On a ground-mounted PV plant, the closer the rows, the more capacity you can fit on the same land. But when rows get too close, the front row casts a shadow on the lower edge of the row behind it, especially in winter. Row spacing is a balance between installed capacity, energy loss and land cost. In this article we explain why inter-row shading matters, how the design sun angle is chosen, the spacing formula, the effect of sloped terrain, and a numerical example.
Why inter-row shading matters so much
A module is made of series-connected cell groups, each protected by a bypass diode. Even a thin shadow along the bottom edge of the rear row can switch off one or more cell groups, depending on module orientation, and other modules in the same string can be affected too. Loss from inter-row shading is therefore not proportional to the shaded area; a small shadow can cost more than it looks.
There are two ways to limit it: space the rows far enough apart, and choose a module layout and stringing that take into account which cell groups the shadow will hit. This article focuses on the first.
Design sun angle: why the winter solstice?
In the northern hemisphere, the sun reaches its lowest noon elevation of the year around 21 December, the winter solstice. Shadows are longest on that day. A common design approach is to avoid inter-row shading on the winter solstice during a chosen time window (for example 10:00–14:00 or 09:00–15:00 solar time). The window is a design decision: the wider it is, the further apart the rows and the fewer modules fit on the land.
Sun elevation at solar noon follows a simple formula:
α (noon) = 90° − φ + δ
where φ is latitude and δ is solar declination. At the winter solstice δ ≈ −23.44°. For other times of day you need both the sun's elevation and its azimuth (its direction in the horizontal plane), calculated with solar position formulas or software. Remember that solar time differs from clock time.
The row spacing formula
Definitions:
- L: length of the module table along its slope (for example, two modules in portrait)
- β: module tilt
- h = L × sin β: height of the table's top edge above its bottom edge
- α: sun elevation
- γ: angle between sun azimuth and array azimuth (for a south-facing array, how far the sun is from due south)
On flat ground, the shade-free distance from the top edge of the front table to the bottom edge of the rear table, measured perpendicular to the rows, is:
d = h × cos γ ÷ tan α
The row pitch (bottom edge of one table to bottom edge of the next) is:
Pitch = L × cos β + d
At solar noon γ = 0, so the formula reduces to d = h ÷ tan α. At other times the sun is lower, but because it comes from the side, the component of the shadow perpendicular to the rows is shortened by cos γ. Both effects have to be considered together. You can also write this with the "profile angle": tan αp = tan α ÷ cos γ, and d = h ÷ tan αp.
Ground coverage ratio (GCR)
Ground coverage ratio is table length divided by row pitch: GCR = L ÷ pitch. A higher GCR fits more capacity on the land but increases inter-row shading loss. A lower GCR reduces shading but raises land, cabling and structure cost per unit of capacity. The right GCR depends on land value and on how much winter production matters.
Worked example (flat ground)
The values below are example values: latitude φ = 38.4° N, table length L = 4.5 m, tilt β = 25°, array facing due south.
- h = 4.5 × sin 25° ≈ 1.90 m
- Horizontal projection of the table: 4.5 × cos 25° ≈ 4.08 m
- Noon sun elevation on the winter solstice: 90 − 38.4 − 23.44 = 28.16°
| Design moment (solar time, 21 Dec) | Sun elevation | Angle from south | d (m) | Pitch (m) | GCR |
|---|---|---|---|---|---|
| 12:00 | 28.16° | 0° | 3.55 | 7.63 | 0.59 |
| 10:00 (and 14:00) | 22.06° | 29.67° | 4.08 | 8.16 | 0.55 |
| 09:00 (and 15:00) | 15.15° | 42.23° | 5.20 | 9.28 | 0.48 |
Checking the 10:00 row: d = 1.90 × cos 29.67° ÷ tan 22.06° ≈ 1.90 × 0.869 ÷ 0.405 ≈ 4.08 m. Widening the design window from 10:00–14:00 to 09:00–15:00 adds about 1.1 m to the pitch and drops GCR from 0.55 to 0.48, meaning roughly 12% less capacity on the same land. That difference shows why the window is an economic decision.
The effect of sloped terrain
On land with a north–south slope s, the rear row stands at a different level from the front row. The shade-free distance, measured horizontally and perpendicular to the rows, becomes:
- South-facing slope (ground falls toward the south, rear row sits higher): d = h ÷ (tan αp + tan s)
- North-facing slope (ground falls toward the north, rear row sits lower): d = h ÷ (tan αp − tan s)
Add a 5° slope to the same example (10:00 design moment, αp ≈ 25.0°): d is 4.08 m on flat ground, drops to about 3.43 m on a south-facing slope and rises to about 5.02 m on a north-facing slope. At noon the same three values are 3.55 m, 3.05 m and 4.25 m. That is why south-facing slopes suit ground-mounted PV, while on north-facing slopes rows must be spaced noticeably wider. As the north slope approaches the sun's profile angle, the required distance grows very quickly.
East–west slope and uneven ground
An east–west slope does not change row spacing directly, but one end of the table ends up higher than the other. There are two options: tilt the table slightly sideways to follow the ground, or keep the table level and step the leg heights. Sideways-tilted tables can change morning and evening shading, so check them with a simulation.
When stepping leg heights on uneven ground, keep an eye on:
- Minimum ground clearance: the lower edge of the table must stay high enough for vegetation, snow build-up, flooding and maintenance access.
- Maximum leg length: longer legs raise the risk of bending and buckling under wind; they may need extra bracing.
- Front, middle and rear legs calculated separately: each leg's length depends on the ground level at that point, and the bill of materials and cutting list must reflect that.
- Grading vs stepping: small irregularities are handled with leg length; large level differences may be cheaper to solve with earthworks.
For the structural side, see our article on wind and snow loads. Any preliminary check of leg lengths, foundations and profile sections does not replace an approved structural design or calculations by a licensed engineer.
Common mistakes
- Calculating only with the noon sun angle and ignoring morning and afternoon shading
- Mistaking clock time for solar time
- Ignoring terrain slope, especially on north-facing slopes
- Treating h as the table's height above ground; in the formula, h is the height of the top edge above the bottom edge
- Confusing pitch with the gap between tables (d)
- Forgetting distant obstacles (hills, tree lines, buildings) and shading at the site boundary
Row spacing and ground-mount design with PVAGE
PVAGE's mounting structure design module uses real terrain elevation data and a slope map for ground-mounted plants. You place platform arrays, adjust row spacing and see inter-row shading in a simulation by choosing the month and hour. Heights and counts for front, middle and rear legs, profile quantities, and clamp and bolt counts are calculated.
On the structural calculation side, you get ground-mount leg and profile dimensions, foundation sizing and a preliminary check for buckling, bending, deflection and shear, exportable as a PDF. This check does not replace an approved structural design. For more on how shading affects production, read our shade analysis article.