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Intersecting spherical pressure tank US 2341044 A IMAGES(5)

DESCRIPTION (OCR text may contain errors) 1944. J. o. JACKSON ET AL 2,341,044 INTERSECTING SPHERICAL PRESSURE TANKS Filed July 28, 1941 s Sheets-Sheet 1 'II/II/ILIIIIIIIIIII a418 ATTORNEYS.

Feb. 8, 1944- J. o. JACKSON ET AL. 2,341,044 INTERSECTING SPHERIQA/L PRESSURE TANKS 5 Sheets-Sheet 2 Filed Ju] .y 28, 1941 INVENTORS 01. M 9 JKMA'ITORNEYS 1944- J. o. JACKSON ETAL v 2,341,044 INTERSECTING SIHERICAL PRESSURE TANKS 7 Filed July 28, 1941 5 SheetS Sheet 5 11%|: im ATTORNEYS 1944- J. o. JACKSON ET AL INTERSECTING SPHERICA L PRESSURE TANKS Filed July 28. 1941 5 Sheets-Sheet 4 2 filVENT R5 1 BY s8 M 9m W WA. ATTORNEYS Feb. 8, 1944. J. o. JACKSON ETVAL I INTERSEC'IING SPHERICAL PRESSURE TANKS Fil ed July 28, 1941 5 sheetssheet 5 11f "A, ATTORNEYS to our present invention; Patented Feb. s, 1944 UNITED STATES PATENT OFFICE lNTERsEcTmGgrPaflnlklucAL li'RESSURE James 0. Jackson, Grafton, and Courtney L. Stone, Pittsburgh, Pa assignors to Pittsburgh- Des Moines Company, a corporation of Pennsylvania Application July 28, 1941, Serial No. 404,434 9 Claims. (01. 220-3) This invention relates to v containers for the sErage of liquids or gases under pressure. Several forms of containers for this purpose are now available including cylindrical-containhas been considered to be the only one that is truly stable elastically, that is, it does not tend to change its symmetry with an increase of internal pressure. The sphere is commonly known to have a minimum of surface for any given volume or content and to require a minimum wall thick-' ness and, therefore, a minimum of weight for the storage of any actual volume of gas compressed to any specified pressure. Moreover, a spherical container is commonly regarded as being the only shape of vessel which has these characteristics. One of the objects of the present invention is to provide a new. composite container for fluids ,producing a container having a .plurality of spherical segmental portions each'of which is bounded on at least one side by a diaphragm-like partition to form a plurality of separatedcompartments and means for equalizing the pressure in such compartments. Other and further objects and advantages reside in the various combinations, subcombinations. and details hereinafter described and claimedand in such other and further matters as will be understood by those skilled in this art or apparent or pointed out hereinafter. In the accompanying drawings, in which like numerals designate corresponding parts throughout the various views: Fig. 1 is a view in elevation of a. tank responding to our invention with parts broken away to show the structure thereof; of a tank responding Fig. 2 illustrates a horizontal-medial section through one of the partial spheres of Fig. land is provided with geometrical indicia by means of which certain calculations can be made relative to a container of this form; k

Figs. 3 and 4 designate in elevation a spherical segment: and a spherical zone whichzare useful in connection with the mathematical aspects of our invention; Fig. 5 is an elevational view of a modified form of'the invention and showing the supports and piping therefor; Fig. 6 is a plan view of a composite tank constituting a further modification of our invention and in which the spherical segments are arranged in the general form of a torus; Fig. 7 is in part an elevational view and in part a sectional view taken on line VII-VII of Fig. 6 and in the direction'of the arrows thereof; Fig. 8 is a view similar to Fig. 6 but of a further modified form of the invention; Fig. 9 is a view partly-in elevation and partly in section taken along the line IX-IX of Fig. 8 and in the direction of the arrows thereof; Fig. 10 is a view similar to Fig. 8 but of a still further modified form of the invention; and Fig. 11 is a view similar to Fig. 9 but taken along the line XI-XI of Fig. 10 and in the direction of the arrows thereof. Referring first to the structural features of our new containers, the simplest form thereof is shown in Fig. 1. In that figure the numerals 20 and 2| designate two partial spheres or spherical shell sections which are joined to a common disc oiplate-like member 22 by means of th continuous welds 23. In this form of tank there are two compartments or storage chambers 24 which are separated from one another by means of the diaphragm 22. It is-to be understood that the welds 23 are fluid-tight. As will be more fully understood from what follows, the container of Fig. 1 is usually provided with inlet and outlet pipes which make it possible to cause the chambers 24 to communicate with one another, thus, ..communication with one another. This automatically equalizes the pressure at all times." In the modified form of container illustrated ,in Fig. 5, it will be noted that there are two, v like end spherical portions 20' and a number of intermediateportions 20" which in this case are in the form of spherical zones. In. other words, end members 20' are incomplete spherical shells. to the extent that the same have a portion thereof removed ,so as to intersect the portions 20" in the manner illustrated, the members 20" being, in effect, the central portions 'of spheres with the diametrically opposite segments removed. A plurality of diaphragms 22' separates the interiorsof members 20' and 20" and, while not visible in Fig. 5. it will be understoodthat the circular welds 2 3 of Fig. l are employed. Thus, the container of Fig: 5 has a plurality or separated compartments or chamof material into the container and for removal of material therefrom, this being effected by suitable valves and by-passes, as will be appreciated by those familiar with piping arrangements.

The fact that all the container portions are thus connected into a common conduit serves to equalize the pressure of the various container portions and twinsure that material supplied to the container portions is stored at the same pressure in all of the various spherical'portions. A suitable relief valve 33 is provided as shown in order to prevent the pressure in the sy tem from exceeding a predetermined maximum. Supports 3'4 are shown as provided at each end of the container and, in general, it is to be understood that we may support the container in any suitable manner which per se forms no part of or restriction upon our present invention. The container need not, however, be elevated. In Figs. 6 and 7 a further modified form of container has been illustrated and which has the general configuration of a torus. This container .is made up of a plurality of spherical segmental portions arranged in ring form with a hollow center and in which each spherical container portion 20a is bounded by and has secured thereto a pair of diaphragms 22a which converge radially inwardly, thus producing a spherical container portion which has the general configuration of a truncated sector. Each diaphragm 22a is to be understood as being secured in place in the same manner as the diaphragm 22 previously described. The plurality of separated compartments or chambers thus provided in this form of the invention are provided with means for equalizing the pressure in each such either by a piping system of the character of Fig. or by providing one or more apertures in each diaphragm. This particular form of container is especially useful for the storage of liquids under pressure where it is an. vantageous to have acontainer with a diameter .which is large as compared to its height. In this arrangement also pumping costs are reduced. The still further modified form of container of Figs. 8 and 9 is, in general, similar to that of Figs. 6 and 7. There are, however, at least two notable distinctions. In the first place, the diaphragms 22b bounding the spherical container portions 20b are all interconnected and merge into a polygonal central diaphragm 22b which is, so to speak, inscribed in the center of the torus and in which is the additional spherical container 2lb. As will be noted from Fig. 9, the container compartments or chambers thus formed arev in communication with each other by means of theopenings 26 provided in the diaphragms 22b and 22b, these openings being reinforced by means of the apertured washerlike elements 25 which are secured to the dia phragms; This form of container is also provided with a piping system like that described in connection with Fig. 5. Under these conditions the piping system may be used solely for charging and discharging the container portions and the matter of pressure equalization is taken care of independently by the apertures 2i aforesaid. The virtue of this form of container is that it is capable of storing large volumes of liquids or gases under pressure and has unusual efiiciency in that all the space occupied by the container is usefully employed. Supporting means such as the braces or columns 21 may be provided and a relief valve 33 prevents excessive pressure condition within the container. - The modified container of Figs. 10 and 11 is substantially the same as that of Figs. 8 and 9 except mainly for the arrangement and disposition of the diaphragms 220 which are arranged to cross each other at right angles and in such manner as to, in effect, form a plurality'of containers of the type of Fig. 5. The nature of of "P" pounds per square inch greater than the atmospheric pressure exerted on

the outside surface of the sphere. In this case if the shell of the sphere is very thin as compared with its radius the said shell will be stressed substantially in tension due to the internal pressure, such teninherent symmetry of the sphere and such tension being numerically equal to PR/2, where P is the sphere. square inch and R in inches the tensional stress T will be expressedin pounds per lineal inch of circumference at the center of the shell thickness at any point on the sphere. Let it be further assumed that the spherical shell 20 is cut by a plane (BCE) and that the larger portion of the-sphere ABCEA is closed by means of a flat circular diaphragm 22 attached to the said portion of the sphere as, for example, by welding around the circle of intersection as shown at 23. Plane BCE will intersect the spherical shell in the form of a. circle. Now referring to the complete spherical shell it is known that such spherical shell has at all points around the circle caused by the intersection of the said plane a tensile stress equal as previously shown to PR/2. This stress has been indicated on Fig. 2 as T acting upward and to the left and is exactly 65 balanced and counteracted by a like but opposite force T1 acting downward and to the right of the intersecting plane. These forces T and T1 are. andT5 acting radially inwardly toward central urface BDE is removed it is apparent that strucint C. Now when the portion of the spherical e having the ability to resist forces '1: and '1': must be substituted in order to maintain equilibrium conditions. If X is assumed to be the angle subtended by the radius BC of the said in- 7 tersecting plane to the center of the sphere 0 assumed that the sphere contains a gas Pressure sion being equal in all directions because of thethe internal gas pressure and R is the radius of If P is expressed in pounds per it is apparent that the angle between the force T and its component Ta'will also be X. The mag-. nitude of force Ta is, therefore T cos X. The diaphragm I2 is, accordingly, stressed by a force having the magnitude of T cos X acting radially away from the center of the circular diaphragm and its thickness must necessarily be sumcient to resist such force. If the thickness of diaphragm I2 is assumed to be suiflcient to resist such force, it is apparent that the structure ABCEA will be out of equilibrium by the sum of the horizontal forces T: around the circumfel'ence of the diaphragm. Now if .the said structure ABCEA including the portion of the sphere and the circular diaphragm is placed in contact with another exactly similar structure placing the two diaphragms together and fastening them oause the horizontal forces T2 will be exactly offset by similar horizontal forces equal to T4. from the adjoining sphericalsegment and each diaphragm will adequately resist the radial forces T cos X. One important feature 'of our invention is based on the fact that if two or more spheres of the same or of different sizes are attached together in the manner we have described the weight of the material required in the shell plus the weight of the material required for the diaphragm for each of the spherical portions divided by the volume or contents of each of the spherical portions will be approximately the same as the weight of the material required to form the shell of any of the entire spherical shells divided by their volume. This can be demonstrated by showing that in Fig. 2 the ratio of .the weight per unit of volume of the segment including its circular diaphragm to the volume of that segment is identical with the ratio of the weight of the material of the entire sphere to its volume.

