Mathematical links between optimum solar collector tilts in isotropic sky for intercepting maximum solar irradiance

• We modeled the optimum tilt of collectors for intercepting maximum irradiance.
• Mathematical link between optimum tilts under two models assumptions are proven.
• Ground reflectance influence on optimum tilt difference between models is presented.

The paper presents a mathematical modeling of the optimum tilt for solar collectors for intercepting maximum solar irradiance (power density), at different geographical locations, periods of time and different base-ground types. The solar irradiance received by the collector is estimated based on isotropic sky analysis models, namely Hottel & Woertz model and Liu & Jordan model. The optimum value for the tilt is considered for maximum hourly and respectively daily noon incident solar irradiance. This paper emphasizes the mathematical link between the optima computed under the two considered models assumptions. Also the ground reflectance factor influence on the optimum tilt difference between considered models is presented related to latitude.