WO2010063018A2

WO2010063018A2 - Wind uplift resistant module mounting system

Info

Publication number: WO2010063018A2
Application number: PCT/US2009/066030
Authority: WO
Inventors: Robert Stancel; Martin R. Roscheisen
Original assignee: Robert Stancel; Roscheisen Martin R
Priority date: 2008-11-26
Filing date: 2009-11-27
Publication date: 2010-06-03
Also published as: WO2010063018A3; US20100218441A1

Abstract

Methods and devices are provided for improved rooftop solar module mounting assemblies. In one embodiment, an assembly is provided for mounting a plurality of photovoltaic devices over a roof surface. The assembly comprises of a plurality of elongate metal rods, wherein the elongate metal rods are connected together to define a support grid; a plurality of non-roof penetrating grid supports configured to elevate the support grid above the roof surface, wherein the panels are grouped to define a rigid combination of modules and beams wherein the combination covers sufficient area and has sufficient rigidity which minimizes the risk of module lift off. Some embodiments are non-ballasted systems without features added to increase the weight of the system above a minimum required for conventional wind load ballasting for solar installations.

Description

WIND UPLIFT RESISTANT MODULE MOUNTING SYSTEM

FIELD OF THE INVENTION

[0001] This invention relates generally to photovoltaic devices, and more specifically, to wind resistant mounting systems for photovoltaic devices or modules.

BACKGROUND OF THE INVENTION

[0002] Solar cells and solar cell modules convert sunlight into electricity. These devices are traditionally mounted outdoors on rooftops or in wide-open spaces where they can maximize their exposure to sunlight. Rooftop mountings are of particular interest in urban settings where open space is limited for traditional ground-mounted installations. Rooftops provide much of the sunlight receiving surfaces in such urban settings and low cost module mountings for such rooftops would drastically increase the number of installations that can be made in such environments.

[0003] A central challenge for providing low cost solar modules arrays for roof ops, in particular flat rooftops, lies in part on not only in reduced material costs for the solar panels themselves, but also reduced installation costs. One aspect may involve using simplified mounting techniques and minimizing the number of roof surface penetrations. Lift-off of solar modules from the roof is possible due to wind, and hence weight or locking down/connecting the modules to the roof is desired. As seen in Figure 1, traditional roof mounts includes roughly one mount 10 per module 12. This creates numerous moisture entry points when such mounts are secured to the rooftop. Each of these entry points needs to be properly sealed to maintain the integrity of the roof and prevent moisture penetration through the roof. The large number of penetrations associated with conventional rooftop mountings creates additional points of failure for the roof and increases the installation time to secure each of the mounts to the roof and seal any and all roof penetrations.

[0004] If given the option, many consumers would generally prefer not to have or at least minimize the number roof penetrations to lock down panels, due to the risk of leaks etc. Therefore, ballasted or weighted systems are common to keep panels from lifting off from the roof. This has the disadvantage of these heavier ballasted systems is that the increased load on the roof may be too high for the structural design of roof, requiring reinforcement, seismic retrofits, ballast material, or simply not mounting on such roofs. Although such a system may reduce the number of roof penetrations, it does so at the cost of additional structural reinforcements that add to final bottomline costs of the installation.

[0005] Due to the aforementioned issues, improved rooftop mounting schemes are desired for solar cell modules, and/or similar photovoltaic devices.

SUMMARY OF THE INVENTION

[0006] Embodiments of the present invention address at least some of the drawbacks set forth above. The present invention provides for the simplified installation of solar modules generally, and glass-glass and/or glass-foil solar modules on an existing rooftop. The modules may be framed or frameless, but the embodiments herein are not limited to any particular solar module configuration. It should be understood that at least some embodiments of the present invention may be applicable to any type of solar cell, whether they are rigid or flexible in nature, flat or rod- shaped, or the type of material used in the absorber layer. Embodiments of the present invention may be adaptable for flexible, semi-rigid, or fully rigid solar modules. At least some of these and other objectives described herein will be met by various embodiments of the present invention.

[0007] In one embodiment of the present invention, an assembly is provided for mounting a plurality of photovoltaic modules over an installation surface. The assembly comprises of a plurality of non-roof penetrating grid supports configured to elevate a support grid above the installation surface.

[0008] In yet another embodiment of the present invention, an assembly is provided for mounting a plurality of photovoltaic modules over an installation surface. The assembly comprises a rigidly interconnected array of PV modules laid up on top of a roof without penetration into the roof where the array is large enough in horizontal area for weight of the array to be high enough to resist wind uplift based only on area and weight of the array, without additional ballast and without any roofing penetration

[0009] It should be understood that any of the embodiment herein may be adapted to include one or more of the following features. In one embodiment, the assembly has module weight is at least 16 kg/ m2, with a minimum area of 25 square meters and a minimum lowest dimension of 5 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2. Optionally, these sizes are sufficient for those rooftops with parapets. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array height. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array grid. Optionally, module weight to module area is at least 16 kg/ m2, with a minimum area of 36 square meters and a minimum lowest dimension of 6 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2. Optionally, the assembly is characterized by an area that is at least 16 kg/ m2, with a minimum area of 36 square meters and a minimum lowest dimension of 6 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2. Optionally, the module weight to area is at least about 50% of the weight of the entire array. Optionally, the module weight to area is at least about 40% of the weight of the entire array. Optionally, the minimum horizontal area is at least 5m x 5m. Optionally, the minimum horizontal area is at least 6m x 6m. Optionally, the minimum weight of the modules is at least 14kg/m2. Optionally, the array has a configuration that resists wind uplift at lateral winds of up to 85 mph. Optionally, the array has a configuration that resists wind uplift at lateral winds of up to 100 mph. Optionally, the array comprises of the PV modules, a support grid beneath the PV modules, and non-roof penetrating grid supports for lifting the support grid above the roof. Optionally, the modules are mounted over junction points of elongate elements in the grid to provide rigidity to the grid by rigidly coupling the module over the grid to use the module as a stiffening member. Optionally, the array includes angled flaps that minimize wind flow to the underside of the modules. Optionally, a downward pressure is created in about a center 70% area of the array. Optionally, a downward pressure is created in about a center 60% area of the array. Optionally, overall maximum edge deflection during wind load is less than about 10 degrees from horizontal. Optionally, overall maximum edge deflection during wind load is less than about 5 degrees from horizontal.

