Flexible shipping container

March 23, 1954

2,672,902

W. PRAGER

FLEXIBLE SHIPPING CONTAINER

Sheets-Sheet 1

Filed Feb. 1, 1952

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March 23, 1954 w. prager 2,672,902

FLEXIBLE SHIPPING CONTAINER

Filed Feb. 1, 1952 2 Sheets-Sheet 2

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.ΑΤΤΟΒΝΈΤ

Patented Mar. 23, 1954

2,672,902

UNITED STATES PATENT OFFICE

2,672,902

FLEXIBLE SHIPPING CONTAINER

William Prager, Hoxsie, R. 1., assignor to United States Rubber Company, New York, N. Y., a corporation of New Jersey

Application February 1, 1952, Serial No. 269,461 (CI. 150—0.5) thereof remains substantially constant throughout the greater portion of the container. A still further object of this invention is to form such a container having the cords of the fabrics form5 ing the plies arranged so that full advantage is taken of the unidirectional strength of the cord fabric forming the walls of the container.

These objects are achieved by substituting for the flat end container heretofore used, a con10 tainer having elongated end portions which taper inwardly gradually toward the longitudinal axis of the container. Since the ends taper gradually, the effective area of the end portion available as a base when the container is placed on 15 end, is reduced slightly, but this is still sufficiently large to provide a stable body when it is so positioned. When the ends are elongated, however, it is possible to eliminate sharp curves from the container body surface, and when this 20 is done the container may be made free of compressive stresses. Although the resultant container is not precisely cylindrical, for the elongated end portions have a gradual inward taper, it is substantially so because for practical pur15 poses the gradually tapered end portions constitute a containuation of the cylindrical body portion; consequently the practical advantages of the Cunningham cylindrical container are achieved in a container which is free of compressive stresses.

Bending stresses are eliminated from the container by forming it in such a manner that the radius of curvature of a meridian through the container does not vary discontinuously. As will be pointed out more fully hereinafter, this is of particular importance at the circles where the end portions join the body portion of the container. A practical -construction, which eliminates bending stresses at this circle, and which 40 provides a gradual taper for the end portion, is one in which the surface of the end portion is shaped in the form of a fifth order parabola. Other constructions which would satisfy these requirements are parabolic curves of the third •15 or seventh order, although as will be pointed out, curves of this nature have certain disadvantages which make them less desirable in barrel constructions.

Since the container of this invention is sub50 stantially cylindrical, it has the great utility of the Cunningham cylindrical construction; but since the end portions of the container are elongated gradually tapering members, the container may be made free of bending and compressive 55 stresses caused by pressurization of the container.

Claims.

This invention relates to flexible shipping containers and more particularly to collapsible shaping containers which preferably are made of rubber coated cord fabric that are adapted to be pressurized in use.

A flexible shipping container and. a method of making this container are disclosed and claimed in the copending Cunningham applications Serial No. 131,407, filed December 6, 1949, now Patent No. 2,612,924, issued October 7, 1952, and Serial No. 144,523, filed February 16, 1950, now Patent No. 2,613,169, issued October 7, 1952, respectively. This Cunningham container is made of rubber coated cord fabric and has a generally cylindrical body and fiat convex-concave ends which are connected and held concave by a central cable that limits the distance between these ends. In use, the: Cunningham barrel is filled with a liquid or dry material to be shipped or stored, and it may be internally pressurized by air'or another suitable gas so that it is in a sense inflated and hence substantially rigid.. This pressurized container which is substantially cylindrical may be handled and stored in the same manner that metal barrels are handled and stored, yet it may be collapsed when empty so that great savings are realized in shipping and storing the empty containers.

Because of these. characteristics of the Cunningham construction, it is a desirable one for flexible containers, and it is an object of the present invention to provide an improved form of this Cunningham construction for flexible containers - More particularly this invention contemplates a container utilizing the. Cunningham construction, in which full advantage is taken of the strength characteristics of the material forming the walls, of the' container.. The exact construction.' disclosed, in the., above-mentioned patents is such'that when the container is pressurized, ..compressive and bending stresses may be induced in the container walls near the ends of the . container by the. internal pgressure. These stresses tend to deform or wrinkle the flexible material forming the walls of the container and to split the plies of the cord fabric which in turn weaken the container and induce failures in the container walls.

It is the primary object of this invention to form a substantially cylindrical container in which the walls will not be subjected to compressive or bending stresses when the container is pressurized.: It is a ftsrther object of this invention to form.· such a container in which the optimum cord angle of the fabric forming the walls

2,672,902

Inasmuch as these latter forces tend to weaken flexible containers, a flexible container constructed according to this invention will have a much longer useful life than those heretofore constructed, and it will be better able to withstand internal pressure and the abuses to which it is subjected in ordinary usage. This latter advantage of the container of this invention is particularly important, for these containers are intended to be used in railway shipment where they will be subjected to very rough usage.

