# Wind Loading of Photovoltaic Panels Installed on Hip Roofs of Rectangular and L-Shaped Low-Rise Buildings

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## Abstract

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## 1. Introduction

_{panel}= 2 mm; the geometric scale, λ

_{L}, of the model was 1/100. The clearance, H

_{panel}, between the panel’s underside and the roof surface was varied from 0.25 to 3 mm in the experiment. The results indicated that the net wind forces on the PV panel were not significantly affected by H

_{panel}. This feature may be related to the fact that the roof pitch was as high as 42°. Aly and Bitsuamlak [15] experimentally investigated the wind forces on PV panels mounted parallel to gable roofs of residential houses; the roof pitches were 14° and 22.6°, and the geometric scale of the wind tunnel models was 1/15. Three sizes of PV panels (small, medium and large) were tested. The value of H

_{panel}was fixed to about 0.15 m at full scale. It was found that the wind load on individual panels was strongly dependent not only on the roof pitch, β, but also on the location and dimensions of the panel. Aly and Bitsuamlak recommended avoiding mounting PV panels near roof edges because large up-lift forces would be generated on the panels. Stenabough et al. [16] carried out a wind tunnel experiment to measure wind forces on PV panels mounted parallel to the gable roof (β = 30°) of a low-rise building. The full-scale dimensions of the tested panels were 50 cm wide and 145.5 cm long. The geometric scale of the wind tunnel models was 1/20, and the thickness, t

_{panel}, was 3 mm (6 cm at full scale). The researchers focused on the effects of the horizontal gap width, G, between PV panels and the clearance, H

_{panel}, on the net wind loads of PV panels. The values of G and H

_{panel}were varied from 0 to 12 cm and from 0 to 20 cm at full scale, respectively. It was found that the net wind loads on PV panels decreased with an increase in G and/or with a decrease in H

_{panel}. Such a wind load reduction is thought to be due to pressure equalization. Leitch et al. [17] measured the net wind forces on PV panels mounted parallel to gable roofs (β = 7.5°, 15°, 22.5°) of domestic buildings and the wind pressures on the underlying roof surface in a wind tunnel. The geometric scale of the wind tunnel models was 1/20. An array consisting of seven panels (1.0 m wide and 7.0 m long at full scale) was arranged at one of two positions on the roof. The thickness, t

_{panel}, was 6 mm (120 mm at full scale), and the clearance, H

_{panel}, was either 5 mm or 10 mm (100 mm or 200 mm at full scale). The aerodynamic shape factors for different array positions and roof pitches were provided. An interesting finding is that the maximum and minimum peak pressures on the roof were close to those on the bottom surface of the panel. Naeiji et al. [18] investigated the net wind forces of PV panels mounted on flat, gable and hip roofs. They used large models with a geometric scale of 1/6 in a large wind tunnel at Florida International University. The PV panel was 2 m in length, 1 m in width and 0.15 m in thickness at full scale. The effects of building height, H, panel clearance, H

_{panel}, and panel tilt angle, β

_{panel}, on the panel wind loads were investigated. It should be mentioned that the angle, β

_{panel}, did not necessarily coincide with the roof pitch, β. The clearance, H

_{panel}, tested was 0.3 m or 0.45 m at full scale, which was much larger than practical values. Takamori et al. [19] measured the wind forces on PV panels mounted parallel to gable roofs of low-rise buildings using 1/30 scale models. The thickness, t

_{panel}, was 3 mm (90 mm at full scale). The panels were installed with no horizontal gap (i.e., G = 0 mm). The clearance, H

_{panel}, and the roof pitch, β, were varied from 30 mm to 150 mm at full scale and from 10° to 40°, respectively. The wind pressure on the PV panels’ bottom surface was replaced by that on the underlying roof surface. This method is thought to be reasonable, judging from the above-mentioned findings of Leitch et al. [17]. The specifications of wind loads in JIS C 8955 [1] are mainly based on a study by Takamori et al.

