Compressed core-wound paper product having a core opening and a process of making the same

Disclosed is a compressed core-wound paper product such as toilet tissue or paper towels. The core-wound paper product comprises a paper product wound about a generally tubular core. The core-wound paper product is compressed, so that the core is flattened to form vertices. By selecting the proper combination of core materials and thickness, to form a core of the proper stiffness; paper product caliper and quantity, to provide hoop forces against the core which are not too great; and total packaging dimensions, so that the core-wound paper product is not too tightly constrained, the core-wound paper product may be made to open to an inside core dimension of about 0.16 centimeters (0.06 inches) to about 1.27 centimeters (0.5 inches). The invention may be utilized with either single roll or multiple roll packages.

FIELD OF THE INVENTION 
This invention relates to core-wound paper products, particularly to 
compressed core-wound paper products and the cores used in compressed 
core-wound paper products, and more particularly to compressed core-wound 
paper products having cores with an opening and the cores therefor. 
BACKGROUND OF THE INVENTION 
Core-wound paper products are in constant use in daily life. Particularly, 
toilet tissue and paper towels have become a staple in home and industry. 
Such products comprises a roll of the consumer goods wrapped in a spiral 
around a hollow center core. The hollow center core has a a volume which 
is not used until the product is inserted onto a spindle for dispensing by 
the consumer. 
One factor affecting the pricing and usage of core-wound paper products is 
the costs of transportation, storage and shelving for such products. These 
costs reflect the size of the core-wound paper product and are increased 
by the volume of the core. One attempt in the art to reduce the costs 
associated with the contribution of the package volume to the size of the 
core-wound paper product is to compress the product, reducing or 
eliminating the void space of the hollow core. 
For example, as early as 1889, U.S. Pat. No. 401,233 issued Apr. 9, 1889 to 
Wheeler disclosed a flattened roll of toilet paper having a comparatively 
rigid interior reinforcement. This arrangement is to allow the incisions, 
which facilitate insertion of a suspensory device, to lie in the same 
plane. As early as 1911, U.S. No. Pat. 1,005,787 issued Oct. 10, 1911 to 
Sibley disclosed a corrugated core for packages of wound fabric. The 
package is compressed into a flattened state to occupy less space during 
transportation and stocking. U.S. Pat. No. 1,316,041 issued Sep. 16, 1919 
to Johnson disclosed a straight flattened roll of toilet tissue having a 
core of flexible material with overlapped ends. The flat state was used 
for shipping, then the roll was bent into a kidney shape for application 
onto a dispensing fixture. 
Compressed core-wound paper product was also used in World War II, per 
government specifications. As described in the May, 1944 edition of Tissue 
Topics, the Hoberg Paper Mills Company intra-company newsletter, 
government toilet tissue was collapsed or flattened and packed in 1,000 
sheet rolls with 60 rolls per case. This arrangement was said to have 
conserved enough space to account for nine months of movement of a Liberty 
class cargo ship. 
One problem associated with compressed core-wound paper products is that of 
rerounding the cores to a generally cylindrical shape having a circular 
cross section. Rerounding is necessary to allow a spindle to be inserted 
through the core, so it can be used on an ordinary dispenser. Rerounding 
is often effected, as disclosed in U.S. Pat. No. 4,909,388 issued Mar. 20, 
1990 to Watanabe, by applying lateral compressive forces to the sides of 
the compressed core-wound paper product. 
When lateral compressive forces are applied to the product, the opposed 
sides of the core are expected to pop outwardly and away from each other. 
Each half of the core is then oriented concave towards the center of the 
core and the other half. However, frequently both halves of the core will 
buckle in the same direction, forming a somewhat crescent-shaped cross 
section. This phenomenon is known as core inversion and occurs when both 
sides of the core buckle such that the two halves of the core are concave 
in the same direction. 
When core inversion occurs upon rerounding, it is very difficult for the 
consumer to insert the spindle through the opening in the center of the 
core. The opening is too small to freely admit the spindle and the opposed 
halves of the core do not readily expand outwardly to be concave in 
opposite directions once inversion has occurred. 
