Lattice Screen

What is modelled

A square lattice of bars of width b with gaps g has an open area of (g / (b + g))^2 when seen straight on. Seen at an angle the bars are deep, so each bar hides part of the neighbouring gap: a ray can only get through if it stays inside one gap along the whole depth d of the lattice. That makes the direct sun drop quickly as the sun gets lower or moves to the side, while the open area that lets the breeze through stays the same. The air moves through two screens, driven by the wind pressure on the front of the house and by the stack effect of the warm air rising between a low and a high opening.

Equations

• Open area φ = [g / (b + g)]2.
• Direct transmission T = max(0, g − d tanθh) / (b + g) × max(0, g − d tanθv) / (b + g), tanθh = tan(azimuth), tanθv = tan(height) / cos(azimuth).
• Diffuse transmission as the cosine-weighted average of T over the upper sky.
• Screen loss ζ = [0.707 √(1 − φ) + 1 − φ]2 / φ2, pressure Δp = ½ ρ (2ζ) v2.
• Wind Δp = ½ ρ U2 ΔCp, stack Δp = ρ g Δh ΔT / T.

Checks run in the page

• Hundreds of thousands of random rays through the full depth against the product formula.
• Cosine-weighted sky rays against the numerical integral.
• Random points against the open-area formula.
• The airflow found from the summed pressures against the root-sum-square of the two parts.

Honest simplifications

The lattice is a perfect square grid of rectangular bars, the sky is a uniform bright hemisphere, the sun power values are fixed typical numbers, the pressure coefficient difference and the indoor-outdoor temperature difference are constants, and carved patterns, glass and curtains are left out.

• Press Dense and deep to see how depth blocks a low sun.
• Press Open and thin and compare the airflow.
• Press Still hot day and see that the stack effect still moves air.