Using the following nomenclature in the English system of units: Vs is the volume of a sphere or spherical container. R is the radius of that sphere or spherical element in inches. P is the pressure in pounds per square inch. S is the allowable unit working stress in pounds per square inch. ts is the spherical shell thickness in inches. i is the diaphragm thickness in inches. As is the area of the spherical surface. Ad. is the area of the diaphragm. w is the weight of the membrane material in pounds per cubic inch. We is the weight of the spherical shell or spherical element. We is the weight of diaphragm. WT is the total combined weight of the shell and diaphragm. - N is any number of spheres or spherical elements. X is the angle formed between the axis of the' section. T is the stressper lineal inch in the spherical membrane. Ta is the stress in diaphragm in a radial direction. An is the area of a circular ring as contrasted with a diaphragm. W3 is the weight of such circular ring. The following fundamental equations for the solution of the geometry of spheres and spherical elements will be used. Spherical segment 'Volume=V,= (1 1rb(3a"+3c +4b Complete sphere It has been stated that the weight-volume ratio for any number of spheres is the same as though they were combined in one single sphere and also that the same remains true for spherical elements; We will first prove and derive the -constant for a complete sphere and then prove that any portion of a sphere may be removed and the structure closed by the use of a disk member forming part of our invention without changing the weight-volume ratio. Let it be assumed that the problem is to store a certain volume V of gas under a given pressure of P pounds per square inch, and further let it be assumed that the gas is to be contained in one sphere or N spheres, whichever combination gives the least weight for the desired volume.

.weight of one sphere Now the stress per lineal inch is and the thickness required to withstand this stress is equal to the stress per lineal inch divided by the allowable working stress in pounds per square inch or 5 T PR Substituting Equation 5 in Equation 3 we have. as an expression for the weight We equal to the following: . PR 6. W,=A.( )w and substituting Equation 2 for A; in Equation 6 we have weight of one sphere and for the total weight of N spheres s. W,= 'i yv Now from Equation 1 '9. ram- 4 2,841,044 4 and substituting this value of R for R in Equa-' The area of the disk is equal to a circular area tion 8 we have for the weight of N spheres of which BC is the radius or but which reduces to BC=OB m x a X 1.5 PwV 80 that l1, WT=T Ad=wR Sill X and expressing Equation 11 in terms of weight but sin-3 x x) per unit volume of gas stored we have or 12 ll l.5 Pw Ari=irR (1-cos X) V S Now the thickness of the spherical shell is equal This equationshows the weight/volume ratio of to the stress per inch divided by the allowable a sphere is independent of the number of spheres, unit stress or that is, one sphere would not weigh more or less T PR than N spheres whose total volume is equal to t,=the one sphere. Now it will be proved that a. portion of a sphere and the thickness q e f the dis i equa may be isolated and that the same ratio holds to the stress per oi elreumference multiplied true. In Fig. 2, as previously described, volume by the length ov which it acts divided y the EABCE is an isolated portion oi the sphere allowable unit stress ip ed by the len th EABDE with a plate-like member or. disk 22 comover which the unit stress i efleetive all in like pleting the inclosure. Now this disk is located units 0! as expressed by at any point C on the AD axis in such a manner 25 B that radial lines from the center of the sphere O i to the outer periphery of the disk makes a constantangle x with the AD axis. Now'the volume of EABCE is equal to the vol- 1 Pll cos X R sin X ume of the complete sphere minus the volume 28 R sin X of EDBCE and using the fundamental equations or for the geometry of the sphere we have Vs=%1rR -%1rb" (3R-b) e g' where r Y J and the weight of the disk is equal to the area of the disk multiplied by the thickness and weight per cubic unit all in like units or expressed by but Wa=Astirw X and the total weight of the complete structure so then i8 7 V.=%a-R %a-(RR cos X) (3R-(RR cos x A Collecting all the equations in a group we have: -rR 1-eos X)(3RR+R cos X) v.=''(2'+a cos X-Cos' x 4 f 2. Ar=2irR=(1+cos x) E "Ti' X) M a. Ad=IR'(1-COSX) PR =,R 2-3 cos X+cos'X) ifi PR +%1R'(3 cos X-cosX) 3 X a 6- w|=Artrw=2IR'(1-i-00S X) to!!! ='-g 2+3 cos Xcos X) v. wi=At-ts-w=s1i=(l-eos=x) -tc-w The spherical surface area of the above volume T=WI+Ws is equal to the area ofthe whole sphere minus Now substituting tin Equation 4 for to in Equathe area of the isolated smaller portion or tion 6 we have 2 l l 4.411% 21121 W: (1 HO. X) 2%; w where R. and b have the same values as above or '5 1 Ar=4rR21rR (R-R cos x) V =4'II'R -2'I'R (1-008 X) ,PRI =11? (4-2+2 cos x) I P- (1+eo X)w I and substitu A.= 21R= (1+cos x) 10- flon 7 we 5 f i The weight of the spherical shell is equal to the area multiplied by the thickness by the weight mama-00.: %;L per cubic unit all in like units or 'PR,

and then from Equation 8 we have 'I' PR3!!! 2s I Now from Equation 1 it is shown that and substituting this value of R for R in the above equation we have (2+3cos X.cos X) which is the same constant as that found in the previous proof. This proves then that if a portion of a spherical shell is removed and the spheres attached to each other regardless of their size or the angle ofattachment provided only that the pressure in all of the spheres is'the same. In actual practice we place one or more small reinforced intercommunicating holes in. each diaphragm so that the pressures will properly equalize or, in some cases, we findit convenient to attach the inlet and outlet piping to all of the spheres which accomplishes the same result. Referring to Formula 5 t cos X since that'the distance of the center of the disk'from the center of curvature of the spherical shell bears to the radius of the spherical shell. For two adjoining truncated spherical shells of the same radius, the required thickness of a single disk to give to the container the elastic stability of a single sphere would therefore vary 5 with the radius of the circle of intersection of the two spherical shells. When the radius of the circle of intersection approaches zero,-the thickness approaches two times the thickness of the spherical shell. When the radius of the intersection approaches the radius of the spherical shell the thickness approaches zero. When the radius of the intersection is equal to the square root of .75 or about .86603 times the diameter of the spherical shell, the thickness of the disk 15 would be the same as that of the spherical shell. If a circular ring were used to reinforce the spherical shell at the circle of intersection instead of our solid diaphragm it may be designed to adequately resist the force T cos X indicated as Tsin Fig. 2. In this type of construction, which is not new, it can be proved that the ring if designed to resist the forces T: transmitted to it from each of the spherical segments, will weigh twice as much as the diaphragm which is the basis of our invention. Further the ring would, in the cases of some forms of our invention, interfere with other essential members. Following is a demonstrationof the fact that the ring will weigh approximately twice that'of a flat circular diaphragm which will withstand the same radial loading.Assume two spheres I ii and H as in Fig. 1 except Joined together and reinforced by a circular ring in lieuof a diaphragm. Now from our previous solutions we knowthat -the radial stress per inch of circumference from one sphere is r3= (PR/2) cos X but since we have two spheres T3 becomes and if As. is used to designate the cross-sectional area of the ring we have Now if it be assumed that the center of gravity of the ring is on the theoretical intersecting point of the two spheres then the weight of the ring is equal to the volume generated as the cross section moves along the circumference of a circle passing through the center of gravity of the ring, the said circle having a radius equal to the perpendicular distance from an axis joining the centers of the two spheres to their common circle of intersection, multiplied by the weight per cubic volume of the ring, or a f =A -21-(R sin X)w (PR cos I-R sin X) sin X), 7o Referring to the weight of a diaphragm we have V I structure. since there are two spheres the weight of two diaphragms I 3 W 2( gg (l cos X) (cos X) W w(1 cos X) cos X ,and comparing the weight of the ring against that of a diaphragm we see that the weight of a ring is twice as much as that required for a diaphragm for the same loading condition.

One ofthe principal advantages of our invention is that comparatively large structures may be built without requiring much, if any, additional support for the relatively thin sheet metal The circular diap'nragms which a each individual spherical segment maybe very simply supported by a central column and radial girder-like members such as are commonly used in large containers. From the foregoing, it will be apparent to those skilled in this art that by making assemblies of our truncated sphericalshells and diaphragms, containers may be built to suit certain conditions, particularly as to space limitations, such as the diameter and height. Such assemblies will be much more efficient and much'less costly than a single container having the saine diameter and height. Such single containers will require much more material for their construction than our assemblies. This is especially so in cases where the single containerhas relatively flat upper and lower surfaces and is to take the place of the container of Fig. 6. In many cases, it would be impractical to either design or build a single container where it would not only be possible to design but to build a container embodying our invention. It is to be understood that the foregoing is presented as illustrative and not as limitative and that we may resort to other and further additions, omissions, substitutions and modifications without departing from the principle or scope hereof. fined by the appended claims. Having thus described our invention, what we claim as new and desire to secure by Letters Pat'- ent is: 2. A container comprising a series of truncated intersecting spherical shell sections and plate-like reinforcing disk members forming partitions between such shell sections and to which such shell sections are joined at their truncations; each such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shells when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell bears to the radius of that shell. 3. A container as defined in claim 2 in which the truncated spherical shell sections are so arranged as to approximate a rectangular structure. 4. A container as defined in claim 2 in which the truncated spherical shell sections are arranged in the form of a toms. - 5. A container as defined in claim 2 in which a number of the plate-lik reinforcing disk members are arranged in' parallel spaced relation. 6. A container as defined in claim 2 in which a number of the plate-like reinforcing disk members lie in planes radiating from the common center of the containen f ,7. A pressure tank comprising at least two truncated intersecting spherical. shell sections having the same radius and thickness and a platelike disk shell reinforcing member forming a partition between such shell sections and to which 4 such shell sections are welded at their truncations, said reinforcing member having a thickness equal to the thickness of one of such shell sections; such shell sections being attached together and to such

reinforcing member at their truncations to form a fiuid tight container; each reinforcing member having a radius at the circle of attachment approximating seven eighths of the The invention is rather that de1. A container comprising truncated intersecting spherical shell sections and a plate-like reinforcing disk member which forms a partition between such, shell sections and is welded to the adjacent intersecting edges thereof; such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shell sections when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell section bears to th radius of that shell section. v radius of the spherical shell sections. 8. A pressure container comprising a series of truncated intersecting spherical shell sections having the same radius and thickness, and circular plate-like disk reinforcing members welded to adjoining shell sections at their intersection and forming partitions between such shell sections; each such reinforcing member having a thickness equal to the thickness of one such shell section multiplied by the distance between the centers of curvature of adjacent shell sections (11- vided by the radius of one such shell section. 9. A pressure container comprising a series of truncated intersecting spherical shell'sections and circular plate-like disk members located between and joined to adjacent shell sections at their intersection to form reinforcements for and partitions between such shell sections; the'plate-like member between each two adjacent shell sections of the series having a thickness equal to the thicknesspf one such shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided y the radius of curvature of such shell section, plus the thickness of the other shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided by the radius of curvature of such other shell section. JAMES O. JACKSON.- COURTNEY L. STONE

Filament wound spherical pressure vessel US 3655085 A ABSTRACT A spherical, multi-layer, fibre reinforced plastic pressure vessel, each layer being a helix inclined at a different angle to the polar axis with each convolution in each layer following substantially a great circle, constructed so that the layer which extends closest to the poles of the sphere resists meridianal force of a given amount at a preselected horizontal plane, the layer most remote from the poles of said sphere resists, together with all other windings cooperating therewith, hoop force of said given amount along the equator, and the intermediate layers resist, together with the layers cooperating therewith, at selected horizontal planes only, either a meridianal force or a hoop force of said given amount.

