 675 \|\| 2025
	\|-		\|-
	\| Spherical earth \|\| 564 ~~yards~~		\| Spherical earth \|\| 516 \|\| 564 \|\| 1691
	\|-		\|-
	\| Ellipsoidal earth \|\| 565 ~~yards~~		\| Ellipsoidal earth \|\| 516 \|\| 565 \|\| 1694
	\|}		\|}

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	];		];

	const ~~result~~ = predictDistance(point1GPS, point2GPS);		const results = predictDistance(point1GPS, point2GPS);

	console.~~table~~([~~result~~]);		printWikiTable(results);
			}

			/**
			* Output a table of the results in the wikitable format.
			*
			* @param {Map<string, number>} results For each model, the distance prediction in meters.
			* @returns {void}
			*/
			function printWikiTable(results) {
			console.log('{\| class="wikitable"');
			console.log("\|+ Line-of-sight distance prediction");
			console.log("\|-");
			console.log("! Earth model !! meters !! yards !! feet");

			const YARDS_PER_METER = 1 / 0.9144;
			const FEET_PER_YARD = 3;

			for (const [model, distanceMeters] of results) {
			const distanceYards = distanceMeters * YARDS_PER_METER;
			const distanceFeet = distanceYards * FEET_PER_YARD;

			console.log("\|-");
			console.log(
			"\| " +
			[
			model,
			`${distanceMeters.toFixed(0)}`,
			`${distanceYards.toFixed(0)}`,
			`${distanceFeet.toFixed(0)}`,
			].join(" \|\| "),
			);
			}

			console.log("\|}");
	}		}

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	* @param {[number, number, number][]} point1GPS The samples for the first GPS coordinate.		* @param {[number, number, number][]} point1GPS The samples for the first GPS coordinate.
	* @param {[number, number, number][]} point2GPS The samples for the second GPS coordinate.		* @param {[number, number, number][]} point2GPS The samples for the second GPS coordinate.
	* @returns {~~{"Flat earth":~~ string, ~~"Spherical earth": string, "Ellipsoidal earth": string}~~} The distance predictions.		* @returns {Map<string, number>} The distance predictions in meters.
	*/		*/
	function predictDistance(point1GPS, point2GPS) {		function predictDistance(point1GPS, point2GPS) {
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	);		);

	return {		return new Map([
	"Flat earth"~~: formatDistance(~~distanceFlatEarth),		["Flat earth", distanceFlatEarth],
	"Spherical earth"~~: formatDistance(~~distanceSphere),		["Spherical earth", distanceSphere],
	"Ellipsoidal earth"~~: formatDistance(~~distanceEllipsoid),		["Ellipsoidal earth", distanceEllipsoid],
	};		]);
	}		}

Ion: /* Ion */ Add predicted results

2026-03-11T01:26:19Z

Ion: Add predicted results

← Older revision		Revision as of 21:26, 10 March 2026
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	A prediction for the line-of-sight distance between two GPS coordinates.		A prediction for the line-of-sight distance between two GPS coordinates.

			The methodology follows below. The results are:

			{\| class="wikitable"
			\|+ Line-of-sight distance
			\|-
			! Earth model !! Prediction
			\|-
			\| Flat earth \|\| 675 yards
			\|-
			\| Spherical earth \|\| 564 yards
			\|-
			\| Ellipsoidal earth \|\| 565 yards
			\|}

	==== Flat earth prediction ====		==== Flat earth prediction ====

Ion: /* Code */ Add the now published coordinates

2026-03-11T01:21:58Z

Code: Add the now published coordinates

← Older revision		Revision as of 21:21, 10 March 2026
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	<pre>		<pre>
	function main() {		function main() {
	~~// To be filled in with the measurements.~~		const point1GPS = [
	const point1GPS = [[0, 0, 0]];		[30.332329, -87.131779, 1],
	const point2GPS = [[0, 0, 0]];		[30.332330, -87.131783, 1],
			];
			const point2GPS = [
			[30.331353, -87.137035, 3],
			[30.331352, -87.137029, 3],
			];

	const result = predictDistance(point1GPS, point2GPS);		const result = predictDistance(point1GPS, point2GPS);

