modelHorizontalFins

Information

Shading model for exterior horizontal fins in front of a window, in function of the fin angle. The control input Ctrl can either be used for controlling the fin angle, or its horizontal displacement. The horizontal displacement option assumes that the fins can be displaced horizontally at the exterior of the window such that they are either in front or next to the window.

Assumption and limitations

We assume that the fins fully cover the window unless the horizontal displacement option is used. The fin angle beta should be positive. We compute the shaded fraction of the direct solar irradiation and assume that indirect reflect effects are negligible. The diffuse solar irradiation is correct by assuming that the diffuse solar irradation originates from a solar altitude angle of 30 degrees, which is an approximation to reality. The ground diffuse solar irradation is not modified.

Typical use and important parameters

Parameter t is the fin thickness, s is the vertical spacing between the fins and w is the fin width. The model assumes that s <= w. If use_betaInput=true, the input Ctrl is used to control the angle beta in the figure, such that Ctrl = 0 corresponds to beta = 0 and Ctrl = 1 corresponds to beta = acos(t/s), which is the maximum value for beta. Note that beta must have radians as a unit. If use_displacementInput=true, the input 0 < Ctrl < 1 is used to control the horizontal displacement of the fins. For Ctrl=0, the fins are moved away from the window, into the plane of the figure below, such that no sun light is blocked. Either use_displacementInput or use_betaInput should be false. See the figure below for an illustration.

Dynamics

This model has no dynamics.

Implementation

The implementation is illustrated using this figure:

Parameters

Connectors

Components

Revisions

• Febrauri 24, 2025 by Filip Jorissen:
  Added Ctrl_to_beta_internal=0 when not using beta input. Otherwise the variable is undefined, resulting in a singular system. See #1426.
• July 1, 2024 by Lucas Verleyen:
  Added Ctrl_to_beta_internal to linearly map the Ctrl input [0,1] onto the fin inclination angle [0,beta_max].
  Removed dispLim as disp_internal is automatically in the range [0,1] due to the definition of Ctrl.
  See #1290.
• April 4, 2023 by Jelger Jansen:
  Updated figure in documentation. See #1186.
• July 18, 2022 by Filip Jorissen:
  Refactored for #1270 for including thermal effect of screens.
• November 10, 2019 by Filip Jorissen:
  Added simplified computation for diffuse solar shading. See #874.
• March 18, 2019 by Filip Jorissen:
  Added control option for horizontal displacement. Fixed bug in the implementation. See #992.
• April, 2017 by Iago Cupeiro:
  Cleaned up implementation and documentation.