PACKAGE OF RECLOSABLE BAGS WITH STAGGERED SLIDERS

20250326563 ยท 2025-10-23

Assignee

Inventors

Cpc classification

International classification

Abstract

A package of reclosable bags and method of packaging the same including a roll having a number x of reclosable bags each having opposite first, and second panels joined along corresponding first and second sides thereof and a mouth having a width defined therebetween. The mouth having a closure member along its width, and a slider for opening and closing the reclosable bag offset along the closure member relative to the slider of each adjacent reclosable bag in the roll. The roll of reclosable bags rolled about an axis parallel with the mouth of each bag and housed in a container having a plurality of walls defining a compartment. The container having a cross-sectional area linearly correlated with the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b.

Claims

1. A package of reclosable bags, the package comprising: a roll of reclosable bags, the roll comprising a number x of reclosable bags, wherein each reclosable bag has: a first panel and a second panel opposite the first panel, the first panel and the second panel joined along corresponding first and second sides thereof with a mouth defined therebetween, the mouth having a width less than about 9 inches, and a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth, wherein the roll is rolled about an axis parallel with the mouth of each bag, and further wherein the slider of each reclosable bag in the roll is offset along the closure member relative to the slider of each adjacent reclosable bag of the roll; and a container comprising a plurality of walls defining a compartment, the plurality of walls including a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall, wherein the container has a cross-sectional area in side view, the cross-sectional area being linearly correlated with the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, wherein m is about 0.17 and b is about 3.16, and wherein the cross-sectional area is in square inches.

2. The package of claim 1, wherein the reclosable bags of the roll are arranged in an overlapping shingled arrangement.

3. The package of claim 1, wherein the sliders of adjacent reclosable bags of the roll are staggered in a repeating pattern.

4. The package of claim 1, wherein each slider has a slider length measured along the width of the mouth and each slider is offset along its respective closure member relative to the slider of each adjacent reclosable bag a distance greater than the slider length, and wherein the first side of each reclosable bag of the roll is aligned with the first side of each adjacent reclosable bag of the roll.

5. The package of claim 1, wherein the container has a spatial efficiency defined by a second equation of X the cross - sectional area , the spatial efficiency being measured in bags/unit cross-section value, wherein x is between 20 and 30 when the spatial efficiency is above 3, and wherein x is between 31 and 40 when the spatial efficiency is above 3.3.

6. The package of claim 1, wherein the container has an overall width at least equal to but less than 10% greater than the width of the mouth of each reclosable bag of the roll.

7. The package of claim 1, wherein the mouth each of each reclosable bag of the roll has a width between 7.5 and 8.5 inches.

8. A package of reclosable bags, the package comprising: a roll of reclosable bags, the roll comprising a number x of reclosable bags, wherein each reclosable bag has: a first panel and a second panel opposite the first panel, the first panel and the second panel joined along corresponding first and second sides thereof with a mouth defined therebetween, the mouth having a width greater than about 9 inches, and a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth, wherein the roll is rolled about an axis parallel with the mouth of each bag, and further wherein the slider of each reclosable bag in the roll is offset along the closure member relative to the slider of each adjacent reclosable bag of the roll; and a container comprising a plurality of walls defining a compartment, the plurality of walls including a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall, wherein the container has a cross-sectional area in side view, the cross-sectional area having a linear correlation to the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, wherein m is about 0.26 and b is about 2.48, and wherein the cross-sectional area is in square inches.

9. The package of claim 8, wherein the reclosable bags of the roll are arranged in an overlapping shingled arrangement.

10. The package of claim 8, wherein the sliders of adjacent reclosable bags of the roll are staggered in a repeating pattern.

11. The package of claim 8, wherein each slider has a slider length measured along the width of the mouth and each slider is offset along its respective closure member relative to the slider of each adjacent reclosable bag a distance greater than the slider length, and wherein the first side of each reclosable bag of the roll is aligned with the first side of each adjacent reclosable bag of the roll.

12. The package of claim 8, wherein the container has a spatial efficiency defined by a second equation of X the cross - sectional area , the spatial efficiency being measured in bags/unit cross-section value, and wherein x is between 15 and 30 when the spatial efficiency is above 2.3, and wherein x is between 31 and 40 when the spatial efficiency is above 3.