[0010] In yet another embodiment of the present invention, an assembly is provided for mounting a plurality of photovoltaic modules over an installation surface, the assembly comprises a rigidly interconnected array of PV modules laid up on top of a roof without penetration into the roof where the array has a horizontal area of at least 25 square meters with a minimum of 5 meters in both the x and y axis, and weight of the array to be at least 3.31bs/ft2 to resist wind uplift based only on area and weight of the array, without additional ballast and without any roofing penetration, total weight not to exceed 6.6 Ibs/ft2.

[0011] In yet another embodiment of the present invention, an assembly is provided for mounting a plurality of photovoltaic modules over an installation surface. The assembly comprises a support grid defined by a plurality of elongate members; a plurality of non-roof penetrating grid supports configured to elevate the support grid above the installation surface; wherein the support grid when coupled to the photovoltaic modules, creates a stiffly interconnected block of PV modules in a non-bending geometry in winds of up to 80mph that prevents wind up lift.

[0012] In yet another embodiment of the present invention, an assembly is provided for mounting a plurality of photovoltaic modules over an installation surface. The assembly comprises a support grid defined by a plurality of discrete elongate members and a plurality of non-roof penetrating grid supports, the supports positioned at locations where the elongate members cross or intersect; wherein the support grid is configured to receive the PV modules at locations where the elongate members are joined whereby when the grid is coupled to the photovoltaic modules, creates a stiffly interconnected block of PV modules in a non-bending geometry in winds of up to 85mph that prevents wind up lift; wherein the modules weigh more that the support grid, total weight not to exceed 4 Ibs/ft2.

[0013] In one embodiment, the minimum array size is about 6 x 6 m is a good size for 80mph wind speeds, based on initial analysis, which when using Im by 2m panels, comprises 3 panels x 6 panels (to form a square panel). Some embodiments may use 4 m x 4 m, but that may be for lower wind speeds. 8 x 8 m array when used with a rigid support grid at 80 mph will be sufficient regardless of the weight of the support grid (even if such grid is very minimal in weight). The larger it is, however, the safer, so bigger will work for sure. 5 m x 5 m and 7m x 7m will work as well.

[0014] It should be understood that in some embodiments, a ratio other than square does not make much sense, as the lower of the two values will be the relevant one for the load consideration. So a 5 x 6 m unit really behaves like a 5 x5 m unit, if the wind shifts.

[0015] Weight is of relevance, of course, but above a certain size, the down-pressure in the center will always outweigh the uplift at the edges. A size at 8 x 8 m of the array is such that the down-pressure in the center will always outweigh the uplift at the edges. [0016] In one embodiment, the weight load of the panel is panel weight (16 kg/ m2 or 1.5 kg/sqf or 3.3 lbs/sft), double that when adding mounting structure. With that weight, a 6 x 6 m should resist 80 mph lateral winds. The wind speeds, depending on the calc and situation between 80 and 120 mph, and the array size may be scaled as appropriate to make 80mph wind resistant arrays also resistant at 120mph based a linear size expansion.

[0017] A further understanding of the nature and advantages of the invention will become apparent by reference to the remaining portions of the specification and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic showing a solar module mount.

[0019] Figure 2 shows a side view schematic of ferees acting on rooftop mounted array.

[0020] Figure 3 shows wind flow over a PV array on a rooftop.

[0021] Figure 4 shows a side view schematic of ferees acting on a PV array.

[0022] Figure 5 shows a side view schematic of pressure acting on a PV array.

[0023] Figures 6 through 11 show various support grids for use with solar modules according to embodiments of the present invention.

[0024] Figures 12 through 16B show various embodiments for use in angle mounting solar modules according to embodiments of the present invention.

[0025] Figures 17 through 21 show various rotatable module mounting apparatus according to embodiments of the present invention.

[0026] Figure 22 shows one embodiment of an angle mounting apparatus for use to be coupled to elongate members of support grids according to embodiments of the present invention.

[0027] Figures 23 through 26 shows side views of module attachments according to embodiments of the present invention.

[0028] Figures 27 through 29 show perspective views of arrays using support grids according to embodiments of the present invention.

[0029] Figures 30A-30G show various methods of using module as part of a stiffening member of the array according to embodiments of the present invention.

[0030] Figures 31 A-3 IB show a perspective view of an array using a support grid according to one embodiment of the present invention. [0031] Figures 32-34 show a perspective view of an array anti-uplift spacers according one embodiment of the present invention.

DESCRIPTION OF THE SPECIFIC EMBODIMENTS

[0032] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed. It may be noted that, as used in the specification and the appended claims, the singular forms "a", "an" and "the" include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to "a material" may include mixtures of materials, reference to "a compound" may include multiple compounds, and the like. References cited herein are hereby incorporated by reference in their entirety, except to the extent that they conflict with teachings explicitly set forth in this specification.

[0033] In this specification and in the claims which follow, reference will be made to a number of terms which shall be defined to have the following meanings:

[0034] "Optional" or "optionally" means that the subsequently described circumstance may or may not occur, so that the description includes instances where the circumstance occurs and instances where it does not. For example, if a device optionally contains a feature for an anti-reflective film, this means that the anti-reflective film feature may or may not be present, and, thus, the description includes both structures wherein a device possesses the anti-reflective film feature and structures wherein the anti-reflective film feature is not present.

