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CROSS-REFERENCE TO RELATED APPLICATION 
     The present application constitutes a utility application for Letters Patent to that certain Provisional Application Serial No. 60/095,147, filed Aug. 3, 1998. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to elevated decks for residential buildings, and more particularly to a rain water collection system for the underside of such decks to maintain a dry space there beneath. 
     DISCUSSION OF THE PRIOR ART 
     Exterior structures, such as decks, gratings and walkways, are typically designed to allow water to fall through the spacing between adjacent decking boards or other apertures. It may be desirable to otherwise collect this water to thereby make the space under such surfaces dry. The object of the present invention is to provide an impermeable assembly which may be easily mounted to the underside of existing decks, gratings or walkways, which collects and routes rain water to a discharge point while maintaining the area under the deck free of dripping water. 
     The closest prior art of which we are aware is the Moore U.S. Pat. No. 5,511,351. The patent describes a water collection and drainage system that is adapted to be attached to the underside of a residential deck and comprises flexible sheets that are affixed to deck joists so that they present concaved upper surfaces and convexed lower surfaces. While this structure may be suitable for use in climates that are not subject to freezing, the underdeck water collection system described in the Moore patent is unsuitable for use in freezing climes. In freezing climes, water from melting snow on the deck will fall between adjacent deck boards onto the concave collector structure suspended therebeneath. When out of the rays of the sun, the temperature beneath the deck very often is below freezing temperature, resulting in a build-up of ice thereon. Over a period of several days of thawing and freezing temperatures, the weight of the ice can cause the suspension structure to fail. 
     Another drawback of the apparatus described in the Moore &#39;351 patent is that the flexible connectors extend below the bottom of the deck joists, thereby limiting the head room under the deck. 
     It is a further object of the invention that the impermeable assembly be comprised of a versatile system of components which may be easily assembled on site by a single person to form an aesthetically pleasing surface beneath the deck which drains all water to the perimeter of a deck, grating or walkway and which can be used in climates where frequent freezing and thawing occurs. 
     It is a further object of the invention to minimize the encroachment of the headroom space beneath the deck by the impermeable assembly. 
     It is a further object of the invention that at least some of the elements of the impermeable assembly be removable for maintenance and repair. 
     SUMMARY OF INVENTION 
     The invention will be taught with respect to residential decks which are typical of other exterior structures which could benefit from the invention. FIG. 1 shows a typical residential deck comprised of joists  10 , end plates  12  and deck boards  14 . Actual decks have a wide variety of sizes and shapes, however, between centers, the joist-to-joist spacing is typically 16″, and if not that then typically 24″. The description of various embodiments will be with orienting reference to a typical deck structure. As used herein longitudinal refers to the orientation along a line parallel to the deck joist while transverse refers to the orientation along a horizontal line perpendicular to the deck joist. With reference to the boundary edges of the deck the side edges are longitudinal while the front and back edges are transverse. 
     FIG.  2 ( a ) shows, conceptually, the surface contour of an impermeable water collection assembly constructed according to certain aspects of the disclosed embodiments. FIG.  2 ( b ) shows the end view of the surface of FIG.  1 . The surface is comprised of periodic peaks and valleys. 
     Water flows transversely into the gutter and then longitudinally to the perimeter of the deck. By controlling the slope or pitch of the assembly, water may be directed to flow to a single edge where it may undergo further collection by means which are not part of this invention. The realization of an impermeable assembly suspended to the underside of an existing structure presents problems not found in art which might otherwise be considered related. For example, prior art impermeable roofing systems which are applied to the top side of an underlying supporting structure are not adaptable to a suspended system. Further, the prior art structure and methods used to realize a permeable suspended ceiling are not amenable to modification which would render them impermeable. The subject invention realizes the impermeable surface of FIG.  2 ( a ) in a novel way which results in an attractive, yet inexpensive system which is exceptionally easy to install and to maintain beneath decks and walkways. In certain of the embodiments disclosed herein, the impermeable assembly is sectioned according to FIG.  2 ( c ). Collectors  20  are convexed on their upper surface to define peak regions which direct water transversely to their side edges and, thus, into inclined gutters  22  which comprise the valley regions directing water longitudinally to the edge of the deck. Gutters  22  are disposed directly beneath deck joists  10  and are attached thereto by various means. Collectors  20  are attached, or otherwise constrained so that their side edges are vertically overlapping with respect to gutters  22  to prevent leakage and to thus render the resulting assembly water impermeable for a typical rain shower. “Impermeability”, as used herein, does not require a watertight tight seal which would withstand gale force winds even though this capability is present in certain embodiments. Collector  20  may have an inverted V or a more crowned convex shape which provides useful stiffness, allowing relatively thin and inexpensive materials to withstand the stress of wind when so shaped. The crowned shape is achieved without loss of headroom in that the crown resides in the cavity between adjacent joists. 