_{panel}and H

_{panel}are both as small as several centimeters (see Figure 1). Furthermore, to accurately obtain the net wind pressures on PV panels, it is necessary to install pressure taps on both the top and bottom surfaces of the model. Generally speaking, making wind tunnel models of PV panels with the same geometric scale as that for buildings (e.g., 1/100) is quite difficult. Therefore, it is necessary to use deformed models of PV panels in wind tunnel experiments [19], which may significantly affect the wind pressure distributions on the PV panels. Thus, we proposed a numerical simulation using the unsteady Bernoulli equation to estimate the pressure in the space between PV panels and the roof, which is called ‘layer pressure’ [22,23]. In the numerical simulation, we used the time histories of external pressure coefficients on the roof without PV panels (bare roof), which had been obtained from a wind tunnel experiment. It was confirmed that this simulation method could be used effectively to estimate the wind loads on PV panels, provided that t

_{panel}and H

_{panel}were both as small as several centimeters. Therefore, we applied this simulation method to the wind load estimation of PV panels mounted on hip roofs of residential houses with rectangular and L-shaped plans, which are widely used in Japan. The roof pitch was fixed to 25° as a representative value for residential houses. PV panels installed in the edge zones were also considered. We propose to install PV panels with small gaps between them along the short sides. It is expected that the pressure equalization caused by the gaps will significantly reduce the net wind loads on PV panels, as well as on the wind pressures on the roof. This study contributes to the rational wind resistant design of PV systems installed on hip roofs, including edge zones, of low-rise buildings as well as to the reduction in wind-induced damage to roofing.

## 2. Wind Tunnel Experiment

#### 2.1. Investigated Buildings and Wind Tunnel Models

_{L}was 1/100 (see Figure 3). Figure 4 shows the pressure tap arrangements on the roofs. Considering the symmetry of the model, the pressure taps were arranged on Roofs A and B for Building 1 and on Roofs A–C for Building 2. The number of pressure taps was 120 for Building 1 and 176 for Building 2. The diameter of pressure taps was 0.6 mm. The pressure taps were connected to pressure transducers (Wind Engineering Institute, MAPS-02) via flexible vinyl tubes of 1 m length and 1 mm ID.

#### 2.2. Wind Tunnel Flow

_{ref}, and the integral scale, L

_{x}, of turbulence at a reference height of z

_{ref}= 10 cm (10 m at full scale, which is nearly equal to the height of the rooftop of the buildings) were about 0.17 and 0.2 m, respectively. Comparing these values of α, I

_{ref}and L

_{x}with the specified values in the AIJ Recommendations for Loads on Buildings [24] (referred to as ‘AIJ-RLB’, hereafter) for suburban exposure (Terrain Category III), we found that α is larger, whereas I

_{ref}and L

_{x}were smaller. In particular, the value of L

_{x}was much smaller than the target. The similarity of the wind tunnel flow with natural winds was discussed in our previous paper [23]. Regarding the integral scale of turbulence, the wind tunnel flow satisfied the criteria specified by Tieleman et al. [25,26,27] for wind tunnel flow. It was concluded that the wind tunnel flow was acceptable for the purpose of the present study. The blockage ratio, Br, defined as the ratio of the model’s vertical cross section to the wind tunnel’s cross section (1.4 m $\times $ 1.0 m), was about 2%, at most. The mean wind speed, U

_{H}, at the mean roof height, H (=9.45 cm), was about 8.5 m/s. The Reynolds number, Re, defined in terms of U

_{H}and H, was about 5.4 × 10

^{4}. The values of Br and Re satisfied the conditions specified by the ASCE Wind Tunnel Testing for Buildings and Other Structures [28], i.e., Br < 5% and Re > 1.1 × 10

^{4}. The wind direction, θ, defined as shown in Figure 5, was varied at an increment of 5°. The range of θ depends on the roof, considering the symmetry of the building, for example, from 0° to 180° for Roof A of Building 1 and from 0° to 355° for all roofs of Building 2. The pressure coefficient distributions on the whole roof area at various wind directions can be obtained from the measured distributions on the half area of the roof (hatched areas in Figure 5a,b).

#### 2.3. Wind Pressure Measurement

_{H}, at the mean roof height, H, was 27.8 m/s, which was determined based on the AIJ-RLB, with an assumption that the ‘basic wind speed’, U

_{0}was 35 m/s and the terrain category was III. The mean wind speed, U

_{H}, was set to 8.5 m/s in the wind tunnel experiment, as mentioned above. Therefore, the velocity scale, λ

_{V}, of the wind tunnel flow was 1/3.27. Consequently, the time scale, λ

_{T}, was calculated as 1/30.6. The sampling frequency and period of pressure measurements were 800 Hz and 19.6 s (26 Hz and 600 s at full scale), respectively. A low-pass filter with a cut-off frequency of 300 Hz was used to eliminate high-frequency noise included in the output of pressure transducers. The measurements were carried out 10 times.

