The off-grid angle: why 70° wins winter.

Two systems, two questions

A grid-tied system can bank its summer surplus on the grid and draw it back in December. Its designer asks one question: which tilt collects the most energy over a year? At 50° north the answer is roughly 35–40°.

An off-grid system has no such bank. Batteries bridge a few cloudy days, not a season. If the array cannot cover the load in the darkest month, the lights go out in the darkest month — however much energy it made in June. The designer of an off-grid system asks a different question: which tilt gives the most energy in the month that has the least?

That month is usually December in the northern hemisphere and June in the southern. Everything below follows from pointing the panels at it.

Where the winter sun stands

At solar noon on the winter solstice the sun's elevation is

α_noon = 90° − |φ| − 23.44°

where φ is your latitude and 23.44° is the tilt of the Earth's axis. At 50° N that is 16.6°. A panel faces a sun at elevation α head-on when its tilt from horizontal is 90° − α — here 73.4°. At 45° N the same rule gives 68.4°; at 55° N, 78.4°.

That is where the round number comes from: 70° points a panel at the winter noon sun for most of Europe, Canada and the northern United States. The textbook annual tilt of 35–40° meets that low sun at an angle of incidence of about 35°, which alone costs around 18% of the direct light through the cosine law — and more through reflection at the glass.

Three effects that favour steep panels in winter

1. Geometry

The sun is low for the whole winter day, not only at noon. A steep panel keeps a small angle of incidence from mid-morning to mid-afternoon, which is when nearly all winter energy arrives.

2. Snow slides off

A panel covered by snow produces nothing, whatever its tilt. At 60–70° snow rarely settles, and what does settle slides off within hours of the first sun. At 30–35° a cover can stay for days. In a snowy climate this effect alone can outweigh everything else.

3. Snow on the ground reflects

A tilted panel sees part of the ground in front of it. The reflected light it receives is

G_ground = GHI × ρ × (1 − cos β) / 2

where ρ is the albedo — about 0.2 for grass and 0.6–0.9 for fresh snow. At β = 35° the panel sees 9% of the horizontal light reflected off the ground; at β = 70°, 33%. With snow on the ground, that is roughly 6% extra for the shallow panel and 23% extra for the steep one. Our calculators switch the albedo to snow values automatically in months with a mean temperature below freezing.

What it costs in summer — and why that is fine

Tilting to 70° typically gives up 10–15% of the yearly energy at mid-latitudes. For a grid-tied system that is money lost. For an off-grid system it is energy that would have been wasted anyway: batteries are full by noon on most summer days, and the charge controller throttles the array. A steep array produces a flatter year — less surplus in June and less deficit in December — which is exactly what a battery-based system wants.

Size an off-grid array for the month with the least sun, and tilt it for that month too.

Computed for fourteen places

The table below comes from the same model as every page on this site: NASA POWER monthly climatology (sunshine, diffuse share, temperature) turned into hourly irradiance, transposed onto the tilted plane with the Hay–Davies model, then through a temperature-dependent module model. "Off-grid best" is the tilt that maximises the worst month.

Four patterns stand out. Between about 45° and 55° north — London, Berlin, Warsaw, Seattle, Toronto — the tilt that maximises the darkest month lies between 67° and 75°, and 70° gives 15–20% more in December than the year-round optimum, cloudy maritime winters included. Further north — Oslo, Stockholm, Anchorage — the answer climbs past 80° towards a vertical wall. Nearer 40° — Denver, New York, Madrid — it falls to 50–66°: tilt any steeper and June, with its high sun, becomes the weakest month. And in Johannesburg, at 26° S with rainy summers, 70° is simply wrong: the darkest month there is a wet summer month, and the best off-grid tilt is 28°.

When 70° is the wrong answer

• Below about 35° latitude. The winter sun stands high, and the worst month is often a rainy one rather than a dark one — in summer, in monsoon or southern-African climates. The off-grid optimum can be as low as the latitude itself.
• Year-round loads that peak in summer. Cooling, irrigation pumps or a summer cabin make summer the design season. Use the calculator with your real monthly pattern.
• Around 40° latitude. A very steep panel turns June into the weakest month. The best compromise there is usually 50–65°.
• Heavy diffuse light. Diffuse light comes from the whole sky, and the sky a panel sees shrinks as (1 + cos β)/2 — 67% at 70° against 91% at 35°. Overcast climates still favour steep tilts in winter, but by a smaller margin than bright, snowy ones.
• Above about 60° latitude. The December sun barely rises; the design month moves to November or January and the answer approaches a vertical wall (90°).

A rule of thumb, then a calculation

Then check your own coordinates: the off-grid calculator finds the tilt that maximises your darkest month and sizes the array and battery for it, and the sun map shows the December sun path over your roof.

Calculate for my location