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equation-of-time.html
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<!DOCTYPE html>
<html>
<head>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r125/three.min.js"></script>
<script src="solar.js"></script>
<script src="meuusjs.1.0.3.min.js"></script>
<script src="meeus-easy.js"></script>
<title>Equazione del Tempo - Equation of time</title>
</head>
<body>
<center><big><big><big>Equazione del Tempo - Equation of time</big></big></big><br>
<i>
v. 1.1.0 - 3/7/2023<br>
<a href="https://github.com/jumpjack/heliostat/blob/main/equation-of-time.html">Source code</a><br>
<br>
<br>
</i></center>
<table border = 1>
<tr>
<td>
Equazione del tempo in coordinate cartesiane
</td>
<td>
Camma "a rene" ("kidney cam")
</td>
<td>
Camma Greubel/Forsey
</td>
</tr>
<tr>
<td>
<span id="cartesian-chart" style="width:600px;height:400px;"></span>
</td>
<td>
<span id="polar-chart" style="width:400px;"></span>
<br>
<button onclick="downloadCamProfile(1)">DOWNLOAD PROFILE</button><a target="#" href="https://anyconv.com/it/convertitore-da-png-a-stl/">Click here to convert to STL</a>
</td>
<td>
<span id="polar-chart2" style="width:400px;"></span><br>
<button onclick="downloadCamProfile(2)">DOWNLOAD PROFILE</button><a target="#" href="https://anyconv.com/it/convertitore-da-png-a-stl/">Click here to convert to STL</a>
</td>
</tr>
<tr>
<td>
Equazione del tempo - componente 1<br>
<span id="eot1-chart" style="width:400px;"></span><br>
<br>
<button onclick="downloadCamProfile(4)">DOWNLOAD PROFILE</button><a target="#" href="https://anyconv.com/it/convertitore-da-png-a-stl/">Click here to convert to STL</a>
</td>
<td>
Equazione del tempo - componente 2<br>
<span id="eot2-chart" style="width:400px;"></span><br>
<br>
<button onclick="downloadCamProfile(5)">DOWNLOAD PROFILE</button><a target="#" href="https://anyconv.com/it/convertitore-da-png-a-stl/">Click here to convert to STL</a>
</td>
<td>
</td>
</tr>
<tr>
<td>
Declinazione in coordinate cartesiane:<br>
<span id="cartesian-chart2" style="width:600px;height:400px;"></span>
</td>
<td>
Camma declinazione:<br>
<span id="polar-chart3" style="width:400px;"></span>
<br>
<button onclick="downloadCamProfile(3)">DOWNLOAD PROFILE</button><a target="#" href="https://anyconv.com/it/convertitore-da-png-a-stl/">Click here to convert to STL</a>
</td>
<td>
</td>
</tr>
<tr>
<td>
Analemma Decl/EoT:<br>
<span id="analemma-chart" style="width:400px;"></span>
</td>
<td>
Analemma Alt/Az:<br>
<span id="analemma-chart2" style="width:400px;"></span>
</td>
</tr>
</table><br>
JSON cam profile:<br>
<textarea id="camProfileJSON" cols = 50 rows = 20></textarea><br>
Use this site to import the JSON cam profile above and simulate cam/follower mechanism: <a href="https://jumpjack.github.io/CamFollowerJS/">link</a><br>
<br>
References:<br>
<ul>
<a href="https://equation-of-time.info/">Theory and real mechanisms (cams, gears, clocks,...)</a><br>
<a href="https://www.wikiwand.com/en/equation_of_time">Wikiwand</a><br>
<a href="https://equation-of-time.info/copy-of-equation-clocks-forerunners">Kidney cam, Greubel/Forsey cam</a><br>
<a href="https://equation-of-time.info/cams">Obliquity and Eccentricity cams mechanically summed up</a><br>
<a href="https://www.renatoweb.it/renatomeridiane/gnomon13.htm">Formula di Cooper per declinazione solare</a><br>
<a href="https://www.tecnologica.altervista.org/php5/index.php?title=Declinazione_solare">Formula e valori tabulati</a><br>