However, the prior art related to compressed core-wound paper products has 
done little, if anything, to address this phenomenon. For example, 
commonly assigned U.S. Pat. No. 5,027,582 teaches away from the present 
invention by disclosing a method of packaging a compressed core-wound 
paper product by flattening the rolls, securing the flattened rolls to 
preclude substantial expansion, then relieving the loading used to flatten 
the rolls. 
Other art teaches away as well. For example U. K. Patent Application 
709,363 published May 19, 1954 in the name of Samson teaches diametrically 
flattening the cores and product. U.S. Pat. No. 4,909,388 issued Mar. 20, 
1990 to Watanabe teaches flattening the roll product to one-half its 
original volume or less and maintaining the roll in a particular flattened 
shape. This patent further teaches that rerounding occurs due to crepes 
and embosses in the paper product. 
One attempt in the art to promote rerounding is found in U.S. Pat. No. 
4,762,061 issued Aug. 9, 1988 to Watanabe et al. This patent teaches 
flattening the paper product through multi-stroke bilateral compression 
will improve the capability of the core-wound paper product to properly 
reround. 
However, it has been found that rerounding is greatly improved and 
occurrences of core inversion are obviated if the core is not presented to 
the consumer in a flattened state--as taught by the aforementioned art. 
Instead the compressed core-wound paper product should be presented to the 
consumer with the opposed sides of the core slightly opened and spaced 
apart from each other as specified below. The size of the opening should 
not be too small, otherwise the congenital inversion failures noted in the 
aforementioned prior art will still appear. Conversely, the size of the 
opening should not be too great, otherwise, in addition to defeating the 
desired economies of space savings, the core-wound paper product will 
appear to be product which has been inadvertently damaged, rather than 
deliberately compressed to a slight degree. Such appearance may evoke a 
negative consumer reaction without providing an offsetting benefit of 
economization. 
Cores for core-wound paper products having an opening are taught in the 
aforementioned U.S. Pat. No. 1,005,787 issued Oct. 10, 1911 to Sibley. 
This patent discloses a corrugated core which is somewhat elastic, yet 
either flexible or yielding. However, this patent does not teach the 
relationship between the corrugated core and the material wound thereon 
necessary to achieve a core opening which minimizes core inversions. 
Instead this patent simply teaches that the relationship between the core 
and the material wound thereon should permit the core to be inserted into 
the packages after the rolls are expanded, so that no difficulty is 
experienced in changing the roll shape. Clearly the step of inserting the 
core after expanding the product is an added inconvenience most consumers 
would find unacceptable. 
It is an object of this invention to improve the ability of the consumer to 
reround, with fewer occurrences of core inversion, the core of a 
compressed core-wound paper product to a generally cylindrical shape 
having a circular cross section. It is an object of this invention to 
produce a compressed core-wound paper product which encounters reduced 
occurrences of core inversion when the consumer attempts to reround the 
core to a generally cylindrical shape having a circular cross section. 
BRIEF SUMMARY OF THE INVENTION 
This invention relates to core-wound paper products which have been 
compressed to reduce the volume of the core void space. The compressed 
core-wound paper product has a generally tubular core with a cross section 
having diametrically opposed vertices. The vertices define the major axis 
of the core. A minor axis having dimensions of about 0.16 centimeters to 
about 1.27 (0.06 to 0.50 inches) and preferably about 0.51 centimeters to 
about 0.89 centimeters (0.20 to 0.35 inches) is orthogonal the major axis. 
Both the major and minor axes lie within the cross section of the core. 
A cellulosic paper product is wound about the core in a spiral pattern. The 
compressed core-wound paper product also has a constraining means for 
maintaining the compressed core-wound paper product in a compressed state. 
The compressed core-wound paper product further has a means for opening the 
core to the aforementioned dimensions of the minor axis after the core has 
been flattened until opposing halves of the core are in contact with one 
another.

DETAILED DESCRIPTION OF THE INVENTION 
As illustrated in FIG. 1 and as used herein, a "core" refers to a hollow 
tubular member about which another component is wound in a spiral pattern 
for later dispensing and removal. As used herein, a "paper product" refers 
to a cellulosic base product wound onto the core 20 and is removed, 
typically, in batch form, i.e., one or more sheets at a time, for usage 
and eventual discard. Used paper product 24, when taken from the core 20, 
is not returned. 
