The global shift towards renewable energy has placed solar photovoltaic (PV) technology at the forefront of sustainable power generation. As the deployment of large-scale solar farms accelerates, the structural integrity and longevity of the supporting infrastructure become paramount. Among the various environmental loads, wind action is often the dominant and most critical force governing the design of solar panel arrays and their support structures. An overly conservative design can lead to excessive material use and cost, while an underestimation can compromise safety and lead to structural failure. Therefore, a precise understanding of the wind pressure distribution and the associated aerodynamic shape coefficients on solar panels, especially when arranged in multi-row arrays, is essential for economical, safe, and reliable design.
This analysis focuses on a crucial operational scenario for tracking solar panel systems: the stow or flattening position. During high-wind events or at night, solar panels are often rotated to a near-horizontal position to minimize the projected area and thus the wind load. However, the question of the optimal angle for this flattened position—the angle that minimizes the net wind force or shape coefficient—requires detailed investigation. Furthermore, in large installations, solar panels are deployed in arrays where rows interact aerodynamically, leading to sheltering or blocking effects that significantly alter the wind load on downstream rows. This study employs Computational Fluid Dynamics (CFD) to numerically simulate wind flow around a multi-row array of solar panels at small inclination angles to determine the optimal flattening angle and to quantify the inter-row sheltering effects.
1. Numerical Methodology and Model Setup
To accurately capture the flow physics, a three-dimensional numerical model was developed based on a common engineering configuration for ground-mounted solar panel arrays.
1.1 Physical Geometry and Computational Domain
The array consists of 8 rows of solar panels, subdivided into two groups of 4 rows each. Each row contains 7 individual solar panel modules. The key geometric parameters are summarized below:
| Parameter | Value | Unit |
|---|---|---|
| Single Panel Length | 1.650 | m |
| Single Panel Width | 0.992 | m |
| Panel Thickness | 0.032 | m |
| Gap between Panels in a Row | 0.015 | m |
| Row Spacing (within a group) | 4.5 | m |
| Group Spacing (between row 4 & 5) | 8.0 | m |
| Panel Center Height above Ground | 1.2 | m |
The computational fluid domain was sized to minimize boundary interference, extending 90m in the streamwise (x) direction, 10m in the spanwise (y) direction, and 12m in the vertical (z) direction. The solar panels were modeled as smooth, no-slip walls.
1.2 Governing Equations and Turbulence Modeling
The wind flow is governed by the fundamental principles of fluid mechanics, expressed through the Reynolds-Averaged Navier-Stokes (RANS) equations for incompressible flow. The continuity and momentum equations are:
Continuity Equation:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{U}) = 0 $$
Since the flow is incompressible and air density ($\rho$) is constant, this simplifies to:
$$ \nabla \cdot \vec{U} = 0 $$
Momentum Equation:
$$ \frac{\partial (\rho \vec{U})}{\partial t} + \nabla \cdot (\rho \vec{U} \otimes \vec{U}) = -\nabla p + \nabla \cdot \tau + \vec{S_M} $$
where $\vec{U}$ is the velocity vector, $p$ is the pressure, $\vec{S_M}$ is a momentum source term, and $\tau$ is the stress tensor. For a Newtonian fluid, $\tau$ is related to the strain rate. The $k-\omega$ Shear Stress Transport (SST) turbulence model was employed for its good performance in predicting flows with adverse pressure gradients and separation, which are relevant for flows around inclined bluff bodies like solar panels.
1.3 Boundary Conditions and Simulation Cases
The boundary conditions were set to simulate an atmospheric boundary layer flow. The inlet was prescribed a velocity profile following a power law:
$$ V(z) = V_{ref} \cdot \left(\frac{z}{z_{ref}}\right)^{\alpha} $$
where $V_{ref}$ is the reference wind speed at height $z_{ref}$, and $\alpha$ is the ground roughness exponent (taken as 0.12 for open terrain). The outlet was set as a pressure outlet. The top and sides of the domain were set as symmetry planes, and the ground was a no-slip wall.
Two primary wind directions were analyzed: 0° (wind normal to the panel’s long side, creating positive pressure on the front/upper surface) and 180° (wind from the back, creating negative pressure/suction on the upper surface). Four panel inclination angles ($\beta$) were studied: 0°, 5°, 10° (for high-wind stow conditions at 33 m/s) and 45° (for normal operation at 18 m/s).