<a href="https://www.desmos.com/calculator/hbsrvo4bkv?lang=it">Grafico su Desmos</a><br>
<a href="https://anyconv.com/it/convertitore-da-png-a-stl/">PNG to STL converter</a><br>
</ul>
<script>
// min/max in second column have been manually set after first run of the script
minVal = 9999; minC = -15;
maxVal = -9999; maxC = 16
minValG = 9999; minG = -16;
maxValG = -9999; maxG = 0;
minValK = 9999; minK = -15;
maxValK = -9999; maxK = 16;
minValDc = 9999; minDc = -23;
maxValDc = -9999; maxDc = 23;
minValD = 9999; minD = 15;
maxValD = -9999; maxD = 53;
minValEot1 = 9999; minEot1 = -10;
maxValEot1 = -9999; maxEot1 = 10;
minValEot2 = 9999; minEot2 = -8;
maxValEot2 = -9999; maxEot2 = 8;
const ZERO_OFFSET = 5;
const step = 10;
thisYear = new Date().getFullYear();
capodanno = new Date(thisYear + "/01/01 00:00");
var cartesianData = [];
var cartesianDataDeclination = [];
var polarData = [];
var polarData2 = [];
var polarData3 = [];
var EoTcompo1 = [];
var EoTcompo2 = [];
var analemmaData = [];
var analemmaDataAltAz = [];
var colors = []; // Array di colori per ogni punto
var colorsDownload = [];
downloadPolarLayout = {
polar: {
radialaxis: {
showline: false, showgrid: false, showticklabels: false, ticks: ""
},
angularaxis: {
showline: false, showgrid: false, showticklabels: false, ticks: ""
}
},
mode : "lines",
}
function restoreLayout(c) {
return {
polar: {
radialaxis: {
title: "",
//range: [0, ZERO_OFFSET + 20],
showline: true,
showgrid: true,
showticklabels: true
},
angularaxis: {
showline: true,
showgrid: true,
showticklabels: true
}
},
showlegend : false,
marker :{
symbol: "circle",
size: 4,
colors: c,
}
}
};
function generateData() {
var data = [];
var originalLayout;
for (var dayOfYear = 0; dayOfYear <= 365; dayOfYear += step) {
// 81 is 22nd March
var BB = (2 * Math.PI * (dayOfYear - 81))/365;
var cart1 = 9.87 * Math.sin(2*BB);
var cart2 = 7.53 * Math.cos(BB) + 1.5 * Math.sin(BB);
var cartesianVal = cart1 - cart2;
var B = 360 * (dayOfYear - 81) / 365; // B is in degrees; 360 are degrees; 81 is 22nd March
var compo1 = 9.87 * Math.sin(2*B*Math.PI/180);
var compo2 = 7.53 * Math.cos(B*Math.PI/180) + 1.5 * Math.sin(B*Math.PI/180)
var cartesianVal2 = compo1 - compo2;
var y = 2023;
var component1 = 9.863 * Math.sin( 2 *(6.24004077 + 0.01720197 * (365.25*(y-2000) + dayOfYear)) + 3.5932 );
var component2 = -7.659 * Math.sin( 6.24004077 + 0.01720197 * (365.25*(y-2000) + dayOfYear)) ;
var preciseEoT = component1 + component2;
cartesianVal = preciseEoT;
///// Find EoT min/max values:
if (component1 < minValEot1) {
minValEot1 = component1
}
if (component1 > maxValEot1) {
maxValEot1 = component1
}
if (component2 < minValEot2) {
minValEot2 = component2
}
if (component2 > maxValEot2) {
maxValEot2 = component2
}
///// Find cartesian min/max values:
if (cartesianVal < minVal) {
minVal = cartesianVal
}
if (cartesianVal > maxVal) {
maxVal = cartesianVal
}
///////// kidney /////////
kidneyVal = cartesianVal + ZERO_OFFSET - minK;
///// Find kidney polar min/max values:
if (kidneyVal < minValK) {
minValK = kidneyVal
}
if (kidneyVal > maxValK) {
maxValK = kidneyVal
}
/////// Greubel /////
if (cartesianVal>0) {
var GreubelForseyVal = -cartesianVal + ZERO_OFFSET - minG;
colors.push('red'); // Colore rosso per punti con y > 0
} else {
var GreubelForseyVal = cartesianVal + ZERO_OFFSET - minG;
colors.push('blue'); // Colore blu per punti con y <= 0
}
if (GreubelForseyVal < minValG) {
minValG = GreubelForseyVal
}
if (GreubelForseyVal > maxValG) {
maxValG = GreubelForseyVal
}
