About Sun Paths
2D Projections
1. Orthographic Projection
A vertical projection of the sky dome onto a horizontal plane. Commonly used in architecture, it visually represents the sun’s position relative to the observer and is ideal for solar design and daylighting studies.
2. Stereographic Projection
A mathematical projection that maps the celestial hemisphere onto a plane from the opposite pole. It preserves angular relationships (conformal) and is primarily used in astronomy, celestial navigation, and advanced solar geometry analysis.
| Feature | Orthographic Projection | Stereographic Projection |
|---|---|---|
| Projection type | Vertical from zenith to ground | From celestial pole onto a flat plane |
| Visual style | Dome-like, natural-looking | Flat, mathematically even |
| Angle preservation | No (not conformal) | Yes (conformal projection) |
| Sun path distortion | Slightly distorted near horizon | More compressed near horizon |
| Common use | Architecture, daylighting, passive design – Preferable near tropics/equator | Astronomy, celestial navigation, astrolabes – Suitable near poles |
| Horizon representation | Edge of the circular diagram | Lower boundary of the projection |
| Tools using it | Ladybug Tools, Ecotect, Climate Consultant | Celestial mapping tools, astrolabe simulators |
Solar Charts
Solar charts are the record of the solar trajectory for a complete year (although only some representative dates are plotted, such as equinoxes and solstices), based on the daily traces that they allow to be marked on the celestial vault (which are projected onto a polar plane) and are specific to a given latitude.
Image Ref: Solar Chart, Santiago de Chile
Thus, it is possible to link each human location to a given solar chart. It consists of the following parts:
a Cartesian coordinate system, which allows us to orient ourselves with respect to the cardinal points;
a circumference concentric to the origin of the coordinates (divided into 360º), which represents the theoretical horizon of the observer;
a system of virtual concentric rings, which indicate a height scale with respect to the theoretical horizon (with a maximum height of 90º at the origin);
daily curves, which indicate the solar path for certain days of the year; and finally, hourly curves, which allow us to identify the position of the sun at a certain time, when they intersect with the daily curves.
Analemmas
An analemma is a diagram showing the position of the Sun in the sky at the same hour of the day (e.g., 9 a.m.) over the year, as seen from a fixed location on Earth.
- It typically has a figure-eight shape.
- The shape results from two main factors:
- Earth’s axial tilt (~23.5°)
- Earth’s elliptical orbit (not a perfect circle)
In sun path diagrams, the analemma helps visualize how:
- The solar altitude (height of the sun), and
- The solar azimuth (sun’s compass direction)
change throughout the year at a given location.
In practice (e.g., architecture, solar studies):
- Sun path diagrams often include analemmas for different times of the day.
- They help determine sunlight exposure, shading design, and solar energy potential at specific times and dates.
Solar Trajectory
Two coordinates are used to fix the position of the sun on the celestial vault at a given point in its path: altitude and azimuth.
- Altitude indicates the vertical angle of the sun with respect to the theoretical horizon line.
- Azimuth is the angle of the sun above the horizon measured with respect to the true north.
Legend:
a = celestial vault
b = horizontal plane
c = parabolic projection surface
d = sun path on any given date
e = projection of the sun path on the parabolic surface
f = meridian
g = geographic north
h = projection of the parabolic surface onto a horizontal surface: sun chart
- Knowledge Base