Model scope and corrections — read first

Noon shadow direction depends on observer latitude φ relative to solar declination δ, not on hemisphere alone. If φ > δ, the Sun is due south and the shadow points north; if φ < δ, the Sun is due north and the shadow points south; if φ = δ, the Sun is at the zenith and an ideal pole casts no shadow. Thus tropical Southern Hemisphere shadows do not always point in one fixed direction. L = h/tan(H) assumes a vertical pole, level ground, ideal sunlight, and 0° < H ≤ 90°. When H ≤ 0°, the formula should not be interpreted as giving a finite physical ground shadow.

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Geographic Time · Module 04

ShadowDirection and length

L = h / tan(H) · Noon shadow direction

Key concepts

Observer latitude φ

Beijing 39.9°N +39.9°

Date

March equinox δ = +0.0°

Pole height h

Pole height 1.0 m

L = h / tan(H)

L = shadow length (m)
h = pole height (m)
H = noon solar altitude
H = 0° → infinitely long shadow (Sun on horizon)
H = 90° → zero-length shadow

Concept explanations

geo · shadow · L = h/tan(H)

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