For a better understanding of these and other characteristics and advantages of the present invention, reference should be had to the following description and the accompanying drawings; wherein,

Fig. 1 is a side view of the container of this invention having a portion of the outer ply of cord fabric broken away to show the disposition of the cords of an underply of fabric in the container walls;

Fig. 2 is a sectional view of a part of an end of the container of this invention;

Fig. 3 is a perspective view of a portion of the cord fabric forming the walls of the container of this invention;

Fig. 4 is a diagrammatic sectional view of a median layer of material forming the end portion of the container;

Fig. 5 is a view similar to Fig. 4 of an end portion of a flat end container heretofore used;

Fig. 6 is a diagrammatic view of a loaded string used for purposes of analysis;

Fig. 7 is a diagrammatic perspective view of a segment of a median layer of fabric of the end portion of a container; and

Fig. 8 is a diagrammatic view of a single mesh of the cord fabric in the body portion of the container of this invention.

Referring to the drawings and to Figs. 1, 2 and 3 in particular, there is shown the flexible shipping container of this invention having a cylindrical body portion 10 and elongated convexconcave end portions 11 and 12. A fill opening (3 is disposed in one end of the container, and fixtures 14 consisting of outer plates 15 and inner plates 16 grip the fabrics of the end portions. The nuts and bolts 17 serve to compress the fabric of the end portions between the plates 15 and 16, and to fix the straps !9 and lifting eyes 20 to the container. Joining the fittings 14 and holding the end portions dished at their center is a cable 18 of rope or wire or other suitable material of such a length as to be just slack when no pressure differential exists across the walls of the container.

The walls of the container are formed of a plurality of layers of cord fabric 21, in which each layer is formed of closely spaced warp yarns 22 and loosely spaced weft yarns embedded in rubber 23. Since a single layer of this fabric has strength in the warp direction only, several plies are used to build a wall in which each ply has its warp yarns placed at a substantial angle to the warp yarns of the adjacent layers so that the wall has two directional strength. This construction is well known in the tire industry. The inner and outer layers of cord fabric of the walls of the container preferably are coated with surface layers of rubber or other suitable material to protect the cord fabric against the material to be shipped in the container as well as against external abrasions. The container walls may be built up by the method disclosed in the above mentioned method Patent 2,613,169, or by any other suitable method, but the fabric forming the body portion 75 of the container is made of such a length that the seams 24 and 25 fall along the end portion of the container a substantial distance from the body portion for a reason which will be more fully ⁵ pointed out hereinafter.

Referring now to Figs. 1 and 4 there is shown a container according to this invention having elongated convex-concave end portions, and in particular a container having the shape of a body 19 of revolution in which a meridian through the end portions conforms substantially to a fifth order parabola between the point a where the end portion joins the cylindrical body portion and „ the point b; from the point b to the point d where ⁰ the fabrics of the end portions enter the fittings 14, the end portions are shaped in the form of a circular arc. For an understanding of the advantages of this form of a container, consider Fig. 4 and the stresses on a generic point P on an ⁰ end portion of the container when it is pressurized with an internal pressure p.

The fabric of the container wall at this point is subjected to three principal directional stresses which are (1) the stress along the tangent of the -⁵ meridian of the container which passes through P; (2) the stress along the tangent of the parallel circle of the container which passes through P; and (3) the normal of this surface at P. This last stress is principally compressive and varies in intensity from p at the inner surface of the layer to zero at its outer surface. It will be seen that the other two principal stresses are considerably larger than this compressive stress, hence it can be ignored. To find the meridional ^ύί&gt; stress resultant M per unit length of the parallel circle, consider the vertical equilibrium of that portion of the fabric bounded by the parallel circle through P and the topmost parallel circle. In Fig. 4 this portion is represented by the arc PQ. Since only horizontal forces are transmitted across the topmost parallel circle, under equilibrium conditions the vertical resultant of the forces transmitted across the parallel circle through P must equal the vertical resultant of 4-&gt; the pressure forces acting on the considered portion of the lid. With the notations of Fig. 4 this condition takes the form (27r7cr)M sin W = p[v(kr}² — _T(cr)²] or, since the diameter of the cylindrical body portion, D, equals 2r, substitution of this value and solution for M gives fc² — r²

M=*-^.p_D (1)

