Solar Radiation Performance of Courtyard Proportions in a Hot-Dry Climate: A Validated Simulation Study of Ameri’s House, Kashan

Courtyard geometry is among the passive design variables governing solar radiation exposure in hot-dry climates, yet its effect remains insufficiently quantified in the context of heritage buildings. This study investigates the solar radiation performance of varying courtyard proportions in Ameri's House, Kashan, Iran, through a simulation-based approach validated against site-specific measurements. Illuminance data collected from a prior daylighting study were converted to solar irradiance values using an established conversion factor of 120 lux per W/m², enabling direct comparison with simulation outputs generated by Ladybug Tools within a Rhino-Grasshopper environment. Model accuracy was assessed using the Coefficient of Variation of the Root Mean Square Error (CV-RMSE), yielding a value of 20.2%, which falls within the accepted threshold (<30%), confirming the reliability of the computational framework. Following validation, annual and seasonal solar radiation simulations were conducted on four representative dates, the spring equinox, summer solstice, autumnal equinox, and winter solstice, examining courtyard floor surfaces at 10:00, 12:00, 14:00, and 16:00 to capture both seasonal and diurnal variation. The results indicate that among the investigated courtyards, those with a length-to-width ratio of 1.34-1.35 and height-to-width 0.29-0.30 achieve the most balanced solar performance, providing effective summer shading while preserving passive solar gain in winter. Courtyards with ratios below this range suffer from over-shading that limits winter passive heating, while those with higher ratios risk thermal stress through excessive summer exposure. These findings offer evidence-based geometric guidelines for climate-responsive courtyard design and contribute a methodology applicable to heritage refurbishment and sustainable design in dry regions.