     Thus, in a general sense, the present invention comprises rain water collection apparatus that is adapted to be affixed to an underside of an elevated, water-previous, deck structure of the type where a plurality of parallel, regularly-spaced, longitudinally extending joists project from a building structure and with a plurality of deck boards secured to an upper edge surface of the joists and which extend generally transversely to the joists. The collection apparatus comprises resilient, water-impervious, rectangular collector sheets having a predetermined length dimension and a width dimension between opposed side edges that is greater than the regular spacing between adjacent ones of the joists. Means are provided for mounting the collector sheets between adjacent ones of said joists for supporting the sheets in a space between adjacent joists with an upper surface of the sheets convex and a lower surface of the sheets concave. A plurality of gutter members are attachable to the joists and span the bottom edge of the joists to vertically overlap side edges of the collector sheets, such that water seeping between adjacent deck boards falls on the upper convex surface of the collector sheets and then flows laterally into the gutter members disposed beneath the side edges of the collector sheets. The gutter members are at a pitch such that the water therein flows to the outer perimeter of the deck structure. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing features, objects and advantages of the invention will become apparent to those skilled in the art from the following detailed description of the preferred embodiments, especially when considered in conjunction with the accompanying drawings in which like numerals in the several views refer to corresponding parts. 
     FIG. 1 is a perspective view, partially sectioned, to show the general construction of a typical residential deck; 
     FIGS.  2 ( a ),  2 ( b ) and  2 ( c ), respectively, show a perspective view of a collector component of one embodiment of the invention, an end edge view of the collector of FIG.  2 ( a ) and the gutter component thereof; 
     FIG.  3 ( a ) is an end view of a pair of adjacent deck joists with a collector and gutters suspended therefrom; 
     FIG.  3 ( b ) is a partial perspective view of a mounting bracket for connecting a gutter component to a joist; 
     FIG.  3 ( c ) is an end edge view of the mounting bracket affixed to a joist; 
     FIG. 3 ( d ) is an end view of a gutter design suitable for the outer side edges of the decks; 
     FIG.  3 ( e ) is a cross-sectional view of an alternative embodiment for a mounting bracket for connecting a gutter component to a joist; 
     FIG.  3 ( f ) is a front view of the mounting bracket of FIG.  3 ( e ); 
     FIG.  3 ( g ) is a front elevation showing a different style of mounting bracket suspending a pair of collectors and a gutter from a joist; 
     FIG.  3 ( h ) shows the mounting bracket of FIG.  3 ( g ) when used to suspend a specially designed gutter from a rim joist; 
     FIG. 4 is a perspective view of the collector component in coiled form prior to installation beneath a deck structure; 
     FIGS.  5 ( a ) through  5 ( h ) illustrate the components of an alternative embodiment of the invention; 
     FIGS.  6 ( a ) through  6 ( d ) show the components of an alternative embodiment of the invention; 
     FIGS.  7 ( a ) and  7 ( b ) show an alternative gutter component and mode of attachment to a deck joist; 
     FIGS.  8 ( a ) through  8 ( d ) illustrate yet another embodiment for attaching collectors and gutters to the underside of a deck or walkway; 
     FIG.  9 ( a ) illustrates a continuous gutter support member in an exploded view; 
     FIG.  9 ( b ) is an end view of the gutter engaging the support member; 
     FIGS.  10 ( a ) through  10 ( d ) graphically illustrate the necessity of maintaining control over the collector contour to prevent puddling; 
     FIGS.  11 ( a ) through  11 ( d ) illustrate components for mounting a continuous collector sheet designed to span a plurality of joists so that water will drain from the surface of the collector without puddling; 
     FIGS.  12 ( a ) through  12 ( e ) show a tensioning apparatus for controlling the profile or contour of the collector sheets; 
     FIGS.  13 ( a ) through  13 ( e ) illustrates an arrangement for imparting a desired contour to pliable collector sheets; 
     FIGS.  14 ( a ) through  14 ( d ) schematically illustrates the manner in which the system of the present invention can be applied in different size modules; 
     FIGS.  15 ( a ) through  15 ( f ) illustrate a combined configuration of mounting and shaping devices for affixing a compliant sheet collector to the undersurface of a deck or elevated walkway; 
     FIGS.  16 ( a ) through  16 ( e ) illustrates another alternative configuration for securing collectors and gutters to the underside of an elevated deck structure; and 
     FIGS.  17 ( a ) through  17 ( c ) illustrate other shape profiles for coilable collector panels useable with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     With reference to FIGS.  2 ( a ) through  2 ( c ), the rain water collection apparatus of the present invention comprises a plurality of collector sheets  20  that are formed so as to be convex on their upper surface and concave on their lower surface when installed between joists  10  of an elevated deck structure. The collectors may be thin aluminum sheets or preferably roll-formed, generally rectangular plastic sheets of a sufficient thickness and resiliency so that when bowed, they will provide a counteracting force tending to return the sheet material to a planar condition. To provide longitudinal rigidity, the individual sheets spanning adjacent joists can be corrugated as indicated in FIGS.  2 ( a ) and  2 ( b ), but in most instances, this is unnecessary unless, of course, the sheet material of the collector  20  is quite thin. 
     FIG.  3 ( a ) shows a collector and gutter system wherein collector  32  is compressively retained by mounting brackets  30  in a position which allows water to drain between the side edge of collector  32  and joist  10 . Gutter  36  is also retained by mounting brackets  30 . It is formed of a resilient material with a radius somewhat smaller than the installed radius such that, when being installed, it must be spread so that when released, there is a compressive force acting to maintain contact with the bracket. 
