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Insolation & Angle

5 min read

Insolation is the solar energy that lands on a surface, quoted in kWh per square metre per day, and it has no single value: it falls with distance from the equator, with winter, with cloud and with a poorly chosen tilt. Aim the collector so the noon sun hits it square-on, using a tilt of latitude minus the sun’s declination, and measure your own site’s daily total with a water-filled test box rather than trusting a figure from another place.

Part of Solar Energy Fundamentals

Insolation is the sunlight energy arriving on a surface; the angle between the surface and the sun’s rays decides how much of it the surface keeps.

A Surface Keeps The Cosine Of The Angle Away From The Sun

A surface facing the sun squarely receives the full beam, about 1,000 W/m² at a clear noon (the parent page’s figure). Tilt it away by an angle θ from facing the sun and the power it receives falls to 1,000 W/m² × cos θ. At θ = 60° the cosine is 0.5, so the surface receives 500 W/m². At θ = 8° the cosine is 0.990, a loss of 1%.

This is why aim matters little for small errors and a great deal for large ones.

Tilt Follows Latitude And Season

At solar noon the sun’s height above the horizon is 90° − |latitude − declination|, where declination is the sun’s angle north or south of the equator on that date, between +23.44° and −23.44° over the year (Seasonal Sun Angle Calculation derives it). A collector tilted up from horizontal by |latitude − declination| faces the noon sun squarely. Face it toward the equator: true south in the northern hemisphere, true north in the southern.

Worked at latitude 45° N:

  • Equinox (declination 0°): tilt = 45 − 0 = 45°.
  • Winter solstice (declination −23.44°): tilt = 45 + 23.44 = 68.4°.
  • Summer solstice (declination +23.44°): tilt = 45 − 23.44 = 21.6°.

The parent page’s rule of latitude ±15° gives 60° for winter and 30° for summer. At noon on the solstice, 60° is 8.4° from the ideal 68.4°, and cos 8.4° = 0.989, so the shortcut costs about 1%. A fixed tilt equal to latitude is a sound compromise; if you only use the heater in winter, tilt steeper than latitude.

Daily Totals Cover A Wide Range

Over a day the received energy is the sum of the sun’s power through the hours. Published solar-resource atlases (recalled, not taken from this wiki) put the daily total on a well-aimed surface from well under 1 kWh/m² in a high-latitude midwinter to roughly 7-8 kWh/m² on a clear desert summer day. The parent page notes summer delivers 2-3 times winter at temperate latitudes, and an overcast day delivers 10-25% of a clear day.

No figure in this wiki is a universal local value. Four things drive it: latitude, season, cloud, and tilt.

Method: Measure Your Own Site

Step 1: Build a test box. A shallow black-painted metal tray holding a known mass of water, insulated beneath and at the sides, covered with one pane of glass, tilted as above. Use about 10 kg of water per 0.25 m² of tray (40 kg per square metre).

Step 2: Measure the starting temperature at dawn, and the maximum at the end of the afternoon. Stir the water before each reading.

Step 3: Compute the energy. Energy gained per square metre = (mass per m² × 4.18 kJ/kg·K × temperature rise) ÷ 3,600 kJ/kWh.

Step 4: Convert to insolation by dividing by the box’s efficiency. A plain glazed box is perhaps 40% (assumed); an untested box is not a precise meter, so repeat on several clear days and keep the highest reading.

Worked Example: A Test Box Result

Inputs: 10 kg of water in a 0.25 m² tray, a rise of 25 K over the day, 4.18 kJ/kg·K.

  1. Water per square metre = 10 ÷ 0.25 = 40 kg/m².
  2. Energy per square metre = 40 × 4.18 × 25 = 4,180 kJ/m² = 4,180 ÷ 3,600 = 1.16 kWh/m².
  3. That is the least the day delivered. At an assumed 40% efficiency, 1.16 ÷ 0.40 = 2.9 kWh/m².

Without a thermometer, count clear days and compare how long a known volume of water takes to warm to bathing temperature; that gives a ratio, not a figure.

Common Mistakes

  • Using the climate of another place. Two sites at the same latitude can differ by a factor of two in cloud.
  • Facing magnetic south. The compass points to magnetic north, which is not true north; find true north with the sun (Shadow Stick).
  • Shading in winter. The sun is low; a tree that is harmless in June can shade the collector from November (Sun Exposure & Shadows).

Safety

A tilted, glazed test box heats water to scalding

The test box is a small solar collector: stagnant water in it can pass 60°C, which scalds in seconds. Test water by hand only after mixing and checking with a thermometer, and cover the box when not measuring.

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