#### 2.4. Wind Pressure Distribution on the Roof

_{b}and R

_{c}, however, the present results are somewhat larger in magnitude than the specified values. The difference may be attributed to the effect of roof’s overhang on the pressures. Note that the AIJ-RLB specification is based on the results for buildings with no overhangs.

## 3. Numerical Simulation of Layer Pressures under PV Panels

#### 3.1. Basic Concept and Assumptions

_{pe}, at the gaps were obtained from the above-mentioned wind tunnel experiment. The C

_{pe}value at the center of the gap between two PV panels was used as a representative value for the gap. However, the C

_{pe}values at these points were not directly obtained from the wind tunnel experiment because the location of pressure taps on the wind tunnel model did not coincide with that of these points. Hence, a spatial interpolation using the cubic spline function was employed. Furthermore, because the time step used in the numerical simulation of layer pressures was much smaller than the sampling interval of pressure measurements in the wind tunnel experiment, a temporal interpolation using the cubic spline function was employed. The shape resistance coefficient, C

_{L}, for the cavity flows in the x and y directions and the pressure loss coefficient (shape resistance coefficient), C

_{Le}, for the gap flows in the z direction depend on the cavity and gap configurations. However, they were assumed to be 1.0 for simplicity [23]. This assumption should be validated by a test with full-scale specimens of cavity and gap, as was done in our previous study [38]. This is a subject left for our future study.

#### 3.2. Practical Application

_{panel}, and the clearance, H

_{panel}, were 30 mm and 70 mm, respectively. The space under the PV panels was divided into many small rooms of 990 mm × 294 mm in plane, as shown in Figure 13, which made it possible to evaluate the spatial variation of layer pressure in the PV panels’ long-side direction.

_{panel}, is small. The bottom-surface pressure is equal to the layer pressure obtained from the numerical simulation. Therefore, the wind force coefficient (pressure difference coefficient) C

_{f}of the PV panel may be given by the following equation:

_{pl}represents ‘layer pressure coefficient’ defined in terms of q

_{H}. The net wind force, F, on a PV panel, called ‘panel force’ in this paper, is calculated by integrating the pressure difference over the panel area. F is normalized by q

_{H}and the area of the panel (A

_{panel}) to yield the panel force coefficient C

_{f}

_{,panel}.

#### 3.3. Wind Force Ccoeffcients of PV Panels

_{a}, of PV panels mounted parallel to sloped roofs as a function of roof pitch, β (deg). The negative wind force coefficients for regular rectangular modules (panels) and triangular end modules on a hip roof (see Figure 17) are specified as follows:

_{f}. The value of G

_{f}depends on the terrain of the construction site. For terrain category III (suburban exposure), G

_{f}is specified as 2.5. As mentioned above, the wind force coefficients are not specified for PV panels placed in the edge zones up to 0.3 m from the roof edges because such panels may be subjected to large up-lift forces, and therefore, installing PV panels in the edge zones is not recommended. In a strict sense, we cannot make a direct comparison between the present results for PV panels installed along the edges and the specified values in JIS C 8955. However, it seems interesting to compare these two values with each other. The minimum peak panel force coefficient, ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$, obtained in this study should be compared with the product of ${C}_{a}$ and ${G}_{f}$, which is −2.8 for regular modules and −3.7 for end modules. The values of ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$ for small panels, such as Panel 1 on Roof A, can be compared with −3.7 for the end modules, whereas those for the other panels can be compared with −2.8 for the regular modules. Figure 15 and Figure 16 indicate that the values of ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$ are generally smaller in magnitude than the specified values in JIS C 8955 [1].

