Skip to content

sideFinsSunlitFraction

Fraction of a window lit by the direct sun between two side fins: the superposition of rectangles of Buildings.HeatTransfer.Windows.BaseClasses.SideFins, with its smooth minima, maxima and steps, explicit

FastSmoothBuildings.Envelope.Functions.sideFinsSunlitFraction, function (source)

Purpose

Fraction f of the area of a window lit by the direct sun between two side fins of depth dep, at the distance gap from the side edges of the window and extending h above its top. The sun is given by its altitude alt and the angle verAzi between the horizontal projection of its rays and the normal of the wall; both fins being alike, the side of the sun is not needed.

Equations

With tan(verAzi), cos(verAzi) and tan(alt) bounded below by δ = 10−6, and λ = tan(alt)/tan(verAzi), the tangent of the angle between the horizontal and the sun's rays projected on the wall, the corner of the shadow of a fin is at

y2 = dep tan(alt)/cos(verAzi),   x2 = dep tan(verAzi).

The shaded area is the superposition of four rectangles of heights H = {h + hWin, h, h + hWin, h} and widths W = {gap + wWin, gap + wWin, gap, gap}; for each,

mx = min(H/λ, x2, W),   my = min(H, y2, W λ),   a = H mx − mx my/2,

Ashd = a1 + a4 − a2 − a3, and f = 1 − Ashd/Awin, the whole window Awin = hWin wWin in the shade when the sun is behind the wall (verAzi > π/2) or below the horizon (alt < 0).

Smoothing

  • min is smoothMin over a hundredth of the width of the window; the bounds at δ are smoothMax, and the tangents a sine over a cosine bounded below by 10−3.
  • The shade behind the wall and below the horizon is chosen by regStep over 0.01 rad, the larger of the two shaded areas by smoothMax over 10−4 Awin.

Relation to Buildings

The superposition of rectangles of Buildings.HeatTransfer.Windows.BaseClasses.SideFins, written explicitly with smooth minima, maxima and steps.

Use

Window with haveSideFins = true; Validation.ShadingFractions.

Revisions

  • October 2026: moved from trano's FastModel.Envelope.Functions.