13. The package of claim 8, wherein the container has an overall width at least equal to but less than 10% greater than the width of the mouth of each reclosable bag of the roll.

14. The package of claim 8, wherein the mouth of each reclosable bag of the roll has a width between 9.5 and 11.5 inches.

15. A method of packaging reclosable bags comprising: stacking a number x of reclosable bags, each of the reclosable bags having opposite first and second panels joined along corresponding first and second sides thereof, and a mouth having a width defined therebetween, the mouth having a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth; staggering the positions of each slider offset along the closure member relative to the slider of each adjacent reclosable bag, rolling the stacked reclosable bags about an axis parallel with the mouth of each bag; and inserting the roll of reclosable bags into a container having a plurality of walls defining a compartment, the plurality of walls including a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall, wherein the container has a cross-sectional area in side view, the cross-sectional area having a linear correlation to the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, m being about 0.17 and b being about 3.16 when x is a number of reclosable bags in the roll each having mouth widths less than about 9 inches and m being about 0.26 and b being about 2.48 when x is a number of reclosable bags in the roll each having mouth widths greater than about 9 inches, wherein the cross-sectional area is in square inches.

16. The method of claim 15, wherein the reclosable bags of the roll are arranged in an overlapping shingled arrangement.

17. The method of claim 15, wherein the sliders of adjacent reclosable bags of the roll are staggered in a repeating pattern.

18. The method of claim 15, wherein each slider has a slider length measured along the width of the mouth and each slider is offset along its respective closure member relative to the slider of each adjacent reclosable bag a distance greater than the slider length, and wherein the first side of each reclosable bag of the roll is aligned with the first side of each adjacent reclosable bag of the roll.

19. The method of claim 15, wherein the container has an overall width at least equal to but less than 10% greater than the width of the mouth of each reclosable bag of the roll.

20. The method of claim 15, wherein the cross-sectional area is defined by the equation 0.17x+3.16 when each reclosable bag in the roll has a mouth width between 7.5 and 8.5 inches, and wherein the cross-sectional area is defined by the equation 0.26x+2.48 when each reclosable bag in the roll has a mouth width between 9.5 and 11.5 inches.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 is a front, left perspective view of an exemplary package in accordance with the disclosed subject matter, including an exemplary container and exemplary reclosable bags.

[0016] FIG. 2 is a front view of a reclosable bag of the package in FIG. 1.

[0017] FIG. 3 is a front view of reclosable bags of the package in FIG. 1 arranged in an overlapping shingled arrangement.

[0018] FIG. 4 is a side view of a roll of reclosable bags.

[0019] FIG. 5 is a front, left perspective view of the container of the package in FIG. 1.

[0020] FIG. 6 is a cross-section of the side of the container in FIG. 5.

[0021] FIG. 7 is a graph illustrating the linear correlation between cross-section and reclosable bags for bags having a mouth width less than about 9 inches.

[0022] FIG. 8 is a graph illustrating the linear correlation between cross-section and reclosable bags for bags having a mouth width greater than about 9 inches.

DETAILED DESCRIPTION

[0023] Reference will now be made in detail to the various exemplary embodiments of the disclosed subject matter, which are illustrated in the accompanying drawings. The structure and corresponding method of operation of the disclosed subject matter will be described in conjunction with the detailed description of the system. The accompanying drawings, where like reference numerals refer to identical or functionally similar elements throughout the separate views, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the disclosed subject matter.

[0024] The package and methods presented herein can be used to store and dispense reclosable bags having sliders for opening and closing the bags. The positioning of the sliders during manufacturing and packaging can impact the packaging efficiency and size of the containers, which can cause increased shipping and materials costs. The package and methods of the disclosed subject matter can reduce the cross-section of the container and increase the packaging efficiency.

[0025] The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout separate views, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the disclosed subject matter. For purpose of explanation and illustration, and not limitation, exemplary embodiments of the reclosable bags and container, as well as the various methods for packaging the reclosable bags, are shown in FIGS. 1-8.