As used herein a "core-wound paper product" refers to the aggregation of a 
"core" and a "paper product" wound thereon. A "compressed core-wound paper 
product" refers to a "core-wound paper product" which is diametrically 
loaded and deformed from a round cross section. A compressed core-wound 
paper product 28 which has been "flattened" has been compressed until the 
core 20 is no longer generally hollow, and has portions of the two major 
faces in contact with one another at any point along the longitudinal 
axis. 
As is well understood by one skilled in the art, the core-wound paper 
product 28 may further comprise a wrapping, banding or other packaging 32 
to maintain the compressed configuration illustrated by FIG. 1. This 
wrapping, banding or other packaging 32 serves as a constraining means to 
maintain the core-wound paper product 28 in the compressed configuration 
and the desired cross section. 
A core 20, according to the present invention, may advantageously be used 
for paper products 24 such as toilet tissue or paper towels. The core 20 
is generally cylindrical prior to compression and flattening, has an axial 
length defined by two oppositely disposed ends. The ends of the core 20 
are circular in cross section prior to flattening. The line connecting the 
centers of these circles is the "longitudinal axis" of the core 20. As 
used herein "axial" refers to the direction of the longitudinal axis. 
When toilet tissue is wound on the core 20, the resulting core-wound paper 
product 28 of toilet tissue typically has a diameter of about 10.2 
centimeters to about 12.7 centimeters (4.00 to 5.00 inches) and a length 
of about 11.4 centimeters (4.50 inches) between the ends. If a core 20 
embodying the present invention is used for paper towels, the core-wound 
paper product 28 of paper towels typically has a diameter of about 10.2 to 
about 15.2 centimeters (4.00 to 6.00 inches) and a length of about 27.9 
centimeters (11.0 inches) for the embodiments described herein. 
It is preferred, but not necessary that the core 20 and the paper product 
24 used for the present invention have the same axial lengths. If there is 
a discrepancy between the axial lengths, generally, but not necessarily 
the core 20 or the paper product 24 having the greater axial length will 
control the performance of the other. 
The core 20 may be made of two layers of a paper having any suitable 
combination of cellulosic fibers such as bleached krafts, sulfites, 
hardwoods, softwoods, and recycled fibers. The core 20 should exhibit 
uniform strength without weak spots. Preferably, the core 20 is not 
calendared, so that it is relatively stiff and retains adhesive deposited 
thereon. The core 20 should have a mullen strength of at least 60 and 
preferably at least 70 as measured according to ASTM Test Method D2529. 
The core 20 may have a thickness of at least about b0.05 centimeters 
(0.020 inches) and preferably has a thickness of at least about 0.07 
centimeters (0.028 inches). The core 20 should be free of objectionable 
odors, impurities or contaminates which may cause irritation to the skin. 
The core 20 may be made of paper having a basis weight of about 0.19 to 
about 0.21 kilograms per square meter (38 to 42 pounds per 1,000 square 
feet), although cores 20 having a basis weight as high as 0.23 kilograms 
per square meter (47 pounds per 1,000 square feet) have been found to work 
well in the present invention. For the embodiments described herein, the 
core 20 should have a cross machine direction ring crush strength of at 
least about 74.4 kilograms per meter (50 pounds per inch) and preferably 
at least about 89.3 kilograms per meter (60 pounds per inch) as measured 
according to Tappi Standard T818 OM-87. 
As illustrated in FIG. 2, when compressed, the core 20 is subjected to 
diametrically applied compressive forces. As used herein, "diametrically 
applied compressive forces" refer to opposed compressive forces applied at 
any diameter of any cross section of the core 20. The diametrically 
applied compressive forces may occur at any point along, or throughout the 
entire axis of, the core 20. It is, of course, to be recognized that 
compressive forces may be applied along a chord of the cross section and 
not be coincident a diameter. 