[0035] Referring now to Figure 2, one embodiment of the present invention will now be described. Figure 2 shows a typical force profile over an array of photovoltaic (PV) modules 1 mounted on beam supports 3 and 4. As seen in Figure 2, the array of modules 1 on beam supports 3 and 4 may encounter a force profile as indicated by the arrows shown in Figure 2 when under wind load from a substantially lateral direction. Figure 2 shows that along the perimeter of the array, the windflow may create upward wind lift forces on the array. In a standard rectangular rooftop installation, the strongest wind uplift forces are present at the corner modules which may be exposed to winds from more than one axis. Moderate uplift forces are present along the modules not at the corners but still along the outer perimeter of the array. The downward forces toward the middle of the array may be attributed to stiffness of the array, the weight of the modules, downward pressure from wind flow, and any load thereon.

[0036] Referring now to Figure 3, the force profile of Figure 2 is caused in part by the turbulent wind flow illustrated in Figure 3. Figure 3 shows that on a building top or rooftop mounting, wind flow 6 over substantially flat mounted modules 1 of the array can create wind load issues due to turbulence and other wind created load or lift. In one non-limiting example, the turbulent flow 7 may have a uplifting effect on the perimeter area of the array. These variable loads from lift and drag forces generated by the wind are countered by the weight of the array and the structural rigidity of the array.

[0037] Figure 4 more clearly shows that the wind flow 6 over the modules 1 can create a shift 13 in the loading on the modules 1 and increase the likelihood of lift off of arrays due to the equal or greater uplift forces 11 that can act on arrays or modules of insufficient weight and area.

Photovoltaic Device Mounting System

[0038] Referring now to Figure 5, it should be understood that in some embodiments of the present invention, while a gust of wind can create local uplift on a roof, there will never be a wind formation such as to create sufficient uplift, when integrated over the entire roof or array surface, to lift the equivalent of the entire array. Thus, those areas 14 have negative pressures due to uplift conditions. Figure 5 shows that it is desirable that the integral of pressure represented by the area under the curve is sufficient to keep the modules of the array down on the roof or other support surface.

[0039] Referring now to Figure 6, one embodiment of the present invention creates a rigid structure of beams or elongate members with multiple modules attached to it (e.g. a total surface area of 5m x 5 m, or 10m x 10 m, or 20m x 20 m etc.). Figure 6 is an underside view showing the grid structure beneath the modules 1 (shown in phantom). In this embodiment, a plurality of support rails 8 are used in conjunction with a plurality of cross beams 9 to create the supporting grid structure. In the present embodiment, the combined structure of beams, rails, and modules is rigid enough that even if 2400 Pa uplift may pull up panels on the edges, the uplift will never be sufficient to lift up the entire structure at once. Therefore in this embodiment, no ballast or penetrations are needed for mounting and operating the array on this roof, although such ballasts or penetrations are not excluded in alternative embodiments. It should be understood that the beams and rails may have cross-sections of various shapes such as but not limited to rectangular, n-polygonal, round, oval, triangular, I-shape, T-shape, C-shape, U- shape, E-shape, other shaped, or any single or multiple combination of the foregoing. Some embodiments may have shapes that maximize rigidity while minimizing weight. The failure mode of the embodiment herein is that the array does not uplift, but instead, prior to uplift, it will slide laterally. Although not limited to any particular method, this is the typical result when wind uplift conditions exist; the array will shift laterally but will not uplift. The array may be pushed against a parapet or the array may be anchored at one or more locations using penetrating or non-roof penetrating anchors.

[0040] Figure 6 also shows that the modules 1 may be mounted in some embodiments, over the junction points where the elongate elements 8 and 9 cross or intersect. In this manner, the module 1 itself becomes a stiffening member by resisting motion at these intersections 15.

[0041] Figures 7 and 8 show that some embodiments may have multiple support rails 8 tied to a fewer number of cross-beams 9. The dark areas 16 indicate clip or mounting locations of the modules 1 to the various beams. These may be used to define groups of modules that are rigidly secured together. Figure 8 shows that there is only a single beam in the x axis and y axis beneath the modules. In this manner, the modules 1 are coupled at only four locations, two on each beam.

[0042] Referring now to Figure 9, yet another embodiment of the present invention will now be described. Figure 9 shows an embodiment of a solar panel mounting configuration. Figure 9 is an underside view of solar panels mounted on supports and shows that there is only a single beam 500 positioned to support each column of solar panels or solar panels. The use of a beam 500 not located to couple to the lateral edge of the solar panel allows for some tolerance during the installation of these beams 500. Those beams 500 that do need to couple to the lateral edge of the solar panel have less leeway between spacing of the beam 500 as too much spacing will create a gap that cannot be spanned by the solar panel, while too little spacing may create a space that is too small for the solar panel. The non-edge positioned beam configuration of Figure 9 allows for greater tolerance during the installation of the beams. An attachment apparatus 502 such as but not limited to a clip, clamp, or bracket will couple the solar panel to the beam 500. The attachment apparatus 502 may be sized as desired to simultaneously couple or contact two panels to the beam 500 or only couple a single panel to the beam 500. [0043] Without an edge positioned beam configuration, additional backside support may be provided by a tensioned or un-tensioned support member 510 that is positioned to span along the backside surface the solar panels. In one embodiment, the tensioned or un-tensioned member 510 will span across multiple solar panels and in doing so will extend across the gaps 512 between the solar panels and support the edges of these solar panels from excessive deflection. Some embodiments, it may span across the entire row of solar panels. Optionally, some embodiments are configured so that the support member does not span entire rows, but supports portions of each row. By way of nonlimiting example, this support member 510 may be beneath the solar panels and support them from behind. Some embodiments may have additional support members 520 (shown in phantom) if additional support is desired. These additional support members 520 may or may not be coupled by a member 540 to the solar panel.