///// declination /////
declination = 23.45 * Math.sin(((360*3.14/180)/365) * (284 + dayOfYear)); // Day 284 is 11th October
declinationPolar = declination + ZERO_OFFSET - minDc;
if (declination < minValDc) {
minValDc = declination
}
if (declination > maxValDc) {
maxValDc = declination
}
if (declinationPolar < minValD) {
minValD = declinationPolar
}
if (declinationPolar > maxValD) {
maxValD = declinationPolar
}
lat = 42; // debug
lon = 12; // debug
declinationRad = declination*3.14/180;
T0 = 12;
EoT = cartesianVal;
HA = (15 * (T0 - 12) + EoT)*3.14/180; // Angolo orario
//elevation = (Math.asin(Math.sin(lat) * Math.sin(declinationRad) + Math.cos(lat) * Math.cos(declinationRad) * Math.cos(HA)));
//azimuth = (Math.acos((Math.sin(declinationRad) - Math.sin(elevation) * Math.sin(lat)) / (Math.cos(elevation) * Math.cos(lat))));
sunData = suncalcMeeus(new Date(capodanno.getTime() + dayOfYear * 86400000 +86400000/2), lat,lon, 100);
elevation = sunData.sunAltitudeDegrees;
azimuth = sunData.sunAzimuthDegrees;
colorsDownload = "#AAAAAA";
cartesianData.push({
x: dayOfYear,
y: cartesianVal
});
cartesianDataDeclination.push({
x: dayOfYear,
y: declination
});
polarData.push({ r: kidneyVal, theta: dayOfYear });
polarData2.push({ r: GreubelForseyVal, theta: dayOfYear });
polarData3.push({ r: declinationPolar, theta: dayOfYear });
EoTcompo1.push({ r: component1 + ZERO_OFFSET - minEot1, theta: dayOfYear });
EoTcompo2.push({ r: component2 + ZERO_OFFSET - minEot2, theta: dayOfYear });
analemmaData.push({
x: cartesianVal,
y: declination
});
analemmaDataAltAz.push({
x: azimuth,
y: elevation
});
}
// Cartesian EoT
data.push({
type: "scatter",
mode: 'lines',
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2 // Dimensione del cerchietto
},
name: "Cartesian",
x: cartesianData.map((point) => point.x),
y: cartesianData.map((point) => point.y),
});
// kidney cam
data.push({
type: "scatterpolar",
mode: "lines+markers",
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 4, // Dimensione del cerchietto
color: colors,
},
name: "Polar",
r: polarData.map((point) => point.r),
theta: polarData.map((point) => point.theta),
fill: "toself",
fillcolor: '#AAAAAA'
});
console.log(colors);
// Greubel cam
data.push({
type: "scatterpolar",
mode: "lines+markers",
/* line : {
color: colors,
width : 2,
},
*/
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 4, // Dimensione del cerchietto
color: colors, // Assegna l'array di colori ai punti
},
name: "Polar2",
r: polarData2.map((point) => point.r),
theta: polarData2.map((point) => point.theta),
fill: "toself",
fillcolor: '#AAAAAA',
});
// declination cartesian
data.push({
type: "scatter",
mode: 'lines',
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2 // Dimensione del cerchietto
},
name: "Cartesian",
x: cartesianDataDeclination.map((point) => point.x),
y: cartesianDataDeclination.map((point) => point.y),
});
// declination cam
data.push({
type: "scatterpolar",
mode: "lines+markers",
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2, // Dimensione del cerchietto
color: colors, // Assegna l'array di colori ai punti
},
name: "Polar3",
r: polarData3.map((point) => point.r),
theta: polarData3.map((point) => point.theta),
fill: "toself",
fillcolor: '#AAAAAA',
});
// analemma cartesian
data.push({
type: "scatter",
mode: 'lines',
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2 // Dimensione del cerchietto
},
name: "Analemma",
x: analemmaData.map((point) => point.x),
y: analemmaData.map((point) => point.y),
});