47c sm W ^{v 7}

Next to determine the circumferential stress resultant N per unit length of the meridian at the point P, consider first an element of a string as represented in Fig. 6. Using the notation shown in the figure for the radius of curvature, the tension on the.string, and the central angle, the forces S acting on this string at K and F have the resultant of magnitude Sdv directed from the midpoint of the arc KF towards O’’. _;5 The equilibrium of this string requires therefore that p'Hdv= Sdv oi· ,

H=T' (2)

As a rule an element of the fabric forming the end surface of the container will have a double curvature. Consider the portion GPIJ of this

2,872,902 surface shown in Fig. 7. GP and IJ are elements of two neighboring meridians or axial sections, ahd GJ and PI are elements of two neighboring parallel circles, i. e. the circles defined by the intersection of the container walls and planes at right angles to the container axis, The normals of the surface at the adjacent points G and P of the meridian intersect in the first Center of curvature O, and the normals of the surface at the adjacent points P and I of the parallel circle intersect in the second center of curvature O' which lies on the axis of the container. OP and O'P are the principal radii of curvature at the point P of the surface; they are denoted T and L respectively in Fig. 7. If M and N denote the meridional and circumferential stress resultant unit length of the parallel circle and meridian respectively) the equilibrium of the elements shown in Fig. 7 requires that

M. AT T⁺L ^P

This equilibrium condition is an obvious generalization of the simpler condition of Equation 2 which is valid for a string. The dotted center line in the part of the container end shown in Fig. 7 may be visualized as elements of two strings; the meridional string is under tension M and carries the portion

M T of this load p; the other string is under the tension N and carries the remainder if L

Of the load. Equation 3 states that, between them, the two strings must carry the entire load.

Let the first radius of curvature T of the point P Of Fig. 4 be denoted by gr. From the geometry of Fig. 4 the second radius of curvature L equals kr (4) sin w

Substitution of these values, and the value of M given in Equation 1 in Equation 3, and solution for N gives _λ k Γ₁ ' sin TfL ¹ 2kg sin W.

Equation 4 shows that N will vary discontinuously whenever the radius of curvature of the meridian and hence g varies discontinuously. Since discontinuities in stress cannot actually arise in the container wall, bending forces are induced; and if it is to withstand these bending forces, the container wall should be reinforced where they occur.

Furthermore since M remains continuous, and since the proper Cord angle depends oh the ratio M/N as will be pointed out more fully below, if N varies discontinuously in any area of the wall, the optimum cord angle varies discontinuously. As a practical matter the cord angle cannot be made to vary in the container walls, hence a container in which the radius of curvature Varies discontinuously does hot utilize the strength characteristics of the cord fabric of the walls efficiently. Further, it is neither economical nor acceptable to reinforce the walls Of flexible containers, for to do so increases both material ahd produdtioh coSts Aiid decreases flexibility· of the container.

Bending stresses may arise at any point on the container wall, but they normally occur at the parallel circles where one meridional curve joins another. At these circles, the two curves should have the same radii of Curvature. Thus where the end portions join the cylindrical body portion, a meridian through the former should have an Infinite radius of curvature. By making a container having elongated rather than fiat end portions, discontinuities in the radius of curvature may be eliminated; yet the container may be given a shape which is substantially cylindrical.

Equation 4 signifies further the condition under which compressive stresses will be induced in the walls of the container, for if the value in the brackets of this equation becomes negative, N becomes negative. Primarily this signifies that sharp curves must be avoided in the container. Thus, consider the point P' on the wall shown in Fig. 5. It will be observed that the. approximate values of k', W, and g' at this point are .9, 45° and .2 respectively, while c' equals .55, The expression in brackets of Equation 4 becomes —.992, and the container wall at the point P' is subjected to compressive forces.

I have found that sharp curves may be eliminated from a container which has a substantially cylindrical shape if elongated convex-concave end portions are substituted for the flat end portions heretofore used in cylindrical containers. One practical construction Of a Substantially cylindrical container in which the fabric of the walls is not subjected to bending or compressive stresses consists of a container having a cylindrical body portion and end portions which are shaped throughout a part of their length adjacent the body portion in the shape of a fifth order parabola curve, and throughout the remainder thereof in the shape of a circular arc,

A satisfactory container of this type is one in which the end portions are shaped so that a meridian therethrough between the points a and b of Fig, 4 conforms substantially to the equation

V D and between the points b and d to a circular arc of radius .2863D. Point &amp; has the coordinates x—AD and y=.1024D, and point a is the origin. In this equation y is the distance from a projection of the cylindrical body portion to the surface of the end portion and a: is the distance from i the point of intersection of the end and body portions to the surface of the end portion as indicated in Fig. 4, Some representative points on this end portion and the meridional and circumferential stress resultants in terms of pD ob) taining at these points are a.s follows:

Table

Pdirits z/b v!b

Μ/ρΰ

0.