[0044] This embodiment of Figure 9 also shows that the support member 510 may be configured to tension each of the solar panels. This may be achieved by physically coupling the support members 510 to the solar panel in manner than transfers the tension in the member 510 to the solar panel. Optionally, in some embodiments, the tensioned support member 510 does not tension the solar panels, but merely supports them if there is any significant load placed on them. The solar panels may have connectors 530 which are coupled to the solar panel and are also coupled to the member 510. In one embodiment, this may be achieved by couplers 540 (shown in phantom). This coupler 540 may be a single piece that is rigidly secured to the solar panel and either slidably or rigidly coupled to the member 510. Optionally, the coupler 540 may be slidably or flexibly coupled to the solar panel and then either slidably or rigidly coupled to the member 510.

[0045] By way of nonlimiting example, it should be understood that the tensioned member 510 may be a cable, wire, or other flexible elongate member. Some embodiments may be fibers, sheets, meshes, strips, or other materials. Some other embodiments use solid beams, I- cross-section beams, C-cross-section beams,

[0046] In another embodiment, the modules 1 are glass-glass panels and some of the heaviest per square meter, but still use ballast if one assumes the standard 2400 Pascals of pressure from top OR bottom, i.e. the assumption that wind can reverse-load the panel and make it lift off the roof. 2400 Pa corresponds roughly to the calculated load for 80 mph wind. In one embodiment, the panel weight is approximately 16 kg/m2. Modules may of various sizes such as but not limited 1 meter by 1 meter, 1 meter by 2 meter, 1.5 meter by 3 meter or other sizes.

[0047] In one embodiment, the ratio between panels and beam structure may be between such that more than 30% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 40% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 50% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 60% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 70% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 80% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1. Optionally in another embodiment, more than 90% of the weight of the combined structure such as that of Figures 7 or 8 comes from the weight of the modules 1.

[0048] In one embodiment, the deflection of any of the beams does not exceed 3 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 4 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 5 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 6 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 7 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 8 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 9 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the beams does not exceed 10 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. [0049] The present embodiment assumes that the panels are mounted flat/ parallel to the roof with a maximum angle of 3/5/7/10 degrees for water run-off. This will not work at steep mounting angles such as tilted 30 degree commercial rooftop installations.

[0050] Aerodynamics may be such as to create downward force. In one nonlimiting example, the underside of the module may have a curved shaped of an airfoil so that downward lift may be created as wind flow blow laterally across the module. This may be made by membranes or other material attached to ribs or struts on the backside of the module to create such airfoil shapes. Optionally, these shapes may be part of the support grid.

[0051] The size of the area of the array is really about when the unit can slide, tip over etc. The weight of the array acts substantially universally over the array, but the uplift may only be present at the edges. So if there is enough overall area, the edge area vs. the center is ok. If the unit is too small, the uplift at the edges makes the unit overturn. In one nonlimiting example, the edge for the array may comprise of a single row of modules that constitute less than 30% of the horizontal area of the array occupied by modules. In one nonlimiting example, the edge for the array may comprise of modules that constitute less than 20% of the area of the array. In one nonlimiting example, the edge for the array may comprise of modules that constitute less than 15% of the area of the array. In one nonlimiting example, the edge for the array may comprise of modules that constitute less than 10% of the area of the array.

[0052] In another embodiment, the idea is basically to have beams, in x and y direction, which are sufficiently stiff, onto which our panels are mounted. Think of a interconnected 5m x 6m unit, a total of 300 sqft, call it "panel", with e.g. 5*3=15 of our utility panels. The point here is that this plane can simply be laid onto a flat rooftop without attachment and without ballast because the area is chosen of an area size sufficiently large and the stiffness of the structure sufficiently high, so that with the weight of our glass/glass panels, no xy mph wind can do anything with it, as the wind would primarily have localized effect within this area and not be strong enough to lift off the structure.

[0053] Referring now to Figure 10, another embodiment of the present invention is shown where a 4x2 array of solar modules 1 are shown coupled to the rails 20 and beam 22. Some embodiments may have rails 20 that are of greater thickness. Optionally, the modules 1 are clamped to the rails 20 or they may be slid into slots on the rails 20. This 4x2 array may be part of a larger array. [0054] Referring now to Figure 11, another embodiment of the present invention is shown where a 4x2 array of solar modules 1 are shown coupled to the rails 20 and beam 22, wherein the rails 20 are positioned along the edges of the module 1 instead of down the centerline as seen in Figure 10. Some embodiments may have rails 20 that are of greater thickness. Optionally, the modules 1 are clamped to the rails 20 or they may be slid into slots on the rails 20.

[0055] Referring now to Figures 12 through 14, embodiments are shown how the modules 1 may be received at an angle on rail 20. Figure 12 shows how a plurality of modules 1 may be coupled to the rail 20. Figure 13 shows a portion of the rail 20 wherein at least one slot 24 is in the rail 20 and sized to receive the module 1. It should be understood that the beam may have any of the cross-sectional shapes previously mentioned herein. Figure 14 shows a top down view of the portion of the rail 20 with slot 24.

[0056] Referring now to Figures 15 through 16, embodiments are shown how the modules 1 may be received at an angle on rail 34. Figure 15 shows how the module 1 may be coupled to shaped connectors 30 that are to be received by shaped slots 32 in the rail 34. Figure 16A shows a portion of the rail 34 wherein at least one slot 36 is in the rail 34 and sized to receive the shaped connector 30. It should be understood that the beam may have any of the cross-sectional shapes previously mentioned herein. Figure 16B shows a top down view of the portion of the rail 34 with slot 36. This embodiment advantageously leaves a portion 38 of the rail 34 intact to improve structural rigidity.