[0026] For purpose of illustration, and not limitation, reference will be made to an exemplary embodiment of a package of reclosable bags having a container and a roll of reclosable bags therein. As used herein, the terms front, end, side, top, and bottom are used for the purpose of illustration only, and not limitation. That is, it is recognizable that the terms front, end, side, top, and bottom are interchangeable and are merely used herein as a point of reference.

[0027] The disclosed subject matter is generally directed to a package of reclosable bags having a container and a roll of reclosable bags therein. The package of reclosable bags in accordance with the disclosed subject matter generally includes a roll of reclosable storage bags. The roll having a number of x reclosable bags each having a first panel and a second panel opposite the first panel, the first panel and the second panel joined along corresponding first and second sides thereof with a mouth defined therebetween. The reclosable bags further include a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth. The roll is formed by rolling the reclosable bags about an axis parallel with the mouth of each bag, and the slider of each reclosable bag in the roll is offset along the closure member relative to the slider of each adjacent reclosable bag of the roll.

[0028] The disclosed subject matter further includes a container having a plurality of walls defining a compartment. The plurality of walls includes a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall. The container has a cross-sectional area in side view defined in square inches.

[0029] The cross-sectional area in side view of the container is linearly correlated with the number of reclosable bags in the roll. As described further herein, the linear correlation between the number of reclosable bags in the roll and the cross-sectional area of the container can be different for reclosable bags of different sizes. In accordance with an aspect of the disclosed subject matter, for reclosable bags having a mouth width less than about 9 inches the cross-sectional area is linearly correlated with the number of bags in the roll as defined by an equation of cross-section=m(x)+b, where m is about 0.17 and b is about 3.16. In accordance with another aspect of the disclosed subject matter, for reclosable bags having a mouth width greater than about 9 inches the cross-sectional area is linearly correlated with the number of bags in the roll as defined by an equation of cross-section=m(x)+b, where m is about 0.26 and b is about 2.48.

[0030] The disclosed subject matter further includes a method of packaging reclosable bags comprising. The method including stacking a number x of reclosable bags, staggering the positions of each slider offset along the closure member relative to the slider of each adjacent reclosable bag, rolling the stacked reclosable bags about an axis parallel with the mouth of each bag, and inserting the roll of reclosable bags into a container having a plurality of walls defining a compartment. As noted above, the container has a cross-sectional area, and the cross-sectional area of the container can be different for reclosable bags of different sizes. In accordance with an aspect of the disclosed subject matter, the cross-sectional area has a linear correlation to the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, where x is a number of reclosable bags in the roll each having mouth widths less than about 9 inches, m is about 0.17 and b is about 3.16. In accordance with another aspect of the disclosed subject matter x is a number of reclosable bags in the roll each having mouth widths greater than about 9 inches, m is about 0.26, and b is about 2.48.

[0031] For the purpose of illustration, and not limitation, reference is made to the exemplary package 100 shown in FIG. 1-6. Additionally, for purpose of understanding, reference is made in conjunction to the linear equations depicted in the graphs in FIGS. 7 and 8, which can be used to define the linear correlation between the cross-section of the container 120 and the number of reclosable bags 104 in a roll of reclosable bags 102 that form the exemplary package 100 in FIGS. 1-6.

[0032] With reference to FIGS. 1 and 2, the package 100 includes a container 120 configured to store a roll of x reclosable bags 102 (not shown) within a compartment 122 therein, with x representing the number of reclosable bags. Each reclosable bag 104 in the roll of reclosable bags 102 has a first panel 106a opposite a second panel 106b (not shown). The first and second panels 106a,b are joined along corresponding first and second sides 112a,b thereof. As embodied herein, the first and second panels 106a,b can have an overall thickness of between 0.001 inches and 0.003 inches. The reclosable bags can be made of any suitable blend of flexible resin material. For purpose of example and not limitation the reclosable bags can be made of a material including, but not limited to, polyethylene, silicone, and polypropylene. A mouth 110 is defined between the first and second sides 112a,b of the reclosable bag 104, the mouth 110 having a width w.sub.1 in inches. As embodied herein, the width w.sub.1 of the mouth 110 is less than about 9 inches. For purpose of example, and not limitation, the width w.sub.1 can be between 7.5 and 8.5 inches. Extending along the mouth 110 is a closure member 116 including a slider 118 for opening and closing the mouth 110, the slider 118 having a length/measured along the width w.sub.1 of the mouth 110.