#### 3.4. Wind Pressure Coeffcients on the Roof

#### 3.5. Effect of Gap Width on the Wind Loads on PV Panels

## 4. Concluding Remarks

_{panel}, between PV panels and roof, it is difficult to make wind tunnel models of PV panels with the same geometric scale as that for buildings. Hence, we focused on a numerical simulation using the unsteady Bernoulli equation to estimate the layer pressures between PV panels and the roof. The simulation used the time histories of wind pressure coefficients on the roof without PV panels (bare roof), which had been obtained in a turbulent boundary layer. Furthermore, we proposed installing PV panels with small gaps between them along the short sides. It was expected that the gaps might produce pressure equalization, resulting in a significant reduction in the net wind forces on PV panels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- JIS C 8955:2017; Japanese Industrial Standard. Load Design Guide on Structures for Photovoltaic Array. Japanese Standards Association: Tokyo, Japan, 2017.
- Wood, G.S.; Denoon, R.; Kwok, K.C.S. Wind loads on industrial solar panel arrays and supporting roof structure. Wind. Struct.
**2001**, 4, 481–494. [Google Scholar] [CrossRef] - Kopp, G.A.; Farquhar, S.; Morrison, M.J. Aerodynamic mechanisms for wind loads on tilted, roof-mounted, solar arrays. J. Wind Eng. Ind. Aerodyn.
**2012**, 111, 40–52. [Google Scholar] [CrossRef] - Kopp, G.A.; Banks, D. Use of the wind tunnel test method for obtaining design wind loads on roof-mounted solar arrays. J. Struct. Eng.
**2013**, 139, 284–287. [Google Scholar] [CrossRef] - Banks, D. The role of corner vortices in dictating peak wind loads on tilted flat solar panels mounted on large, flat roofs. J. Wind. Eng. Ind. Aerodyn.
**2013**, 123, 192–201. [Google Scholar] [CrossRef] - Browne, M.T.L.; Gibbons, M.P.M.; Gamble, S.; Galsworthy, J. Wind loading on tilted roof-top solar arrays: The parapet effect. J. Wind. Eng. Ind. Aerodyn.
**2013**, 123, 202–213. [Google Scholar] [CrossRef] - Cao, J.; Yoshida, A.; Saha, P.K.; Tamura, Y. Wind loading characteristics of solar arrays mounted on flat roofs. J. Wind. Eng. Ind. Aerodyn.
**2013**, 123, 214–225. [Google Scholar] [CrossRef] - Kopp, G.A. Wind loads on low-profile, tilted, solar arrays placed on large, flat, low-rise building roofs. J. Struct. Eng.
**2014**, 140, 04013057. [Google Scholar] [CrossRef] - Stathopoulos, T.; Zisis, I.; Xypnitou, E. Local and overall wind pressure and force coefficients for solar panels. J. Wind. Eng. Ind. Aerodyn.
**2014**, 125, 195–206. [Google Scholar] [CrossRef] - Wang, J.; Yang, Q.; Tamura, Y. Effects of building parameters on wind loads on flat-roof-mounted solar arrays. J. Wind. Eng. Ind. Aerodyn.
**2018**, 174, 210–224. [Google Scholar] [CrossRef] - Wang, J.; Phuc, P.V.; Yang, Q.; Tamura, Y. LES study of wind pressure and flow characteristics of flat-roof-mounted solar arrays. J. Wind. Eng. Ind. Aerodyn.
**2020**, 198, 104096. [Google Scholar] [CrossRef] - Wang, J.; Yang, Q.; Phuc, P.V.; Tamura, Y. Characteristics of conical vortices and their effects on wind pressures on flat-roof-mounted solar arrays by LES. J. Wind. Eng. Ind. Aerodyn.
**2020**, 200, 104146. [Google Scholar] [CrossRef] - Alrawashdeh, H.; Stathopoulos, T. Wind loads on solar panels mounted on flat roofs: Effect of geometric scale. J. Wind. Eng. Ind. Aerodyn.
**2020**, 206, 104339. [Google Scholar] [CrossRef] - Geurts, C.; Blackmore, P. Wind loads on stand-off photovoltaic systems on pitched roof. J. Wind. Eng. Ind. Aerodyn.
**2013**, 123, 239–249. [Google Scholar] [CrossRef] - Aly, A.M.; Bitsuamlak, G.T. Wind-induced pressures on solar panels mounted on residential homes. J. Archit. Eng.
**2014**, 20, 04013003. [Google Scholar] [CrossRef] - Stenabaugh, S.E.; Iida, Y.; Kopp, G.A.; Karava, P. Wind loads on photovoltaic arrays mounted parallel to sloped roofs on low-rise buildings. J. Wind. Eng. Ind. Aerodyn.
**2015**, 139, 16–26. [Google Scholar] [CrossRef] - Leitch, C.J.; Ginger, J.D.; Holmes, D.J. Wind loads on solar panels mounted parallel to pitched roofs, and acting on the underlying roof. Wind. Struct.
**2016**, 22, 307–328. [Google Scholar] [CrossRef] - Naeiji, A.; Raji, F.; Zisis, I. Wind loads on residential scale rooftop photovoltaic panels. J. Wind. Eng. Ind. Aerodyn.
**2017**, 168, 228–246. [Google Scholar] [CrossRef] - Takamori, K.; Nakagawa, N.; Yamamoto, M.; Okuda, Y.; Taniguchi, T.; Nakamura, O. Study on design wind force coefficients for photovoltaic modules installed on low-rise building. AIJ J. Technol. Des.
**2015**, 21, 67–70. (In Japanese) [Google Scholar] [CrossRef] [Green Version] - Agarwall, A.; Irtaza, H.; Shahab, K. 2020, Aerodynamic wind pressure on solar PV arrays mounted on industrial pitched roof building. In Proceedings of the International Conference on Recent Advances in Engineering & Science (ICRAES-2020), Aligarh, India, 4–6 September 2020. [Google Scholar]
- Li, J.; Tong, L.; Wu, J.; Pan, Y. Numerical investigation of wind influences on photovoltaic arrays mounted on roof. Eng. Appl. Comput. Fluid Mech.
