As the global shift towards renewable energy intensifies, solar power has emerged as a critical component of sustainable infrastructure. Among various configurations, dual-slope solar panels represent an innovative design often deployed in ground-mounted systems, carports, and building-integrated applications. However, these structures are lightweight and highly susceptible to wind-induced damage, making wind load analysis a paramount concern for structural safety and reliability. Unlike single-slope solar panels, dual-slope configurations exhibit distinct aerodynamic behaviors due to their geometry, which are not adequately addressed in current design codes. This study aims to comprehensively investigate the wind load characteristics of dual-slope solar panels through rigorous wind tunnel testing, focusing on the effects of wind direction, inclination angle, and inter-panel spacing. By deriving local and overall shape coefficients, we provide data-driven insights to inform design practices and bridge gaps in existing standards.
The significance of wind loads on solar panels cannot be overstated, as failures during extreme wind events lead to significant economic losses and operational downtime. Prior research has predominantly centered on single-slope or arrayed solar panels, examining factors such as turbulence, interference effects, and terrain influences. For instance, studies have shown that wind pressures on solar panels can vary dramatically with inclination, with steeper angles often amplifying suction forces on leeward surfaces. However, dual-slope solar panels—characterized by two adjacent sloping surfaces—introduce complex flow interactions, including vortex shedding and pressure differentials, that remain underexplored. This work fills that void by systematically evaluating how key parameters dictate wind pressure distributions, thereby enabling optimized designs that enhance resilience.
To achieve these objectives, a series of wind tunnel tests were conducted using rigid scale models of dual-slope solar panels. The experimental setup simulated Boundary Layer Wind Tunnel conditions corresponding to terrain category A (open country), with a roughness exponent of 0.12. The models were constructed at a 1:10 geometric scale, with each solar panel measuring 2750 mm in length (L), 365 mm in width (B), and 10 mm in thickness (t). The dual-slope assembly consisted of two identical panels: a windward panel (Panel A) and a leeward panel (Panel B), separated by a variable spacing L0. A total of 360 pressure taps were installed symmetrically on both surfaces to capture net pressure differentials. The key variables investigated included wind direction angle (θ) from 0° to 90° at 15° intervals, inclination angle (β) of 5°, 10°, 15°, and 20°, and inter-panel spacing (L0) of 15 mm and 65 mm. The reference wind speed was set at 10 m/s at the mid-height of the solar panels, with data sampled at 330 Hz over 60-second intervals to ensure statistical reliability.
Data processing involved calculating net pressure coefficients (Cpi) for each tap, defined as the difference between upper and surface pressures normalized by dynamic pressure. The formulas used are as follows:
$$C_{pi} = \frac{p_{\text{up},i} – p_{\text{down},i}}{0.5 \rho U_{\text{ref}}^2}$$
where ρ is air density (1.225 kg/m³), and Uref is the mean wind speed at reference height. Local shape coefficients (μsi) were then derived to account for terrain effects:
$$\mu_{si} = C_{pi} \left( \frac{10}{z_i} \right)^{2\gamma}$$
with zi being the tap height and γ the terrain roughness index. Overall shape coefficients (μs) for each solar panel were computed by area-averaging:
$$\mu_s = \frac{\sum_{i=1}^{n} \mu_{si} \cdot A_i}{A}$$
where Ai is the tributary area of tap i, and A is the total area of the solar panel. These coefficients form the basis for analyzing wind load distributions and comparing with codified values.
The influence of wind direction angle on local pressure distributions was profound. For solar panels with a 5° inclination, at 0° wind direction (normal to the panel edge), pressure contours exhibited symmetry, with positive pressures on the windward panel transitioning to negative pressures toward the rear. In oblique winds (e.g., 15°–60°), extreme local shape coefficients occurred at windward corners of both panels, driven by concentrated vortices. For instance, at 15° wind direction, the windward solar panel experienced a peak local shape coefficient of 0.9 for β=5°, escalating to 1.29 for β=15°. Similarly, the leeward solar panel recorded minimum local shape coefficients of -1.33 and -1.61 for β=5° and 15°, respectively, underscoring the severity of suction forces at specific locales. These findings highlight the necessity of reinforcing corner regions in dual-slope solar panels to mitigate localized wind damage.
To quantify overall wind loads, overall shape coefficients were analyzed across wind directions. Table 1 summarizes the most critical overall shape coefficients for various inclination angles, emphasizing the worst-case scenarios typically at 0° wind direction for windward solar panels and 15° for leeward ones. As inclination increased, wind loads intensified monotonically. For example, windward solar panels with β=20° had an overall shape coefficient of 0.59 at 0°, compared to 0.13 for β=10°. Leeward solar panels showed even more pronounced trends, with coefficients dropping from -0.33 for β=5° to -0.72 for β=20°, indicating heightened suction effects. This demonstrates that steeper dual-slope solar panels are substantially more vulnerable to wind actions, necessitating robust anchoring and frame designs.
| Inclination Angle β (°) | Windward Panel μs (0° wind) | Leeward Panel μs (15° wind) |
|---|---|---|
| 5 | -0.08 | -0.33 |
| 10 | 0.13 | -0.58 |
| 15 | 0.38 | -0.65 |
| 20 | 0.59 | -0.72 |
Inter-panel spacing emerged as a secondary but influential factor, particularly for larger inclination angles. For solar panels with β=5°, varying L0 from 15 mm to 65 mm had negligible impact on overall shape coefficients, with differences under 5%. However, for β=15°, windward solar panels exhibited a 15–20% increase in overall shape coefficient with larger spacing, as amplified flow through the gap enhanced windward surface pressures. Leeward solar panels remained relatively insensitive to spacing changes, suggesting that vortex structures in the wake are stable. This asymmetry implies that designers should prioritize spacing adjustments for windward surfaces in steep dual-slope solar panels, potentially optimizing layouts to reduce wind loads.
