A Mathematical Characterization of Partial Shading Factor under Building-Vegetation Interaction

  • Hessa Ali Al-Ali

Student thesis: Master's Thesis


The shading factor of an object such as building and vegetation has an important influence on indoor cooling load and outdoor thermal comfort specifically in regions with hot climate. Existing literature that studies the effects of shading over indoor cooling load and outdoor thermal comfort tends to use a sky view factor or a simplified partial shading factor to distinguish areas directly versus indirectly exposed to sunshine. This thesis presents an exact mathematical characterization on the partial shading factor under building-vegetation interaction. We identify 5 critical angles that separate the shading area by shading source (i.e. far-end building and tree) and shaded surface (i.e. near-end building façade and road pavement), and prove the generic relationships among the critical angles. We then use the critical angles to identify the 3 possible urban layouts that exhibit different shading scenarios (for example, shading from far-end building on near end building façade, shading from tree on road, etc.) and 13 possible shading paradigms. We then identify the ranges of sun location that lead to 81 possible shading scenarios. Finally, we present the linkages between the shading scenario, possible urban layout and the shaded area equation. The result of the analysis is a complete characterization of a partial shading factor that can be introduced in simulation models to analyze building energy consumption as well as passenger mobility and health under different urban layout, building geometry, vegetation distribution and positions on earth.
Date of AwardDec 2016
Original languageAmerican English
SupervisorI-tsung Tsai (Supervisor)


  • Shading Factor
  • Environmental Design
  • Architecture
  • Urban Design.

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