How to Calculate the Louvre Angle That Blocks the Sun: West and South Walls

Step 2: the profile angle

Horizontal slats and overhangs only 'see' the sun in the vertical section at right angles to the wall. First find the horizontal shadow angle = sun azimuth − direction the wall faces; at 18:00 that is 276.9° − 270° = 6.9°. The profile angle = atan(tan elevation ÷ cos horizontal angle) = atan(tan 26.0° ÷ cos 6.9°) = 26.2°. When the sun is off to the side, the profile angle is steeper than the elevation. In the evening the sun shines almost straight onto a west wall, so the two are nearly equal.

Step 3: the cut-off angle of open slats

Horizontal slats at 0° stop any sun that comes in steeper than the cut-off angle atan(spacing ÷ width) = atan(95 ÷ 100) = 43.5°. On the west wall the profile angle is still 47.1° at 16:00, so open slats are enough. From 16:30 until sunset it is lower and the slats have to turn.

Step 4: the minimum tilt

Each slat has to turn until its shadow reaches the next one. In the section that means width × sin(slat angle − sun angle) ≥ spacing × cos(sun angle). At 18:00: 95 × cos 26.2° ÷ 100 = 0.853, arcsin 0.853 = 58.5°, so the minimum tilt is 58.5° − 26.2° ≈ 32.4° (outer edge down).

As the sun sinks the tilt has to grow: 48.4° at 19:00 and 62.2° at 20:00. Slats wider than their spacing (100 > 95 mm) can close completely, so they always stop the low sun before sunset — you just won't see much through them.

South wall at noon

On the south wall at 13:00 the sun is almost due south (azimuth 183.6°), 65.3° above the horizon, and the profile angle is 65.3°. That is well above the 43.5° cut-off, so open slats stop the direct sun — according to the calculator's day chart, for the whole time the sun shines on the south wall on 21 June. You get shade and keep the view.

Winter is the opposite: on 21 December at 12:00 (UTC+1) the sun is only 18.4° high and open slats let it in. A tilt of 45.9° would stop it, but in winter you usually want the sun's warmth.

Why west and east walls need rotating louvres or vertical fins

The Scottish Building Standards Technical Handbook (annex on controlling solar gain) says horizontal devices are most effective on south facades but not suitable for east and west facades, because the sun is too low. For those it recommends vertical fins and adjustable devices such as sliding and rotating shutters.

The calculator shows why. Fixed horizontal slats on the west wall only stop the sun until 16:00. Fixed vertical fins at right angles to the wall only stop sun that comes in from the side at more than 43.5° — but on 21 June the horizontal angle is just 27.7° even at 20:00, so from 18:00 to sunset the sun passes between them. Vertical slats must turn too: 63.7° at 18:00, with a peak of 71.4° around 17:20. On a west wall what matters is that the slats can rotate — vertical or horizontal.

Key points

• Work with the profile angle, not the sun's elevation.
• Cut-off angle of open slats = atan(spacing ÷ width). The smaller the spacing relative to the width, the less the slats need to turn.
• Check the whole day: on a west wall the last hours before sunset are the worst, on an east wall the first hours of the morning.
• This is about direct sun. Diffuse and reflected light still gets through.

The calculator handles shading geometry, not structural design. Fixing, wind load and the louvre system itself must follow the manufacturer's instructions and local regulations.