U.S. patent application number 11/167160 was filed with the patent office on 2007-01-25 for low cost radiant floor comfort systems.
This patent application is currently assigned to DAVIS ENERGY GROUP, INC.. Invention is credited to Richard C. Bourne, Marc Hoeschele.
Application Number | 20070017095 11/167160 |
Document ID | / |
Family ID | 37677734 |
Filed Date | 2007-01-25 |
United States Patent
Application |
20070017095 |
Kind Code |
A1 |
Bourne; Richard C. ; et
al. |
January 25, 2007 |
Low cost radiant floor comfort systems
Abstract
A rapidly assembled pre-fabricated array of heating elements,
such as tubing or wire, on a rigid mesh, for use in radiant panel
heating and/or cooling systems, reduce costs by streamlining both
the design layouts and the labor operations to fabricate and
install the systems. The pre-fabricated arrays may be installed
with the mesh on the finish floor side for additional protection of
the heating elements during and after installation.
Inventors: |
Bourne; Richard C.; (Davis,
CA) ; Hoeschele; Marc; (Davis, CA) |
Correspondence
Address: |
OLIFF & BERRIDGE, PLC
P.O. BOX 19928
ALEXANDRIA
VA
22320
US
|
Assignee: |
DAVIS ENERGY GROUP, INC.
Davis
CA
|
Family ID: |
37677734 |
Appl. No.: |
11/167160 |
Filed: |
June 28, 2005 |
Current U.S.
Class: |
29/890.03 |
Current CPC
Class: |
B29K 2023/0691 20130101;
B65H 2701/331 20130101; B21F 27/00 20130101; B65H 54/56 20130101;
B29C 53/083 20130101; Y10T 29/4935 20150115; B21F 35/04 20130101;
F24D 3/14 20130101; Y02B 30/00 20130101; F24D 3/149 20130101; Y02B
30/24 20130101; B21C 47/00 20130101; B21C 47/28 20130101 |
Class at
Publication: |
029/890.03 |
International
Class: |
B21D 53/02 20060101
B21D053/02 |
Claims
1. A method of fabricating a heating/cooling element for a radiant
comfort system, comprising: forming the heating/cooling element of
a material having a shape memory; winding the heating/cooling
element into a pattern of turn portions and straight portions onto
a winding device; removing the heating/cooling element from the
winding device after a predetermined period so the heating/cooling
element retains the pattern of turn portions and straight
portions.
2. The method of claim 1, wherein winding the heating/cooling
element includes receiving the heating/cooling element about two
mandrels disposed on the winding device so that the turn portions
turn more than 180 degrees about each mandrel and wind alternately
clockwise and counterclockwise about the two mandrels, and the
straight portions are disposed between the mandrels.
3. The method of claim 1, wherein the heating/cooling element is an
extruded polymeric tube.
4. The method of claim 3, wherein the polymeric tube is comprised
of one of a high density polyethylene or a cross-linked
polyethylene.
5. The method of claim 1, wherein the heating/cooling element is a
tube connectable to a fluid source to heat/cool an area.
6. The method of claim 1, further comprising: securing the
heating/cooling element to a substrate in a serpentine pattern with
the turn portions open to approximately 180 degrees and the
straight portions are substantially parallel to one another; and
placing a covering over the heating/cooling element and the
substrate to protect the heating/cooling element and facilitate
heating/cooling transfer.
7. The method of claim 6, wherein the heating/cooling element is a
tube connectable to a fluid source to heat/cool an area.
8. The method of claim 6, wherein the substrate is a rectangular
mesh grid and the straight portions are oriented transverse to a
length of the rectangular mesh grid.
9. The method of claim 6, wherein the substrate is a structural
sheet and the covering is a poured material that covers the
substrate and the heating/cooling element and hardens after
pouring.
10. The method of claim 6, further comprising placing at least one
metallic heating/cooling transfer element in contact with the
heating/cooling element before placing the covering.