Typically, the diametrically applied compressive forces are not directly 
applied to the core 20. Usually, the diametrically applied compressive 
forces are applied to the paper product 24 and radially transmitted 
therethrough to the core 20. However, the principles involved in 
applications through the paper product 24 or along a chord of a diameter 
are substantially similar to those of diametrically applied compressive 
forces applied directly to the core 20 and, will not be further 
distinguished or otherwise repeated. 
Upon application of the diametrically applied compressive forces, the core 
20 will collapse into the flattened condition of FIG. 2. The cross section 
of the flattened core 20 of FIG. 1 has a major axis a--a, and a mutually 
orthogonal minor axis i--i. The major axis a--a and minor axis i--i of the 
cross section are transverse, orthogonal the longitudinal axis of the core 
20 and lie within the cross section of the core 20. The major axis a--a is 
aligned with the longest dimension of the cross section of the paper 
product 24 when flattened, and the minor axis i--i is the perpendicular 
bisector thereto. The resulting flattened core 20 has two vertices 36, one 
located at each end of the major axis a--a. 
It will be recognized by one skilled in the art that the major and minor 
axes a--a and i--i will be unequal in length, unless the cross section of 
the core 20 is circular (or square). Due to variations in the 
manufacturing process, the cross section of the core 20 is usually not 
constant throughout the axial length of the core 20, particularly when the 
core 20 is compressed. However, the major and minor axes a--a and i--i of 
concern in the present invention are those at either end of the core-wound 
paper product 28, for that is where the consumer inserts the spindle into 
the core 20. 
It is necessary to apply the diametrically opposed laterally compressive 
forces to the core-wound paper product 28 until the opposing halves of the 
core 20 are in contact with one another, so that the vertices 36 are 
formed. The vertices 36 define the ends of the major axis a--a. The 
vertices 36 are coincident the inner surface of the core 20. The termini 
of the minor axis i--i are likewise coincident the inner surface of the 
core 20. 
If the diametrically opposed laterally compressive forces are not 
sufficient to form vertices 36 in the core 20, it will have a somewhat 
dog-bone shaped cross section, as illustrated in FIG. 3. A compressed core 
20 having a dog-bone shaped cross section is highly undesirable, because 
such a core 20 is generally more prone to inversion upon rerounding, as 
illustrated in FIG. 4. 
Referring again to FIG. 1, after compressing the core-wound paper product 
28 until the opposed halves of the core 20 contact and the vertices 36 are 
formed, the diametrically opposed laterally compressive forces are 
relieved somewhat, to allow the core 20 to partially reopen, without 
returning to a round cross section. The core-wound paper product 28 is 
then packaged for shipment and sale. 
For the embodiments described herein, core-wound paper products 28 which 
have an opening across the minor axis i--i of about 0.16 centimeters to 
about 1.27 centimeters (0.06 to 0.50 inches), and preferably about 0.51 
centimeters to about 0.89 centimeters (0.20 to 0.35 inches) have been 
found to work well. The compression relieving cycle may be generally 
conducted in accordance with the teachings of U.S. Pat. No. 5,027,582 
issued Jul. 2, 1991 to Dearwester, which patent is incorporated herein by 
reference for the purpose of showing one method of packaging a core-wound 
paper product 28 according to the present invention. 
The dimension of the minor axis i--i may be easily measured by several 
known means. However, the preferred means is to a ordinary scale, such as 
made by the Starrett Instrument Company, and having a resolution with 
graduations approximately one-sixteenth inch (0.16 centimeters) apart. The 
scale is placed against the end of the core 20, in the plane of the cross 
section and visually aligned parallel the minor axis i--i. The dimension 
of the minor axis i--i is then read from the scale as the linear distance 
between the inside surfaces of the core 20 on opposite sides of the 
longitudinal axis. 
It is to be recognized that a suitable compressed core-wound paper product 
28 may be constructed without having the specified minor axis i--i 
dimension. Instead, such compressed core-wound paper product 28 may have a 
lesser dimension of the minor axis i--i (or even be flattened at the minor 
axis i--i) providing an opening of the aforementioned dimension is 
provided near one of the vertices 36. However, such an embodiment is not 
preferred, because it is difficult to achieve the proper spring action of 
a core 20 having such a configuration. 