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DESCRIPTION (OCR text may contain errors) [151 3,655,085 [451 Apnll, 1972 United States Patent Aleck 3,112,234 11/1963 3,144,952 8/1964 Uhll [54] F ILAMENT WOUND SPHERICAL PRESSURE VESSEL 'g et a1. 3,366,522 1/1968 Underwood........ ....156/175X Primary Examiner-Raphael H. Schwartz Attorney-Hubbell, Cohen &. Stiefel [73] Assignee: [22] Filed: [57] 1 ABSTRACT A spherical, multi-layer, fibre reinforced plastic pressure vessel, each layer being a helix inclined at a different angle to the polar axis with each convolution each layle lfollow fighsubstantia yagreat circ e,constructe sot att e ayerw ic ex- [58] Field of Search l 156/148 tends closest to the poles of the sphere resists meridianal force of a given amount at a preselected horizontal plane, the layer most remote from the poles of said sphere resists, together with all other windings cooperating therewith, hoop force of said given amount along the equator, and the intermediate layers resist, together with the layers cooperating therewith, at selected horizontal planes only, either a meridianal force or a hoop force of said given amount.

References Cited UNITED STATES PATENTS Ramberg [52] US. [51] Int. 1 Wiltshire g n u 0 Y 2 6 9 l 7 l 9 1 7 4 3 17 Claims, 5 Drawing Figures ow n PATENTEDAPR 1 1 I972 SHEET 1 UF 2 INVENTOR BENJAMIN J. ALECK #ilmww ATTORNEYS. PATENTEDAPR 1 1 m2 SHEET 2 BF 2 f 00oooo0ooo:. 4 5 INVENT BENJAMIN J. 1. CK MMQEMM ATTORNEYS. Tl (DEGREES) FILAMENT WOUND SPHERICAL PRESSURE VESSEL BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to spherical fibre reinforced plastic pressure vessels. 2. Description of the Prior Art Spherical fibre reinforced plastic pressure vessels are known. Generally speaking, the fibre reinforcement is wound in a random pattern in the hope of yielding a vessel having substantially uniform resistance to meridianal and hoop forces throughout. Some attempt has been made to wind vessels utilizing a multiplicity of layers, each layer being in the form of a helix, the convolutions of which follow substantially great circle paths, but the method of constructing such vessels has been highly empirical, with no reliable theoretical foundation, and the vessels so constructed have been inefficient. SUMMARY The helical winding layer extending closest to the poles of the sphere (that is the layer having its convolutions extending about the sphere at the most acute angle of inclination (a) to the polar axis) is constructed, in accordance with mathematical expressions, to resist a given amount of meridianal force at an analytical plane perpendicular to the polar axis which intersects the surface of the sphere at a given angle to the polar axis (a The winding layer next closest to the poles of the sphere is wound at an angle to the vertical of a and is constructed to resist, together with the first winding, at an analytical plane perpendicular to the polar axis which intersects the surface of the sphere at a selected angle to the polar axis of a said given amount of meridianal force. The layer next closest to the poles of the sphere is then constructed with convolutions disposed at an angle to the vertical equal to a: and is designed to resist, together with the contributions from the first two windings, a meridianal force of said given amount at still another analytical plane perpendicular to the polar axis which intersects the surface of the sphere at an angle to the polar axis of (1 The procedure may be continued for all additional winding layers save the layer (layer m) whose windings are most remote from the poles. Layer m will have its windings disposed to the vertical at an angle a,,, but will be constructed to resist at the diametral plane, together with all other windings, a hoop force of said given amount. Apart from the arbitrarily selected analytical planes no attempt is made to construct the vessel so that it uniformly resists throughout its entire surface both meridianal and hoop forces, this being taken care of by deformation of the completed vessel itself under pressure. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a sectional view of a spherical mandrel with bo'ss hardware disposed thereon ready to receive filament windings in accordance with the present invention;

FIG. 2 is an elevational view showing a few turns of one winding layer; FIG. 3 is a broken elevational view of the vessel partially wound; FIG. 4 is a series of curves for several windings showing the relationship between resistance to meridianal force in pounds per inch versus the location of the analytical plane; and FIG. 5 is a view similar to FIG. 1 showing a modified form of hardware for the vessel. DESCRIPTION OF PREFERRED EMBODIMENTS The present method is directed to a multi-layer filament wound spherical pressure vessel, each layer of which is in the form of a tight helix with each convolution in each layer following substantially the path of a great circle (the deviation from a true great circle path being as a result of the pitch of the helix). It can be shown for any such layer (e.g., a layer 1) that the following equations are true: wherein: f, is the radial pressure which the layer of fibres at tension T would exert on a spherical mandrel; N, is the number of turns in the layer under'consideration; T is the maximum tension to which the filaments in the layer are to be subjected and is therefore constant; a is the radius of the sphere being formed; 1; is an angle to the vertical axis at which an arbitrarily selected plane perpendicular to the polar axis intersects the surface of the sphere being formed; 0: is the angle at which the windings or convolutions in the layer under investigation are disposed to the vertical; N is the resistance in pounds per inch to tensile force in the meridianal direction tending to pull the sphere apart along a plane perpendicular to the polar axis of the sphere; and N is the resistance in pounds per inch to tensile force operating along a parallel of the sphere (i.e., perpendicular to the polar axis) tending to pull the sphere apart along a plane parallel to or including the polar axis. In a multi-layer structure, the contribution of each layer to resistance to meridianal and hoop stresses at any given plane on the surface of the sphere is additive with the contribution of each other layer intersecting said plane. Thus, for example, if there is a two layer structure, to detennine the total resistance to meridianal force per unit length of parallel which both layers can withstand (N equation (2) above would have to be rewritten as:

Obviously, the equations (1) and (3) for two layer structures could be rewritten in a similar manner. Thus it can be shown that in a structure having m layers wound in accordance with the above described great circle helical pattern that where i is the number of any given layer and ranges from 116 I winding layer (N,). This apparently insurmountable problem has been solved in the present method by making certain assumptions which experimentation has proved to be highly satisfactory. Specifically, one assumption is that if the requirements of equation (6) above at a given number of arbitrarily selected analytical plane s w hich intersect the surface of the sphere at angles to the polar axis which vary from zero to 90, are met for a desired value of N the value of N, at the planes in between those selected for analytical pEposes will take on satisfactory values. A second assumption is that if the requirements to achieve a substantially constant N, are met throughout the vessel, the requirements for achieving a substantially constant N are also met. As will be seen hereinafter, the second assumption preferably includes one modification; namely, that in the equatorial region of the sphere where the layer most remote from the poles is layed down, that is the m layer, the requirements of this layer with respect to the number of windings, that is N,,,, are satisfied not with respect to Na, but instead with respect to N9, A detailed analysis indicates that a vessel designed utilizing the equations (6) and (7) above and the assumptions expressed above will yield a vessel THAT will maintain a substantially spherical shape. However, it can be shown that the assumptions are only good approximations and that A6,, and N, do vary over the surface of the sphere when under pressure. This variation is so small that all that results therefrom is that the ideal spherical shape of the vessel becomes somewhat altered when the vessel is pressurized, the alteration taking the form of the appearance of small peaks and valleys in the spherical surface, which peaks and valleys compensate for the actual variations arising from the design assumptions. Turning our attention now to the drawings in detail, the vessel to be formed by the present invention is preferably wound on a mandrel 10 having a radius a. The mandrel may be a hollow metal sphere or the like although preferably, in the present invention, the mandrel is a dissolvable mandrel such as a salt mandrel. As the vessel to be formed is a pressure vessel, it is obvious that it must have at least an inlet-outlet 12 although, as shown in FIGS. 1 and 3, the vessel has an inlet 12 and an outlet 14 of substantially identical configuration. As shown in the drawings, the inlet 12 and the outlet 14 are both cylindrical tubes and each is provided with a flange l6 and 18 of certain proportions to be described hereinafter in greater detail. Naturally other shapes of hardware may be employed. As here shown, and as is preferred, the surface of the mandrel 10 is contoured in order to render it complementary to the flanges 16 and 18 in order to present a substantially spherical outer surface for winding the vessel thereon. The contour cutouts or surface depressions for the flanges l6 and 18 are designated in FIG. 1 by the reference numerals 20 and 22. As already stated, each of the winding layers to be fonned to make the present vessel is to be in the form of a helix with each turn thereof following substantially a great circle of the sphere to be formed, the variation from a true great circle being the result of the pitch of the helix (FIG. 2). To form the first winding layer, which layer is designated by the reference numeral 1 in FIG. 3, it is preferred to pitch the layer so that the upper and lower edges thereof run tangent to the exterior of the tube 12. Thus

04,, that is the angle of inclination of the first layer to the vertical, is preferably determined by the physical dimensions of the inlet 12 and, if included, the outlet 14. Now, in view of the fact that winding number 1, which, as shown, is the winding which extends closest to the poles of the sphere, provides the sole resistance to meridianal force in the areagn the polar s id esofthe second layer, N must be equal to N which is an arbitrarily preselected value that preferably is equal to p x(a/2), wherein p is the maximum pressure to which the vessel will be subjected. Moreover, it is possible to fix the angle of the plane perpendicular to the polar axis at which winding 1 will afford the maximum resistance to meridianal force. This plane intersects the spherical surface at an angle 1; that will subsequently be assigned as the value of 01 The equation t o determine a is a sin"( 1/2 sin a Now equation (2) can be solved for N Once N is known, all of the parameters for the first winding are known. Therefore, a curve can be plotted to determine the contribution of winding 1 to resistance to meridianal force at various planes of contribution of winding 1 is less than the predetermined value of N Since no additional winding will be provided in the polar region between at and 01 means must be provided for yielding additional resistance to meridianal force. This means is the flanges 16 and 18 on the inlet 12 and the outlet 14, respectively. These flanges are preferably metal and are proportioned with respect to thickness and the nature of their material to provide additional N in the polar region to make sure that the polar region does not fail in meridianal stress. Turning our attention now to the second winding, that is winding 2, a is already established as above described. However, inorder to determine the number of turns in winding 2, that is N an assumption must be made with respect to the value of 01 That is to say, it is known that the third winding, winding number 3, will contribute no N at 01 Thus if equation (4) is solved where n is assumed to be a the value of N, can be calculated, as there are no other unknowns in the equation. Thus N45 is known as it has been preselected, N, is known as it has been previously calculated, 01 is known as determined above, and a is known. In order to select a to fulfill the final missing unknown in the equation save for the value of N itself, certain practical considerations must be taken into account. Thus, if a is too close in size to 01 then the number of windings to form the entire vessel will be increased and this will increase the complexity of the winding operations which is undesirable. However, if 01 is unduly large there will be substantial variations in the actual M between a and a as contrasted with the theoretical constant value throughout, and these variations at some practical point become undesirable. l have found that a practical number of windings to yield a desirable vessel falls somewhere in the range of 10 to 14 for most applications. Assuming as a first approximation that the difference in adjacent as is substantially uniform throughout, a reasonable approximation of a can be made. Once a; has been assumed or approximated as above described, equation (4) may be solved to determine N If the solution of the equation (4) for N yields a positive number, then the assumption for 04;, is a workable assumption and the calculation may be employed. If, however, the solution yields a negative number for N which solution would indicate that with the assumed value of angle a the second layer should have a negative number of turns in order to yield an N,,, equal to the desired value, then it becomes clear that the selection for a is wrong in that it is too small an angle and an adjustment in the assumption must be made to enlarge the assumed value of angle a whereupon the

