Hidden World / experimentsCustom SVG baseline · 01

At the edge of the canopy

Why does a tree’s shadow move and change length?

Move the Sun and watch the shadow of a marked point 5 metres above level ground.

Before you try

If the Sun is lower in the sky, does this shadow become longer, shorter, or stay the same?

01 / From aboveFixed scale · grid spacing 5 m
Plan view of the reference shadowA reference beside a tree casts a shadow away from the Sun. NESW 10 m

Dark line: measured reference shadow. Brown dot: Sun direction. The leafy tree provides context.

02 / Along the light rayFixed scale · metres
Side view of the reference and shadowA five-metre reference and its shadow form a right triangle. 5 m Marked reference top

Change the light

Height above the horizon

Clockwise from north: N 0° · E 90° · S 180° · W 270°

Shadow length
5.00 m
Shadow bearing
315°

Follow the light to the ground

The shadow points away from the Sun. Lower sunlight meets the ground farther from the reference, making a longer shadow. Moving the Sun around the horizon changes the shadow’s direction. At a fixed elevation, that rotation does not change its length.

Geometry, assumptions, and sources

In the right triangle, tan(elevation) = height ÷ shadow length. Rearranging gives shadow length = height ÷ tan(elevation).

This model measures the shadow of a marked point on an upright 5 m reference beside a tree. It assumes parallel sunlight and level ground. It does not compute the canopy’s outline, soft shadow edges, slopes, weather, or atmospheric refraction. The controls are independent experiments, not a daily or seasonal solar path.

Try the idea somewhere new

If the reference height doubles while the Sun stays fixed, what happens to its shadow length?