     Mounting brackets  30  are mounted to facing vertical sides of adjacent joists  10 . Additional brackets, not shown, are mounted along the joists at an interval sufficient to provide adequate support. There is a trade off which must be made here. The number of attachment points should be minimized for ease of installation, however a larger interval between mounting brackets requires a stiffer, and thus more expensive, collector and gutter design. FIGS.  3 ( b ) and  3 ( c ) show one type of mounting bracket  30  in more detail. Shown here is tab  34  which functions to partially retain collector  32 . If the collector is fabricated of crimpable material, such as aluminum or galvanized steel, additional retention may be accomplished by crimping the edge of collector upward so as to be locatable behind tab  34  as shown in FIG. 3 ( c ). Collector  32  is installed by transverse compression to snap into mounting brackets  30 . Alternatively, mounting bracket  30  could be modified to accommodate any well known fastening means to retain the collector by piercing it. For example, apertures in the mounting bracket would allow a nail to pierce the collector and attach to the joist. Collector  32  may be any sheet material which will maintain a crowned shape under side-edge compression. 
     As shown in FIG.  3 ( b ) gutter  36  is formed with side lips or flanges  37 . The gutter is suspended from mounting brackets  30  by engaging flange  37  with tabs  38  and  40 . Gutters  36  may be formed of any material and process which results in a semi-rigid structure. As used herein the term semi-rigid refers to a structure which would not sag or otherwise deform as installed. The embodiment of FIGS.  3 ( a )- 3 ( c ) requires a semi-rigid structure, such as extruded PVC, to span the distance between mounting clips without sagging. 
     FIG.  3 ( d ) is an end view of a gutter design suitable for the interior side edges of the decks. As shown, gutter  42  is attached to the inside face of an outermost joist with screw  31 . The gutter can be reversed end-for-end, when attaching it to the inside face of the opposite outermost joist. An elongated slot in gutter  42  provides for thermal expansion and contraction. 
     FIGS.  3 ( e ) and  3 ( f ), respectively, show a front view and a cross-sectional view of an alternative embodiment of a mounting bracket  46  for connecting a gutter component to a joist which may be formed by injection molding of a plastic. Mounting bracket  46  is fastened to the side of joist  10  by nails, not shown, which pass through nail holes  48  and  49 . Slot  47  in bracket  46  receives an edge of collector  32  therein as well as an inwardly turned flange of gutter  36 , each being retained by the aforementioned compressive forces. 
     FIG.  3 ( g ) illustrates by means of an end view a mounting bracket  30 ′ that differs slightly from that shown in FIG.  3 ( a ). The mounting bracket  30 ′ comprises an extruded strip approximately 20 in. in length and which is adapted to affixed to opposed side surfaces of the joist  10  by means of nails or screws. The extrusion includes upper and lower tines  31  and  33 , respectively, which project obliquely at differing angles from the joist  10  to define an elongated slot therebetween. The slot is dimensioned to receive an edge of a collector panel  32 ′ along with the flange  37 ′ of the gutter  36 ′. In that the collector panels are under compression by virtue of the fact that their widths are greater than the spacing between joists and, hence, are bowed upwardly, they stay retained in the slot of the mounting bracket  30 ′. Likewise, because the side edges of the gutter must be spread apart from one another in order to have the flanges  37 ′ fitted into the elongated slots of the two mounting brackets, the spring force tending to return the gutter to its unstressed state insures that they will not pull free of the mounting brackets without manual intervention. 
     FIG.  3 ( h ) illustrates the mounting bracket  30 ′ affixed to a rim joist of a deck structure, the rim joist being the outermost joist of the deck. The bracket  30 ′ is nailed or screwed to an inner side surface of the rim joist and, as can be seen, the inwardly extending nubs  39  and  41  act as stand-offs or spacers allowing the thickness dimension of the uncurved portion  43  of a specially shaped gutter member  45  to be sandwiched between the bracket  30 ′ and the rim joist. A protuberance  47  on the gutter  45  cooperates with a finger-like projection  49  on the bracket  30 ′ to snap or latch the gutter in place when the straight portion  43  thereof is forced upward into the space or pocket created by the stand-offs  39  and  41 . Again, the slot defined by the outwardly and obliquely projecting tines  31  and  33  receives the edge portion of a collector sheet  32 ′. 
     When it is desired to discharge water from only one end of the gutter, discharge from the other end must be blocked by an end cap or end plug, not shown. The end plug is preferably a resilient material, totally contained within gutter  36 , which forms a watertight seal by exerting an expanding force upon the inner surface of the gutter. The end cap may be a plastic structure which pinches the end of gutter  36  to form a watertight seal. 
     For many deck structures, the collector could be very unwieldily to install as a single section due to its length′. To facilitate handling, the collector may be fabricated with both a longitudinal and transverse stress such that it has two stable rest modes. The first rest mode is achieved by rolling the collector in the transverse direction wherein the crown is formed. The second rest mode is achieved by additionally rolling the collector in the longitudinal direction to make it coil. As shown in FIG. 4, the collector maintains a flat mode when coiled, but converts to the semi-rigid crowned or convex mode as it is uncoiled. It is thus possible for a single person to readily handle and install a single piece collector of virtually any length by simply unrolling same as it is being inserted into its joist mounted support brackets. Alternatively, a long collector may subdivided into a plurality of shorter sections to facilitate handling. There are a variety of well-known ways to accomplish a water-tight seal at the end joints of such sections. For example, VHB type 4622 acrylic foam tape, manufactured by Minnesota Mining and Manufacturing (3M), may be applied to the underside of the collectors after they have been installed. Alternatively, collector ends may be joined with a resilient gasket in either an end-to-end configuration or an overlapping configuration. 