**2019**, 13, 905–922. [Google Scholar] [CrossRef] [Green Version] - Uematsu, Y.; Yambe, T.; Watanabe, T.; Ikeda, H. The Benefit of horizontal photovoltaic panels in reducing wind loads on a membrane roofing system on a flat roof. Wind
**2021**, 1, 44–62. [Google Scholar] [CrossRef] - Uematsu, Y.; Yambe, T.; Yamamoto, A. Application of a numerical simulation to the estimation of wind loads on photovoltaic panels installed parallel to hip roofs of residential houses. Wind
**2022**, 2, 129–149. [Google Scholar] [CrossRef] - Architectural Institute of Japan. Recommendations for Loads on Buildings; Architectural Institute of Japan: Tokyo, Japan, 2015. [Google Scholar]
- Tieleman, H.W.; Reinhold, T.A.; Marshall, R.D. On the wind-tunnel simulation of the atmospheric surface layer for the study of wind loads on low-rise buildings. J. Wind. Eng. Ind. Aerodyn.
**1978**, 3, 21–38. [Google Scholar] [CrossRef] - Tieleman, H.W. Pressures on surface-mounted prisms: The effects of incident turbulence. J. Wind. Eng. Ind. Aerodyn.
**1993**, 49, 289–299. [Google Scholar] [CrossRef] - Tieleman, H.W.; Hajj, M.R.; Reinhold, T.A. Wind tunnel simulation requirements to assess wind loads on low-rise buildings. J. Wind. Eng. Ind. Aerodyn.
**1998**, 74–76, 675–686. [Google Scholar] [CrossRef] - ASCE/SEI 49-12; Wind Tunnel Testing for Buildings and Other Structures. American Society of Civil Engineers: Reston, VA, USA, 2012.
- Meecham, D.; Surry, D.; Davenport, A.G. The magnitude and distribution of wind-induced pressures on hip and gable roofs. J. Wind. Eng. Ind. Aerodyn.
**1991**, 38, 257–272. [Google Scholar] [CrossRef] - Xu, Y.L.; Reardon, G.F. Variation of wind pressure on hip roofs with roof pitch. J. Wind. Eng. Ind. Aerodyn.
**1998**, 73, 267–284. [Google Scholar] [CrossRef] - Ahmad, S.; Kumar, K. Effect of geometry on wind pressures on low-rise hip roof buildings. J. Wind. Eng. Ind. Aerodyn.
**2002**, 90, 755–779. [Google Scholar] [CrossRef] - Ahmad, S.; Kumar, K. Wind pressures on low-rise hip roof buildings. Wind Struct.
**2002**, 5, 493–514. [Google Scholar] [CrossRef] - Takamori, K.; Nishimura, H.; Asami, R.; Somekawa, D.; Aihara, T. Wind pressures on hip roofs of a low-rise building—Case of square plan. In Proceedings of the National Symposium on Wind Engineering, Tokyo, Japan, 3–5 December 2008; pp. 409–414. (In Japanese). [Google Scholar]
- Aihara, T.; Asami, Y.; Nishimura, H.; Takamori, K.; Asami, R.; Somekawa, D. An area correct factor for the wind pressure coefficient for cladding of hip roof—The case of square plan hip roof with roof pitch of 20 degrees. In Proceedings of the National Symposium on Wind Engineering, Tokyo, Japan, 3–5 December 2008; pp. 463–466. (In Japanese). [Google Scholar]
- Terazaki, H.; Katsumura, A.; Uematsu, Y.; Ohtake, K.; Okuda, Y.; Kikuchi, H.; Noda, H.; Masuyama, Y.; Yamamoto, M.; Yoshida, A. Wind force coefficient and gust loading factor for roof and eave. Wind Eng.
**2011**, 36, 343–361. (In Japanese) [Google Scholar] - Shao, S.; Tian, Y.; Yang, Q.; Stathopoulos, T. Wind-induced cladding and structural loads on low-rise buildings with 4:12-splped hip roofs. J. Wind. Eng. Ind. Aerodyn.
**2019**, 193, 103948. [Google Scholar] [CrossRef] - Shao, S.; Stathopoulos, T.; Yang, Q.; Tian, Y. Wind pressures on 4:12-sloped hip roofs of L- and T-shaped low-rise buildings. J. Struct. Eng.
**2018**, 144, 04018088. [Google Scholar] [CrossRef] - Yambe, T.; Uematsu, Y.; Sato, K. Wind Loads on Roofing System and Photovoltaic System Installed Parallel to Flat Roof. In STR-39. In Proceedings of the International Structural Engineering and Construction Holistic Overview of Structural Design and Construction, Limassol, Cyprus, 3–8 August 2020; Vacanas, Y., Danezis, C., Singh, A., Yazdani, S., Eds.; ISEC Press: Fargo, ND, USA, 2020. [Google Scholar]