calculation of N is repeated. Once the solution of equation (4) yields a positive value for N then the parameters for winding 2 are established in that the angle of inclination of the convolutions to the vertical (a is is determined, and the number of turns in the second winding (N is also determined. While the plotting of the curves of FIG. 4 are unnecessary to this analysis, if desired, the N,,, versus 1; curve can be plotted and it would appear as shown in FIG. 4 in dashed line. Turning our attention now to winding number 3, a similar procedure may be employed to determine the number of turns (N in winding number 3 as was employed above to determine the number of turns (N in winding number 2. Specifically, the summation form of the equation for N,,, above set forth as equation number (6), may be written where only three windings (l, 2 and 3) are present in accordance with the following equation: analyses, that is at various 1;, which curve is shown in solid lines in FIG. 4. It will be seen that the polar area between a, and 94 the N, Equation number (9) is presented with 1 already assumed to be 01 This assumption facilitates the calculation as it eliminates winding 4 from consideration in arriving at the parameters for winding 3 in the same way that 17 was selected to be 01;, in the solution of equation (4) for N Again, some arbitrary value for a, must be assigned prior to the solution of the equation (9) for N;;. The factors determining the selection of a, are the same as those set forth above with respect to a, and when a selection or first approximation for the value is made, equation (9) is readily solvable for N Again, if N;, should prove to be a positive number then the assumption as to the value of a is a useful and workable one and the calculations may be adhered to. Of course, with the assumption, if the value of N should prove to be negative, then it is obvious that a 4 has been chosen to be too close to the angle a and it must be enlarged. Again, as was true in the solution of N it will be seen that the solution of the equation for N is made by analyzing the sphere at a very convenient plane, namely the plane at which the contribution of winding 4, the next winding to be wound after winding 3, will be zero, whereby to enable the designer to ignore the contribution of winding 4 in calculating the number of turns in winding N The manner of determining the parameters of the remaining windings 4, 5, 6 save for the winding most remote from the poles, that is winding m, is precisely as that described above with respect to the second and third windings, and is a mere application of equation (6) presented above. The manner of solving the parameters of winding m will be described below. It should be noted that the sphere has been redesigned to yield constant N only at a preselected number of planes and no attempt has been made to determine whether the actual N at other analytical planes, that is at planes perpendicular to the polar axis which intersect the spherical surface at other angles 1 would be equal to the N chosen for the particular sphere. However, a review of the data and an observation of the results of the of the design method indicate that there is not substantial variation in M, over the entire surface of the sphere if the sphere is constructed in accordance with the method. Moreover, it should be noted that throughout the description to this point, no attempt has been made to determine whether N0, that is the hoop strength of the sphere, is constant throughout and whether

it is equal to the meridianal strength of the sphere in order to yield a substantially 100 percent efficient vessel. The reason for the absence of such calculations is the assumption previously mentioned that when the vessel is designed for a constant N a substantially constant Nml ,rssuln dflN'a, willbesah i t all jgua to Na.l-lowever, in order to insure that the hoop strengt of the sphere does meet the design requirements for a highly efficient vessel, the winding with the maximum a, that is the winding m, is preferably designed to satisfy the requirements of equation (7) and not of equation (6). That is to say equation is r r tten as +1; Nm 01 2311.". A i 711 1" J ln solving equation (1) for N,,,, n will be chosen to be 90 in order to determine that the hoop strength at the diametral plane of the vessel is equal to N is equal to Na, Thus in equation (10) the value of sin n will be 1. It will be obvious that between the expression in the equation beginning with N and the expression in the equation beginning with N,,, may appear a number of additional expressions similar to those already presented but for the other windings in the vessel. However, all of the parameters for these windings will be known (having been arrived at by the previously described procedure) and the entire equation 10) is readily solvable for N,,, in order to yield a winging m which will yield the proper hoop strength for thevessel in the equatorial area. This gives' added assurance that the vessel will be a highly efficient one. Utilizing the design procedures above described, a highly satisfactory pressure vessel has been wound in accordance with the present invention to yield a vessel with a radius (a) of 6.75 inches and the ability to withstand a pressure of 6,530 psi. Such a vessel was formed of Owens Corning 8-994 fiberglass prepreged with US. Polymeric E790 epoxy resin The winding layers were wound one at a time and after the complete vessel had been formed it was subjected to the curing temperature for the epoxy resin carried by the prepreged fiber glass to cause the resin to form a substantially continuous rigid matrix for the filament winding. After the resin had been set or cured, water was introduced into the interior of the vessel through the inlet 12 to dissolve and flush out the salt mandrel whereby to yield the desired vessel. It will be obvious that the plastic need not be incorporated in the vessel being formed as a coating on the filament winding although this is highly desirable. Thus uncoated reinforcing filament such as fiber glass could be employed and after the winding layers are formed, the winding layers could be impregnated with liquid polymeric material as by spraying or brushing, and thereafter the plastic could be cured. Moreover, as is well known in the art, it is not necessary that the plastic be epoxy, although this is desirable. For example, any rigid or semi-rigid thermoplastic or thermosetting plastic material such as, for example, ABS (acrylonitrile, butadiene, styrene) plastic; acrylic plastic such as polymethyl methacrylate; polystyrene; vinyl plastics, urea-formaldehyde condensates; phenol-formaldehyde condensates; polyoxymethylene plastics; or polyolefins; etc., may be employed. The epoxy resin used in the specific example is a condensate of epichlorhydrin and bis phenol A, although other epoxies could be employed. While fiberglass is the preferred reinforcement due to its high tensile strength, it will be obvious to anyone skilled in the art that other types of reinforcing filaments can be employed within the present invention. Thus, any of the well known continuous filaments, whether synthetic or natural, may be employed, including, by way of example, polyamides, such as polyhexamethylene adipamide and

polycaproamide; polyesters, such as ethylene terephthalate polymers and copolymers; acrylic polymers and copolymers such as polyacrylonitrile; vinyl polymers such as polyvinyl alcohol, polyvinyl chloride and polyvinylidene chloride; fluorinated ethylene polymers such as polytetrafluoroethylene and polytrifiuoromonochloroethylene; polyhydrocarbons such as linear polyethylene, linear polypropylene and copolymers of ethylene with other polymerizable monomers; regenerated cellulose; cellulose acetate; polyurethanes; and the like. In addition, biconstituent filaments made up of polyamid and polyester, e.g., nylon polyester or the like, may be employed. Such biconstituent filaments are produced commercially, for example, by Allied Chemical under the trade name BF-121. (Frequently such biconstituent filaments of nylonpolyester are referred to as merged filaments) Generally, these filaments are obtained by the simple expedient of melt mixing polyamide and polyester, e.g., nylon and polyethylene Lastly, if desired, metal fibers and such naturalfibers as silk, may be employed. While in the preferred method above described all of the layers save the layer N are designedby utilizing equation (6) with an eye to maintaining M constant at preselected planes at angles a a etc., and only the last winding, that is the m winding is designed utilizing equation (7) for hoop strength, a satisfactory vessel can be designed by aiming for a substantially constant N at the various planes of analysis determined by the angles 11 ,01 etc., by utilizing eaQUATlON (7), and a similarly efficient vessel can be obtained. If such a procedure is elected, however, the layer closest to the polar regions, that is winding 1, should nevertheless be designed in order to yield an appropriate meridianal strength at the angle a, in order to insure that the vessel is reasonably efficient in the meridianal direction as well as in the hoop direction. Thus, as a generalization, it can be said that winding number 1, that is the winding closest to the polar region of the vessel, must be designed in accordance with the equation (6) to yield a desirable meridianal strength for the vessel in the polar region, and winding number m closest to the equatorial region of the vessel must be designed in accordance with equation number (7) to yield a vessel having a desirable hoop strength. The windings in between the first winding and the m winding may be designed in accordance with either equation (6) or equation (7) utilizing, of course, the assumptions and procedures above described. However, it will be obvious that to facilitate calculations, all of the windings between winding 2 and winding m-l are preferably designed with respect to the same equation, that is either with respect to equation (6) or with respect to equation (7). One exception to the above statement may be that if desired the first two windings closest to the polar region of the vessel, that is winding 1 and winding 2 may be both designed utilizing equation (6) to yield a substantially constant meridianal strength and the two windings most remote from the polar regions, that is windings m and m-l may both be designed by the utilization of equation number (7), that is to yield in the equatorial region substantially constant hoop strength for the vessel. In such a method, thewindings 3 through m-Z may be designed in accordance with either equation (6) or equation (7) or any combination thereof, although, as already mentioned above, it is more desirable to utilize the same equation throughout the intermediate layers or windings.

Once the calculations for all of the windings are completed in accordance with any of the above embodiments of the invention, the mandrel is set with the bosses 12 and 14, placed as shown in FIG. 1, and layer 1 is wound at an angle of inclination of a, and with a number of turns of N as calculated. The winding may be wound by hand although it is preferred that it be wound by machine as conventional winding machines will maintain more uniform spacing of the adjacent turns in the particular winding. During winding a mild tension is applied to the filaments in order that they lay snugly on the mandrel but this tension is relieved almost immediately after removal of the mandrel if it is a dissolvable mandrel such as a salt mandrel. If the mandrel 10 happens to be a metal sphere, the amount of tension applied to the windings is of such small amount that it leaves the metal sphere forming the mandrel substantially unstressed. After winding 1 is completed, the machine is readjusted to wind the second winding pattern at an angle and with a number of turns N Thereafter the machine is reset for each additional winding through winding m. In view of the fact that a number of resetting's must be made, and each of these takes time in fabrication, it is desirable to keep the number m relatively small, always, of course, taking into account the requirement for a substantially uniform N and N9, throughout the surface of the vessel. As already noted, if the number of windings, that is if the number m, is between about l0 and about 14, satisfactory results with a pra namb r ofr pes ac i 7 It will be obvious that upon completion of winding and the curing of the plastic resin, the mandrel, if removable as would be true of a salt mandrel, is dissolved by flushing water into the interior of the vessel through inlet 12 Naturally, if a metal liner is employed in the mandrel, the metal liner will remain as an integral part of the vessel. As already indicated, the completed sphere is spherical under no stress, but when it is subject to its intended operating pressures, it will not maintain a truly' spherical shape. Instead, a vessel made in accordance with the present method will under pressure deform to exhibit small peaks and valleys in its surface that are not readilyv visible to the naked eye. The appearance of the small peaks and valleys is the adjustment of the vessel itself to compensate for variations in N and N over the surface of the vessel arising as a result of the fact that the procedure for designing and making the vessel is based on assumptions that are good approximations but not perfect ones. The desirability of the method is that it yields a vessel which through these minute distortions in shape adjusts itself to correct for these variations. While the description presented with respect to FIGS. 1 and 3 was with respect to a vessel having an inlet 12 and an outlet 14, a similar method may be employed where the vessel has only one portal to the interior thereof which serves at various times as an inlet and outlet. The hardware for such a vessel is shown in FIG. 5, wherein the boss 12 with its flange 16 set in a depression 20 in the surface of a salt mandrel 10 identical to the mandrel 10 of FIG. 1. However, in view of the fact that the vessel to be formed on mandrel 10 of FIG. 5 is to have only one opening, a problem arises with respect to the opposite polar regions. If symmetry is to be maintained in the winding, and this is highly desirable for practicing the present method, there would be an opening at the opposite polar region but this would render the vessel useless. There are various ways of avoiding this problem and one of them is illustrated in FIG. 5 wherein asolid concave plate 114 having a diameter and curvature equal to the diameter and curvature of flange 16 is set in the opposite polar region to the hardware 12. If desired,