     FIGS.  5 ( a ) and  5 ( h ) show an alternative means for retaining the collector. With reference to FIG.  5 ( a ), an end view of a U-shaped mounting bracket  50  is shown attached to a bottom edge surface of joist  10  with screw  52 . Spacers  54  may be optionally interposed to add slope or pitch to the system. FIG.  5 ( b ) shows a bottom plan view of mounting bracket  50 , including slots  55  which receive the compression member  58  of FIG.  5 ( d ). The mounting bracket is comprised of relatively stiff resilient material which behaves as a spring to be the source of a compressive force to retain the collector acting through compression member  58 . The heavy solid line indicates the position of the bracket under compression as installed, while dashed lines  56  indicate its position prior to installation of the collector sheets. FIGS.  5 ( c ) and  5 ( d ) show a side view and plan, respectively, of one of the compression members  58 . Compression member  58  is comprised of relatively compliant material. Its wings  60  transmit the compressive force of mounting bracket  50  to region  64 , via hinge points  62 . Dotted lines  63  in FIG.  5 ( c ) show the rest position of wings  60  when unflexed. Connection to mounting bracket  50  is accomplished by ears  61  on the ends of wings  60  which engage slots  55  in the mounting bracket. Compression member  58  operates most efficiently when flexure is confined to hinge points  62 . Toward this end, elements  60  and  64  are stiffened by embossed ribs  66  and  68  while hinge point  62  is made more compliant by reducing the width of the compression member  58  in this region. The result is that only a small fraction of the force from mounting bracket  50  is required to overcome hinge points  62  and a persistent downward retaining force is transmitted to the domed portion of collector  69  (FIG.  5 ( f )). 
     FIGS.  5 ( e )- 5 ( h ) show the range of flexure of elements  50 ,  60 , and  64 . In FIG.  5 ( e ) the compression member  58  has been wedged between the mounting clips  50  and is under a slight compression to hold it in place prior to installing the collector  69 . In FIG.  5 ( f ) these elements have flexed to allow the installation of collector  69 , while in FIG.  5 ( g ) the collector has been set in its installed position. 
     The system of FIGS.  5 ( a )- 5 ( h ) may be designed to provide a relatively low retaining force sufficient for nominal extremes of wind velocity since the collector is positively retained at the limit of flexure as shown in FIG.  5 ( h ) where mounting bracket  50  has been compressed to an almost vertical position, such that it is now in contact with a joist  10 . This arrangement reduces the susceptibility of the collector to exceptionally severe wind. With collector  69  positively retained with a relatively light retaining force, it may be easily removed for maintenance and repair. 
     FIG.  6 ( a ) through  6 ( d ) show an alternative embodiment of the deck rain diverter system which could be used in combination with the collector retaining system of FIG.  5 . FIG.  6 ( a ) shows a partial section of a U-shaped gutter  70  having regularly spaced mounting slots  74  formed therein. Mounting slots  74  are pre-formed on the opposed sides of gutter  70  and are periodically spaced along the length of the gutter at an interval sufficient to adequately support it. A mounting clip  76  may be formed from a plastic extrusion which is subsequently cut and drilled. Resilient tabs or fingers  78  are provided to captively mount the clips in the slots  74  while leaving them free to slide within the limits of the slots. 
     FIG.  6 ( b ) shows a section of a convexly bowed collector component  80 . The side edges of the collector are comprised of joist-contact regions  82  and notch regions  84  being defined therebetween. The contact regions provide a substantially continuous line of side edge support for the collector while the notch regions provide a slot-like opening for water to drain from the domed surface of the collector to the gutter  70 . FIG.  6 ( c ) shows a cross-sectional view of gutter  70  attached to joist  10 . Gutter  70  may be preformed according to the cross-sectional view of FIG.  6 ( d ), such that the mounting clips  76  frictionally engage the joist to temporarily hold the gutter in position. When the gutter is set in final position with a desired pitch for draining water to the free end of the deck, it is attached with screws for permanent placement. The mounting clips are registered in the center of slot  74  to provide for limited movement of the gutter due to the large differential thermal expansion and contraction of plastic material from which the gutter may be formed. For metal gutters, where differential thermal expansion is negligible, the width of slot  74  may be the nominal width of bushing  76 . 
     Collector  80  is pressed into a continuous linear contact with inclined flange  72  by the action of the collector retaining system of FIG.  5 ( a ). The contact force at this interface is non-uniform, due to deformation of both the collector and the gutter. However, this effect is mitigated and the integrity of the joint is enhanced by placing the attachment point of the collector retaining system midway between the attachment points of clips  76  to the joists. The integrity of this joint may be additionally enhanced by making flange  72  more compliant relative to the stiffness of the total gutter  70  and the collector  80 . If it is desirable to achieve a joint which is watertight in a high wind environment, it can be achieved with the embodiment of FIGS.  6 ( a ) through  6 ( d ). 
     For this embodiment, the preferred order of assembly is to first install the collector retaining system of FIGS.  5 ( a )-( h ). Next the gutter mounting clips  76  are added to the gutter and the gutter is mounted to the joist. Finally, the collector  80  is snapped into position as shown in FIG.  6 ( c ) in the manner described with reference to FIGS.  5 ( f ) and  5 ( g ). 