11. The method of claim 6, wherein the substrate is a structural
sheet and the covering is a rigid panel.
12. The method of claim 6, wherein the substrate is a corrugated
metal sheet having troughs narrower than an outer dimension of the
heating/cooling element and the heating/cooling element is placed
into the troughs before placing the covering.
13. A method of installing a pre-fabricated radiant comfort system,
comprising a mesh grid and a flexible linear heating/cooling
element attached to one side of the grid to form a pre-fabricated
assembly, the method comprising: installing the pre-fabricated
assembly at an installation location with the grid disposed between
the heating/cooling element and the finish surface; and covering
the assembly with a finish surface.
14. The method of claim 13, wherein the grid element is held in a
substantially vertical position while the element is being attached
thereto to form the pre-fabricated assembly.
15. The method of claim 13, wherein the element is attached to the
grid using a motorized wire-wrapping tool.
16. The method of claim 13, wherein the heating/cooling element is
a flexible tube for conveying a liquid heating/cooling transfer
fluid.
17. The method of claim 13, wherein the heating/cooling element is
an electrical wire.
18. The method of claim 13, wherein the mesh grid is comprised of a
metal and the finish surface is concrete.
19. The method of claim 13, further comprising joining at least two
pre-fabricated assemblies by the heating/cooling element.
20. The method of claim 19, wherein the two assemblies are foldable
about the joining element without damaging the element.
21. The method of claim 20 where the folded assembly allows a
required minimum bend radius of the heat transfer element at the
fold line.
Description
[0001] This invention was made with State of California support
under California Energy Commission contract number 500-02-026. The
Energy Commission has certain rights to this invention.
BACKGROUND
[0002] This subject matter of this application relates to radiant
floor heating and cooling systems, and particularly to systems that
place hydronic tubing or electrical heating cables in contact with
indoor room or outdoor surfaces.
[0003] Radiant floors are widely recognized as the most comfortable
choice among heating systems. As a result, the radiant floor market
has grown rapidly. However, the market could be much larger if
installed system costs could be lowered significantly.
Installations have been largely limited to custom homes where the
owners are willing to pay more for improved comfort. Current
radiant heating systems are more likely to be installed at sites
where cooling systems are not necessary. Cooling is generally
provided by ducted forced air systems, which for a modest
additional expense can deliver heating as well. By comparison,
combining radiant heating with forced air cooling is much more
expensive to install. However, there is the potential in dry
climates to install ductless systems that can deliver cooling as
well as heating through floor tubing. Many rapidly growing housing
market areas are in the dry climates of the U.S. southwest and
mountain states. Production builders construct more than 75% of new
homes in these areas. These volume homebuilders are more likely to
consider radiant systems if costs can be reduced, because
homebuyers are attracted to many radiant system features including
superior comfort, high energy efficiency, and low noise.
[0004] There are additional market opportunities for lower-cost
outdoor panel heat transfer systems. These include snow-melt and
patio heating systems, patio cooling systems, and swimming pool
solar heating systems that circulate pool water through tubing in
surrounding or nearby concrete paving.
[0005] The most economical radiant floor systems place linear
tubing or electrical conductors (wires) in concrete slabs, where
reinforcing steel provides a matrix for securing the linear heat
transfer elements in a desired pattern. The concrete transfers heat
laterally, allowing wider spacing of the elements. For concrete
slab construction, a typical method involves a concrete crew
placing steel reinforcing wire, which is typically a grid-type
reinforcing mesh that arrives in a rolled form and then is
straightened, cut, and laid throughout the formed area. A radiant
floor specialty crew then manually secures the tubing or wire onto
the top of the reinforcing grid at 2' to 3' intervals with wire or
cable ties. Tying the tubes or wires in place is a labor intensive,
time consuming, process. The installers must either repeatedly bend
over or be on their hands and knees for extended periods of time.
