Solar Bus Shelter Energy

What is modelled

The sun moves on a path set by the latitude and the day of the year. A south-facing roof tilted by the chosen angle receives direct light in proportion to the cosine of the angle between the sun and the roof normal, plus diffuse sky light and a little light reflected from the ground. The panel turns a fraction of it into power, which charges the battery; the display runs all day and the LED lamp runs from dusk to dawn.

Equations

• Declination δ = 23.45° sin(360 (284 + n) / 365), zenith cos θz = sin φ sin δ + cos φ cos δ cos ω.
• Incidence on a south roof cos θ = sin δ sin(φ − β) + cos δ cos(φ − β) cos ω.
• Clear-sky beam 1361 e0 0.7AM0.678 times the clearness, diffuse 10 % of it.
• Panel power P = A η × 0.85 × Groof; battery dE = Pin − Pload, limited to 0 and the capacity.

Checks run in the page

• Daily energy above the atmosphere, numerical against closed form.
• Head-on incidence at the optimum tilt.
• The battery energy ledger over three days.
• The day length from counting minutes against the hour-angle formula.

Honest simplifications

A simple clear-sky model scaled by one clearness number, no shading by buildings, no temperature, soiling or inverter detail, a 0.85 system factor and a 92 % charge efficiency chosen for illustration. Real yield depends on the local weather record, so this is a sizing sketch, not a design.

• Press Mid-winter dark day and see the daily energy and the unmet lighting appear.
• Sweep the roof tilt on the yield-against-tilt graph and notice that the best tilt changes with the season.
• Press Oversized battery, tiny panel and see that a big battery does not fix a small panel.