Ion: /* Code */ Average the samples in Euclidean coordinates; document and type function inputs and outputs;

2026-02-28T02:52:22Z

Code: Average the samples in Euclidean coordinates; document and type function inputs and outputs;

Show changes

Ion: /* Code */ Average multiple coordinates; output in yards

2026-02-28T02:12:27Z

Code: Average multiple coordinates; output in yards

@@ Line 151: / Line 151: @@
 <pre>
 /**
   * Output flat earth and globe predictions for the straight-line distance
   * between a pair of GPS coordinates.
   */
-function main() {
+function predictDistance(point1GPS, point2GPS) {
    const distanceFlatEarth = euclideanDistance(
      euclideanFlatEarth(point1GPS),
@@ Line 173: / Line 200: @@
    );
-   console.table([
+   return {
-     { model: "Flat earth", distance: Math.round(distanceFlatEarth) },
+    "Point 1": formatGPSCoordinate(point1GPS),
-     { model: "Spherical earth", distance: Math.round(distanceSphere) },
+     "Point 2": formatGPSCoordinate(point2GPS),
-     { model: "Ellipsoidal earth", distance: Math.round(distanceEllipsoid) },
+    "Flat earth": formatDistance(distanceFlatEarth),
-   ]);
+     "Spherical earth": formatDistance(distanceSphere),
+}
@@ Line 199: / Line 246: @@
 /**
-  * Compute the Euclidean coordinates for the given GPS coordinates on a spherical
+  * Compute the Euclidean coordinates for the given GPS coordinates on a
-  * earth.
+  * spherical earth.
   */
 function euclideanSphere([latitudeDeg, longitudeDeg, altitudeMeters]) {

Ion: /* Flat earth prediction */ Better wording

2026-02-25T14:15:29Z

Flat earth prediction: Better wording

← Older revision		Revision as of 10:15, 25 February 2026
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	* the distance from the North Pole to the equator is 10,002 km,		* the distance from the North Pole to the equator is 10,002 km,
	* lines of latitude are equally spaced concentric circles around the North Pole,		* lines of latitude are equally spaced concentric circles around the North Pole,
	* lines of longitude extend outward from the North Pole at equally ~~spaced~~ angles, and		* lines of longitude extend outward from the North Pole at equally increasing angles, and
	* all verticals are perpendicular to the plane (and thus parallel with each other).		* all verticals are perpendicular to the plane (and thus parallel with each other).

Ion: /* 1. Calculating the Euclidean coordinates from the GPS coordinates */ Describe the FE model more precisely

2026-02-25T10:16:09Z

1. Calculating the Euclidean coordinates from the GPS coordinates: Describe the FE model more precisely

← Older revision		Revision as of 06:16, 25 February 2026
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	* the equator is a circle,		* the equator is a circle,
	* the distance from the North Pole to the equator is 10,002 km,		* the distance from the North Pole to the equator is 10,002 km,
	* lines of latitude are equally spaced,		* lines of latitude are equally spaced concentric circles around the North Pole,
	* lines of longitude extend outward from the North Pole at equally spaced angles, and		* lines of longitude extend outward from the North Pole at equally spaced angles, and
	* all verticals are perpendicular to the plane (and thus parallel with each other).		* all verticals are perpendicular to the plane (and thus parallel with each other).

Ion: /* 1. Calculating the Euclidean coordinates from the GPS coordinates */ Describe the FE model more precisely

2026-02-25T10:13:28Z

1. Calculating the Euclidean coordinates from the GPS coordinates: Describe the FE model more precisely

← Older revision		Revision as of 06:13, 25 February 2026
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	===== 1. Calculating the Euclidean coordinates from the GPS coordinates =====		===== 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.		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,
			* lines of latitude are equally spaced,
			* lines of longitude extend outward from the North Pole at equally spaced angles, and
			* all verticals are perpendicular to the plane (and thus parallel with each other).

	[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Flat_1.png\|frameless]]		[[File:Ion_Pensacola_2026-02_GPS_Distance_Prediction_Flat_1.png\|frameless]]