In addition to working for long periods in uncomfortable positions,
the installers must have considerable dexterity to secure the ties
without damaging the tubing or wires.
[0006] The heating elements typically arrive at the site in rolls,
and if the element is hydronic tubing, its "memory" of the rolled
shape complicates the task of securing it in straight runs on the
mesh. Radiant floor designs typically use customized serpentine and
rectangular spiral layouts. These layouts or circuits can be
complex because interior wall locations must be marked before the
circuits are placed. The layout patterns are usually configured
room-by-room with connecting lines entering through doorways to
avoid passing under interior walls, thereby minimizing the danger
that wall framing fasteners will penetrate and damage the tubing or
wire.
[0007] The ends of the heating elements ultimately meet at a
manifold or panel that becomes the distribution point for a group
of "circuits," whether hydronic or electrical. After the circuits
are run, the concrete crew that formed the slab edges returns to
pour the slab over the heating elements. During the pour, they
typically reach blindly through the wet concrete with "J-hooks" to
pull the reinforcing mesh up near the horizontal centerline of the
slab. Because the mesh is not typically flat, and the ties are
widely spaced, this operation sometimes results in pulling heating
elements too near the surface, where they are more vulnerable to
damage. If the system is hydronic, the tubing is pressurized during
the pour, and a sudden loss in pressure indicates that the tubing
has been punctured.
[0008] Radiant systems that are not placed in concrete slabs are
relatively more expensive because they require the addition of a
layout matrix to guide the layout patterns. Such systems usually
require either closer spacing of the heating elements or additional
components to spread heat laterally. The prior art includes several
novel strategies for reducing the cost of "raised floor" radiant
technologies that do not surround the linear heat transfer elements
with concrete. For example, the Applicant's "low mass" radiant
system shown in U.S. Pat. No. 4,782,889 uses a corrugated deck that
spans across the framing members to hold the tubing, and spread
heat laterally across the floor. A subsequent technology (U.S. Pat.
No. 5,788,152) uses a composite plywood-aluminum deck to accomplish
the same three functions. Both of these systems would benefit from
use of a tubing product that arrives in a serpentine pattern rather
than in rolls.
[0009] The above factors suggest a need and opportunity for
improved radiant panel methods that reduce costs and enhance
installation reliability.
SUMMARY
[0010] The subject matter of this application is directed to an
improved heating element product and methods for fabricating and
installing such elements, including radiant panel systems that
reduce costs by streamlining both the design layouts and the labor
operations to fabricate and install the systems. The improved
products and methods include forming a heating element, such as
hydronic tubing in a "figure-8" pattern that facilitates
installation of the tubing in certain layouts. The subject matter
of the application also provides, a method of rapidly assembling
pre-fabricated arrays of heating elements, such as tubing or wire,
on a rigid mesh. According to the subject matter of this
application, the pre-fabricated arrays may be installed with the
mesh on the finish floor side for purposes of protection of the
heat transfer elements. These and other improvements will be
further described in the following sections.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The subject matter of this application will be described in
detail with reference to the following drawings in which like
reference numerals refer to like elements and where:
[0012] FIG. 1 is an isometric view showing an exemplary method for
winding figure-8 tubing;
[0013] FIG. 2 is a plan view showing an exemplary method for
deploying tubing from a narrow figure-8 pattern;
[0014] FIG. 3 is a plan view showing an exemplary method for
deploying tubing from a wide figure-8 pattern;
[0015] FIG. 4 is an isometric view showing an exemplary method for
pre-fabricating tubing in a narrow figure-8 pattern to a grid
substrate;
[0016] FIG. 5 is a cross-sectional view showing an exemplary method
for placing a pre-fabricated assembly and enclosing it in a
concrete slab;
[0017] FIG. 6 is a cross-sectional view showing an exemplary method
for placing the pre-fabricated assembly on a framed floor with
cementitious topping; and
[0018] FIG. 7 is an isometric view showing an exemplary method for
folding two pre-fabricated assemblies that form a single tubing
circuit.
