Solar Geometry & Shading
Where the sun is — and how to keep it out.
Sun is welcome in winter and a problem in summer — and a shading device only works if it matches where the sun actually is. So you first set out the sun's geometry, then size the device. A south window is easy; an east or west window is the hardest thing to shade.
Learning objectives
By the end of this lesson, you will be able to — mapped to the course outcomes for Climatology & Building Physics:
Define the solar angles and describe the sun's seasonal path.
Read a sun-path diagram and the horizontal and vertical shadow angles.
Size a horizontal overhang for a window from its shadow angle.
Choose the right shading device for an orientation.
Where the sun is
Altitude and azimuth locate the sun, from declination, hour angle and latitude; the sun is high in summer and low in winter. The sun-path diagram maps it, and the shadow angles relate it to a wall.[9, 10]
Locating the sun
The sun's position is fixed by its altitude (height above the horizon) and azimuth (compass bearing), computed from declination (the sun's tilt, ±23.45° over the year), hour angle (15° per hour from solar noon) and latitude. At solar noon the altitude is 90° − |latitude − declination|.[9, 10]
Shading devices
A horizontal overhang shades high south sun (the vertical shadow angle sets its depth); vertical fins shade the low east-west sun (the horizontal shadow angle); an egg-crate does both.[9]
For the high south sun
A horizontal overhang or chajja shades a window from high-altitude sun — ideal for the south façade, where the sun is high (large VSA) when it strikes, so a shallow projection casts a deep shadow. The required projection P = window height H ÷ tan(VSA).[9]
Size an overhang
Enter the window height and the design vertical shadow angle to get the overhang projection: P = H ÷ tan(VSA). A 1.2 m window at VSA 60° needs about 0.69 m.[9, 10]
Overhang shading calculator
Depth of a horizontal overhang to fully shade a window: P = H ÷ tan(VSA).
At a glance
| Aspect | One | The other |
|---|---|---|
| Device vs sun | Horizontal overhang: blocks high sun (VSA) | Vertical fin: blocks low, oblique sun (HSA) |
| Best façade | Overhang: south (high sun) | Fins/louvres: east & west (low sun) |
| Shadow angle | VSA: profile height → overhang depth | HSA: bearing off wall → fin spacing |
| Ease of shading | South: easy, shallow chajja | East/West: hard, deep fins needed |
| Seasonal sun | Summer: high, north of east/west | Winter: low, south of east/west |
Key terms
The sun's vertical height above the horizon (0–90°).
The sun's horizontal compass bearing, measured from north or south.
The sun's angle to the equatorial plane; varies ±23.45° over the year.
Angular time from solar noon — 15° per hour.
When the sun crosses the local meridian — its highest point that day.
A stereographic map of the sun's daily and seasonal positions for a latitude.
The sun's bearing off the wall; governs vertical fins.
The sun's profile (apparent) height; governs horizontal overhangs and their depth.
A horizontal projection above a window that shades high sun.
A vertical blade beside a window that shades low, oblique sun.
A combined horizontal + vertical grid for the harshest façades.
Think it through
Use the calculator to size an overhang for a 1.5 m window at VSA 70°, then at 45°. Why does the shallow-angle case need an impractically deep overhang — and what would you use on an east window instead?
Self-assessment
1. The best device to shade a SOUTH window is —
2. For a window of height H below the overhang and design vertical shadow angle VSA, the projection is —
3. Solar declination at the equinox is —
Recap
References & further reading
- [9]O.H. Koenigsberger et al., Manual of Tropical Housing and Building. Orient Longman.
- [10]S.V. Szokolay, Introduction to Architectural Science. Architectural Press / Routledge.
Further reading
- S.V. Szokolay, Introduction to Architectural Science. Routledge.
- O.H. Koenigsberger et al., Manual of Tropical Housing and Building.
- G.Z. Brown & M. DeKay, Sun, Wind & Light. Wiley.
Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.