[0033] With reference to FIGS. 3 and 4, prior to rolling, the reclosable bags 104 are stacked and the slider 118 of each reclosable bag 104 is offset along its respective closure member 116 relative to the slider 118 of each adjacent reclosable bag 104. For example, the stack can include a first reclosable bag 104a, a second reclosable bag 104b adjacent the first reclosable bag 104a, and a third reclosable bag 104c adjacent the second reclosable bag 104b. he slider 118 of the first reclosable bag 104a can be spaced a first distance d.sub.1 from the first side 112a of the first reclosable bag 104a. The slider 118 of the second reclosable bag 104b can be spaced a second distance d.sub.2 from the first side 112a of the second reclosable bag 104b, the second distance d.sub.2 being greater than the first distance d.sub.1 by at least the slider length l. The slider 118 of the third reclosable bag 104c can be spaced a third distance d.sub.3 from the first side 112a of the third reclosable bag 104c, the third distance d.sub.3 being greater than the second distance d.sub.2 by at least the slider length l.

[0034] As embodied herein, a fourth reclosable bag 104d can be stacked adjacent the third reclosable bag 104c. For example, and as embodied herein, the slider 118 of the fourth reclosable bag 104d can be spaced a fourth distance d.sub.4 from the first side 112a, the fourth distance d.sub.4 being equal to the first distance d.sub.1, thereby creating a staggered repeating pattern. The staggered slider pattern illustrated in FIG. 3 is exemplary. Sliders can be staggered in any desirable pattern. In another example, the sliders 118 can be staggered along the entirety of the width w.sub.1 of the mouth 110 before restarting the pattern on another adjacent reclosable bag 104. Those having skill in the art will appreciate that the sliders 118 can be positioned in a variety of staggered patterns without departing from the spirit or scope of the disclosed subject matter.

[0035] As illustrated in FIGS. 3 and 4, during stacking, the reclosable bags 104 can be arranged in an overlapping shingled arrangement. For example, and as embodied herein, the bags can be stacked on top of one another and arranged such that the first and second panels of adjacent bags overly one another and mouths of adjacent bags do not overly one another. As embodied herein, when the reclosable bags are rolled about an axis parallel with the mouth 110 of each bag, each adjacent reclosable bag 104 in the roll 102 can be overlapping in a shingled arrangement. As further embodied herein, the first side 112a of each reclosable bag 104 in the roll 102 can be aligned with the first side 112a of the other reclosable bags 104 of the roll 102. As embodied herein, the roll of reclosable bags 102 can have a cylindrical shape. Furthermore, the roll 102 has a number of x reclosable bags 104. In some instances, x is between 1 and 49.

[0036] With reference to FIG. 5, the container 102 of the package 100 includes a plurality of walls defining a compartment 122. The plurality of walls includes a bottom wall 124 having a depth d and a width w.sub.2, a front wall 126 having a height h extending upwardly from the bottom wall 124 and a back wall (not shown) opposite the front wall 126. The plurality of walls further includes a first side wall 128 having a height extending upwardly from the bottom wall adjacent the front and back walls 126, 132, a second side wall 129 (not shown) having a height extending upwardly from the bottom wall 124 opposite the first side wall 128, and a top wall 130 having a depth opposite the bottom wall 124.

[0037] With reference to FIGS. 6-8, the plurality of walls of the container 102 define an internal compartment 122 for storing the roll of reclosable bags 102 therein. Accordingly, the width w.sub.2 of the container 120 is large enough to accommodate the width w.sub.1 of the reclosable bags 104. As embodied herein, the overall width w.sub.2 of the container 120 can be at least equal to but less than 10% greater than the width w.sub.1 of the mouth 110 of each reclosable bag 104 of the roll 102. For example, and as embodied herein, the first side of each reclosable bag of the roll can be aligned with the first side of the other reclosable bags of the roll. As embodied herein, having the first sides of each reclosable bag of the roll aligned can reduce the overall width w.sub.2 of the container 120 that can be required to accommodate the width of the roll of reclosable bags.