1.4 Data Reduction: Pressure, Shape Coefficient, and Reduction Factor
The surface pressure on the solar panels was extracted from the CFD solution. The mean pressure coefficient $C_{p,i}$ at a point *i* is defined as:
$$ C_{p,i} = \frac{P_i – P_\infty}{\frac{1}{2} \rho V_{ref}^2} $$
where $P_i$ is the static pressure at point *i*, $P_\infty$ is the reference static pressure far upstream, and $V_{ref}$ is the reference wind speed.
The shape coefficient ($C_f$), often used in structural codes, is essentially the area-averaged pressure coefficient. For low-height structures, it can be considered equal to the wind load shape coefficient. The net shape coefficient for a panel is the difference between the average coefficients on its upper and lower surfaces.
To quantify the sheltering effect between rows, a reduction factor ($R_j$) for row *j* is defined as the ratio of its net shape coefficient to that of the first row in its group:
$$ R_j = \frac{C_{f, net, j}}{C_{f, net, 1}} \quad \text{(for rows 2-4 and 6-8)} $$
A lower reduction factor indicates a greater sheltering effect from the upstream row.
2. Results and Analysis: Wind Load Characteristics
2.1 Mean Pressure Distribution
The analysis of mean pressure reveals clear trends based on wind angle and panel tilt. For a 0° wind angle (positive pressure on the windward face), the upper surfaces of the solar panels experience positive pressure, while the lower surfaces experience suction (negative pressure). The magnitude of this pressure increases with the inclination angle at a given wind speed; a 10° tilt induces higher pressure than a 5° or 0° tilt under the same 33 m/s wind. This is due to the increased frontal projected area and more pronounced flow separation at higher angles. The 45° tilt case under 18 m/s wind shows a comparable pressure magnitude to the 5° tilt at 33 m/s, highlighting the strong non-linear dependence on both angle and speed.
For a 180° wind angle (leeward/back pressure), the flow separates at the leading edge, creating a region of suction (negative pressure) on the upper surface of the solar panels. The lower surface, now facing the oncoming wind, experiences positive pressure. Similar to the positive pressure case, the magnitude of the net pressure difference is greatest for the 10° tilt and smallest for the 0° tilt.
A critical finding is that for both wind directions (0° and 180°), the smallest net pressure force on the solar panels among the small angles (0°, 5°, 10°) occurs at the 0° inclination. This identifies 0° as the optimal flattening angle from a pure wind load minimization perspective, as orienting the solar panels parallel to the wind direction presents the smallest effective cross-section.
2.2 Shape Coefficients and Optimal Flattening
Normalizing the pressure by the dynamic pressure yields the shape coefficient, which is independent of wind speed and thus more suitable for design code application. The table below summarizes the net shape coefficients for the first row under different conditions, illustrating the effect of tilt angle.
| Wind Angle | Panel Tilt ($\beta$) | Net Shape Coeff. ($C_{f,net}$) – Row 1 | Note |
|---|---|---|---|
| 0° (Positive) | 0° | ~0.35 | Minimum value |
| 0° (Positive) | 5° | ~0.75 | |
| 0° (Positive) | 10° | ~1.10 | |
| 0° (Positive) | 45° | ~1.50 | At 18 m/s |
| 180° (Leeward) | 0° | ~-0.40 | Minimum magnitude |
| 180° (Leeward) | 5° | ~-0.85 | |
| 180° (Leeward) | 10° | ~-1.20 | |
| 180° (Leeward) | 45° | ~-1.45 | At 18 m/s |
The data confirms that the shape coefficient magnitude increases monotonically with tilt angle for both wind directions. The agreement between the calculated values for 10° tilt and available experimental data from literature is reasonable, validating the numerical approach. The significant rise in the coefficient from 0° to 10° underscores the importance of precise flattening. For structural design, using a single conservative coefficient (e.g., 1.3 as in some codes) for all small angles is uneconomical. A more nuanced approach, where the shape coefficient for solar panels is taken as a function of the stow angle, is justified. For optimal flattening at 0°, a net coefficient of approximately $\pm$0.4 is suggested for design.
2.3 Multi-Row Sheltering Effect and Reduction Factors
The presence of multiple rows of solar panels creates complex wake interactions. The first row experiences the full, unperturbed wind flow. The second row lies within the turbulent wake of the first, resulting in a significantly reduced wind velocity and altered pressure distribution. This sheltering effect propagates downstream but diminishes as the flow gradually recovers. The group spacing (8m) acts as a reset, allowing the flow to partially re-energize before impacting the first row of the second group (Row 5).