3.4..

5.-..

.7..0 .10 .15 .2 .25 .3 .$5 .4 o

.0022 .0062 .0128 .0227 .0378 . 0622 .1024 .211 .210 .208 .206 .203 .202 .205 .214 .500 .407 .396 .3.68 .303 .200 .110 .143

In the above table points 0 and 7 correspond to points a and b respectively.

From point b to point d, since this is an arc

2,672,902 of a circle, N remains constant and M increases toward infinity which would occur at a point of intersection on the container axis between the arcs of the two circular curves forming the right and left parts of the end portions. To avoid the unreasonably large stresses which would occur near the longitudinal axis of the container, the fabric of the end portions is gripped by the fixtures 14 at the circumferences of the plates 15 and 16. To further reinforce the end portions in this area of increased strain an additional ply of heavy cotton duck 26 may be bonded to the cord fabric of the end portions. The ratio e of the diameter of the parallel circle of maximum end projection to the diameter of the cylindrical body portion of this container is .395, and the maximum end projection is .4815D.

From the foregoing table it will be seen that up to the point 2, a distance equal to roughly % of the maximum projection of the container ends, the ends depart only minutely from cylindricality, and that up to the point 7, where the end projection is more than % its maximum value, the departure of the container end from cylindricality is only about y_s the radius of the container. Thus this exemplary container is substantially cylindrical throughout most of its length. The effective diameter of the container base is approximately .4 the maximum diameter of the container; so that the container is stable when placed on end. The above table for this container shows further that the walls at no point are subjected to compressive forces. Furthermore, since the end has the shape of a fifth order parabola near the cylindrical body portion, an inflection point occurs at the intersection of these portions, and the container is free of bending stresses at this circle of intersection. Further, the circular arc has a radius of curvature equal to the radius of curvature of the parabolic curve at the intersection of these curves, so that the radius of curvature of a meridian of the container does not vary discontinuously.

Although the curve described here does not require a particular size of container, a satisfactory size is one in which the body portion has a length equal to its radius. Thus, a 55 gallon container m this size would have a diameter of 23 y₂' ’. This container size is compact, stable and easy to handle; hence it is an extremely desirable ship- - -. ping container.

To determine the proper cord angle in the cylindrical body portion of the container consider Fig. 8. The sides AB and CE are small segments of neighboring parallel circles, and the sides AC -and BE are small segments of neighboring gen- '’° erators of the cylindrical body portion. If the lengths AB and AC are denoted by e and f respectively, the total axial and circumferential stresses acting on the cord mesh shown are Me and N/ respectively. These forces may be visualized as acting at the centers of AB and AC where the cords of the fabric overlap. Let U denote the product of the force in a typical cord by the number of plies having cords in the same direc- _ction. Vertical equilibrium at the center of AB requires

Me=2U sin Z(6) and horizontal equilibrium at the center at AC that

Nf=2U cos Z(7)

It follows from, Fig. 8 that //e=tan Z (8) 75

Dividing 6 by 7 and substituting 8 gives tan Z=\/M/N (9) _r Inasmuch as Equations 1 and 4 are valid for ·' any portion of the container wall, to find the values of M and N in the cylindrical body portions the appropriate values of k, w and g should be substituted in these equations. In the cylindrical body portion fc=l, W=90° and 3=infinity.

¹⁰ Substitution of these values in Equations 1 and 4 gives _ _r2 (io) and

N=^P^ (11)

Substituting these values of M and N in Equation ²⁰ 9 gives

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₂₅ Thus the cord angle in the cylindrical body portion depends only upon the ratio of radius of the circle of maximum end projection to the radius of the cylindrical body portion. For the typical container given above, the value c=.395 and ^Z=33°·

From a comparison of Equations 12 and 9, it will be apparent that although the cord angle in the cylindrical body portion is constant and depends only upon the ratio c, the optimum cord 35 ^a^^gle for any part of the end portion will vary with the values of the ratio M/N at that point. Since as a practical matter the cord angle of the fabric forming the walls of the container cannot vary, if the angle determined by Equation 9 ,,θ differs materially from the angle determined by Equation 12 the fabric of the container walls is being used inefficiently. A comparison of the above table with the requirements of these equations reveals another important advantage of the container shape prescribed by that specific embodiment. The optimum cord angle for the fabric of the end portion as determined by the ratio M/N varies from 33° at the cylindrical center portion to approximately 40° at point 4; in effect for practical purposes the cord angle is substantially constant up to the point 4, and this optimum cord angle is substantially that required by the cylindrical body portion. Thus, if the seams 24 and 25 are placed at or near the parallel circle passing through the point 4 the cord fabric forming the body portion will be used most efficiently. It will be noted further that the minimum value of M, which determines the strain on the seam, occurs at the parallel circle through point 5. However, between point 5 and point 4 the meridional stress varies less than 1%; hence, the seam may be placed at that circle which permits the most efficient use of the fabric forming the container walls.

