Calculation of Length of Shadow.

Figure

Keyword

Solar Declination,Equation of Time,Solar hour angle,Solar elevation,Solar azimuth,Length of Shadow,Azimuth of Shadow,Vertical Length,Horizontal length.

Reference

・『建築設計資料集成　環境1』（日本建築学会・丸善株式会社）.
・『建築気候』（斎藤平蔵・共立出版株式会社）.
・『有害紫外線モニタリングネットワーク活動報告』（独立行政法人国立環境研究所）.

Remarks

・θ0=2*π*Number of days elapsed/365(or 366)
・Solar Declination(δ) Approximation Formula：
δ=0.006918-0.399912*cos(θ0)+0.070257*sin(θ0)-0.006758cos*(2*θ0)+0.000907*sin(2*θ0)-0.002697*cos(3*θ0)+0.001480*sin(3*θ0).

・Equation of Time(Eq) Approximation Formula：
Eq=60*12*{0.000075+0.001868*cos(θ0)-0.032077*sin(θ0)
-0.014615*cos(2*θ0)-0.040849*sin(2*θ0)}/π.

・Solar Elevation(α) Formula：
α=arcsin{sin(φ)*sin(δ)+cos(φ)*cos(δ)*cos(h)}.

・Solar azimuth(β) Formula：
β=arctan[cos(φ)*cos(δ)*sin(h)/{sin(φ)*sin(α)-sin(δ)}].

History

・2014/08/07：layout change.
・2009/10/05：Correction about Remarks.The braces({,}) are added to the Solar Elevation Formula.
・2009/03/20：Moved from www.am-consulting.co.jp to here.