DETAILED DESCRIPTION OF EMBODIMENTS
[0019] Although features of the subject matter of this application
may be implemented use in a variety of deployment patterns,
standardization can be maximized using a serpentine pattern in
which the linear heat transfer element, such as tubing or wire,
enters near one corner of a rectangular grid and is placed in a
repetitive back-and-forth alignment of parallel runs. The "memory"
problem for plastic tubing wound on a spool can be minimized an/or
eliminated with a "figure-8" winding, which can be accomplished
according to the subject matter of this application.
[0020] FIG. 1 is an isometric view showing an exemplary method for
winding figure-8 tubing. As shown in FIG. 1, tubing 1 is extruded
from an extruder 2. The tubing 1 is received on a winder 6 having
two mandrels 3a and 3b. Because the extruder 2 is typically a large
machine that must remain fixed in position, a preferred exemplary
embodiment uses a two-mandrel winder 6 with double-axis movement.
The exemplary version of the winder 6 has two vertical mandrels 3a,
3b and a bed 6a that tilts about a horizontal axis 6b. The spacing
between the mandrels 3a, 3b can vary from as little as about 3' to
as much as about 20', as shown in exemplary applications further
described with reference to FIGS. 2 and 3.
[0021] During the winding process, tubing 1 being produced by the
extruder 2 is wound on two mandrels 3a and 3b of a winder 6 rather
than on one larger mandrel as used in a standard tubing extrusion
process. The diameter of the mandrels 3a, 3b will typically range
from 6'' to 12''. As the tubing 1 from the extruder 2 is freshly
wound about the mandrels 3a and 3b, the tubing 1 takes a "set" such
that curved tubing segments 4 remain curved and straight sections 5
remain straight after removal from the winder 6. In an embodiment,
the winder 6 tilts and rotates relative to the extruder 2 so that
the tubing 1 clears the mandrels 3a, 3b as winding proceeds. As
shown in FIG. 1, the winder 6 next rotates counter-clockwise about
axis 9 as viewed from above. As rotation proceeds, the tubing 1
winds about the mandrel 3b and the winder 6 continues to rotate
counterclockwise until the mandrel 3a approaches the tubing 1. An
end 7 of winder 6 then pivots downward until the tubing 1 fully
clears the top of mandrel 3a. The end 7 then pivots back up before
rotation reverses, and clockwise rotation continues until the
mandrel 3b approaches the tubing 1. An end 8 of the winder 6 then
pivots downward until the tubing 1 fully clears above the mandrel
3b. The end 8 pivots back up, and rotation changes back to
counter-clockwise.
[0022] The winding process continues until the winder 6 is full.
The tubing 1 is then cut and the cut end from the extruder 2 is
connected to a second winder. The coiled tubing 1 is then removed
from the first winder 6. If the heating element being extruded from
the extruder 2 is a cross-linked polyethylene tubing (PEX), the
coil of tubing then proceeds to a cross-linking operation. The
completed coil of tubing may either be packaged for shipment or
deployed and secured immediately to a grid in a process to be
described below.
[0023] FIGS. 2 and 3 are plan views showing exemplary methods for
deploying tubing from narrow and wide figure-8 patterns,
respectively. In FIG. 2, tubing 1 from a bundle 10 is partially
secured to a mesh grid 11. In FIG. 3, tubing 1 is shown secured to
the grid 11. In various exemplary embodiments, the grid 11 will
typically serve both as a base for attaching the tubing 1 and as a
source of reinforcement for a concrete slab or other floor topping,
and is usually made of steel in a square grid pattern, e.g.,
reinforcing wire. For example, a mesh of rigid #10 steel wires
(approximately 0.10'' diameter) are often used in a 6''.times.6''
spacing arrangement, and the grid is typically produced in the U.S.
in 5' and 7' widths. Heavier wire and/or tighter grid spacing can
be used where stronger reinforcement is required. The mesh is
relatively rigid but can be obtained in either rolls or flat
sheets. Flat sheets are preferred for use with the subject matter
of this application because such sheets more reliably retain the
tubing 1 in a flat plane. The most common and appropriate sheet
size is 7' by 20', as shown in FIGS. 2 and 3.