From the foregoing it will be apparent that I have devised a shipping container which has a good practical construction in that it may be handled, stored and shipped easily, yet which will give greatly improved wearing qualities and should have a very long life in use. In particular a container may be made which has a substantially cylindrical shape, yet which is free of bending or compressive, or both bending and compressive forces. These advantages are achieved by abandoning the flat end portion and substituting in its stead the elongated end pOr2;672.902 shaped such that a container meridian therethrough conforms substantially to the curve , i-KJ)-ⁱ²G)‘⁺²⁰(s)‘ between the points x=0 and x—AD and to the arc of the circle of: radius .2863D from the point ¢=.41) to the point where said means embraces said end portion, wherein x is tne distance from 10 the plane of intersection of the end portion and the cylindrical body portion to the meridian through the end portion, y is the distance from a projection of the cylindrical body portion to the meridian through the end portion, and D is the 15 diameter of the container, whereby the cord fabric is subjected only to tensile stresses when the container, is pressurized.

3. A collapsible container designed to withstand high internal fluid pressures, comprising a 20 cylindrical body portion and two elongated rounded end portions formed of a plurality of layers of coated cord fabric wherein the cords of one layer form an angle with the cords of adjacent layers, said container being formed so 25 that internal pressures subject the walls thereof to tensile stresses only, means holding said end portions dished centrally of their parallel circles of maximum end projection, each said end portion conforming substantially to the curve

F²'²G)-&gt;²®‘⁺O‘ throughout a portion of its length adjacent the body portion, wherein ¢15 the distance from the 35 plane formed by the intersection of the cylindrical body portion and the end portion to the end wall, y is the distance from a projection of the cylindrical body portion to the end portion, and D is the diameter of the cylindrical body ⁴⁰ portion. , . , .

A collapsible shipping container designed to withstand high internal fluid pressures, comprising a cylindrical body portion and two rounded end portions formed of a plurality of layers of 45 coated cord fabric wherein the cords of each layer form a substantial angle with the cords of adjacent layers, means holding said end portions dished centrally of their parallel circles of maximum end projection, said container being 50 shaped so that internal pressures subject the walls thereof to tensile stresses only, each said end portion conforming substantially to a fifth order parabola throughout a portion of its length, adjacent to the body portion, and having a para55 allel circle of maximum end projection whose diameter is approximately A the diameter of the body portion.

5. A collapsible shipping container designed to withstand high internal hydraulic pressures, com60 prising a cylindrical body portion and convexconcave end portions formed of a plurality of layers of coated cord fabric in which the cords of one layer are angularly disposed relative to the cords of adjacent layers, means holding said end 05 portions dished near their centers, said end portions being formed such that the fabric forming the walls of the container is subjected to only tensile stresses when the container is pressurized internally and being formed throughout a sub70 stantial portion of their lateral projection adjacent to the cylindrical body portion substantially in the shape of a parabolic curve.

6. A collapsible shipping container designed to be pressurized in use, comprising a cylindrical 75 body portion and two elongated end portions tion of the present invention which is well adapted to resist internal pressures.

Although a specific embodiment of a container according to this invention has been described, changes may be made in the constructional details Without departing from the spirit or scope Of this invention. In particular, although a specific fifth order parabola curve has been described, other curves may be devised within the teaching of this invention without departing from the spirit or scope of the invention.

Thus, although a fifth order curve has been described, other curves which provide a gradually inwardly tapering end portion may be substituted therefor, so long as sharp curves are eliminated from the end. Further, other curves are known which could be substituted for the fifth order parabola to provide an inflection point at the circles where the ends meet the body. Thus, parabolic curves of the third or seventh order would eliminate bending stresses in this area. However, in general these curves require rather sharp curves near the centers of the end portions so that compressive stresses occur. If in particular circumstances these stresses are not objectionable, these curves may be used advantageously in a container end,

Although in the description of the curve of the specific embodiment illustrated, a single layer Of fabric is described; it will be appreciated that, as shown in Figs, 1 and 2, the walls of the container are made up of several layers of cord fabric, in no event less than two, and that a container according to this invention would have its walls conforming substantially to the desired curve. x. , * _T