Interactive model
Watch the balance change.
Move from direct sunlight to diffuse sky light. See how winter transmission changes for your courtyard and a square reference.
Enable JavaScript to explore the model. The published comparison above and results below remain available.
Diffuse fraction is a prescribed scenario, not a weather observation. Fixed 32°N latitude and 100 m² floor. The reference is a square courtyard at the selected wall height and 0° bearing. Direct and diffuse components follow the published model.
Results
What the analysis shows
For the square and north–south 4:1 plans at 32°N and 5 m height, the modelled winter ranking reverses at a diffuse fraction of 36.8%. Below that fraction the elongated plan admits more; above it the square admits more.
| Diffuse fraction | Square: winter | 4:1 north–south: winter |
|---|---|---|
| 0.0% | 19.1% | 23.2% |
| 36.8% | 27.4% | 27.4% |
| 50.0% | 30.3% | 28.9% |
| 100.0% | 41.5% | 34.6% |
At the all-diffuse endpoint, orientation disappears from the model. Different aspect ratios still retain different sky-view factors. This separation provides a check on the physical interpretation.
Methods and study design
We combine the seasonal direct-beam transmission and isotropic sky view factor using a prescribed diffuse fraction d of unobstructed horizontal exposure. The mixture is normalized against that same total exposure:
The crossover uses the winter difference between the north–south 4:1 plan and the square. It is meaningful only when d* lies between zero and one. The diffuse fraction is held fixed within each scenario; it is not inferred from climate data.
The released table covers five aspect ratios, three wall heights, seven bearings and eleven diffuse fractions at 32°N: 1,155 configurations. It includes annual, winter and summer values. The calculation also enumerates non-dominated choices at 0%, 50% and 100% diffuse under two simultaneous objectives: greater winter admission and lower summer admission, holding wall height at 5 m. Ties are retained; a preferred design cannot be selected without an explicit objective.
Mixture endpoints recover the direct-only and diffuse-only studies exactly. Linearity makes the crossover analytical; numerical precision remains inherited from the seasonal integration and view-factor calculation.
Interpretation and scope
The result explains why a single geometric ranking should not be generalized across sky conditions. Direct and diffuse components measure different pathways; choosing one while ignoring the other can change which plan appears favourable.
The comparison is a controlled sensitivity analysis, not a weather simulation. Seasonal diffuse fractions in an actual location need measured or credible meteorological inputs. Anisotropic skies, reflections, occupancy and thermal effects can change practical conclusions. The report does not identify a universally optimal courtyard or claim measured cooling or energy savings.
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.
- Direct–diffuse scenarios — 1,155 rows
- Summary, crossover and non-dominated comparisons
- 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). Direct–diffuse trade-offs in courtyard solar access. ABLAQ-R04, version 1.0.0. https://ablaqstudios.com/direct-diffuse-tradeoffs. Download citation (BibTeX)