2.2 View factor calculation
In this study , a solid angle method [ 9,10 ] was adopted to calculate the VF between the window and the hemisphere . A solid angle ( Ω ), expressed in steradians , can be calculated using vectors oriented from a point �aa � ) on a plane of an exposed glazed area to the vertices on a plane of a shade element . The solid angle ( ΩΩ ������ ) from a point ( aa � ) on the glazing to the unobstructed hemisphere ( see Fig . 3 ( a )) can be calculated using Eq . ( 3 ). The solid angle can differ based on the geometric relationships between the surface of the shading devices and the location of the point ( aa � ). Therefore , the solid angle should be calculated for multiple points ( n ) on the exposed glazing area . The VF at a specific shading state can be calculated using Eq . ( 4 ).
Fig . 3 . The concept for sky view factor calculation : the solid angle from point ( aa � ) to the unobstructed hemisphere ( a ) and the number of measurement points ( n ) on the exposed glazing area ( b ).
�� � �
∑ � ��
ΩΩ ������ ���ΩΩ �������� ( 3 )
��� �� � ΩΩ ������� �
� � �� � �� �� � � �� ( 4 )
3 . Application
Evaluation of adaptive façade was performed by applying Method Three to a two‐axis folding type shading device . The shading device was designed with two dynamic folding elements which could fully close and open based on X and Y‐axis ( see Fig . 4 ). The shading layer of the adaptive façade was designed with a width of 2 m and a height of 4 m ; and the curtain wall layer was designed to be the same size as the shading layer ( including a frame width of 28.6 mm ). The movements of the shade were divided among 11 operational states having equal position displacements as shown in Fig . 4 .
Fig . 4 . The phased states of the two‐axis folding system .
Calculation Method for Evaluating Diffuse Solar Heat Gains Through Adaptive Façades 86