[0024] FIG. 2 shows how the bundle 10 of "figure-8" tubing 1 can be
deployed into a narrow serpentine pattern 13a. Compared to a wide
serpentine pattern 13b shown in FIG. 3, the narrow serpentine
pattern 13a requires less factory space for the winding process,
and facilitates pre-fabrication of the tubing/grid arrays, as
discussed with reference to FIG. 4. The tubing 1 is sufficiently
flexible that the curved tubing segments 4, which in packing make
turns of more than 180.degree., quite easily open to 180.degree.
during deployment of the tubing 1. In an exemplary preferred
layout, "tails" of the heating elements from each pattern 13
connect to a supply box or "manifold center". Thus, it is
beneficial to have both the supply end 16 and the return end 15
leaving the grid 11 in close proximity to one another. For example,
FIG. 2 shows a "tail" 15 of the heating element that proceeds
straight from the left end to the right end of the grid 11. When
installed at the job site, the tail 15 will proceed with the second
tail/supply end 16 to the manifold center connection point.
[0025] A common spacing of the tubing 1 on the grid 11 is 12'' on
center. The configuration or pattern shown in FIG. 2 uses tubing
nominally wound on 12'' mandrels with axes spaced 4' apart, so that
the "outside-to-outside" serpentine pattern is 5' wide. Located on
the grid 11 as shown, this pattern allows side-by-side grid
placement that essentially maintains a spacing of about 12''
between the tubing 1 including the tail 15. In FIG. 2, tubing
segments 17 and the tail 15 have already been secured to the grid
11 with ties 18. Various devices can be used for the ties 18.
Field-placed tubing is typically held to the mesh grids 11 with
either wire ties or ("zip") cable ties placed by hand. An example
of a motorized wire tie system is discussed with respect to FIG. 4.
Spacing of the ties 18 varies with location of the tubing 1 on the
grid 11. For example, along the straight segments 5, the ties may
be spaced up to 36'' apart, but at the 180.degree. curved segments
4, ties 18 are recommended at the intersection of the straight and
curved segments 5, 4. A spacing of about 24'' between the ties 18
is recommended along the tail 15 (FIG. 2) where the curved segments
4 have been opened to form a continuous straight segment 5. The
dotted line 19 shows where the "not yet secured" tubing will be
placed, and how the other tail 16 will leave the grid parallel to
the first tail 15.
[0026] FIG. 3 also shows the tubing 1 placed 12'' on center. In
this exemplary embodiment, the tubing 1 having a figure-8 pattern
was wound on 12'' diameter mandrels spaced 17' apart, and the
"outside" serpentine dimension is 18'. Most features of this wide
figure-8 pattern 13b are similar to those discussed with respect to
FIG. 2, including tails 15 and 16 leaving the grid 11 at the same
corner. However, this wide or "long serpentine" pattern 13b would
better integrate with grid sheets 11 of even footage width
increments (for example, 6' or 8' wide) so that identical
grid/tubing panels 11 could provide even spacing of the tubing 1 in
side-by-side placement. With the 7' grid 11 or other "odd" footage
widths, uniform spacing of the tubing 1 across multiple panels can
only be achieved by adding an extra serpentine element to each
alternate sheet 11. For example, alternating 7' panels can have
four serpentine pairs each, and their alternating neighbors can
have three pairs, like the panel shown in FIG. 3.
[0027] FIG. 4 is an isometric view showing an exemplary method for
pre-fabricating tubing 1 in the narrow figure-8 pattern 13 to a
grid substrate 11. The pre-fabricated tubing/grid panel 24, shown
in FIG. 4, is similar to the grid 11 discussed with respect to FIG.
