Sun Path Polar Chart

Excel Polar Chart
Polar Coordinate Chart

Thestereographic solar charts allow us to determine when sunlight falls through awindow or a skylight. Previously, I made a brief entry which set out how theyshould be used:

As can beseen, its handling is easy. However, each solar chart serves only to a givenlatitude, so we must learn to build our own solar chart. As it is a laboriousprocess, I will discuss it in two different entries.

Sun Charts: Projections of Solar Events and Shadowing from the Sky Dome. The emphasis of this lesson is the Sun Chart tool (or Sun Path). These flat diagrams are found in many solar design tools, but may look completely foreign to the new student in solar energy. A sun path chart shows the position of the sun at a specific location during different times of the year. Once oriented properly, the sun path chart can tell you when a tree, hill or building will cast a shadow on a potential greenhouse location. The difference between the location of magnetic north and polar north changes based on location.

The firstthing to know is that the stereographic solar chart is a representation of theecliptic, or sun path on a horizontal plane. However, the paths are directed toa central point, instead of using an orthogonal projection. This singularprojection allows us to discern the sun path in the lower latitudes.

The firststep is to draw the Sun's path on a sphere in the days of the equinox. Thispath corresponds to an arc, which is projected as a line on the sphererepresenting the sky. Then we draw the solstice paths, which are alsocircumference arcs, which are separated from the equinox by the tilt angle ofthe axis of the Earth; 23.44º.

When drawingcircumference arcs equidistant from both solstices, we obtain the trajectoriesof the Sun in each month.

The secondstep is to project the position of the hours on the ecliptic equinox, knowingthat every hour is separated from the previous 15 degrees.

The thirdstep is to tilt the solar paths, according to the latitude where we are. Followingthe example we consider latitude 40º. Accordingly, the ecliptic will be tilt40º.

In this samestep we will project the ecliptic on the horizontal plane of the sphere. To dothis, the points that are on the plane are projected directly onto the ground,while the points on the sphere will be directed to lower vertex. Thus, we drawthe sun path on the day of the equinox.

In the fourthstep, we operate in the same way with the trajectories of the solstices: thepoints on the horizon are projected directly onto the ground, while the pointson the sphere are directed towards the lower vertex.

In the fifthstep, we operate in the same way with the rest of the year. Thus, we have sunpaths drawn every month for a latitude of 40 °.

In the nextpost I will explain how to find the hours in solar paths. Soon.

The map shows day and night on Earth and the positions of the Sun (subsolar point) and the Moon (sublunar point) right now.

UTC time = Thursday, 10 December 2020, 12:04:00.

March equinox | June solstice | September equinox | December solstice

= The Sun's position directly overhead (zenith) in relation to an observer.

= The Moon's position at its zenith in relation to an observer (Moon phase is not shown).

= Civil Twilight (lightest shade)

= Nautical Twilight

= Astronomical Twilight

= Night, no twilight (darkest shade)

Excel Polar Chart

Position of the Sun: Subsolar Point

On Thursday, 10 December 2020, 12:04:00 UTC the Sun is at its zenith at Latitude: 22° 58' South, Longitude: 2° 45' West

The ground speed is currently 427.13 meters/second, 1537.7 kilometres/hour, 955.5 miles/hour or 830.3 nautical miles/hour (knots). The table below shows position of the the Sun compared to the time and date above:

Time	Longitude Difference			Latitude Difference			Total
Later	Degrees	Distance	Direction	Degrees	Distance	Direction	Distance
1 minute	0° 14' 59.7'	25.63 km	West	0° 00' 00.2'	0.01 km	South	25.63 km
1 hour	14° 59' 42.8'	1536.98 km	West	0° 00' 12.6'	0.39 km	South	1536.96 km
24 hours	0° 06' 55.6'	11.84 km	East	0° 04' 50.6'	8.94 km	South	14.83 km

Position of the Moon: Sublunar Point

On Thursday, 10 December 2020, 12:04:00 UTC the Moon is at its zenith at Latitude: 4° 12' South, Longitude: 59° 06' West

Polar Coordinate Chart

The ground speed is currently 446.92 meters/second, 1608.9 kilometres/hour, 999.7 miles/hour or 868.7 nautical miles/hour (knots). The table below shows position of the the Moon compared to the time and date above:

Time	Longitude Difference			Latitude Difference			Total
Later	Degrees	Distance	Direction	Degrees	Distance	Direction	Distance
1 minute	0° 14' 29.3'	26.81 km	West	0° 00' 15.0'	0.46 km	South	26.81 km
1 hour	14° 29' 21.1'	1608.60 km	West	0° 15' 03.8'	27.77 km	South	1608.57 km
24 hours	12° 30' 45.6'	1389.17 km	East	5° 54' 34.0'	653.54 km	South	1528.23 km

Locations With the Sun Near Its Zenith

The following table shows 10 locations with Sun near zenith position in the sky.

Location	Local Time	Distance			Direction
Jamestown	Thu 12:04	840 km	522 miles	454 nm	NNW
Windhoek	Thu 14:04	2035 km	1265 miles	1099 nm	E
Luanda	Thu 13:04	2314 km	1438 miles	1250 nm	NE
Cape Town	Thu 14:04	2395 km	1488 miles	1293 nm	SE
São Tomé	Thu 12:04	2776 km	1725 miles	1499 nm	NNE
Kinshasa	Thu 13:04	2834 km	1761 miles	1530 nm	NE
Brazzaville	Thu 13:04	2837 km	1763 miles	1532 nm	NE
Libreville	Thu 13:04	2903 km	1804 miles	1568 nm	NNE
Gaborone	Thu 14:04	2921 km	1815 miles	1577 nm	E
Maseru	Thu 14:04	3095 km	1923 miles	1671 nm	ESE