// analemma cartesian Alt/Az
data.push({
type: "scatter",
mode: 'lines',
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2 // Dimensione del cerchietto
},
name: "Analemma alt/az",
x: analemmaDataAltAz.map((point) => point.x),
y: analemmaDataAltAz.map((point) => point.y),
});
// EoT component 1 cam
data.push({
type: "scatterpolar",
mode: "lines+markers",
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2, // Dimensione del cerchietto
color: colors, // Assegna l'array di colori ai punti
},
name: "EoT1",
r: EoTcompo1.map((point) => point.r),
theta: EoTcompo1.map((point) => point.theta),
fill: "toself",
fillcolor: '#AAAAAA',
});
// EoT component 2 cam
data.push({
type: "scatterpolar",
mode: "lines+markers",
marker: {
symbol: 'circle', // Imposta la forma del marcatore a cerchio
size: 2, // Dimensione del cerchietto
color: colors, // Assegna l'array di colori ai punti
},
name: "EoT2",
r: EoTcompo2.map((point) => point.r),
theta: EoTcompo2.map((point) => point.theta),
fill: "toself",
fillcolor: '#AAAAAA',
});
return data;
}
function createCartesianChart() {
allData = generateData();
originalCartesianLayout = {
title: "",
xaxis: { title: "Giorno dell'anno" },
yaxis: { title: "" },
};
Plotly.newPlot("cartesian-chart", [allData[0]], originalCartesianLayout).then(function(gd) {
gdCartesian = gd;
// Aggiungi l'evento plotly_hover al primo grafico
gd.on('plotly_hover', function(eventData) {
// Recupera l'indice del marker selezionato nel primo grafico
var indiceMarker = eventData.points[0].pointNumber;
// Recupera le coordinate del marker evidenziato
var x = eventData.points[0].x;
var y = eventData.points[0].y;
// Aggiunge linea verticale nel grafico cartesiano quando passa il mouse:
var lineLayoutUpdate = {
shapes: [
{
type: 'line',
x0: x,
y0: 0,
x1: x,
y1: y ,
line: {
color: 'red',
width: 2
}
}
]
};
Plotly.relayout('cartesian-chart', lineLayoutUpdate);
// Aggiungi la linea dal centro al marker evidenziato nel grafico polare Kidney/1
Plotly.addTraces('polar-chart', {
r: [0, allData[1].r[indiceMarker] ], // Coordinate r della linea (0 per il centro)
theta: [0, x], // Coordinate theta della linea (0 per il centro)
mode: 'lines',
type: "scatterpolar",
line: {
color: 'red',
width: 2
}
});
if (y>0) {
var G = -y;
} else {
var G = y;
}
// Aggiungi la linea dal centro al marker evidenziato nel grafico polare Greubel/2
Plotly.addTraces('polar-chart2', {
r: [0, allData[2].r[indiceMarker] ], // Coordinate r della linea (0 per il centro)
theta: [0, x], // Coordinate theta della linea (0 per il centro)
mode: 'lines',
type: "scatterpolar",
line: {
color: 'red',
width: 2
}
});
});
// Aggiungi l'evento plotly_unhover al primo grafico
gd.on('plotly_unhover', function(eventData) {
Plotly.deleteTraces('polar-chart', [-1]); // Rimuove l'ultima traccia aggiunta
Plotly.deleteTraces('polar-chart2', [-1]); // Rimuove l'ultima traccia aggiunta
});
});
Plotly.newPlot("cartesian-chart2", [allData[3]], originalCartesianLayout);
}
function createPolarChart() {
// Kidney cam
//var data = generateData();
originalPolarLayout = restoreLayout();
Plotly.newPlot("polar-chart", [allData[1]], originalPolarLayout).then(function (gd) {
gdPolar1 = gd;
Plotly.relayout(gd, {aspectratio:1, polar : { radialaxis : {range : [0, maxValK]}}});
addAxis(gd);
});
}
function createPolarChart2() {
// Greubel/Forsey cam
// www.youtube.com/watch?v=hs4Jt44x6Pw
// It can't be used as a real cam because some arcs represent negative values, other represent positive ones, depending on arc color!