The paper product 24 compressed and utilized with the core 20 may be a 
toilet tissue having a basis weight of about 0.183 to about 0.324 grams 
per square meter (0.004 to 0.008 pounds per square foot). Such a paper 
product 24 may be made of one laminae or of two superimposed laminae 
having an aggregate basis weight within the aforementioned limits. The 
paper product 24 may be made of a mixture comprising cellulosic fibers. 
As used herein, a core 20 or a paper product 24 is considered cellulosic if 
it comprises at least about 50 weight percent or at least about 50 volume 
percent cellulosic fibers. Cellulosic fibers include, but are not limited 
to cotton linters, rayon, bagasse, wood pulp, such as softwoods 
(gymnosperms and coniferous) or hardwoods (angiosperms and deciduous) and 
aggregations of the foregoing. Noncellulosic fibers which may be 
incorporated into a cellulosic core 20 or a cellulosic paper product 24 
include without limitation synthetic fibers such as polyolefins, 
polyesters and nylons. A cellulosic mixture comprising about 30 percent 
softwood fibers and about 70 percent hardwood fibers has been found to 
work well for the core-wound paper product 28 described and claimed 
herein. 
The paper product 24 may be made with layered cellulosic fibers on a blow 
through drying papermaking machine. Particularly, a paper product 24 made 
in accordance with the teachings of commonly assigned U.S. Pat. No. 
3,994,771 issued Nov. 30, 1976 to Morgan Jr. et al.; commonly assigned 
U.S. Pat. No. 4,529,480 issued Jul. 16, 1985 to Trokhan; and commonly 
assigned U.S. Pat. No. 4,637,859 issued Jan. 20, 1987 to Trokhan, all of 
which patents are incorporated herein by reference for the purpose of 
showing how to make a paper product 24 suitable for use with the claimed 
invention, has been found to work well with the present invention. 
The construction of the core-wound paper product 28 provides a means for 
opening the core 20 to the dimensions across the minor axis i--i specified 
above after the core 20 has been flattened until the opposing halves of 
the core 20 contact with one another. Such a means for opening the core 20 
is easy to understand if the core 20 and the paper product 24 are 
considered to be two springs arranged in series along the direction the 
diametrically applied compressive forces are applied, which direction is 
generally parallel the minor axis i--i. 
As is well known to one skilled in the art the force (f) exerted by a 
spring is the product of its spring rate (k) multiplied by any deflection 
(x). In a core-wound paper product 28 according to the present invention, 
the core 20 acts as a compression spring, resisting the diametrically 
applied compressive forces by expanding outwardly until any restraining 
force constrains the core 20 from further expansion. Conversely, the paper 
product 24 exerts a radial force against the core 20 which must be 
overcome for the core to expand to the minor axis dimensions specified 
above. 
Note that it is necessary for the core-wound paper product 28 to maintain 
the specified dimension after the core 20 has been compressed until 
opposing halves are in contact with one another. It is not recommended to 
compress the core 20 directly to the specified dimensions, without passing 
through the specified dimension--as the core 20 is preferably flattened 
until contact occurs. If the core-wound paper product 28 is made in this 
manner, as noted above the undesired dog bone shaped cross section of FIG. 
3 will likely result. 
Any combination of spring rates, spring forces, and deflections which 
produces a minor axis dimension of about 0.16 centimeters to about 1.27 
centimeters (0.06 to 0.50 inches), and preferably about 0.51 centimeters 
to about 0.89 centimeters (0.200 to 0.350 inches) is suitable. It is only 
necessary that the core 20 be able to overcome the restraining forces and 
expand to this dimension after flattening until contact has occurred. Of 
course, it will be apparent to one skilled in the art that the final 
package dimensions will be a critical parameter which determines selection 
of the other variables. 
In a particularly preferred embodiment according to the present invention, 
the means for opening the core 20 to the desired dimension comprises a 
spring integral with the core 20. As used herein, a spring is considered 
"integral" with the core 20 if the core 20 does not require the addition 
of a separate or independent element to incorporate the spring. In a 
particularly preferred embodiment, the spring results from the stiffness 
of materials used to construct the core 20. 