[0057] Referring now to Figure 17, one embodiment of a module support 40 is shown which can receive the module while in one orientation and allow the module to rotate to a flat or angled orientation while still be clamped or other wise in contact with the module 1 during the movement. The ends 42 and 44 are attached to a first module and a second module respectively. The modules are shown in phantom for ease of illustration. The end 42 is connected to an already installed module. The module connected to end 44 is about to be installed and is positioned into place by lowering the module about the hinge as indicated by arrow 46 to a horizontal position, sub-horizontal position, or near horizontal position. The ends 42 and 44 may be a clamp or other structure defining an opening into which the module 1 is lowered or a clamp attached to module 1 is lowered. The install position to end 44 may be a vertical or near vertical position. Another set of legs may be coupled to the module about to be installed at an end opposite of the end 4. In one embodiment, the ends 42 and 44 may be locked in place by tabs 48 and 49 which may mechanically fasten, chemically glue, or otherwise secure the ends 42 and 44 into position. Various module gripping designs for the ends 42 and 44 may be found in U.S. Patent Application 12/203,901 filed Sept 3. 2008 and fully incorporated herein by reference for all purposes. U.S. Patent Application 12/126,836 filed May 23, 2008 is also fully incorporated herein by reference for all purpose. These hinged module supports 40 may be coupled together by the elongate elements of the support grid. In this manner, the supports 40 provide an easy mechanism to couple modules together onto the support grid.

[0058] Referring now to Figure 18, another embodiment may use a separate top down connecting bracket 50 or angle locking mechanism to hold the two ends 42 and 44 in a horizontal position, sub-horizontal position, or near horizontal position.

[0059] Figures 19 and 20 shows yet another variation of the embodiment of Figure 17 wherein a rotatable top piece 55 may be used to secure the modules. The piece 55 may have a first position as shown in Figure 19 wherein the modules can be laid down. Figure 20 shows that piece 55 may be rotated into a second position wherein it will extend over the modules and prevent lift-off of the modules. Piece 55 may be lowered to be in contact with the modules or it may be kept above the surface, only interacting when module becomes angled.

[0060] Figure 21 shows that any of the embodiments from Figures 17-20 may be a wide clip with large underside attachment but with only partial coverage of the front side of the module to minimize shadowing. Thus, the ratio of top side area of the clip to bottom side area of the clip may be between about 1 :2 to about 1 :20 in one nonlimiting example.

[0061] Referring now to Figure 22, yet another mounting system is shown wherein slots are shaped in posts 60 and the posts are themselves coupled to rails 62 to secure the posts 60 in position. Some embodiments may have rails 62 that are coupled to the posts 60 after the posts 60 are all in position. Optionally, other embodiments may use posts 60 which will couple to the rails 62 as the posts 60 are installed. The modules 1 may secured in a flat or an angled configuration. Optionally, the posts 60 maybe installed to the rails and/or to or integrated with the grid supports 40. Some embodiments may use a combination of rail mounted and grid support mounted posts 60 to provide angled positioning of modules over the support grid.

[0062] Referring now to Figures 23 and 24, a still further embodiment of the present invention will now be described. This embodiment shows that the modules 1 may be coupled to legs or supports 80 and 82. The legs or supports 80 and 82 may interlock. Optionally, they may also be interlocked or otherwise coupled to the rails 60. Figure 24 shows that the rails 60 may be placed first and then the legs coupled to the rails 60. Optionally, the rails 60 are added after the legs 80 and 82 are all in place. In some embodiments, the legs are of different length so that the module may be angled when interlocked into place.

[0063] Referring now to Figures 25 and 26, a still further embodiment of the present invention will now be described. This embodiment shows that the modules 1 may be coupled to legs or supports 80 and 82. The legs or supports 80 and 82 may interlock. Optionally, they may also be interlocked or otherwise coupled to the rails 60. This provides a structure that limits the travel or angle of the modules in any wind uplift condition. Figure 24 shows that the rails 60 may be placed first and then the modules 1 coupled to the rails 60. Optionally, the rails 60 are added after the legs 80 and 82 are all in place and the modules 1 are in place. The rails 60 may be slidably coupled to the modules 1 through couplings on each module 1. Optionally, the rails 60 are only connected at the ends to the two modules at the ends.

[0064] Referring now to Figure 27, one example of a rooftop mounting device 20 with a simplified installation technique will now be described. This embodiment shows a plurality of latitudinal elongate members 30 and longitudinal elongate member 32 joined together to define an array. In the present embodiment, the array is a rectangular array. It should be understood of course that different types or shapes of arrays (square, rectangular, triangular, oval, hexagonal, etc...) may be used as desired, singly or in combination, to define the appropriate shape to cover the rooftop in a desired manner. It should also be understood that some rooftops or other mounting locations may use one or more arrays that are structurally connected or not connected together.

[0065] By way of example and not limitation, the elongate members 30 and 32 may be comprised of iron bars such as reinforcing steel bar (rebar). Optionally, the elongate members may be stiffened and be beams with any of the cross-sectional shapes previously mentioned herein. Of course, shorter lengths may also be used. The elongate members may be straight, curved, bent, or contain multiple bends as desired for particular installations. The elongate members 30 and 32 may be textured or surface shaped to improve contact with the mounting members. In some embodiments of the present invention, the rebar or other elongate members material may be bare/non-surface treated, epoxy coated, zinc-plated, otherwise surface treated, or otherwise treated material. Optionally, other readily available material may be used for the elongate members such as but not limited to zinc plated conduits, PVC piping, plastics, polymers, metallized polymers, aluminum extension, pretreated wood rods or beams, copper, or other material. These other elongate members may be of cross-sectional shapes such as but not limited to circular, square, rectangular, triangular, other shaped, or single or multiple combinations of the foregoing.