[0038] Furthermore, the container 102 can have a cross-sectional area in side view in square inches, as seen in FIG. 6. As embodied herein, the cross-sectional area can be calculated by multiplying the height h of the front wall 126 by the depth d of the bottom wall 124. Although the disclosed embodiments include containers having rectangular cross-sections, it is to be understood that containers having alternative configurations can be used with the disclosed subject matter and the cross-sectional area of such configurations can be calculated as is known in the art.

[0039] The cross-sectional area of the container is linearly correlated with the number of reclosable bags 104 in the roll 102. The linear correlation between the number of reclosable bags in the roll and the cross-sectional area of the container can be different for reclosable bags of different sizes. In accordance with an aspect of the disclosed subject matter, for reclosable bags having a mouth width less than about 9 inches the cross-sectional area is linearly correlated with the number of reclosable bags 104 in the roll 102 as defined by an equation of cross-section=m(x)+b, where m is about 0.17 and b is about 3.16. As used herein, m being about 0.17 means that m is between 0.15 and 0.19 and b being about 3.16 means that b is between 3.1 and 3.2. This linear correlation is depicted in FIG. 7. FIG. 7 depicts measured cross-sectional areas and reclosable bag counts for exemplary packages in accordance with the discloses subject matter. A linear trend line illustrates the linear correlation between the number of reclosable bags in the package and the cross-sectional area of the container.

[0040] According to another aspect of the disclosed subject matter, the container 120 can further include a spatial efficiency defined by a second equation of

[00003] X the cross - sectional area .

As with the relationship between cross-sectional area and the number of reclosable bags in the roll, the spatial efficiency of the container can be different for reclosable bags of different sizes. As embodied herein, the reclosable bags can have a mouth width less than about 9 inches, and when x is between 20 and 30 the spatial efficiency can be above 3, and when x is between 31 and 40 the spatial efficiency can be above 3.3.

[0041] Additionally, or alternatively, the reclosable bags 104 can have a mouth width w.sub.1 greater than about 9 inches. For purpose of example, and not limitation, the mouth width w.sub.1 can be between 9.5 and 11.5 inches. In accordance with an aspect of the disclosed subject matter, the linear correlation between the cross-section of the container 102 and the reclosable bags 104 in the roll 102 for reclosable bags having a mouth width w.sub.1 greater than about 9 inches can be defined by the equation of cross-section=m(x)+b, where m is about 0.26 and b is about 2.48. As used herein, m being about 0.26 means that m is between 0.2 and 0.3 and b being about 2.48 means that b is between 2.4 and 2.5. This linear correlation is depicted in FIG. 8. FIG. 8 depicts measured cross-sectional areas and reclosable bag counts for exemplary packages in accordance with the discloses subject matter. A linear trend line illustrates the linear correlation between the number of reclosable bags in the package and the cross-sectional area of the container.

[0042] In accordance with the disclosed subject matter described above, the reclosable bags 104 can have a mouth width w.sub.1 greater than about 9 inches and the container 120 can include a spatial efficiency defined by a second equation of

[00004] X the cross - sectional area .

The spatial efficiency is measure in bags/unit cross-section value, and when x is between 15 and 30 the spatial efficiency can be above 2.3, and when x is between 31 and 40 the spatial efficiency can be above 3.

[0043] As embodied herein, the disclosed subject matter further includes a method of packaging the reclosable bags 104. In accordance with the described subject matter above, the method includes stacking a number x of reclosable bags 104 and staggering the positions of each slider 118 located on each of the reclosable bags 104 offset along the mouth 110 of the closure member 116 relative to the slider 118 of each adjacent reclosable bag 104. The method further includes rolling the stacked reclosable bags 104 about an axis parallel with the mouth 110 of each bag 104 creating a roll of reclosable bags 102. The method also includes inserting the roll of reclosable bags 102 into a container 120.