the central polar part designated by the reference character 116 may be slightly thickened whereas the annular remainder 118 may have precisely the same dimensions and properties as the flange 16 above. The purpose for the slight recess between the portions 116 and 118 is to provide a guide or shoulder for the first winding, that is winding 1. However, it will be obvious that such a shoulder is not necessary to practicing the present method. It will also be obvious that such a solid disc need not be employed. In lieu thereof, if there is to be only one inlet outlet, the vessel may nevertheless be formed with two as in FIG. 1 and then one of them may be closed as by a metal plug or the like. However, it is important in considering the present method to realize that there is no fibre in the immediate vicinity of the poles of the vessel and some form of insert to provide the necessary meridianal and hoop strength in the polar regions must be included in order to yield a useable vessel. Throughout this description it has been assumed that the first layer to be wound on to the mandrel is winding 1 that extends closest to the poles of the sphere. It has further been assumed that each successive winding 10 be wound on to the mandrel is the one extending next closest to the poles and that the final winding to be placed on the mandrel is the winding m which is most remote from the polar regions. While this is the preferred method of laying down the windings, it is not the only method embodying the invention. For example, the order of laying down the windings, once the calculations have been made, could be reversed. In the alternative a relatively random selection of layers to be wound'could be employed such as, for example, winding 3, winding 7, winding 5, winding 9, winding 1, etc. However, such a pattern would require more adjustment of a winding machine and would therefore not be as desirable as the preferred order described or the reverse thereof. With the method of the type herein described, a highly efficierit, fibre reinforced, spherical plastic vessel can be formed. What is claimed is: 1. A substantially spherical filament reinforced plastic pressure vessel wherein said vessel is to withstand a preselected meridianal force of M pounds per inch and a preselected hoop force of Na, pounds per inch, said vessel including means for permitting defonnation of said vessel upon pressurization thereof to exhibit throughout the entire vessel an ability at all planes perpendicular to the polar axis to withstand a substantially constant meridianal force of M and at all planes parallel to said polar axis to withstand a substantiallY constant hoop force of N9, said last mentioned means comprising a plurality (m) of lielically wound layers of filament, the convolutions of which follow substantially great circle paths, each winding layer being composed of windings disposed in planes which intersect the center of the polar axis of said sphere at an angle of inclination (a), that is different from said angle of inclination of the windingsof the other of said layers, said winding layers being designated progressively from 1 to in in accordance with their respective angles of inclination, said winding layer 1 satisfying the equation Ni Vsin 1 sina at 1; 90; and windings (2) through (m-l) satisfying together with the windings of more acute angles of inclination, one of said two equations at analytical planes intersecting the surface of said sphere at 1 a t-l.

2. The pressure vessel of claim 1, wherein N is substanilfl Y/QQL QLI JYH i H 3. The pressure 'vessel of claim 2, wherein saidwindings (2) .t ir l..) waist!thesame qua isa. 4. The pressure vessel of claim 3, wherein said same equation is said first presented equation. 5. The pressure vessel of claim 2, wherein said winding (2) satisfies together with winding (1) the first presented equation at n a said winding (ml satisfies together with windings (1) through (m-2) the second presented equation at 11 a and the windings (3) through (m-2), together with the windings of more acute angles of inclination, satisfies one of said two equations at analytical planes intersecting the surface of said sphere at 1 a 6. The pressure vessel of claim 1, wherein said filament is fiber glass. 7. The pressure vessel of claim 4, wherein said filament is fiber glass. 8. The pressure vessel of claim 7, wherein (m) is between 10 and 14. 9. The pressure vessel of claim 1, wherein said plastic is a substantially continuous matrix for said winding layers and is at least semi-rigid. 10. The pressure vessel of claim 7, wherein said plastic is rigid or semi-rigid and is a substantially continuous matrix for said winding layers. 11. The pressure vessel of claim 1, further comprising a flanged boss disposed at one of the poles of said sphere, said boss having a radius of, a sina,, said flange having a radius of a slna 12. The pressure vessel of claim 11, further comprising a second flanged boss disposed at the other of the poles of said sphere, said second boss having a radius of a sinoq, the flange of said second boss having a radius of a sina 13. The pressure vessel of claim 11, further comprising a concave imperforate disc disposed at the other of said poles of said sphere and having a radius of a sina 14. The pressure vessel of claim 10, further comprising a flanged boss disposed at one of the poles of said sphere, said boss having a radius of a sina said flange having a radius of a sma 15. The pressure vessel of claim 14, further comprising a second flanged boss disposed at the other of the poles of said sphere, said second boss having a radius of a sina the flange of said second boss having a radius of a sina 16. The pressure vessel of claim 14, further comprising a concave imperforate disc disposed at the other of said poles of said sphere and having a radius of a sina 17. The pressure vessel of claim 14, wherein (m) is between 10 and 14.

DESCRIPTION DETAILED DESCRIPTION The entire polymerization reaction is preferably carried out in the polymerization zone defined by an essentially spherical wall. In fact, the inventors have found that by carrying out the polymerization reaction under the conditions of the process according to the present invention, it is possible to obtain, in a reproducible manner and using a single agitator, polymers and copolymers based on vinyl chloride which after screening possess interesting characteristics in terms of high apparent density, mean particle diameters adjustable to need and a low weight percentage of fine particles, despite the fact that the reaction mixture successively has four different states from the beginning to the end of the polymerization reaction; liquid state, suspension of solid particles in a liquid, pasty state, and powdered state, and its consistency changes considerably. According to the present invention, it is possible to vary the speed of rotation of the blade-type turbine assembly as a function of the state of the reaction mixture and its consistency, the desired mean particle diameter of the polymer or copolymer or any other parameter of the processor the quality of the resins to be prepared. The speed of rotation of the blade-type turbine assembly is generally reduced between the beginning andthe end of the polymerization reaction to a value lower than one-third the initial value and to as low as one-fourth the initial value. Also according to the present invention, the polymerization reaction may bestarted in the polymerization zone defined by an essentially spherical wallwith a very small initial volume of reaction mixture, which makes it possible to carry out polymerization operations in which part of the monomer or monomers and/or part of the polymerization initiator or polymerization initiators and/or at least part of any other additive can be introduced into the said polymerization zone during the polymerization or the degassing of the polymer obtained. According to a first variant o the process according to the present invention, the polymerization reaction is carried out in two steps, which are carried out in different devices, carrying out a prepolymerization operation with a monomer composition based on vinyl chloride in the first step and a final polymerization operation in the second step, the said first step being carried out in the polymerization zone defined by the essentially spherical wall. According to an embodiment of the first variant of the process according tothe present invention, the prepolymerization operation is carried out in the polymerization zone defined by the essentially spherical wall until the degree of conversion of the monomer composition reaches 3% to 15%, a supplementary monomer composition based on vinyl chloride, which is identical to or different from that used during the first step, is added to the reaction mixture if desired, after which the final polymerization operation is carried out with the reaction mixture thus formed while stirring slowly. According to this embodiment, the final polymerization step can be carried out, e.g., in a polymerizer of the conventional type as described, e.g., in French Patent No. 1,382,072

and its above-referenced Certificates of Addition; in French Patent No. 73 05537, published as Nos. 2,218,350 and No. 75 32124, published as No. 2,328,722 and in French Patent No. 85 05429, published as No. 2,580,192. According to a second variant of the process according to the present invention, the polymerization reaction is carried out in two steps, which are carried out in different devices, carrying out a prepolymerization operation in the first step with a monomer composition based on vinyl chloride and a final polymerization operation in the second step, the second step being carried out in the polymerization zone defined by an essentially spherical wall. According to an embodiment of the second variant of the process according to the present invention, the prepolymerization operation is carried out with highly turbulizing agitation until the degree of conversion of the monomer composition reaches 3% to 15%, a supplementary monomer compositionbased on vinyl chloride, which is identical to or different from that used during the first step, is added to the reaction mixture if desired, after which the final polymerization operation is carried out with the reaction mixture thus formed in the polymerization zone defined by an essentially spherical wall. According to this embodiment, the prepolymerization step can be carried out, e.g., in a prepolymerizer of the convention type as described, e.g., in French Patent No. 1,382,072. The inventors have also found that if the process according to the present invention is employed either by carrying out the entire polymerization reaction in the polymerization zone defined by an essentially spherical wall or by carrying out the polymerization reaction in two steps, which are performed in different devices, the second step being carried out in the polymerization zone defined by an essentially spherical wall, the duration of the degassing treatment is noticeably reduced under otherwise identical conditions. In practice, the space between the blades and the wall of the spherical polymerization zone of the reactor, in which the process according to the present invention is carried out, is advantageously between 2 mm and 50 mm. The length of the blades of the turbine assembly is such that the distance between their tips and the lowest point of the spherical wall, measured vertically, is at least equal to one-tenth the diameter of the sphere, in which case the diameter of the circle described by their tips during rotation is at least equal; with regard to the play, to threefifths the diameter of the sphere, which means that the said blades pass by in the vicinity of the spherical wall over at least 10% of the surface. The blades may pass by in the vicinity of the sherical wall such that they reach an equatorial plane, in which case the diameter of the circle described by their tips during rotation is equal; without regard tothe play, to the diameter of the sphere. The blades may also extend slightly beyond the equatorial plane perpendicular to the axis of rotation. The turbine assembly generally comprises one to six blades, especially three blades, which are preferably disposed regularly around the axis of rotation and are advantageously profiled so as to facilitate intensive mixing. In addition, the reactor may be, but does not need to be, equipped with an additional scraping system consisting of one or several rotated members inthe part of the spherical polymerization