While it is generally contrary to the conventional wisdom of providing 
relatively thinner gauge core 20 materials for purposes of economy and 
land-fill minimization, it has been found, as noted above, generally 
heavier gauge core 20 materials work well with the present invention to 
provide the requisite stiffness. Further, the core 20 can be stiffened to 
incorporate the aforementioned integral spring by proper selection of 
adhesive and fibers in its construction. 
Alternatively, rather than stiffen the core 20 to provide a means for 
opening the core 20 to the specified minor dimensions, the paper product 
24 may be constructed to provide less resistance to the opening of the 
core 20. For example, hoop stresses associated with winding the paper 
product 24 onto the core 20 will restrain the core 20 from expanding. 
Therefore, a more loosely wound paper product 24 will work well with a 
core 20 of relatively lesser stiffness. 
Alternatively, the outside dimension, taken parallel the minor axis i--i, 
of the constraining means may be adjusted to suit the selected combination 
of core 20 and paper product 24. For example, for a given amount of paper 
product 24 wound about the core 20 at a particular tension, a particular 
radial dimension (the distance from the outside of the core 20 to the 
outside of the paper product 24) will result. This radial dimension may be 
adjusted for the final dimension of the constraining means taken parallel 
the minor axis i--i by increasing or decreasing the caliper of the paper 
product 24. 
Caliper changes naturally occur over time in paper products 24. Therefore, 
it may be desirable to calendar the paper product, so that time dependent 
caliper changes are minimized. 
If it is not desired to adjust the caliper of the paper product 24, so a 
particular radial dimension can be achieved, the final dimension of the 
constraining means may be adjusted instead. It will be apparent to one 
skilled in the art that either a reduction in the radial dimension of the 
paper product 24 or an increase in the final dimension of the constraining 
means may be used with a relatively less stiff core 20, than in a 
core-wound paper product 28 where these parameters were not so adjusted. 
While the foregoing discussion has been directed to individually packaged 
compressed core-wound paper products 28, as illustrated in commonly 
assigned U.S. Pat. No. B1 4,886,167 issued Jun. 11, 1991 to Dearwester and 
commonly assigned U.S. Pat. No. 5,027,582 issued Jul. 2, 1991 to 
Dearwester, it is often desirable to utilize compressed roll paper 
products 28 in multiple roll packages. Particularly, an array of four 
compressed core-wound paper products 28 arranged in a single row with 
parallel longitudinal axes has been found advantageous, although the 
present invention includes single roll configurations, and configurations 
having a plurality of rolls less than, equal to and more than four rolls. 
By way of example, an illustrative package containing four identical 
core-wound paper products 28 according to the present invention is 
described. Both the cores 20 and the paper products 24 had an axial length 
of about 11.43 centimeters (4.5 inches). Prior to compression and 
flattening, the core-wound paper product 28 had an outside diameter of 
about 10.4 centimeters (4.1 inches) and a radial dimension of about 3.1 
centimeters (1.24 inches). 
The cores were made of 0.21 kilogram per square meter (42 pound per 1,000 
square foot) mottled white tubestock supplied by the Menominee Paper 
Company of Menominee, Mich. The tubestock had a width of about 7.3 
centimeters (2.88 inches) and a caliper of about 0.36 centimeters (0.14 
inches). 
The cores 20 were spiral wound edge to edge at an angle of about 34 degrees 
from the longitudinal axis and adhered throughout with a 0.03 millimeter 
(0.001 inch) thick layer of 48 percent solids dextrin adhesive supplied by 
The National Starch and Chemical Company of Bridgewater, N.J. The cores 20 
had an inside diameter of about 4.13 centimeters (1.63 inches) and a 
thickness of about 0.07 millimeters (0.028 inches). 
The paper product 24 utilized in this example was Charmin brand toilet 
tissue manufactured by The Procter & Gamble Company of Cincinnati, Ohio. 