[0044] As described above, the container 120 has a cross-sectional area that can differ for reclosable bags of different sizes. In accordance with an aspect of the disclosed subject matter, the cross-sectional area has a linear correlation to the number of reclosable bags 104 in the roll 102 defined by an equation of cross-section=m(x)+b, where x is a number of reclosable bags 104 in the roll 102 each having mouth 110 widths less than about 9 inches, m is about 0.17 and b is about 3.16. In accordance with another aspect of the disclosed subject matter x is a number of reclosable bags 104 in the roll 102 each having mouth 110 widths greater than about 9 inches, m is about 0.26, and b is about 2.48.

Example 1

[0045] For purpose of illustration and not limitation, exemplary packages of reclosable bags in accordance with the disclosed subject matter were prepared as outlined below. Each package included a roll of reclosable bags. The number of reclosable bags in each roll is denoted in Table 1 below. Each reclosable bag in the roll included a first panel and a second panel opposite the first panel, the first panel and the second panel joined along corresponding first and second sides thereof with a mouth defined therebetween, the mouth having a width less than about 9 inches. Each reclosable bag in the roll included a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth. The roll was rolled about an axis parallel with the mouth of each bag. The slider of each reclosable bag in the roll was offset along the closure member relative to the slider of each adjacent reclosable bag of the roll. The exemplary packages each included a container comprising a plurality of walls defining a compartment, the plurality of walls including a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall. The dimensions of the exemplary containers are included below in Table 1. Each of the exemplary containers has a cross-sectional area in side view, the cross-sectional area being linearly correlated with the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, wherein m is about 0.17 and b is about 3.16, and wherein the cross-sectional area is in square inches. For further purposes of illustration, and not limitation, a container having a bag count of 25 and a cross-section of 7.72 square inches would be in accordance with the disclosed subject matter and the linear correlation recited above.

TABLE-US-00001 TABLE 1 Bag Count Cross-Section 18 6.47 22 6.47 25 7.72 26 7.72 35 9.77 40 9.77

Example 2

[0046] For purpose of illustration and not limitation, exemplary packages of reclosable bags in accordance with the disclosed subject matter were prepared as outlined below. Each package included a roll of reclosable bags. The number of reclosable bags in each roll is denoted in Table 2 below. Each reclosable bag in the roll included a first panel and a second panel opposite the first panel, the first panel and the second panel joined along corresponding first and second sides thereof with a mouth defined therebetween, the mouth having a width greater than about 9 inches. Each reclosable bag in the roll included a closure member extending along the mouth, the closure member including a slider configured to open and close the mouth. The roll was rolled about an axis parallel with the mouth of each bag. The slider of each reclosable bag in the roll was offset along the closure member relative to the slider of each adjacent reclosable bag of the roll. The exemplary packages each included a container comprising a plurality of walls defining a compartment, the plurality of walls including a bottom wall having a depth, a front wall having a height extending upwardly from the bottom wall, and a side wall having a height extending upwardly from the bottom wall and adjacent the front wall. The dimensions of the exemplary containers are included below in Table 2. Each of the exemplary containers has a cross-sectional area in side view, the cross-sectional area being linearly correlated with the number of reclosable bags in the roll defined by an equation of cross-section=m(x)+b, wherein m is about 0.26 and b is about 2.48, and wherein the cross-sectional area is in square inches. For further purposes of illustration, and not limitation, a container having a bag count of 40 and a cross-section of 12.71 square inches would be in accordance with the disclosed subject matter and the linear correlation recited above.

TABLE-US-00002 TABLE 2 Bag Count Cross-Section 15 6.47 17 6.47 20 7.72 22 7.72 25 9.77 30 9.77 40 12.72

[0047] In addition to the specific embodiments claimed below, the disclosed subject matter is also directed to other embodiments having any other possible combination of the dependent features claimed below and those disclosed above. As such, the particular features presented in the dependent claims and disclosed above can be combined with each other in other manners within the scope of the disclosed subject matter such that the disclosed subject matter should be recognized as also specifically directed to other embodiments having any other possible combinations. Thus, the foregoing description of specific embodiments of the disclosed subject matter has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosed subject matter to those embodiments disclosed.

[0048] It will be apparent to those skilled in the art that various modifications and variations can be made in the method and system of the disclosed subject matter without departing from the spirit or scope of the disclosed subject matter. Thus, it is intended that the disclosed subject matter include modifications and variations that are within the scope of the appended claims and their equivalents.