zone not occupied by the turbine assembly. The shape of the industrial reactions which are suitable for usefor the process according to the present invention is not necessarily that of a complete integral sphere. According to the present invention, the only important thing is that the polymerization zone be defined by an essentially spherical wall. However, the spherical shape of the reactor may be interrupted by various tubes, pipe connections or openings. Thus, for the convenience of use and especially cleaning, the reactor may comprise openings of sufficient size to permit access to the inside and, e.g., the entry of a person in the case of large reactors. The reactor maybe, e.g., of the type described in French Patent No. 1 22425, published as No. 2,517,313. The descriptions illustrating the embodiments of the process according to the present invention will be described below in an illustrative rather than a limitative manner with reference to FIGS. 1a through 1d of sheet 1 of the appended drawings, and a reactor suitable for use for carrying out the process according to the present invention will be described with reference to FIGS. 2 and 3 of the drawings. FIG. 1a shows a closed polymerization zone Z.sub.1 defined by a spherical wall S.sub.1. A turbine assembly T.sub.1, provided with blades disposed regularly around a pivot B essentially located in the bottom point of the sphere, is mounted to rotate around the said pivot. A motor M drives the turbine T.sub.1. In this example, the tips of the blades of the turbine assembly T.sub.1 extend beyond the equatorial plane (line E--E) perpendicular to the axis of rotation (which is essentially vertical in the case of FIG. 1a) and pass by in the vicinity of the internal sphericalwall over 60% of the surface of the sphere. FIG. 1b shows a closed polymerization zone Z.sub.2 defined by a spherical wall S.sub.2. A turbine assembly T.sub.1, mounted to rotate around a pivotB, is driven by a motor M in the same manner as shown in FIG. 1a. In this example, the tips of the blades of the turbine assembly T.sub.2 describe acircle whose diameter is at least equal; without regard to the play, to threefifths the diameter of the sphere S.sub.2. FIG. 1c shows a diagram analogous to FIGS. 1a an 1b showing a polymerization zone Z.sub.3 defined by a sphere S.sub.3. The turbine assembly T.sub.3, driven by the motor M, rotates around a pivot B which isshifted relative to the bottom point of the sphere. In this example, the axis of rotation of the turbine T.sub.3 is not vertical. The equatorial plane (line E--E), perpendicular to this axis of rotation, is oblique. Thetips of the blades of the turbine T.sub.3 describe a circle whose diameter is equal; without regard to the play, to that of the sphere S.sub.3. FIG. 1d illustrates an essentially spherical polymerization zone Z.sub.4 defined by a spherical wall S.sub.4 and by a cylindrical extension C.sub.4which can serve as a screen or permits access to zone Z.sub.4. The turbine T.sub.4, which is driven by the motor M to rotate around a pivot B, is mounted in the same manner as in FIG. 1c.

The spherical reactor 1 shown in FIG. 2 comprises two hemispheres, an upperhemisphere 2 and a lower hemisphere 3. The hemispheres 2 and 3 are assembled and maintained by bolts 4 distributed in a diametrical plane over the respective flanges 5 and 6 and the hemispheres 2 and 3. A synthetic rubber gasket 7 ensures tight sealing between the two hemispheres. The reactor 1 is equipped with a magnetically operated drive assembly 8 driving a shaft 9 disposed vertically along one diameter of the reactor 1,with insertion of a coupling 10. The shaft is sealed by a polytetrafluoroethylene packing 11. A turbine assembly carried b a projection 12 mounted in the bottom point of the lower hemisphere 3 comprises three blades 13 connected to the base 14 which is rigidly attached to the shaft 9. The turbine assembly is mounted so that the blades pass by in the vicinity of the internal wall of the lower hemisphere 3 and extend to the level of the equatorial plane (line E--E) of the reactor 1. The reactor 1 is surrounded by two jackets 15 and 16 which are fastened to the hemispheres 2 and 3, respectively, in which a heat exchange fluid circulates, entering via the tubes 17 and 18 and leaving via the tubes 19 and 20. In its upper part, the reactor 1 comprises a tube 21 for feeding in the monomers, the polymerization initiators and any other additive used, as well as a tube 22 for discharging the nonreacted monomer composition. In its lower part, the reactor 1 comprises a tube 23 controlled by a valve 24for discharging the polymer. Any polymerization initiator which can be used to prepare polymers and copolymers based on vinyl chloride by mass polymerization and which generally form free radicals is suitable for use in the process according to the present invention, such as organic peroxides, e.g., lauroyl peroxide, acetyl cyclohexanesulfonyl peroxide, isobutyroyl peroxide, dichloroacetyl peroxide, trichloroacetyl peroxide; peroxydicarbonates, such as ethyl peroxydicarbonate, ethyl hexyl peroxydicarbonate, isopropyl peroxydicarbonate, isobutyl peroxydicarbonate, cetyl peroxydicarbonate, cyclohexyl peroxydicarbonate, tert.-butyl cyclohexyl peroxydicarbonate; tert.-butyl perneodecanoate, cumyl perneodecanoate; tert.-butyl permethoxyacetate; tert.-butyl perethoxyacetate; tert.-butyl perphenoxy-2-propionate; 2,4,4-trimethyl pentyl perphenoxy-2-acetate; and azo compounds such as 2,2'-azo-bis-(2,4-dimethylvaleronitrile). The polymerization initiator or polymerization initiators are used, in general, in amounts of 0.001 wt. % to 0.006 wt. %; expressed as active oxygen, relative to the total weight of the monomer composition used. The polymerization temperature is, in general, between 10 100 The invention will be further described in connection with the following examples which are set forth for purposes of illustration only.

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DESCRIPTION (OCR text may contain errors) 1944. J. o. JACKSON ET AL 2,341,044 INTERSECTING SPHERICAL PRESSURE TANKS Filed July 28, 1941 s Sheets-Sheet 1 'II/II/ILIIIIIIIIIII a418 ATTORNEYS.

Feb. 8, 1944- J. o. JACKSON ET AL. 2,341,044 INTERSECTING SPHERIQA/L PRESSURE TANKS 5 Sheets-Sheet 2 Filed Ju] .y 28, 1941 INVENTORS 01. M 9 JKMA'ITORNEYS 1944- J. o. JACKSON ETAL v 2,341,044 INTERSECTING SIHERICAL PRESSURE TANKS 7 Filed July 28, 1941 5 SheetS Sheet 5 11%|: im ATTORNEYS 1944- J. o. JACKSON ET AL INTERSECTING SPHERICA L PRESSURE TANKS Filed July 28. 1941 5 Sheets-Sheet 4 2 filVENT R5 1 BY s8 M 9m W WA. ATTORNEYS Feb. 8, 1944. J. o. JACKSON ETVAL I INTERSEC'IING SPHERICAL PRESSURE TANKS Fil ed July 28, 1941 5 sheetssheet 5 11f "A, ATTORNEYS to our present invention; Patented Feb. s, 1944 UNITED STATES PATENT OFFICE lNTERsEcTmGgrPaflnlklucAL li'RESSURE James 0. Jackson, Grafton, and Courtney L. Stone, Pittsburgh, Pa assignors to Pittsburgh- Des Moines Company, a corporation of Pennsylvania Application July 28, 1941, Serial No. 404,434 9 Claims. (01. 220-3) This invention relates to v containers for the sErage of liquids or gases under pressure. Several forms of containers for this purpose are now available including cylindrical-containhas been considered to be the only one that is truly stable elastically, that is, it does not tend to change its symmetry with an increase of internal pressure. The sphere is commonly known to have a minimum of surface for any given volume or content and to require a minimum wall thick-' ness and, therefore, a minimum of weight for the storage of any actual volume of gas compressed to any specified pressure. Moreover, a spherical container is commonly regarded as being the only shape of vessel which has these characteristics. One of the objects of the present invention is to provide a new. composite container for fluids ,producing a container having a .plurality of spherical segmental portions each'of which is bounded on at least one side by a diaphragm-like partition to form a plurality of separatedcompartments and means for equalizing the pressure in such compartments. Other and further objects and advantages reside in the various combinations, subcombinations. and details hereinafter described and claimedand in such other and further matters as will be understood by those skilled in this art or apparent or pointed out hereinafter. In the accompanying drawings, in which like numerals designate corresponding parts throughout the various views: Fig. 1 is a view in elevation of a. tank responding to our invention with parts broken away to show the structure thereof; of a tank responding Fig. 2 illustrates a horizontal-medial section through one of the partial spheres of Fig. land is provided with geometrical indicia by means of which certain calculations can be made relative to a container of this form; k

Figs. 3 and 4 designate in elevation a spherical segment: and a spherical zone whichzare useful in connection with the mathematical aspects of our invention; Fig. 5 is an elevational view of a modified form of'the invention and showing the supports and piping therefor; Fig. 6 is a plan view of a composite tank constituting a further modification of our invention and in which the spherical segments are arranged in the general form of a torus; Fig. 7 is in part an elevational view and in part a sectional view taken on line VII-VII of Fig. 6 and in the direction'of the arrows thereof; Fig. 8 is a view similar to Fig. 6 but of a further modified form of the invention; Fig. 9 is a view partly-in elevation and partly in section taken along the line IX-IX of Fig. 8 and in the direction of the arrows thereof; Fig. 10 is a view similar to Fig. 8 but of a still further modified form of the invention; and Fig. 11 is a view similar to Fig. 9 but taken along the line XI-XI of Fig. 10 and in the direction of the arrows thereof. Referring first to the structural features of our new containers, the simplest form thereof is shown in Fig. 1. In that figure the numerals 20 and 2| designate two partial spheres or spherical shell sections which are joined to a common disc oiplate-like member 22 by means of th continuous welds 23. In this form of tank there are two compartments or storage chambers 24 which are separated from one another by means of the diaphragm 22. It is-to be understood that the welds 23 are fluid-tight. As will be more fully understood from what follows, the container of Fig. 1 is usually provided with inlet and outlet pipes which make it possible to cause the chambers 24 to communicate with one another, thus, ..communication with one another. This automatically equalizes the pressure at all times." In the modified form of container illustrated ,in Fig. 5, it will be noted that there are two, v like end spherical portions 20' and a number of intermediateportions 20" which in this case are in the form of spherical zones. In. other words, end members 20' are incomplete spherical shells. to the extent that the same have a portion thereof removed ,so as to intersect the portions 20" in the manner illustrated, the members 20" being, in effect, the central portions 'of spheres with the diametrically opposite segments removed. A plurality of diaphragms 22' separates the interiorsof members 20' and 20" and, while not visible in Fig. 5. it will be understoodthat the circular welds 2 3 of Fig. l are employed. Thus, the container of Fig: 5 has a plurality or separated compartments or chamof material into the container and for removal of material therefrom, this being effected by suitable valves and by-passes, as will be appreciated by those familiar with piping arrangements.