**Figure 6.**Contours of the minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe}$, on the roof of Building 1: (

**a**) θ = 0°; (

**b**) θ = 45°; (

**c**) θ = 90°.

**Figure 7.**Contours of the most critical minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe,\mathrm{cr}}$, irrespective of wind direction, on the roof of Building 1.

**Figure 8.**Comparison of the experimental values of ${\widehat{C}}_{pe,\mathrm{cr}}$ and ${\stackrel{\u02c7}{C}}_{pe,\mathrm{cr}}$ with the positive and negative peak pressure coefficients specified in the AIJ-RLB: (

**a**) Definition of zones; (

**b**) Peak pressure coefficients compared with the specifications.

**Figure 9.**Contours of the minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe}$, on the roof of Building 2: (

**a**) θ = 0°; (

**b**) θ = 45°; (

**c**) θ = 90°; (

**d**) θ = 135°; (

**e**) θ = 315°.

**Figure 10.**Contours of the most critical minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe,\mathrm{cr}}$, irrespective of wind direction, on the roof of Building 2.

**Figure 11.**Model of the space under PV panels (conceptual illustration): (

**a**) perspective; (

**b**) x−y plane; (

**c**) x−z plane.

**Figure 14.**Minimum peak panel force coefficients, ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$, on Roof A of Building 1 at θ = 0°, 45° and 90°.

**Figure 15.**The minimum value of ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$ among all panels on each roof of Building 1.

**Figure 16.**The minimum value of ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$ among all panels on each roof of Building 2.

**Figure 17.**PV panels installed on a hip roof as defined in JIS C 8955 [1].

**Figure 18.**Minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe}$, on Roof A of Building 1 at the panels’ centers: (

**a**) θ = 0°; (

**b**) θ = 45°; (

**c**) θ = 90°.

**Figure 19.**Minimum peak pressure coefficients, ${\stackrel{\u02c7}{C}}_{pe}$, on Roof B of Building 1 at the panels’ centers: (

**a**) θ = 0°; (

**b**) θ = 45°; (

**c**) θ = 90°.

**Figure 20.**Effect of gap width, G, on the minimum peak panel force coefficients, ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$, on Roof B of Building 1 at θ = 90°.

**Figure 21.**Effect of gap width, G, on the minimum peak panel force coefficients, ${\stackrel{\u02c7}{C}}_{f,\mathrm{panel}}$, on Roof B of Building 2 at θ = 90°.

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**MDPI and ACS Style**

Uematsu, Y.; Yambe, T.; Yamamoto, A.
Wind Loading of Photovoltaic Panels Installed on Hip Roofs of Rectangular and L-Shaped Low-Rise Buildings. *Wind* **2022**, *2*, 288-304.
https://doi.org/10.3390/wind2020016

**AMA Style**

Uematsu Y, Yambe T, Yamamoto A.
Wind Loading of Photovoltaic Panels Installed on Hip Roofs of Rectangular and L-Shaped Low-Rise Buildings. *Wind*. 2022; 2(2):288-304.
https://doi.org/10.3390/wind2020016

**Chicago/Turabian Style**

Uematsu, Yasushi, Tetsuo Yambe, and Atsushi Yamamoto.
2022. "Wind Loading of Photovoltaic Panels Installed on Hip Roofs of Rectangular and L-Shaped Low-Rise Buildings" *Wind* 2, no. 2: 288-304.
https://doi.org/10.3390/wind2020016