     FIG.  7 ( a ) shows a perspective view of an alternative example of a gutter which is attachable to the bottom of joist. Attachment of gutter  90  is made by a screw inserted through slot  92 . The length of slot  92  provides for differential thermal expansion as described earlier with reference to slot  74  of FIG.  6 ( a ). While it would be possible to achieve a watertight seal for this attachment, it is preferable that the shape of the gutter be modified to provide a dry region which positions the slot above the expected depth of water in the gutter. As shown in FIG.  7 ( a ), a center island is a feature of the extrusion and is thus continuous. Alternatively, discrete islands may be added to gutter  70  of FIG. 6 to achieve the same result, with water flowing in the adjacent U-shaped troughs  93  and  95 . 
     The embodiments considered thus far have employed gutters which must be semi-rigid to span the attachment points without sagging. It would be desirable to ship and otherwise handle gutters in a coilable form in the manner described with reference to FIG. 4 regarding coilable collector  32 . To be coilable, the gutter must be designed with a relatively large transverse radius. Further, the attachment means must be adapted to work with this shape. FIG. 8 shows such an embodiment. 
     In FIG.  8 ( a ) gutter  100  may be fabricated and coiled in the manner of FIG. 4, such that, when uncoiled, it snaps into a semi-rigid shape, as shown in FIG.  8 ( a ). A mounting bracket  102  is attached to the underside of joist  10  as shown in FIGS.  8 ( b ) and  8 ( c ) by nails or screws passing through hole  105 . Collector  100  is retained by tabs  104  on mounting bracket  102 , which provide a supporting ledge. Collector retaining band  106  and spring  108  perform the same function as the collector retaining system of FIGS.  5 ( a ) through  5 ( h ). Thus, the collector may be installed and removed in the manner previously described. 
     Gutter  100  is pre-formed with apertures  110  (FIG.  8 ( a )), which are regularly spaced along the gutter at intervals sufficient to adequately support the gutter. Mounting brackets  102  are first mounted to the bottom of joist  10  by screws or nails passed through aperture  105  at an interval which nominally corresponds to the interval of apertures  110  in tabs  104 . Next, gutter  100  is attached to bracket  102  by plastic or metal spring clips  114 , a perspective view of which is shown in FIG.  8 ( d ). The clips captures the edges of both aperture  110  in gutter  100  and slot  112  in tabs  104 . Slot  112  allows for both the variation in the actual spacing of brackets  102  as well as relative movement due to thermal expansion. As such, gutter  100  can be a plastic material such as PVC having a high coefficient of linear expansion. 
     FIGS.  9 ( a ) and  9 ( b ) show yet another alternative for mounting the collector and gutter components to joists and provide substantially continuous support for the gutter, to thereby reduce the stiffness requirements of the gutter and improving the integrity of the collector/gutter interface. Mounting brackets, as at  120 , attach to the lower end edges of joists  10  in the manner of bracket  102  of FIG.  8 ( a ). Support members  124  are supported at each end by being engaged in horizontal slots  122 . The substantially continuous support provided by support members  124  allows the gutter to be more flexible, thus making it easier to ship and install and less expensive to fabricate. Tabs  125  are spaced periodically along support member  124  to provide an edge stop for collector  32  such that the compressive force imparted by the collector retaining means positions the collector edge in intimate contact with gutter  126  to thereby improve the watertight integrity of this interface and also to assure the retention of the gutter. For this embodiment, the preferable order of assembly is as follows: First mounting brackets  120  and support members  124  are installed in an alternating sequence along each joist. Next, the collector retaining means are installed between each opposing pair of mounting brackets followed by installation of gutters  126  (the relative order of these two steps are not important). Finally, collectors  32  are snapped into position, relying upon the elasticity of the collector retaining means to allow the edge of the collector to pass by the edge of support member  124  and be forced into the notch formed by tabs  125 . 
     The embodiments considered thus far have comprised separate collector and gutter means to facilitated fabrication and installation of an impermeable assembly which does not compromise headroom because the joist cavity is used to crown the collector and thereby achieve the desired contour as shown conceptionally in FIG.  2 . Alternatively, headroom may be conserved by employing a tensional-stressed pliable sheet to establish substantially the same contour. Since the pliable sheet acquires its shape through tension, it is not confined to the joist cavity and may span a plurality of joists. Thus, it is possible to control the contour of a relatively large sheet of pliable material to form peaks and valleys for collecting and draining away water passing between adjacent deck boards. If the geometry of the peaks and valleys is judiciously chosen, there will be a drainage path for each point on the pliable sheet and no puddles will form. 
     It is important to preclude the possibility of puddles, since the weight of any puddle increases the strain on the pliable sheet which may lead to an avalanche type of failure as the size of the puddle increases to further increase the strain. Also, in cold climates, ice formation can present a problem. 
     The requisite contour is achieved by a tensional stress on the pliable sheet sufficient to assure conformity to the contouring means. The underlying principle is illustrated in FIGS.  10 ( a )- 10 ( d ), which show several examples of strain along a line connecting a peak and a valley. FIG.  10 ( a ) shows an ideal condition where the strain is negligible and the slope is constant. This ideal may be approached by increasing the yield strength of the pliable sheet and stressing the sheet near its yield stress to maintain the surface taught. 