The calculated reduction factors clearly illustrate this effect:
| Row Number | Group | Reduction Factor ($R$) – 10° Tilt, 0° Wind | Reduction Factor ($R$) – 45° Tilt, 0° Wind |
|---|---|---|---|
| 2 | 1 | 0.55 | 0.30 |
| 3 | 1 | 0.60 | 0.45 |
| 4 | 1 | 0.65 | 0.50 |
| 5 | 2 | 0.90 | 0.95 |
| 6 | 2 | 0.60 | 0.35 |
| 7 | 2 | 0.65 | 0.50 |
| 8 | 2 | 0.70 | 0.55 |
The key observations are:
- Maximum Shelter: The second row in each group (Rows 2 and 6) experiences the greatest shelter, with the smallest reduction factor. For the 45° tilt, the load on Row 2 can be as low as 30% of the load on Row 1.
- Effect of Tilt Angle: The sheltering effect is more pronounced at larger tilt angles (e.g., 45°) compared to smaller ones (e.g., 10°). The wakes behind more steeply inclined solar panels are larger and more persistent, providing greater protection to downstream rows.
- Effect of Spacing: The larger group spacing (8m) reduces the sheltering effect on Row 5, as seen by its higher reduction factor (~0.9) compared to the downstream rows within the group. This has direct implications for optimizing the layout of solar panel arrays to balance land use and structural loading.
This analysis provides crucial data for applying non-uniform wind loads in the structural design of solar panel array supports. Rather than applying the full first-row load to all rows, engineers can use these reduction factors to size purlins, rafters, and foundations more efficiently, leading to substantial material savings in large solar farms.
3. Implications for Design and Future Perspectives
The findings of this numerical study have direct and significant implications for the design and operation of solar power plants. For engineers, the primary takeaway is the quantitative evidence supporting an optimal stow strategy. Tracking systems should be programmed to orient the solar panels parallel to the forecasted high-wind direction (0° relative angle) to minimize the operational wind load. This simple adjustment can drastically reduce the cyclic stress on actuators and support structures, enhancing system longevity.
From a structural design perspective, the use of a single, conservative shape coefficient for all rows of solar panels is economically inefficient. The presented data supports the development of a more refined set of design guidelines. For example, a tiered approach for ground-mounted arrays could be:
- First Row (Unshielded): Use a shape coefficient based on the specific tilt angle (e.g., $C_f$ = 0.35 for 0°, 1.1 for 10° for positive wind).
- Second & Subsequent Rows (Shielded): Apply a reduction factor to the first-row coefficient. The factor depends on row position, tilt angle, and row spacing. For a 10° tilt and 4-5m spacing, a factor of 0.55-0.65 for rows 2-4 is appropriate.
Future research should expand on this work by investigating a wider range of wind incidence angles (not just 0° and 180°) to develop a complete load map for stowed solar panels. The effect of different array geometries, such as varying row spacing and ground clearance, also warrants detailed parametric studies. Furthermore, coupling these CFD-derived pressure fields with structural finite element models would enable a true fluid-structure interaction analysis, predicting not just loads but also dynamic responses and instabilities. Finally, experimental validation through wind tunnel tests on scaled multi-row models would further solidify the confidence in these numerical recommendations for the safe and cost-effective design of solar panel arrays.
4. Conclusion
This detailed numerical investigation into the wind loads on multi-row solar panel arrays, focusing on small inclination angles relevant for storm stow positions, yields several conclusive and actionable insights. The optimal flattening angle for minimizing wind load on a solar panel is unequivocally 0° relative to the wind direction, i.e., when the panel surface is parallel to the flow. At this orientation, both positive and leeward pressure loads are minimized. The wind pressure and corresponding aerodynamic shape coefficient increase monotonically with the tilt angle of the solar panels for a given wind speed.
Furthermore, the analysis quantifies the significant sheltering effect present in multi-row arrays. The first row of solar panels bears the brunt of the wind load. The immediate downstream row experiences the most substantial load reduction, often 40-70% less than the first row, depending on the tilt angle. This sheltering effect is more pronounced for larger tilt angles. The load recovers partially for rows positioned after a large gap, mimicking the start of a new array group.
These results strongly advocate for moving beyond uniform wind load assumptions in the design standards for solar panel support structures. Incorporating optimal stow angles and row-specific reduction factors can lead to more economical, material-efficient, and yet perfectly safe designs, contributing to the overall sustainability and financial viability of large-scale solar energy projects. The methodology and data presented serve as a foundation for refining engineering practices for the resilient deployment of solar panels across the globe.