2. In an exemplary embodiment of the method, the grid 11 is
supported in a vertical position so that the tubing installer 20
can work in a more convenient and comfortable position compared to
installing the tubing 1 on the floor or at a horizontal table. In
the embodiment, the grid 11 is hung from above its horizontal
centerline on pegs 21 that project from a support rail 22. The
support system may also include a lower support rail (not shown) to
stabilize the grid during assembly. Assembly proceeds starting with
placement of the grid 11 onto the pegs 21 of the support rail 22.
The tubing bundle 10 (not shown) is then deployed onto the grid 11
by hanging the curved segments 4 over the pegs 21, with one peg 21
per serpentine loop. The installer 20 may preferably use a
motorized tie gun 23 to quickly attach the tubing 1 to the grid 11
at ties 18. The top tail 15 may be tied to the grid 11 either
before or after the serpentine loops are tied. After all ties 18
are completed, the "off panel" tubing in the tails 15 and 16 may be
bundled and lightly secured to the edge of tubing/grid panel 24 for
transporting. The assembled grid/tubing arrays 24 may be stacked in
any position for storage and delivery.
[0028] FIG. 5 is a cross-sectional view showing an exemplary method
for placing pre-fabricated panels in a concrete slab. In a typical
slab-on-grade application, edge forms 25 confine the concrete pour,
and are partially supported by a concrete footing 26. Grid/tubing
panels 24 are supported by standoffs 27 above a prepared base layer
28. In an exemplary embodiment, the panels 24 are placed with the
tubing 1 at an underside of, rather than above, the grid 11.
Locating the tubing 1 below the grid 11 is an advantage of the
pre-assembly process as it keeps the tubing 1 lower in the concrete
slab where it is less vulnerable to puncture from above, and it
keeps the tubing 1 from floating upward between its tie points 18.
Before a slab 29 is poured, the tails 15, 16 (not shown) from the
panels 24 are deployed to the manifold center (not shown) and
connected for a leakage test. Typically, the tubing 1 remains
pressurized during the pour, and pressure is monitored to verify
continuing integrity during the labor activities. In a typical 4''
thick slab, the grid panels 24 are placed at a vertical centerline
of the slab 29. Several types of standoffs 27 are available and are
well known in the art. Alternatively, instead of using standoffs,
the panels 24 may be placed directly on the base layer 28, and then
lifted using a "J-hook" during the pour, to place the panels 24
near the vertical centerline of the concrete slab 29.
[0029] FIG. 6 is a cross-sectional view showing an exemplary method
for placing the pre-fabricated assembly on a framed floor with a
cementatious topping in conjunction with metal fins that improve
heat transfer. The floor construction includes joists 30 that
support the subfloor 31 and a cement topping 32. This floor
construction method is used where the mass of a concrete or gypsum
cement topping is valued for its thermal and/or acoustical
benefits. The topping 32 does not as effectively spread heat
laterally compared to the full slab shown in FIG. 5, and the
absence of a steel mesh grid also reduces lateral heat transfer.
Aluminum channel fins 33 may be secured to the subfloor 31 in close
contact with the tubing 1 to improve heat transfer and to minimize
the likelihood that occupants will feel "hot lines" on the floor
surface 34 directly above the tubing 1. The channel fins 33 are
only placed over straight sections 5 of the tubing 1.
[0030] Another advantage of the figure-8 tubing 1 is apparent in
considering installation of the channel fins 33. For example,
conventional rolled tubing must first be secured to a subfloor to
straighten the tubing before the channel fins can be placed. With
the figure-8 tubing 1, the tubing 1 need not be secured to the
subfloor 31 before the channel fins 33 are placed. Instead, the
tubing 1 can be held by the channel fins 33 which are secured to
the subfloor 31. This process works because the channel fins 33 can
readily be snapped over the straight sections 5 of the figure-8
tubing 1.