     FIG.  10 ( b ) shows an example where the weight of the pliable sheet causes an unacceptable strain. A catenary is formed, and the weight of the collected water adds to the strain, thus exacerbating the problem. One solution is to choose a material which is light in weight, has a low modulus of elasticity, and has negligible plastic deformation under stress. This may be best accomplished with a composite material comprising a high performance plastic film and a woven re-enforcing mesh. For example, a woven mesh of fiberglass or graphite could be imbedded between upper and lower layers of Mylar film. 
     Another solution is to increase the slope of the catenary as shown in FIG.  10 ( c ). However, it is generally undesirable to do so since it reduces headroom which us usually at a premium. The preferable solution for a relatively large deck where headroom is important is shown in FIG.  10 ( d ). Here, a plurality of peaks reduce the span of the catenary to control the droop such that complete drainage is accomplished without excessive slope. However, the location of the intermediate peaks must be chosen judiciously since an intermediate peak which provides drainage for one area may block the drainage of another area. A pliable sheet may be contoured to assure complete drainage by a peak-forming device which exerts an upward force on selected regions of the pliable sheet, a valley-forming member which exerts a downward force on other selected regions of the pliable sheet, and a tensioning means which determines the relative elevation of the regions of the pliable sheet which form a catenary between the peak-forming means and the valley-forming means. 
     FIGS.  11 ( a )- 11 ( d ) show one example of well chosen peaks and valleys. Valley-forming members  150 ,  152 ,  154 , and  156  are mounted end-to-end along joists  10  at a slope sufficient to drain collected water to the exit edge. A large surface pliable sheet  151  is stretched across the valley forming members affixed to the underside of the joists and is retained in tension by a tensioning means (not shown). Peak-forming members, as at  158 , are shown in cross-sectional detail in FIG.  11 ( d ). It is comprised of a flexible tapered plate designed to place pliable sheet  151  in waterproof contact with the underside of joist  10  and provide stress relief by distributing the resulting upward force. FIG.  11 ( b ) shows a cross-sectional view through peak-forming member  158 , while FIG.  11 ( c ) shows a cross-sectional view through peak-forming member  160 . Peak-forming members  158 - 168  establish a watershed ridge wherein all water is constrained to flow into and along the valley-forming members  150 - 156 . 
     FIG.  12 ( a ) shows an cross-sectional view of a tensioning apparatus  178  while FIG.  12 ( b ) shows the elements of the apparatus  178  in an exploded cross-sectional view. A portion of joist  10 , to which  178 , is attached, is shown in phantom line  12 ( b ) for reference in FIG.  12 ( b ). Tensioning apparatus  178  is comprised of an inner core member  180  which may be made of wood and which has been treated to inhibit rot. As shown in FIG.  12 ( c ), barbed metal pins  182  are staked into inner core  180  at a periodic interval along its length and the resulting assembly is attached to joist  10  by screws  184 . The interval between barbed pins is chosen to impart a substantially uniform tensional stress to the pliable sheet  192  after it has been impaled on the barbed pins. A spacer  204  may optionally be used to set the elevation of the tensioning means relative to the bottom of joist  10  and thus allow water to drain over the top. If the tensioning apparatus is used at the right side edge then pliable sheet  186  (FIG.  12 ( b )) is stretched to the desired tension, attached to the barbed metal pins and the excess material (indicated by the dashed line extension) is trimmed away. The same may be done to pliable sheet  188  to tension the left side edge. As shown, the tensioning apparatus  178  performs the function of tensioning and additionally joining two sections of pliable sheets  186  and  188  together. 
     A retaining clip  190  is pressed onto the inner core as shown in FIG.  12 ( a ). It is designed to additionally stretch the pliable sheets  186  and  188  after they have been impaled on pins  182 , compressively wrapping around inner core  180  to lock into the position shown in FIG.  12 ( a ), and to provide a decorative cover. If required, retaining clip  190  may be additionally secured by screws. Retaining clip  190  may additionally function to provide a water-tight seal at the side walls of inner core  180 . 
     FIG.  12 ( d ) shows a partial plan view of a system employing tensioning apparatus  178  in various locations while FIG.  12 ( e ) shows an end view of the same system. Joists  10  are shown in dotted lines for reference. Locations  194  and  202  are left-side-edge and right-side-edge tensioning means as previously described. When FIG.  12 ( e ) is considered to be a cell of a wider system comprising a plurality of such cells, then the tensioning apparatus at locations  194  and  202  may additionally function as valley-forming devices. At location  198  the same means functions as a peak-forming device to establish a watershed ridge as previously explained. 
     Pliable sheet  192  may be continuous or, alternatively, may be spliced at any of the locations  194 - 202 . Spacers  204 - 210  set the slope of the pliable sheet while allowing water to drain to the side edges as best seen in FIG.  12 ( e ). Spacers  212  and  214  may be continuous along their respective joists to present a more attractive side-edge view. 