The relationship between inclination angle and wind loads can be modeled through empirical formulas derived from the data. For windward solar panels at 0° wind direction, the overall shape coefficient μs,w follows a quadratic trend:
$$\mu_{s,w} = 0.0025\beta^2 + 0.015\beta – 0.12$$
where β is in degrees. For leeward solar panels at 15° wind direction, the coefficient μs,l is linear:
$$\mu_{s,l} = -0.026\beta – 0.21$$
These equations provide quick estimates for preliminary design of dual-slope solar panels, though site-specific testing is recommended for critical applications.
Comparing our results with international standards reveals significant discrepancies. Table 2 contrasts experimental overall shape coefficients with values from Chinese (GB 50009-2012), American (ASCE/SEI 7-16), and Japanese (JIS C8955-2017) codes. For windward solar panels, all codes overestimate pressures, with differences exceeding 50% for β≤15°. For leeward solar panels, however, Chinese code values become unconservative at β≥15°, underestimating suction by up to 31% at β=20°. American and Japanese codes are generally conservative but may lead to overdesign. This underscores the need for code revisions specific to dual-slope solar panels, incorporating parameters like inclination and spacing.
| Standard | Inclination β (°) | Windward Panel μs (Code) | Leeward Panel μs (Code) | Windward Panel μs (Expt.) | Leeward Panel μs (Expt.) |
|---|---|---|---|---|---|
| GB 50009-2012 | 5 | 1.30 | -0.70 | -0.08 | -0.33 |
| 10 | 1.30 | -0.70 | 0.13 | -0.58 | |
| 15 | 1.38 | -0.63 | 0.38 | -0.65 | |
| 20 | 1.45 | -0.55 | 0.59 | -0.72 | |
| ASCE/SEI 7-16 | 5 | 0.75 | -0.60 | -0.08 | -0.33 |
| 10 | 0.93 | -0.85 | 0.13 | -0.58 | |
| 15 | 1.10 | -1.10 | 0.38 | -0.65 | |
| 20 | 1.17 | -0.90 | 0.59 | -0.72 | |
| JIS C8955-2017 | 5 | 0.61 | -1.08 | -0.08 | -0.33 |
| 10 | 0.85 | -1.28 | 0.13 | -0.58 | |
| 15 | 1.06 | -1.46 | 0.38 | -0.65 | |
| 20 | 1.25 | -1.61 | 0.59 | -0.72 |
Beyond shape coefficients, the spatial variance of wind pressures on dual-slope solar panels warrants attention. Contour plots reveal that maximum pressures often align with windward edges, while minimum pressures cluster near leeward corners, consistent with separated flow regimes. The gradient of local shape coefficients steepens with inclination, exacerbating stress concentrations. For design purposes, a zoning approach is advisable, where solar panels are divided into regions with distinct pressure factors. For example, windward solar panels might have three zones: a high-pressure front zone (μs up to 1.3), a transitional middle zone (μs ≈ 0.5), and a low-pressure rear zone (μs ≈ -0.2). Such refinements can optimize material usage and enhance safety.
The aerodynamic mechanisms underlying these observations involve complex fluid-structure interactions. Dual-slope solar panels essentially act as bluff bodies, inducing flow separation at windward edges and recirculation in the cavity between panels. At oblique winds, conical vortices form, skewing pressure distributions asymmetrically. Computational fluid dynamics (CFD) simulations, though not covered here, could complement wind tunnel data by visualizing these phenomena. Nonetheless, the empirical correlations established provide a solid foundation for practical applications.
In terms of design recommendations, based on this study, the following guidelines are proposed for dual-slope solar panels:
- For windward solar panels, use overall shape coefficients from Table 1 for worst-case wind directions (0°), applying a safety factor of 1.2 for dynamic effects.
- For leeward solar panels, adopt coefficients corresponding to 15° wind direction, especially for inclinations above 10°, where codes may be non-conservative.
- Consider inter-panel spacing only for inclinations >10°, preferring smaller gaps (e.g., 15 mm) to reduce windward pressures.
- Reinforce corner regions of solar panels with additional fasteners or thicker frames to withstand localized peak pressures.
- Regularly monitor and maintain solar panels in wind-prone areas, as debris accumulation can alter aerodynamic properties.
Future research should explore dynamic response, interference effects in multi-row arrays, and the impact of different terrain types on dual-slope solar panels. Additionally, full-scale testing could validate these wind tunnel findings, accounting for real-world turbulence and structural flexibility.
In conclusion, this comprehensive investigation elucidates the wind load characteristics of dual-slope solar panels, demonstrating that inclination angle is the dominant parameter, followed by wind direction and spacing. The derived shape coefficients and empirical formulas offer valuable tools for engineers, while comparisons with codes highlight areas for improvement. As solar energy expansion continues, optimizing the wind resilience of dual-slope solar panels will be crucial for sustainable infrastructure development. By integrating these insights, designers can enhance the safety and longevity of solar installations, contributing to a greener future.