Map a planting site by measuring its slope as rise over run and its shade as the shadow length at the worst day, the winter solstice, using the noon sun altitude of 90 degrees minus latitude minus 23.44 degrees. Divide an object’s height by the tangent of that altitude to get its winter shadow length, then sort the ground into full sun, partial shade and shade zones. Do this before planting, because a tree that shades the rest of the planting cannot be moved.
Sun mapping records where direct sun falls on a site through the year, and slope analysis records how steeply and in which direction the ground falls, together deciding where each layer of a planting can grow.
Winter Shadow Length Sets The Shade Limit On Every Row
The sun is lowest and shadows longest at the winter solstice. At solar noon the sun’s altitude above the horizon is 90 degrees minus your latitude minus 23.44 degrees (Northern Hemisphere, 21 December); at the summer solstice it is 90 minus latitude plus 23.44; at the equinoxes it is 90 minus latitude. A shadow’s length is the object’s height divided by the tangent of the altitude. For the full derivation see Seasonal Sun Angle Calculation and Sun Exposure & Shadows.
Worked Example: A 10 m Tree At 45 Degrees Latitude
Inputs: latitude 45 degrees, tree height 10 m.
- Winter noon altitude: 90 − 45 − 23.44 = 21.56 degrees.
- tan(21.56 degrees) = 0.395.
- Shadow length: 10 ÷ 0.395 = 25.3 m, about 2.5 times the height.
- Summer noon altitude: 90 − 45 + 23.44 = 68.44 degrees; tan = 2.53; shadow = 10 ÷ 2.53 = 4.0 m.
Rows planted 10 m behind a 10 m tree on its north side sit in its winter-noon shadow, and the shadow is longer morning and evening. Your own latitude changes every number here; do not reuse these.
What You Need
- Your latitude. In the Northern Hemisphere it equals the altitude of the pole star above the horizon; North Star Finding shows how to find the star.
- True south (true north in the Southern Hemisphere), from a shadow stick: Shadow Stick.
- Stakes, string, a plumb line and a level — an A-frame level works (A-Frame Level).
Method
Step 1: Mark true south on the site map and peg it on the ground.
Step 2: Measure existing obstacles (trees, buildings, hills): height and distance. An obstacle shades a point if its angle above the horizon from that point, arctan(height ÷ distance), is greater than the sun’s altitude.
Step 3: Record sun hours at several dates. Stand a pole of known height on the site and mark its shadow tip every hour on a clear day near each solstice or in each season. The carrier’s bands: full sun is 6+ hours, partial shade 3-6, full shade under 3.
Step 4: Measure the slope. Percent slope = rise ÷ run × 100; angle = arctan(rise ÷ run). A rise of 10 m over a run of 100 m is 10 percent, an angle of 5.7 degrees. A 100 percent slope is 45 degrees. Note which way the ground faces: in the Northern Hemisphere a south-facing slope receives more winter sun.
Step 5: Mark cold pockets. Cold air drains downhill and pools in hollows (Cold Air Drainage & Frost Pockets); frost-tender blossom should not be planted there.
Common Mistakes
- Mapping only in summer — the summer sun is so high that nearly everything looks sunny.
- Confusing percent and degrees — 45 degrees is a 100 percent slope, not a 45 percent one.
- Using magnetic south as true south — the difference can be large in many places.
- Mapping young trees — map the mature height, not the sapling.
What’s Next
- Learn next: Water Flow and Swale Placement — the slope map becomes a water plan
- Combine with: Canopy and Sub-Canopy Trees — the shading you are mapping for