     For certain embodiments it is preferable to add a peak-forming means to a location intermediate of the joists after the pliable sheet has been attached. In this position, the elevation of the peak may have a wide range of adjustment to control the tension and shape of the pliable sheet. An example of such a devices is shown in FIGS.  13 ( a )- 13 ( e ). As shown in FIGS.  13 ( a ),  13 ( b ), and  13 ( c ), a screw device  250  is joined to a plastic coated cord  254  by plate  252  to suspend the cord from the bottom of a deck board (not shown). Screw  250  is secured to plate  252  by crimping regions  253 , while cord  254  is secured by crimping regions  255 . A side view of a cleat  256  is shown in FIG.  13 ( c ), while a bottom view thereof is shown in FIG.  13 ( d ). As shown in FIGS.  13 ( c ) and  13 ( d ), cord  254  passes through the center of cleat  256 , and is laced in a conventional figure-eight pattern to provide an adjustable tensioning support for pliable collector sheet  257 . Preferably, the interface of the pliable collector sheet  257 , cleat  256  and cord  254  should be water tight. The free end of cord  254  may be tapered such that it may be readily threaded through an aperture of cleat  256  which would result in a interference fit, thus rendering this interface water tight. If required, a gasket may be added to seal the region between the pliable sheet and the cleat. 
     FIG.  13 ( e ) shows a tool which may be used to attach screw  250  to the undersurface of a deck board between joists. The tool is comprised of a hollow tube  260  with slot  262  and handle  264 . Cord  254  is threaded through tube  260  and the side edges of plate  252  engage slot  262 . Pliable sheet  257  is pierced and screw  250  is driven into the deck board by the upward pressure and torque provided by tool  258  acting through plate  252 . When the tool is withdrawn the free end of cord  254  will be accessible for attachment to cleat  256 . 
     The aforementioned means for controlling the contour of the pliable sheet may be combined in a variety of ways to achieve complete drainage. FIGS.  14 ( a )- 14 ( d ) shows some illustrative examples. For each example arrows show the general direction of water flow. The actual direction of flow may vary due to the complex shape of the contour. The joist and end plate structure of the deck are shown as dashed lines for reference. The examples may also be considered as cells to be used in various combinations to extend the area of water collection. 
     With reference to FIG.  14 ( a ), elements  300 - 308  are peak-forming devices while elements  310  and  312  are valley-forming devices which collectively create a contour for a pliable sheet in the manner explained of FIGS.  11 ( a )- 11 ( d ). The peak-forming means  300 - 308  establish a watershed ridge under joist  10  such that water flows transversely to the region of the valley-defining means and, thereafter, longitudinally to the exit edge as indicated by the arrows as at  313 . FIG.  14 ( a ) is considered to be a 2× cell in that the span of water collection is twice the joist-to-joist spacing. With reference to FIG.  14 ( b ), elements  320 - 328  are peak-forming devices, while elements  330  and  332  are valley-forming devices which create a contour for a pliable sheet in the manner of FIG.  11 . Here, the watershed ridge is staggered to provide a 3× cell such as that described with reference to FIG.  10 . The general direction of flow is transverse to the valley-forming regions followed by longitudinal flow along the valley-forming means as shown by the arrows  333 . By combining 2× and 3× cells, a deck having any number of joist cavities can be accommodated. 
     FIG.  14 ( c ) shows a 4× cell wherein element  340  is a continuous member which establishes a peak region, i.e., a ridge at center joist  10 . Element  340  may be comprised of tensioning apparatus  178  as shown in FIG.  12 ( a ). FIG.  14 ( d ) shows a 4× cell which collects water to a single point at the exit end of valley-forming device  364 . Element  362  is also a valley-forming device which functions to allow transverse water flow through it as shown by the arrows  363 . Element  360  is a ridge-forming device in the manner of element  340 . Elements  350 - 358  are adjustable peak-forming members as shown in FIG.  13 ( c ). Valley-forming member  362  is attached to joist  10  such that each point along its length is at an elevation intermediate of the elevations of corresponding points along the top surface of element  360  and the bottom surface of element  364 . Peak-forming members  350 - 358  reduce the span of the catenary to mitigate the formation of puddles as described with reference to FIG. 10, while element  362  assures that, in contrast to FIG.  14 ( b ), the resulting ridge line has a saddle point at an intermediate elevation sufficiently low to completely drain all of the water from the right side and sufficiently high to discharge all of the collected water to the exit point. This condition is best satisfied when the height of peak-forming members  350 - 358  are adjusted to the minimum height necessary to insure complete contact between the impermeable sheet and valley-forming devices  362 . Post-installation adjustment of the height of peak-forming means  350 - 358  is very advantageous in this embodiment since improper height adjustment can create blocking ridges and valleys. After installation, these conditions may be readily detected by testing and then corrected by adjustment. 
     In the embodiments considered thus far, the impermeable assembly has been comprised of discrete means which are collectors and gutters or alternatively continuous pliable sheet means which are contoured to form both collector and gutter regions. The embodiment of FIGS.  15 ( a )- 15 ( f ) shows an example of how elements of the discrete embodiments may alternatively be combined with a pliable sheet and its associated contouring, tensioning, and joining means. In this example the structure of FIGS.  9 ( a ) and  9 ( b ) has been modified to be used with a pliable sheet collector means in a 3× cell configuration. FIG.  15 ( a ) shows an end view of the cell as installed. Gutter  400  corresponds to gutter  126  of FIG.  9 ( a ) while gutter support plate  402  corresponds to bracket  124  of FIG.  9 ( a ). Bracket  402  has been modified to provide attachment points for pliable sheet  404 , as shown in the detailed section of plan view of FIG.  15 ( b ) and the end view of FIG.  15 ( c ). As shown, the bracket  402  is periodically cut and formed to create a pointed hook  408  which impales pliable sheet  404  to retain it in tension in the manner described with respect to the barbed pins of FIGS.  12 ( a )- 12 ( e ). The installation of the pliable sheet may be simplified, and the density of attachment points may be reduced if the side edge of the pliable sheet has a stress distributing cord  406  in a hem thereof. Alternatively, there are many other well known ways to perform this attachment. 