//var data = generateData();
originalPolarLayout = restoreLayout();
Plotly.newPlot("polar-chart2", [allData[2]], originalPolarLayout).then(function (gd) {
gdPolar2 = gd;
Plotly.relayout(gd, {aspectratio:1, polar : { radialaxis : {range : [0, maxValG]}} });
//Plotly.restyle(gd, { 'line.color': colors, 'line.width' : 3});
addAxis(gd);
});
}
function createPolarChart3() {
// Declination cam
//var data = generateData();
originalPolarLayout = restoreLayout();
Plotly.newPlot("polar-chart3", [allData[4]], originalPolarLayout).then(function (gd) {
gdPolar3 = gd;
Plotly.relayout(gd, {aspectratio:1, polar : { radialaxis : {range : [0, maxValD]}}});
addAxis(gd);
});
}
function createPolarChartEot1() {
// Declination cam
//var data = generateData();
originalPolarLayout = restoreLayout();
Plotly.newPlot("eot1-chart", [allData[7]], originalPolarLayout).then(function (gd) {
gdPolarEoT1 = gd;
Plotly.relayout(gd, {aspectratio:1, polar : { radialaxis : {range : [0, maxEot1 + ZERO_OFFSET - minEot1]}}});
addAxis(gd);
});
}
function createPolarChartEot2() {
// Declination cam
//var data = generateData();
originalPolarLayout = restoreLayout();
Plotly.newPlot("eot2-chart", [allData[8]], originalPolarLayout).then(function (gd) {
gdPolarEoT2 = gd;
Plotly.relayout(gd, {aspectratio:1, polar : { radialaxis : {range : [0, maxEot2 + ZERO_OFFSET - minEot2]}}});
addAxis(gd);
});
}
function createAnalemmaChart() {
originalCartesianLayout = {
title: "",
xaxis: { title: "EoT" },
yaxis: { title: "Declination" },
};
Plotly.newPlot("analemma-chart", [allData[5]], originalCartesianLayout).then(function(gd) {
gdAnalemma = gd;
});
}
function createAnalemmaAltAzChart() {
originalCartesianLayout = {
title: "",
xaxis: { title: "Azimuth" },
yaxis: { title: "Elevation" },
};
Plotly.newPlot("analemma-chart2", [allData[6]], originalCartesianLayout).then(function(gd) {
gdAnalemmaAltAz = gd;
});
}
function downloadCamProfile(sel) {
if(sel === 1) {
gd = gdPolar1;
name = "kidneyCam";
dataIndex = 1;
JSONexportData = polarData;
}
if(sel === 2) {
gd = gdPolar2;
name = "GreubelCam";
dataIndex = 2;
JSONexportData = polarData2;
}
if(sel === 3) {
gd = gdPolar3;
name = "declinationCam";
dataIndex = 4;
JSONexportData = polarData3;
}
if(sel === 4) {
gd = gdPolarEoT1;
name = "EoT1cam";
dataIndex = 7;
JSONexportData = EoTcompo1;
}
if(sel === 5) {
gd = gdPolarEoT2;
name = "EoT2cam";
dataIndex = 8;
JSONexportData = EoTcompo2;
}
/*
Cam profile format:
{
"segments" : [
{"x" : 30, "y" : 25},
{"x" : 60, "y" : 60},
{"x" : 90, "y" : 50},
{"x" : 95, "y" : 70},
{"x" : 150, "y" : 50},
{"x" : 180, "y" : 70},
{"x" : 210, "y" : 40},
{"x" : 240, "y" : 50},
{"x" : 270, "y" : 20},
{"x" : 300, "y" : 10},
{"x" : 330, "y" : 5},
{"x" : 360, "y" : 0}
