Judge a site’s sun by its worst day, the winter solstice, when the noon sun is lowest and every shadow longest: shadow length equals object height divided by the tangent of the sun’s altitude. At 40 degrees latitude the winter-noon sun stands 26.6 degrees high, so a shadow is 2.0 times the object’s height, and at 48 degrees it is 2.98 times.
Measuring how much winter sun reaches a building site, and which hills, trees and structures block it, using shadow geometry.
Shadow Length Depends on Latitude, so There Is No Universal Clear Distance
Shadow length L from an object of height h, with the sun at altitude a above the horizon, is L = h / tan(a). At solar noon the altitude is 90 degrees minus the latitude, plus or minus the sun’s declination (the carrier’s formula: winter noon sun angle = 90 - latitude - 23.5, summer = 90 - latitude + 23.5, in the Northern Hemisphere). So the winter-noon shadow multiplier for a given latitude is:
| Latitude | Winter-noon sun altitude | Shadow length / height |
|---|---|---|
| 36 N | 30.6 degrees | 1.69 |
| 40 N | 26.6 degrees | 2.00 |
| 44 N | 22.6 degrees | 2.41 |
| 48 N | 18.6 degrees | 2.98 |
(Altitude = 90 - latitude - 23.44; shadow multiplier = 1 / tan(altitude).) At 40 N the multiplier is 2.0, so a 10 m tree casts a 20 m shadow at winter noon. These are noon values. Away from noon the sun is lower and the shadow longer and swung to the side: at 40 N, three hours after solar noon on the winter solstice, the altitude is 14.0 degrees and the shadow is 4.0 times the height. This page uses Northern Hemisphere conventions, where the sun at noon is in the south and shadows point north. In the Southern Hemisphere swap north and south: the sun is in the north and shadows point south. Near the equator the noon sun can be nearly overhead and shadows are short; the method still works but the notion of a single “sunny side” fades.
What You Need
- A straight pole — 2 m long, set vertical, for measuring shadow ratios.
- A tape — and a sketch map of trees and hills.
- A site visit near midwinter — or the calculation if you cannot wait.
Method: Check the Sun’s Path Against the Obstacles
Step 1: Measure the winter-noon shadow ratio On or near the winter solstice, at solar noon, measure the pole’s shadow. Ratio = shadow / pole height. That ratio is your site’s multiplier. Never look at the sun to measure it.
Step 2: Find the obstacles in the sun’s arc From the building site, look toward the winter sun’s arc (south, from south-east through south-west in the Northern Hemisphere). Measure the height of each tree, ridge or building above the window level and its distance from the site.
Step 3: Compare angles Obstacle angle = arctan(height above window / distance). If it is smaller than the sun’s altitude for the hours you want, the obstacle does not shade you.
Step 4: Check morning and afternoon Obstacles to the south-east or south-west matter at the start and end of the day. Check the sun’s azimuth at those times (see Seasonal Sun Angle Calculation).
Worked Example
At 40 N, a tree 15 m tall stands south of a planned house. Window sill 1 m above ground, so the tree rises 14 m above the sill.
- Noon on the winter solstice: sun altitude 26.6 degrees, tan = 0.50.
- Clear distance needed = 14 / tan(26.6) = 14 / 0.50 = 28 m.
- If the tree is 25 m away: angle = arctan(14 / 25) = arctan(0.56) = 29.2 degrees, which is higher than 26.6 degrees, so the tree blocks the noon winter sun.
- Three hours after noon the altitude is 14.0 degrees at azimuth about 222 degrees clockwise from north (south-west), and the shadow of a 15 m tree is 15 x 4.0 = 60 m long, falling to the north-east.
A tree that does nothing in summer can darken a south wall in winter. For deciduous trees the bare winter branches still block a share of the light; do not count them as clear.
Using Shadows in Site Choice
- Valley floors and north-facing slopes in the Northern Hemisphere get less winter sun, the reason the carrier prefers a gentle south-facing slope and gives solar exposure a weight of 3x because it is hard to change.
- Fields need light as well as buildings: check the shadows of ridges across the fields.
- Plan tree clearing and building positions together. A 28 m clearing south of the house is a large cost; choose a site that already has it.
Common Mistakes
- Using the summer sun — the summer sun is high and shadows are short; winter decides.
- Using a fixed distance for all latitudes — the multiplier changes from 1.69 to 2.98 across the table.
- Ignoring the sides — morning and afternoon shadows come from the east and west quadrants.
Safety
Never look at the sun to measure it
Use shadows, never direct sighting of the sun, and never a telescope or binocular pointed at it. Looking at the sun damages eyes permanently.
What’s Next
- Learn next: Solar Orientation & Geometry — using the sun the site gives you
- Combine with: Cold Air Drainage & Frost Pockets — sunless hollows are also the coldest