[0066] As seen in the embodiment of Figure 27, these various elongate members 30 and 32 are in contact with support members 40. In this embodiment, the support members 40 may be configured to elevate the elongate members 30 and 32 over the rooftop. Optionally, the support members 40 may be height adjustable to configure the array on the rooftop. Optionally, the support members 40 may be selected to be of a height that configures the array in a substantially planar manner. Optionally, the support members 40 may be selected to be of a height that configures each section of the area is in a substantially planar configuration, wherein different sections may be in different planes, plane angles, and/or plane orientation. Optionally, the support members 40 may be used to connect elongate members 30 and 32 together, with or without elevating them above the rooftop. Optionally in some embodiments, the support members 40 are used merely to align the elongate members together without actually locking the items together. In such an embodiment, this may involve a slidable or other non-rigidly locking coupling. The solar module 50 may be mounted to the array by coupling it to the elongate members 30 and 32. Optionally, the solar module 50 is coupled to the support members 40 to secure them to the array. Still further, some embodiments may use a combination of coupling to the elongate members and the support members. Although not limited to the following, the solar modules 50 in Figure 27 are shown as being coupled to the support members 40 at non-corner edges of the module. The support members 40 may be made of various materials such as but not limited to metal, polymer, plastics, PVC, injection moldable material, concrete, stone, structural foam material, fiberglass, wood, other building material, or any single or multiple combinations of the foregoing.

[0067] Figure 27 also shows that in the current embodiment, the corners of the array 20 may optionally, in alternative embodiments, be secured by grid-to-roof or array-to-roof anchors 42 and 44. Some arrays may have 3 or more anchors. Some embodiments may have 4 or more anchors. In one nonlimiting embodiment, the entire array does not have more than one anchor for every 25 square meter of area. Optionally, these sizes are sufficient for those rooftops with parapets. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array height. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array grid.

[0068] Optionally, it should be understood that the elongate members are all rigidly connect together to meet specifications previously mentioned so that wind loads or other loads are distributed more broadly over the array. This structural rigidly may be due to welds, couplers, or other connectors used to secure the elongate member together. Optionally, it may be due to rigidly from the coupling of elongate members to the structural members 40. Optionally, rigidity in the array may come from some combination of both of the above. In some embodiments, instead of the entire array being entirely rigidly connected, some embodiments may be configured that the array is connected in groups or sections, wherein all the elongate members in each section is rigidly connected, but connections from section to section may be rigid, hinged, slidable, or otherwise connected. Sections may all be of the same size. Optionally, sections may be of at least two different sizes. In one embodiment, the entire support array comprises of two sections. Optionally in another embodiment, the array comprises of at least three sections. Optionally in another embodiment, the array comprises of at least four sections. Optionally in another embodiment, the array comprises of at least five sections. Optionally in another embodiment, the array comprises of at least six or more sections. In one embodiment, the array covers at least about 10000 square feet in area (as measured based on dimensions measured around the array perimeter). In one embodiment, the array covers at least about 15000 square feet in area (as measured based on dimensions measured around the array perimeter). In another embodiment, each section is at least 5000 square feet. In another embodiment, each section is at least 7500 square feet.

[0069] Optionally, the limited use of the anchors at select locations minimizes the number of moisture penetrating points on the roof surface. Not every module has all of its support members anchored to the roof. Most embodiments herein do not use anchors. With each anchor 42 or 44, there may optionally be additional cabling, attachment rods, or other connector 46 (shown in phantom) to increase the number of support members 40 engaged by each anchor. There maybe one or more connectors 46 for each anchor. In some embodiments, the connectors 46 are coupled to the support members. In other embodiments, they may be coupled to the elongate members 30/32 or a combination of elongate members 30/32 and support members 40. In other embodiments, they maybe the elongate members. Figure 27 also shows one embodiment for grounding the array 20 may connected to grounding rod(s) 33 on the roof. Optionally, other embodiments may couple the array to other ground elements to direct undesired electrical charges to ground. Grounding elements may be including any and all embodiments disclosed herein.

[0070] Figure 28 show one embodiment wherein the array 20 is shown wherein the modules are sized to be coupled between the elongate members as indicated by modules 360. In another embodiment, it is shown that the modules 370 are sized to fit over the elongate members. As seen in Figure 28, the modules 360 may be mounted to the elongate members in one or both axis. The modules 360 may be connected at the edges by couplers 380 which may be coupled to secure more than one module at a time by spanning over both edges of an elongate member.

[0071] Figure 29 shows yet another embodiment of an array 400 wherein the elongate members 32 are in one axis and aligned and/or spaced to be positioned over support beams in the underlying roof. The elongate members 30 in another axis are aligned and/or spaced to best support the connection the overlying modules 410. The spacing and/or alignment of the elgonate members 30 is different from that of the elongate members 32.

[0072] In one nonlimiting example, a 5m x 6m unit, a total of 300 sqft, call it "panel", with e.g. 5*3=15 of our utility panels. The point here is that this plane can simply be laid onto a flat rooftop without attachment and without ballast because the area is chosen of an area size sufficiently large and the stiffness of the structure sufficiently high, so that with the weight of the glass/glass panels, no 80 mph wind can do anything with it. Optionally, these sizes are sufficient for those rooftops with parapets. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array height. Optionally, these sizes are sufficient for those rooftops with parapets as high as the solar array grid.

[0073] This provides a stiffly interconnected block of PV modules laid up on top of a roof without penetration into the roof where the block is large enough for its weight to be high enough to resist wind uplift without the need of additional ballast and without any roofing penetration. Weight of the module is more than and that the modules glass layer is used as a stiff ener. [0074] Figures 3OA through 30G, show yet another aspect of some embodiments of the present invention. Figures 30A and 30B show embodiments where the "hinge", bending, or intersection points of the support grid are not supported by the structural rigidity of the module 1. Such a structure may be more flexible in upbending in directions 200 than it could be at points 202.

[0075] Referring now to Figures 30C and 30D, another embodiment of the present invention is provided wherein the module 1 is positioned over the point 202 and the module itself is placed into compression when uplift forces as indicated by arrow 200 are present.

[0076] Figures 30E and 30F show that modules 1 may be placed over a single point 202 as seen in Figure 30F or over multiple points 202. Clips 204 may be used to attach the modules 1 to the support grid.

[0077] Figure 30G shows that mounting the module 1 on a bracket 210 or other spacer above the plane of the hinge point will create increasing greater compression load on the module 1, the higher the bracket 210 becomes. The height of the bracket 210 can be such that only compression load are placed into the module 1 during bending. Some embodiments may use a hinge 212 to attach to the module. If the module is mounted too low, then mainly bending loads are placed in the module.