],
"rotSpeed": 2,
"stepsWidth": 10,
"rotationDir": 1
}
*/
camProfileJSON.value='{ "segments" : [\n';
for (var i=0; i < JSONexportData.length-1; i++) {
camProfileJSON.value += '{"x" : ' + parseInt(JSONexportData[i].theta.toFixed(0)) + ', "y" : ' + parseInt(JSONexportData[i].r.toFixed(0)) + '},\n';
}
camProfileJSON.value += '{"x" : ' + parseInt(JSONexportData[i].theta.toFixed(0)) + ', "y" : ' + parseInt(JSONexportData[i].r.toFixed(0)) + '}\n'; // without final comma
camProfileJSON.value +=' ],\n "rotSpeed": 2,\n "stepsWidth": ' + step + ', \n"rotationDir": 1}';
// Rimuovi gli assi dal layout del grafico
Plotly.relayout(gd, downloadPolarLayout)
Plotly.update(gd, { mode : "lines" } );
Plotly.restyle(gd , {marker : { color : colorsDownload } });
if (gd.data.length > 1) { // Elimina la linea radiale che punta al marker, se presente
Plotly.deleteTraces(gd, [1]);
}
addAxis(gd);
// Scarica l'immagine del grafico
Plotly.downloadImage(gd, { format: 'png', width: 800, height: 600, filename: name }).then( function() {
// Applica il layout originale per ripristinare gli assi e la griglia visibili
originalPolarLayout = restoreLayout();
Plotly.update(gd, {
marker: {
size : 2, color: colors
},
});
Plotly.update(gd, { mode : "lines+markers" } )
Plotly.relayout(gd, restoreLayout())
Plotly.restyle(gd , {marker : { color : colors, size : 4 } });
console.log("Tracce:",gd.data.length);
});
}
function addAxis(gd) {
// Aggiunge punto al centro della camma:
Plotly.addTraces(gd, {
r: [0], // Coordinata r del punto (0 = centro)
theta: [0], // Coordinata theta del punto (0 = angolo 0)
mode: 'markers',
marker: {
color: 'white',
size: 8
},
type: 'scatterpolar',
hoverinfo: 'none'
});
}
createCartesianChart();
createPolarChart();
createPolarChart2();
createPolarChart3();
createAnalemmaChart();
createAnalemmaAltAzChart();
createPolarChartEot1();
createPolarChartEot2();
console.log("Cartesian min, max, range:", minVal.toFixed(0),maxVal.toFixed(0),(maxVal - minVal).toFixed(0));
console.log("Kidney min, max, range:", minValK.toFixed(0),maxValK.toFixed(0),(maxValK - minValK).toFixed(0));
console.log("Greubel min, max, range:", minValG.toFixed(0),maxValG.toFixed(0),(maxValG - minValG).toFixed(0));
console.log("Declination cartesian min, max, range:", minValDc.toFixed(0),maxValDc.toFixed(0),(maxValDc - minValDc).toFixed(0));
console.log("Declination min, max, range:", minValD.toFixed(0),maxValD.toFixed(0),(maxValD - minValD).toFixed(0));
console.log("Eot1 min, max, range:", minValEot1.toFixed(0),maxValEot1.toFixed(0),(maxValEot1 - minValEot1).toFixed(0));
console.log("Eot2 min, max, range:", minValEot2.toFixed(0),maxValEot2.toFixed(0),(maxValEot2 - minValEot2).toFixed(0));
</script>
</body>
</html>