The paper product 24 had a basis weight of about 0.253 grams per square 
centimeter (0.006 pounds per square foot) and a caliper of about 0.27 
millimeters (0.011 inches). Each of the four core-wound paper products 28 
had 280 perforated sheets of the paper product 24. Each sheet of the paper 
product 24 was 11.2 centimeters (4.4 inches) long, and, as noted above 
11.4 centimeters (4.5 inches) in width--corresponding to the axial length 
of the paper product 24. 
Each core-wound paper product 28 was individually compressed to a dimension 
of about 5.1 centimeters (2.0 inches) to ensure flattening occurred and 
the vertices 36 were completely formed. The four core-wound paper products 
28 were placed in the package as described above. The package of four 
core-wound paper products 28 was then compressed to a total width, 
aggregating all four minor axes i--i, of about 21.8 centimeters (8.56 
inches). 
While compressed to this dimension, the package of four core-wound paper 
products 28 was wrapped in a single sheet of medium density polyethylene 
film having a thickness of about 0.04 millimeters (0.0015 inches) supplied 
by the Exxon Chemicals Company of Houston, Tex. as model number EW-20S. 
There was minimal, if any, preload or winding tension applied to the 
package of four core-wound paper products 28 while it was wrapped with the 
film. 
Within one minute, the means for opening the cores 20 to the specified 
minor dimensions sua sponte expanded the package to a total width of about 
25 centimeters (10 inches). It was noted that not each core 20 opened to 
the same dimension. The two outboard cores 20 opened slightly more than 
the two central cores 20. However, each core 20 acceptably opened to a 
value within the preferred range set forth above. 
Four of the aforementioned packages, each containing four core-wound paper 
products 28 as described above, were tested according to the following 
procedure to determine the reaction to diametrically applied compressive 
forces and the spring rates (k) of the packages. The results are given 
below in Table I and graphically illustrated in FIG. 5. 
An Instron Model 4500 tensile machine made by the Instron Corporation of 
Canton, Mass. was utilized. The package of core-wound paper product 28 
under consideration was loaded into the tensile machine with the 
longitudinal axis and the major axis a--a perpendicular the direction of 
travel of the crosshead. Each compressed core-wound paper product 28 was 
arranged with the minor axes i--i colinear and parallel the direction of 
travel of the crosshead. 
The core-wound paper product 28 was compressed at a rate of about 5.1 
centimeters per minute (2.0 inches per minute) until the opposed halves of 
the core 20 were visually observed to be in contact. The reactive force of 
the core-wound paper product 28 against the crosshead was measured at 
intervals of 0.64 centimeters (0.25 inches), corresponding to the 
deflection of the core-wound paper product 28 in response to such applied 
force. 
The results given in Table I show the deflection in inches in the first 
column, and the reactive force in pounds of each package at the particular 
deflection in the second through fifth columns. The sixth column gives the 
average force reading for the preceding four columns. 
TABLE I 
______________________________________ 
Reactive Force 
Avg. Pkgs 
Deflection 
Pkg 1 Pkg 2 Pkg 3 Pkg 4 
1-4 
______________________________________ 
0.00 0.0 0.0 0.0 0.0 0.0 
0.25 2.5 2.7 2.5 2.7 2.6 
0.50 4.0 4.4 4.2 4.4 4.3 
0.75 5.8 6.2 5.9 6.3 6.1 
1.00 7.8 8.1 7.8 8.1 8.0 
1.25 10.0 10.1 9.8 10.2 10.0 
1.50 12.6 12.4 12.2 12.5 12.4 
1.75 15.9 15.0 14.7 15.1 15.2 
2.00 19.7 17.9 17.8 18.0 18.4 
2.25 24.2 21.5 21.5 21.4 22.2 
______________________________________ 
These forces and deflections were plotted to yield the spring rate curve 
for the package in parametric units of pounds per inch. Referring to FIG. 
5, it is noted that the response of each package is relatively linear 
throughout approximately the first 1.5 inches of deflection. The packages 
of four core-wound paper product 28 according to the present invention 
exhibited a spring rate (k) of about 9.3 pounds per inch. Of course, since 
the package may be analyzed as four springs in series, with each 
core-wound paper product 28, comprising one spring, it would be expected 
that each core-wound paper product 28 would have a spring rate (k) 
approximately four times as great as that of the total package.