[0078] Referring now to Figure 3 IA, yet another embodiment of the present invention is shown. This shows that the modules 30 are sized to cover at least two support members 40. This allows the module 30 to be used as part of the stiffening members of the array.

[0079] Referring now to Figure 3 IB, yet another embodiment of the present invention is shown. This shows that the modules 30 are sized to cover at least two or more support members 40. Figure 3 IB shows that one module 30 may cover up to three support members and are coupled to the grid using clips as described herein.

[0080] Referring now to Figure 32, one embodiment of a module is shown connected to an adjacent module. The use of the underside mounted edge housing 600 allows the modules to be flush mounted against one another. A spacer or liner 640 may be included therebetween. This flush mounting is particularly useful where it is desirable for aesthetic or weatherproofmg reasons to have the modules closely joined as shown in Figure 32. More importantly, however, in the present embodiment, the spacer or liner 640 provides an anti-flexing purpose for the array by resisting movement of the modules together during wind uplift conditions. The spacer or liner 640 may comprise of a single material, a rigid inner skeleton 652 with a compliant outer surface 654, or a compliant inner with rigid outer area. These may be included in all areas of the array or only between spaces associated with the outer row of the array. Optionally, these may be included in all areas of the array or only between spaces associated with the outer 2 to 4 rows of the array. In one embodiment, the element 640 may be characterized as an anti-uplift spacer or a minimum spacer element between modules. Figure 32 shows that this embodiment of the edge housing 600 is positioned where the housing is located beneath the transparent module layer 602 and is positioned so as not to contact a front side surface 604 of the transparent module layer. In the present embodiment of the invention, the solar cells 606 are located between the transparent module layer 602 and an opposing module layer 608. It should be understood that various encapsulant layers may optionally be included between the cells and the layers 602 and 608 as are not shown for ease of illustration. In the present embodiment, a moisture barrier 610 may be included along the perimeter of the layer 608.

[0081] In one embodiment, the spacers are sized or the thickness of the compliant layer is such that deflection of any of the modules does not exceed 3 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 4 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 5 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 6 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 7 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 8 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 9 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift. Optionally in another embodiment, the deflection of any of the modules does not exceed 10 degrees from horizontal under wind flow sufficient to create 2400 Pa of lift.

[0082] Figure 33 shows a variation on the embodiment of Figure 32. In this embodiment, the adjacent module 650 presents one edge without an edge housing to mate with the module 601. A spacer or liner 640 may be included therebetween. These may be included in all areas of the array or only between spaces associated with the outer row of the array. Optionally, these may be included in all areas of the array or only between spaces associated with the outer 2 to 4 rows of the array.

[0083] Figure 34 shows a variation on the embodiment of Figure 33. In this embodiment, the adjacent module 650 presents one edge without an edge housing to mate with the module 601. A simplified spacer or liner 660 is used that maintains a substantially flush surface between the modules 601 and 650. This provides a more even surface to provide for easier run-off of rain water and minimize debris buildup on the module surface. A smooth surface that minimizes protrusions also allows for easier cleaning and maintenance. Also, aesthetic considerations may be addressed with this configuration such as being a completely flush surface , e.g. of facade. These may be included in all areas of the array or only between spaces associated with the outer row of the array. Optionally, these may be included in all areas of the array or only between spaces associated with the outer 2 to 4 rows of the array.

[0084] While the invention has been described and illustrated with reference to certain particular embodiments thereof, those skilled in the art will appreciate that various adaptations, changes, modifications, substitutions, deletions, or additions of procedures and protocols may be made without departing from the spirit and scope of the invention. For example, with any of the above embodiments, the modules may be at the module corners instead of along non-corner edges of the module. The modules in the array may be configuration in the same orientation or in different orientations (landscape and/or portrait). The support members and array may be used with framed or frameless modules. Although these support arrays are discussed in the context of roof top mounting, it should be understood that they may also be adapted for use in ground mounted installations or on non-roof mounting areas.

[0085] Furthermore, even though thin- film solar cells such as CIGS solar cells are described for the purposes of example, those of skill in the art will recognize that any of the embodiments of the present invention can be applied to almost any type of solar cell material and/or architecture. For example, the absorber layer in solar cell 10 may be an absorber layer comprised of silicon, amorphous silicon, organic oligomers or polymers (for organic solar cells), bi-layers or interpenetrating layers or inorganic and organic materials (for hybrid organic/inorganic solar cells), dye-sensitized titania nanoparticles in a liquid or gel-based electrolyte (for Graetzel cells in which an optically transparent film comprised of titanium dioxide particles a few nanometers in size is coated with a monolayer of charge transfer dye to sensitize the film for light harvesting), copper-indium-gallium-selenium (for CIGS solar cells), CdSe, CdTe, II-VI materials, IB-VI materials, CuZnTe, CuTe, ZnTe, Cu(In,Ga)(S,Se)₂, Cu(In₅Ga, Al)(S, Se₅Te)₂, IB-IIB-IVA-VIA absorbers, and/or combinations of the above, where the active materials are present in any of several forms including but not limited to bulk materials, micro-particles, nano-particles, or quantum dots. The CIGS cells may be formed by vacuum or nonvacuum processes. The processes may be one stage, two stage, or multi-stage CIGS processing techniques. Additionally, other possible absorber layers may be based on amorphous silicon (doped or undoped), a nanostructured layer having an inorganic porous semiconductor template with pores filled by an organic semiconductor material (see e.g., US Patent Application Publication US 2005-0121068 Al, which is incorporated herein by reference), a polymer/blend cell architecture, organic dyes, and/or C₆o molecules, and/or other small molecules, micro-crystalline silicon cell architecture, randomly placed nanorods and/or tetrapods of inorganic materials dispersed in an organic matrix, quantum dot-based cells, or combinations of the above. Many of these types of cells can be fabricated on flexible substrates.

