Interactive model
Follow sunlight through the year.
Change the courtyard, orientation and latitude. Compare monthly direct sunlight with a square courtyard at the same wall height.
Enable JavaScript to explore the model. The published comparison above and results below remain available.
The curves use the published monthly dataset. Summary values are ratios of summed exposure, not averages of monthly percentages. Fixed 100 m² floor; constant direct normal input. Bearings run from north–south (0°) to east–west (90°).
Results
What the analysis shows
At 32°N with 5 m walls, the north–south 4:1 plan has 23.2% winter direct-beam transmission, compared with 19.1% for the square. Its summer value is lower: 37.3% against 54.5%. Turning the elongated plan east–west produces a different seasonal pattern: 0.7% in winter and 62.7% in summer.
| Plan / long-axis bearing | Winter | Summer | Annual |
|---|---|---|---|
| Square / 0° | 19.1% | 54.5% | 41.9% |
| 4:1 / north–south | 23.2% | 37.3% | 32.2% |
| 4:1 / east–west | 0.7% | 62.7% | 38.2% |
The annual value alone conceals this redistribution. The table and figure use the same fixed area, wall height and exposure normalization.
Methods and study design
We hold floor area at 100 m² and vary aspect ratio (1, 1.5, 2, 3, 4), wall height (2.5, 5, 7.5 m), long-axis bearing (0–90° at 15° intervals) and latitude (29, 32, 35°N). The 315 combinations are evaluated over all 365 days of a generic non-leap year.
Solar declination follows NOAA’s fractional-year approximation evaluated at noon for each day. Solar vectors use local apparent solar time, with east, north and up components. Ten-minute midpoint samples are rotated into the courtyard’s width and length axes. No equation-of-time conversion is needed because civil clock time is not an input.
Here e′ and n′ are the rotated horizontal solar-vector components and z is the upward component. Constant direct normal input is assumed, so z supplies the horizontal cosine weight. Monthly and seasonal quantities are ratios of summed exposure components, not unweighted averages of monthly percentages. Winter is December–February; summer is June–August.
A five-minute repeat for 12 representative cases, spanning all latitudes and extreme ratios and bearings at 5 m height, changes monthly transmission by at most 0.0154 percentage points. The open-horizontal time integral is also compared with its closed-form day integral. The full comparison record reports the cases and tolerances.
Interpretation and scope
Orientation changes which part of the daily solar path clears the walls. At low winter elevations, a north–south elongated opening preserves a long noon pathway; an east–west narrow dimension obstructs that pathway. In summer, the higher and longer solar arc changes the comparison.
This report quantifies the consequences of established solar and shading geometry. It does not introduce a new solar-position theory. Latitudes are model inputs, not site observations. Constant direct normal input omits clouds, aerosol, atmospheric attenuation and the actual seasonal radiation budget. Results describe normalized direct access, not measured energy, thermal comfort or climate-optimal design.
The sky-view study adds the diffuse component that is absent here.
Data and reproducibility
The interactive model uses the published data and open browser equations (JavaScript). The executed interactive-model verification records numerical agreement and integration checks. Its interface source is also available. The controls run locally; shared links encode only the chosen model inputs.
All numerical outputs are calculated, not observational measurements. The release contains the complete parameter tables, source and numerical comparison record.
- Monthly results — 3,780 rows
- Annual and seasonal results — 315 configurations
- Python research software
- Numerical comparison report (JSON)
- File manifest and SHA-256 checksums
- Reproduction instructions and data dictionary
Code, numerical data and generated research figures are released under CC0 1.0. The report is institutionally published; numerical verification does not constitute external peer review.
Methodological references
- NOAA Global Monitoring Division, General Solar Position Calculations. Fractional-year declination approximation and solar hour-angle relationships.
- John R. Howell, A Catalog of Radiation Heat Transfer Configuration Factors, C-11. Equal, parallel, directly opposed rectangular surfaces.
- EnergyPlus Engineering Reference, Shading Module. Geometric treatment of solar shading.
- Sandia National Laboratories, PV Performance Modeling Collaborative: Plane of Array Irradiance. Distinguishing beam, diffuse-sky and ground-reflected components.
Institutional authorship
Author and publisher: ABLAQ Studios. Osama Khaled Ahmed Abdel-Qader, Scientific Research Lead, directs the scientific research and its decisions and holds publication accountability. Current team responsibilities are described in the research directory; programme roles are not a substitute for study-specific contribution records.
Computational implementation and execution use the tools documented in Methods. Scientific correspondence: osama.khaled@ablaqstudios.com.
ABLAQ Studios (2026). Seasonal solar exposure across courtyard geometries. ABLAQ-R02, version 1.0.0. https://ablaqstudios.com/seasonal-solar-exposure. Download citation (BibTeX)