The fact that all the container portions are thus connected into a common conduit serves to equalize the pressure of the various container portions and twinsure that material supplied to the container portions is stored at the same pressure in all of the various spherical'portions. A suitable relief valve 33 is provided as shown in order to prevent the pressure in the sy tem from exceeding a predetermined maximum. Supports 3'4 are shown as provided at each end of the container and, in general, it is to be understood that we may support the container in any suitable manner which per se forms no part of or restriction upon our present invention. The container need not, however, be elevated. In Figs. 6 and 7 a further modified form of container has been illustrated and which has the general configuration of a torus. This container .is made up of a plurality of spherical segmental portions arranged in ring form with a hollow center and in which each spherical container portion 20a is bounded by and has secured thereto a pair of diaphragms 22a which converge radially inwardly, thus producing a spherical container portion which has the general configuration of a truncated sector. Each diaphragm 22a is to be understood as being secured in place in the same manner as the diaphragm 22 previously described. The plurality of separated compartments or chambers thus provided in this form of the invention are provided with means for equalizing the pressure in each such either by a piping system of the character of Fig. or by providing one or more apertures in each diaphragm. This particular form of container is especially useful for the storage of liquids under pressure where it is an. vantageous to have acontainer with a diameter .which is large as compared to its height. In this arrangement also pumping costs are reduced. The still further modified form of container of Figs. 8 and 9 is, in general, similar to that of Figs. 6 and 7. There are, however, at least two notable distinctions. In the first place, the diaphragms 22b bounding the spherical container portions 20b are all interconnected and merge into a polygonal central diaphragm 22b which is, so to speak, inscribed in the center of the torus and in which is the additional spherical container 2lb. As will be noted from Fig. 9, the container compartments or chambers thus formed arev in communication with each other by means of theopenings 26 provided in the diaphragms 22b and 22b, these openings being reinforced by means of the apertured washerlike elements 25 which are secured to the dia phragms; This form of container is also provided with a piping system like that described in connection with Fig. 5. Under these conditions the piping system may be used solely for charging and discharging the container portions and the matter of pressure equalization is taken care of independently by the apertures 2i aforesaid. The virtue of this form of container is that it is capable of storing large volumes of liquids or gases under pressure and has unusual efiiciency in that all the space occupied by the container is usefully employed. Supporting means such as the braces or columns 21 may be provided and a relief valve 33 prevents excessive pressure condition within the container. - The modified container of Figs. 10 and 11 is substantially the same as that of Figs. 8 and 9 except mainly for the arrangement and disposition of the diaphragms 220 which are arranged to cross each other at right angles and in such manner as to, in effect, form a plurality'of containers of the type of Fig. 5. The nature of of "P" pounds per square inch greater than the atmospheric pressure exerted on

the outside surface of the sphere. In this case if the shell of the sphere is very thin as compared with its radius the said shell will be stressed substantially in tension due to the internal pressure, such teninherent symmetry of the sphere and such tension being numerically equal to PR/2, where P is the sphere. square inch and R in inches the tensional stress T will be expressedin pounds per lineal inch of circumference at the center of the shell thickness at any point on the sphere. Let it be further assumed that the spherical shell 20 is cut by a plane (BCE) and that the larger portion of the-sphere ABCEA is closed by means of a flat circular diaphragm 22 attached to the said portion of the sphere as, for example, by welding around the circle of intersection as shown at 23. Plane BCE will intersect the spherical shell in the form of a. circle. Now referring to the complete spherical shell it is known that such spherical shell has at all points around the circle caused by the intersection of the said plane a tensile stress equal as previously shown to PR/2. This stress has been indicated on Fig. 2 as T acting upward and to the left and is exactly 65 balanced and counteracted by a like but opposite force T1 acting downward and to the right of the intersecting plane. These forces T and T1 are. andT5 acting radially inwardly toward central urface BDE is removed it is apparent that strucint C. Now when the portion of the spherical e having the ability to resist forces '1: and '1': must be substituted in order to maintain equilibrium conditions. If X is assumed to be the angle subtended by the radius BC of the said in- 7 tersecting plane to the center of the sphere 0 assumed that the sphere contains a gas Pressure sion being equal in all directions because of thethe internal gas pressure and R is the radius of If P is expressed in pounds per it is apparent that the angle between the force T and its component Ta'will also be X. The mag-. nitude of force Ta is, therefore T cos X. The diaphragm I2 is, accordingly, stressed by a force having the magnitude of T cos X acting radially away from the center of the circular diaphragm and its thickness must necessarily be sumcient to resist such force. If the thickness of diaphragm I2 is assumed to be suiflcient to resist such force, it is apparent that the structure ABCEA will be out of equilibrium by the sum of the horizontal forces T: around the circumfel'ence of the diaphragm. Now if .the said structure ABCEA including the portion of the sphere and the circular diaphragm is placed in contact with another exactly similar structure placing the two diaphragms together and fastening them oause the horizontal forces T2 will be exactly offset by similar horizontal forces equal to T4. from the adjoining sphericalsegment and each diaphragm will adequately resist the radial forces T cos X. One important feature 'of our invention is based on the fact that if two or more spheres of the same or of different sizes are attached together in the manner we have described the weight of the material required in the shell plus the weight of the material required for the diaphragm for each of the spherical portions divided by the volume or contents of each of the spherical portions will be approximately the same as the weight of the material required to form the shell of any of the entire spherical shells divided by their volume. This can be demonstrated by showing that in Fig. 2 the ratio of .the weight per unit of volume of the segment including its circular diaphragm to the volume of that segment is identical with the ratio of the weight of the material of the entire sphere to its volume.

Using the following nomenclature in the English system of units: Vs is the volume of a sphere or spherical container. R is the radius of that sphere or spherical element in inches. P is the pressure in pounds per square inch. S is the allowable unit working stress in pounds per square inch. ts is the spherical shell thickness in inches. i is the diaphragm thickness in inches. As is the area of the spherical surface. Ad. is the area of the diaphragm. w is the weight of the membrane material in pounds per cubic inch. We is the weight of the spherical shell or spherical element. We is the weight of diaphragm. WT is the total combined weight of the shell and diaphragm. - N is any number of spheres or spherical elements. X is the angle formed between the axis of the' section. T is the stressper lineal inch in the spherical membrane. Ta is the stress in diaphragm in a radial direction. An is the area of a circular ring as contrasted with a diaphragm. W3 is the weight of such circular ring. The following fundamental equations for the solution of the geometry of spheres and spherical elements will be used. Spherical segment 'Volume=V,= (1 1rb(3a"+3c +4b Complete sphere It has been stated that the weight-volume ratio for any number of spheres is the same as though they were combined in one single sphere and also that the same remains true for spherical elements; We will first prove and derive the -constant for a complete sphere and then prove that any portion of a sphere may be removed and the structure closed by the use of a disk member forming part of our invention without changing the weight-volume ratio. Let it be assumed that the problem is to store a certain volume V of gas under a given pressure of P pounds per square inch, and further let it be assumed that the gas is to be contained in one sphere or N spheres, whichever combination gives the least weight for the desired volume.

.weight of one sphere Now the stress per lineal inch is and the thickness required to withstand this stress is equal to the stress per lineal inch divided by the allowable working stress in pounds per square inch or 5 T PR Substituting Equation 5 in Equation 3 we have. as an expression for the weight We equal to the following: . PR 6. W,=A.( )w and substituting Equation 2 for A; in Equation 6 we have weight of one sphere and for the total weight of N spheres s. W,= 'i yv Now from Equation 1 '9. ram- 4 2,841,044 4 and substituting this value of R for R in Equa-' The area of the disk is equal to a circular area tion 8 we have for the weight of N spheres of which BC is the radius or but which reduces to BC=OB m x a X 1.5 PwV 80 that l1, WT=T Ad=wR Sill X and expressing Equation 11 in terms of weight but sin-3 x x) per unit volume of gas stored we have or 12 ll l.5 Pw Ari=irR (1-cos X) V S Now the thickness of the spherical shell is equal This equationshows the weight/volume ratio of to the stress per inch divided by the allowable a sphere is independent of the number of spheres, unit stress or that is, one sphere would not weigh more or less T PR than N spheres whose total volume is equal to t,=the one sphere. Now it will be proved that a. portion of a sphere and the thickness q e f the dis i equa may be isolated and that the same ratio holds to the stress per oi elreumference multiplied true. In Fig. 2, as previously described, volume by the length ov which it acts divided y the EABCE is an isolated portion oi the sphere allowable unit stress ip ed by the len th EABDE with a plate-like member or. disk 22 comover which the unit stress i efleetive all in like pleting the inclosure. Now this disk is located units 0! as expressed by at any point C on the AD axis in such a manner 25 B that radial lines from the center of the sphere O i to the outer periphery of the disk makes a constantangle x with the AD axis. Now'the volume of EABCE is equal to the vol- 1 Pll cos X R sin X ume of the complete sphere minus the volume 28 R sin X of EDBCE and using the fundamental equations or for the geometry of the sphere we have Vs=%1rR -%1rb" (3R-b) e g' where r Y J and the weight of the disk is equal to the area of the disk multiplied by the thickness and weight per cubic unit all in like units or expressed by but Wa=Astirw X and the total weight of the complete structure so then i8 7 V.=%a-R %a-(RR cos X) (3R-(RR cos x A Collecting all the equations in a group we have: -rR 1-eos X)(3RR+R cos X) v.=''(2'+a cos X-Cos' x 4 f 2. Ar=2irR=(1+cos x) E "Ti' X) M a. Ad=IR'(1-COSX) PR =,R 2-3 cos X+cos'X) ifi PR +%1R'(3 cos X-cosX) 3 X a 6- w|=Artrw=2IR'(1-i-00S X) to!!! ='-g 2+3 cos Xcos X) v. wi=At-ts-w=s1i=(l-eos=x) -tc-w The spherical surface area of the above volume T=WI+Ws is equal to the area ofthe whole sphere minus Now substituting tin Equation 4 for to in Equathe area of the isolated smaller portion or tion 6 we have 2 l l 4.411% 21121 W: (1 HO. X) 2%; w where R. and b have the same values as above or '5 1 Ar=4rR21rR (R-R cos x) V =4'II'R -2'I'R (1-008 X) ,PRI =11? (4-2+2 cos x) I P- (1+eo X)w I and substitu A.= 21R= (1+cos x) 10- flon 7 we 5 f i The weight of the spherical shell is equal to the area multiplied by the thickness by the weight mama-00.: %;L per cubic unit all in like units or 'PR,

and then from Equation 8 we have 'I' PR3!!! 2s I Now from Equation 1 it is shown that and substituting this value of R for R in the above equation we have (2+3cos X.cos X) which is the same constant as that found in the previous proof. This proves then that if a portion of a spherical shell is removed and the spheres attached to each other regardless of their size or the angle ofattachment provided only that the pressure in all of the spheres is'the same. In actual practice we place one or more small reinforced intercommunicating holes in. each diaphragm so that the pressures will properly equalize or, in some cases, we findit convenient to attach the inlet and outlet piping to all of the spheres which accomplishes the same result. Referring to Formula 5 t cos X since that'the distance of the center of the disk'from the center of curvature of the spherical shell bears to the radius of the spherical shell. For two adjoining truncated spherical shells of the same radius, the required thickness of a single disk to give to the container the elastic stability of a single sphere would therefore vary 5 with the radius of the circle of intersection of the two spherical shells. When the radius of the circle of intersection approaches zero,-the thickness approaches two times the thickness of the spherical shell. When the radius of the intersection approaches the radius of the spherical shell the thickness approaches zero. When the radius of the intersection is equal to the square root of .75 or about .86603 times the diameter of the spherical shell, the thickness of the disk 15 would be the same as that of the spherical shell. If a circular ring were used to reinforce the spherical shell at the circle of intersection instead of our solid diaphragm it may be designed to adequately resist the force T cos X indicated as Tsin Fig. 2. In this type of construction, which is not new, it can be proved that the ring if designed to resist the forces T: transmitted to it from each of the spherical segments, will weigh twice as much as the diaphragm which is the basis of our invention. Further the ring would, in the cases of some forms of our invention, interfere with other essential members. Following is a demonstrationof the fact that the ring will weigh approximately twice that'of a flat circular diaphragm which will withstand the same radial loading.Assume two spheres I ii and H as in Fig. 1 except Joined together and reinforced by a circular ring in lieuof a diaphragm. Now from our previous solutions we knowthat -the radial stress per inch of circumference from one sphere is r3= (PR/2) cos X but since we have two spheres T3 becomes and if As. is used to designate the cross-sectional area of the ring we have Now if it be assumed that the center of gravity of the ring is on the theoretical intersecting point of the two spheres then the weight of the ring is equal to the volume generated as the cross section moves along the circumference of a circle passing through the center of gravity of the ring, the said circle having a radius equal to the perpendicular distance from an axis joining the centers of the two spheres to their common circle of intersection, multiplied by the weight per cubic volume of the ring, or a f =A -21-(R sin X)w (PR cos I-R sin X) sin X), 7o Referring to the weight of a diaphragm we have V I structure. since there are two spheres the weight of two diaphragms I 3 W 2( gg (l cos X) (cos X) W w(1 cos X) cos X ,and comparing the weight of the ring against that of a diaphragm we see that the weight of a ring is twice as much as that required for a diaphragm for the same loading condition.