[0086] Additionally, concentrations, amounts, and other numerical data may be presented herein in a range format. It is to be understood that such range format is used merely for convenience and brevity and should be interpreted flexibly to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. For example, a thickness range of about 1 nm to about 200 nm should be interpreted to include not only the explicitly recited limits of about 1 nm and about 200 nm, but also to include individual sizes such as but not limited to 2 nm, 3 nm, 4 nm, and sub-ranges such as 10 nm to 50 nm, 20 nm to 100 nm, etc....

[0087] The publications discussed or cited herein are provided solely for their disclosure prior to the filing date of the present application. Nothing herein is to be construed as an admission that the present invention is not entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided may be different from the actual publication dates which may need to be independently confirmed. All publications mentioned herein are incorporated herein by reference to disclose and describe the structures and/or methods in connection with which the publications are cited. For example, U.S Patent Application Ser. No. 11/465,787 filed August 18, 2006, U.S. Provisional Application Ser. No. 61/118,420 filed November 26, 2008, and U.S. Provisional Application Ser. No. 61/252,128 filed Oct. 15, 2009, are fully incorporated herein by reference for all purposes. U.S. Publication No. 2004/0250491 (Diaz), deflectors may be installed on the north- facing back of every panel in order to reduce the wind-induced uplift forces, when installed in the northern hemisphere.

[0088] While the above is a complete description of the preferred embodiment of the present invention, it is possible to use various alternatives, modifications and equivalents. Therefore, the scope of the present invention should be determined not with reference to the above description but should, instead, be determined with reference to the appended claims, along with their full scope of equivalents. Any feature, whether preferred or not, may be combined with any other feature, whether preferred or not. In the claims that follow, the indefinite article "A", or "An" refers to a quantity of one or more of the item following the article, except where expressly stated otherwise. The appended claims are not to be interpreted as including means-plus-function limitations, unless such a limitation is explicitly recited in a given claim using the phrase "means for."

Claims

WHAT IS CLAIMED IS:

1. An assembly for mounting a plurality of photovoltaic modules over an installation surface, the assembly comprising: a rigidly interconnected array of PV modules laid up on top of a roof without penetration into the roof where the array is large enough in horizontal area for weight of the array to be high enough to resist wind uplift based only on area and weight of the array, without additional ballast and without any roofing penetration

2. The assembly of claim 1 wherein the module weight is at least 16 kg/ m2, with a minimum area of 25 square meters and a minimum lowest dimension of 5 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2.

3. The assembly of claim 1 wherein module weight to module area is at least 16 kg/ m2, with a minimum area of 36 square meters and a minimum lowest dimension of 6 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2.

4. The assembly of claim 1 wherein theto area is at least 16 kg/ m2, with a minimum area of 36 square meters and a minimum lowest dimension of 6 meters in the x or y axis, with a maximum weight of the array not to exceed 32 kg/m2.

5. The assembly of claim 1 wherein the module weight to area is at least about 50% of the weight of the entire array.

6. The assembly of claim 1 wherein the module weight to area is at least about 40% of the weight of the entire array.

7. The assembly of claim 1 wherein the minimum horizontal area is at least 5m x 5m.

8. The assembly of claim 1 wherein the minimum horizontal area is at least 6m x 6m.

9. The assembly of claim 1 wherein the minimum weight of the modules is at least 14kg/m2.

10. The assembly of claim 1 wherein the array has a configuration that resists wind uplift at lateral winds of up to 80 mph.

11. The assembly of claim 1 wherein the array has a configuration that resists wind uplift at lateral winds of up to 100 mph.

12. The assembly of claim 1 wherein the array comprises of the PV modules, a support grid beneath the PV modules, and non-roof penetrating grid supports for lifting the support grid above the roof.

13. The assembly of claim 1 wherein the modules are mounted over junction points of elongate elements in the grid to provide rigidity to the grid by rigidly coupling the module over the grid to use the module as a stiffening member

14. The assembly of claim 1 further comprising angled flaps that minimize wind flow to the underside of the modules.

15. The assembly of claim 1 wherein a downward pressure is created in about a center 70% area of the array.

16. The assembly of claim 1 wherein a downward pressure is created in about a center 60% area of the array.

17. The assembly of claim 1 wherein overall maximum edge deflection during wind load is less than about 10 degrees from horizontal.

18. The assembly of claim 1 wherein overall maximum edge deflection during wind load is less than about 5 degrees from horizontal.

19. An assembly for mounting a plurality of photovoltaic modules over an installation surface, the assembly comprising: a rigidly interconnected array of PV modules laid up on top of a roof without penetration into the roof where the array has a horizontal area of at least 25 square meters with a minimum of 5 meters in both the x and y axis, and weight of the array to be at least 3.31bs/ft2 to resist wind uplift based only on area and weight of the array, without additional ballast and without any roofing penetration, total weight not to exceed 6.6 Ibs/ft2.

20. An assembly for mounting a plurality of photovoltaic modules over an installation surface, the assembly comprising: a support grid defined by a plurality of elongate members; a plurality of non-roof penetrating grid supports configured to elevate the support grid above the installation surface; wherein the support grid when coupled to the photovoltaic modules, creates a stiffly interconnected block of PV modules in a non-bending geometry in winds of up to 85mph that prevents wind up lift.

21. An assembly for mounting a plurality of photovoltaic modules over an installation surface, the assembly comprising: a support grid defined by a plurality of discrete elongate members and a plurality of non-roof penetrating grid supports, the supports positioned at locations where the elongate members cross or intersect; wherein the support grid is configured to receive the PV modules at locations where the elongate members are joined whereby when the grid is coupled to the photovoltaic modules, creates a stiffly interconnected block of PV modules in a non-bending geometry in winds of up to 85mph that prevents wind up lift; wherein the modules weigh more that the support grid, total weight not to exceed 4 1bs/ft2.