[0031] The figure-8 tubing 1 may also benefit installations of the
"Low Mass Hydronic Radiant Floor System" shown in U.S. Pat. No.
4,782,889 (1988). In this application (not shown), tubing is held
by and in the grooves of a corrugated metal deck that replaces the
subfloor in framed construction. As with respect to FIG. 6, the
pre-formed serpentine patterns afforded by the figure-8 tubing 1
simplify installation by eliminating the need to wrestle with
continuously curved tubing. Instead, the tubing 1 can be quickly
deployed in its approximate final position, and then secured by
pushing it down into the grooves in the corrugated metal deck.
[0032] In practice, one of the most cost-effective radiant heat
designs combines low piping and manifold costs with relatively low
pressure drop to minimize pump size and energy use. Optimal circuit
lengths, tubing sizes, and tube spacings often dictate arrays that
require two grid panels. For example, two 7'.times.20' grids may be
placed end-to-end to form a 7'.times.40' assembly, or side-by-side
to form a 14'.times.20' assembly. For U.S. markets where 1/2
diameter (nominal) tubing is most common, the resulting 280 square
foot area is appropriate for the optimal circuit. FIG. 7 shows a
folded panel with a tubing circuit pattern known as a "spiral
pair." This pattern is similar to the "long serpentine" shown in
FIG. 3. For both patterns, folding a "two grid" panel in the middle
requires bends in all the parallel tubes in the array. The narrow
serpentine pattern shown in FIG. 2 only requires two bends, but in
either event, the tubing must not be damaged by bending. Tubing
manufacturers typically specify minimum bend radii for their
products. For example, the minimum bend radius for most
cross-linked polyethylene (PEX) tubes is 10 diameters. Thus, a
1/2'' tube (actually 0.625'' diameter) can be formed to a 6.25''
bend radius- or roughly to a 12'' semi-circle in a serpentine
pattern.
[0033] FIG. 7 is an isometric view showing a method for folding two
grid sections that support a single tubing circuit. With two
end-to-end grids 11a, 11b joined only by the tubing 1, and with the
tubing 1 not joined to the grids 11 near the intersection of the
grids 11a, 11b, one grid 11 may be offset with respect to the other
grid 11 by a predetermined bend diameter. A folded width of the
assembled grids 11a, 11b is then the width of the grid plus the
tubing bend diameter. As shown in FIG. 7, the tubing 1 is secured
to a folded pair of grids 11a and 11b. The two grids 11a, 11b are
folded about line 37. When the pair of grids 11a, 11b is unfolded,
the top corner 40 on the left grid 11a will meet the top corner 41
on the right grid 11b. When folded, the tubing 1 is contained
between the two grids 11a and 11b. With the grids 11a, 11b in the
folded position, the two top corners 40 and 41 are displaced by a
length 19 (typically the minimum tubing bend diameter), allowing
the tubing 1 to form arcs 17 without crimping the tubing 1. In the
case shown where the bend radius equals the grid wire spacing, the
arcs 17 are inset by a distance 18 equal to approximately 0.57
times the bend radius. For the 6'' spacing and bend radius shown,
the distance 18 equals approximately 3.4''. Thus, the ties 38 and
39 should be no closer than 9.4'' (6''+3.4'') to the fold line 37.
After unfolding and placement in the prepared foundation, the grids
11a and 11b may be wired together along the fold line 37, with the
corners 40 and 41 intersecting.
[0034] Although the subject matter of this application has been
described with reference to various exemplary embodiments, it is to
be understood that the subject matter is not limited to the
exemplary embodiments or constructions. To the contrary, the
subject matter of this application is intended to cover various
modifications and equivalent arrangements. In addition, while the
various elements of the exemplary embodiments are shown in various
combinations and configurations, others combinations and
configurations, including more, less, or only a single element, are
also within the spirit and scope of the invention.
* * * * *