     With continued reference to FIG.  14 ( a ), pliable sheet  404  is maintained in tension by means of flexible bracket  410  acting through wire link  412  and a flexible mounting pad  414  secured to sheet  404 . Flexible mounting pad  414 , shown in plan view in FIG.  15 ( d ) and in end view in FIG.  15 ( e ) is a circular rubber or plastic element which is suitably bonded to pliable sheet  404 . Wire link  412  is threaded through eye  416  in pad  414 . Elements  418  position pliable sheet  404  below the bottom surface of joists  10  to provide a transverse flow path in the manner of valley-forming means  150  of FIGS.  11 ( b ) and  11 ( c ). In this embodiment, the height of flexible bracket  410  may be accurately established before the pliable sheet is completely installed. This may be accomplished by measurement from the bottom surface, or other feature of valley-forming means  418 , or it may be set after the right-side edge of pliable sheet  404  has been installed as shown in FIG.  15 ( f ). In this figure, flexible bracket  410  is shown in its light stress position. It is raised to the elevation as shown, wherein, the installed portion of pliable sheet  404  is substantially taut and is fastened to joist  10 . Installation is completed by fastening the left-side edge of pliable sheet  404  to mounting plate  402 , thereby deforming flexible bracket  410  to the desired stressed state as shown in FIG.  15 ( a ). 
     FIGS.  16 ( a )- 16 ( c ) show yet another alternative for mounting the collector and gutter components to joists and providing continuous support for the gutter, to thereby reduce the stiffness requirements of the gutter and improve the integrity of the collector/gutter interface. The mounting system is comprised of a pair of mounting rails  450  constructed according to FIG.  16 ( a ), a two-piece bracket  452  for attaching the rails to the deck joists as shown in FIG.  16 ( b ), and a collector retaining clip  456  as shown in FIG.  16 ( c ). Each of these components may be readily realized using known plastic materials and thermo-forming processes. There are three essential features of rail  450 . Apertures  458  provide vias for water to pass from the collector to the gutter. Projection  462  allows the rail to be captured by the two-piece bracket  452 . Bracket  452  is comprised of a top piece  464  and a bottom piece  466 , each having a mounting hole  468 . Top piece  464  further includes elongated grooves or cavities  470  which receive the rail projections  462  therein. Bracket  452  can be attached at any point along rails  450  thus allowing the rails to run orthogonal to the joists without regard for the joist-to-joist interval. 
     FIG.  16 ( d ) is a cross-sectional view through the center of the bracket  452  as mounted showing how rails  450  are captured by the compression of bracket pieces  464  and  466 . FIG.  16 ( e ) is a cross-sectional view through the center of rail aperture  458  and the center of collector retaining clip  456 . The flexure and geometry of clip  456  is chosen such that when mounted as shown, the cop is held in a fixed position by tap  472  and exerts a downward force to retain collector  10 . Retaining clips  456  may be located at any aperture and the clip-to-clip interval is chosen to assure continuous intimated contact between the gutter and the rail. The final assembly step is to snap gutter  470  into groove  460 . 
     It would be desirable to enhance the transverse stiffness of the coiled collector of FIG. 4 while retaining the natural compliance of a relatively thin material. Well-known manufacturing processes may be used to corrugate, or otherwise add, a transverse rib structure to the collector, such that the transverse stiffness of the collector would be substantially greater than its longitudinal stiffness. FIGS.  17 ( a )- 17 ( c ) are illustrative of such a structure. 
     The embodiments explicitly disclosed are illustrative of the versatility of the individual elements, which may be employed in a wide variety of alternative configurations and combinations to most optimally achieve a desired combination of advantages. For example, various embodiments employing a pliable sheet may be less expensive and easier to install, while embodiments employing flexible or semi-rigid elements may be more durable. 
     While the invention has been described with embodiments intended to drain rainwater from deck structures, the benefits of an aesthetically pleasing ceiling system which is inexpensive and very easy to install is also desirable for dry or interior applications. Any of the disclosed embodiments could be used without modification in dry or interior applications. Further, it is intended that any of the disclosed embodiments may be appropriately modified for dry applications where impermeability is not required or for interior applications where environmental stress is relatively low. 
     This invention has been described herein in considerable detail in order to comply with the patent statutes and to provide those skilled in the art with the information needed to apply the novel principles and to construct and use such specialized components as are required. However, it is to be understood that the invention can be carried out by specifically different equipment and devices, and that various modifications, both as to the equipment and operating procedures, can be accomplished without departing from the scope of the invention itself.

Summary:
A combination of versatile and inexpensive elements are combined on site to create an impermeable assembly which collects water falling through a grating or cracks between adjacent boards of a deck and completely drains it to one or more points at a selected edge. The impermeable assembly is comprised of a plurality of peaks and valleys configured to simplify installation, conserve headroom and provide an aesthetically pleasing finished surface. In a first embodiment, a collector collects the water falling through cracks between boards spanning the space between adjacent joists from which it drains transversely to a gutter positioned beneath the joists. The gutter drains the water longitudinally to the perimeter of the deck.