One ofthe principal advantages of our invention is that comparatively large structures may be built without requiring much, if any, additional support for the relatively thin sheet metal The circular diap'nragms which a each individual spherical segment maybe very simply supported by a central column and radial girder-like members such as are commonly used in large containers. From the foregoing, it will be apparent to those skilled in this art that by making assemblies of our truncated sphericalshells and diaphragms, containers may be built to suit certain conditions, particularly as to space limitations, such as the diameter and height. Such assemblies will be much more efficient and much'less costly than a single container having the saine diameter and height. Such single containers will require much more material for their construction than our assemblies. This is especially so in cases where the single containerhas relatively flat upper and lower surfaces and is to take the place of the container of Fig. 6. In many cases, it would be impractical to either design or build a single container where it would not only be possible to design but to build a container embodying our invention. It is to be understood that the foregoing is presented as illustrative and not as limitative and that we may resort to other and further additions, omissions, substitutions and modifications without departing from the principle or scope hereof. fined by the appended claims. Having thus described our invention, what we claim as new and desire to secure by Letters Pat'- ent is: 2. A container comprising a series of truncated intersecting spherical shell sections and plate-like reinforcing disk members forming partitions between such shell sections and to which such shell sections are joined at their truncations; each such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shells when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell bears to the radius of that shell. 3. A container as defined in claim 2 in which the truncated spherical shell sections are so arranged as to approximate a rectangular structure. 4. A container as defined in claim 2 in which the truncated spherical shell sections are arranged in the form of a toms. - 5. A container as defined in claim 2 in which a number of the plate-lik reinforcing disk members are arranged in' parallel spaced relation. 6. A container as defined in claim 2 in which a number of the plate-like reinforcing disk members lie in planes radiating from the common center of the containen f ,7. A pressure tank comprising at least two truncated intersecting spherical. shell sections having the same radius and thickness and a platelike disk shell reinforcing member forming a partition between such shell sections and to which 4 such shell sections are welded at their truncations, said reinforcing member having a thickness equal to the thickness of one of such shell sections; such shell sections being attached together and to such

reinforcing member at their truncations to form a fiuid tight container; each reinforcing member having a radius at the circle of attachment approximating seven eighths of the The invention is rather that de1. A container comprising truncated intersecting spherical shell sections and a plate-like reinforcing disk member which forms a partition between such, shell sections and is welded to the adjacent intersecting edges thereof; such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shell sections when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell section bears to th radius of that shell section. v radius of the spherical shell sections. 8. A pressure container comprising a series of truncated intersecting spherical shell sections having the same radius and thickness, and circular plate-like disk reinforcing members welded to adjoining shell sections at their intersection and forming partitions between such shell sections; each such reinforcing member having a thickness equal to the thickness of one such shell section multiplied by the distance between the centers of curvature of adjacent shell sections (11- vided by the radius of one such shell section. 9. A pressure container comprising a series of truncated intersecting spherical shell'sections and circular plate-like disk members located between and joined to adjacent shell sections at their intersection to form reinforcements for and partitions between such shell sections; the'plate-like member between each two adjacent shell sections of the series having a thickness equal to the thicknesspf one such shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided y the radius of curvature of such shell section, plus the thickness of the other shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided by the radius of curvature of such other shell section. JAMES O. JACKSON.- COURTNEY L. STONE

Filament wound spherical pressure vessel US 3655085 A ABSTRACT A spherical, multi-layer, fibre reinforced plastic pressure vessel, each layer being a helix inclined at a different angle to the polar axis with each convolution in each layer following substantially a great circle, constructed so that the layer which extends closest to the poles of the sphere resists meridianal force of a given amount at a preselected horizontal plane, the layer most remote from the poles of said sphere resists, together with all other windings cooperating therewith, hoop force of said given amount along the equator, and the intermediate layers resist, together with the layers cooperating therewith, at selected horizontal planes only, either a meridianal force or a hoop force of said given amount.

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DESCRIPTION (OCR text may contain errors) [151 3,655,085 [451 Apnll, 1972 United States Patent Aleck 3,112,234 11/1963 3,144,952 8/1964 Uhll [54] F ILAMENT WOUND SPHERICAL PRESSURE VESSEL 'g et a1. 3,366,522 1/1968 Underwood........ ....156/175X Primary Examiner-Raphael H. Schwartz Attorney-Hubbell, Cohen &. Stiefel [73] Assignee: [22] Filed: [57] 1 ABSTRACT A spherical, multi-layer, fibre reinforced plastic pressure vessel, each layer being a helix inclined at a different angle to the polar axis with each convolution each layle lfollow fighsubstantia yagreat circ e,constructe sot att e ayerw ic ex- [58] Field of Search l 156/148 tends closest to the poles of the sphere resists meridianal force of a given amount at a preselected horizontal plane, the layer most remote from the poles of said sphere resists, together with all other windings cooperating therewith, hoop force of said given amount along the equator, and the intermediate layers resist, together with the layers cooperating therewith, at selected horizontal planes only, either a meridianal force or a hoop force of said given amount.

References Cited UNITED STATES PATENTS Ramberg [52] US. [51] Int. 1 Wiltshire g n u 0 Y 2 6 9 l 7 l 9 1 7 4 3 17 Claims, 5 Drawing Figures ow n PATENTEDAPR 1 1 I972 SHEET 1 UF 2 INVENTOR BENJAMIN J. ALECK #ilmww ATTORNEYS. PATENTEDAPR 1 1 m2 SHEET 2 BF 2 f 00oooo0ooo:. 4 5 INVENT BENJAMIN J. 1. CK MMQEMM ATTORNEYS. Tl (DEGREES) FILAMENT WOUND SPHERICAL PRESSURE VESSEL BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to spherical fibre reinforced plastic pressure vessels. 2. Description of the Prior Art Spherical fibre reinforced plastic pressure vessels are known. Generally speaking, the fibre reinforcement is wound in a random pattern in the hope of yielding a vessel having substantially uniform resistance to meridianal and hoop forces throughout. Some attempt has been made to wind vessels utilizing a multiplicity of layers, each layer being in the form of a helix, the convolutions of which follow substantially great circle paths, but the method of constructing such vessels has been highly empirical, with no reliable theoretical foundation, and the vessels so constructed have been inefficient. SUMMARY The helical winding layer extending closest to the poles of the sphere (that is the layer having its convolutions extending about the sphere at the most acute angle of inclination (a) to the polar axis) is constructed, in accordance with mathematical expressions, to resist a given amount of meridianal force at an analytical plane perpendicular to the polar axis which intersects the surface of the sphere at a given angle to the polar axis (a The winding layer next closest to the poles of the sphere is wound at an angle to the vertical of a and is constructed to resist, together with the first winding, at an analytical plane perpendicular to the polar axis which intersects the surface of the sphere at a selected angle to the polar axis of a said given amount of meridianal force. The layer next closest to the poles of the sphere is then constructed with convolutions disposed at an angle to the vertical equal to a: and is designed to resist, together with the contributions from the first two windings, a meridianal force of said given amount at still another analytical plane perpendicular to the polar axis which intersects the surface of the sphere at an angle to the polar axis of (1 The procedure may be continued for all additional winding layers save the layer (layer m) whose windings are most remote from the poles. Layer m will have its windings disposed to the vertical at an angle a,,, but will be constructed to resist at the diametral plane, together with all other windings, a hoop force of said given amount. Apart from the arbitrarily selected analytical planes no attempt is made to construct the vessel so that it uniformly resists throughout its entire surface both meridianal and hoop forces, this being taken care of by deformation of the completed vessel itself under pressure. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a sectional view of a spherical mandrel with bo'ss hardware disposed thereon ready to receive filament windings in accordance with the present invention;

FIG. 2 is an elevational view showing a few turns of one winding layer; FIG. 3 is a broken elevational view of the vessel partially wound; FIG. 4 is a series of curves for several windings showing the relationship between resistance to meridianal force in pounds per inch versus the location of the analytical plane; and FIG. 5 is a view similar to FIG. 1 showing a modified form of hardware for the vessel. DESCRIPTION OF PREFERRED EMBODIMENTS The present method is directed to a multi-layer filament wound spherical pressure vessel, each layer of which is in the form of a tight helix with each convolution in each layer following substantially the path of a great circle (the deviation from a true great circle path being as a result of the pitch of the helix). It can be shown for any such layer (e.g., a layer 1) that the following equations are true: wherein: f, is the radial pressure which the layer of fibres at tension T would exert on a spherical mandrel; N, is the number of turns in the layer under'consideration; T is the maximum tension to which the filaments in the layer are to be subjected and is therefore constant; a is the radius of the sphere being formed; 1; is an angle to the vertical axis at which an arbitrarily selected plane perpendicular to the polar axis intersects the surface of the sphere being formed; 0: is the angle at which the windings or convolutions in the layer under investigation are disposed to the vertical; N is the resistance in pounds per inch to tensile force in the meridianal direction tending to pull the sphere apart along a plane perpendicular to the polar axis of the sphere; and N is the resistance in pounds per inch to tensile force operating along a parallel of the sphere (i.e., perpendicular to the polar axis) tending to pull the sphere apart along a plane parallel to or including the polar axis. In a multi-layer structure, the contribution of each layer to resistance to meridianal and hoop stresses at any given plane on the surface of the sphere is additive with the contribution of each other layer intersecting said plane. Thus, for example, if there is a two layer structure, to detennine the total resistance to meridianal force per unit length of parallel which both layers can withstand (N equation (2) above would have to be rewritten as:

Obviously, the equations (1) and (3) for two layer structures could be rewritten in a similar manner. Thus it can be shown that in a structure having m layers wound in accordance with the above described great circle helical pattern that where i is the number of any given layer and ranges from 116 I winding layer (N,). This apparently insurmountable problem has been solved in the present method by making certain assumptions which experimentation has proved to be highly satisfactory. Specifically, one assumption is that if the requirements of equation (6) above at a given number of arbitrarily selected analytical plane s w hich intersect the surface of the sphere at angles to the polar axis which vary from zero to 90, are met for a desired value of N the value of N, at the planes in between those selected for analytical pEposes will take on satisfactory values. A second assumption is that if the requirements to achieve a substantially constant N, are met throughout the vessel, the requirements for achieving a substantially constant N are also met. As will be seen hereinafter, the second assumption preferably includes one modification; namely, that in the equatorial region of the sphere where the layer most remote from the poles is layed down, that is the m layer, the requirements of this layer with respect to the number of windings, that is N,,,, are satisfied not with respect to Na, but instead with respect to N9, A detailed analysis indicates that a vessel designed utilizing the equations (6) and (7) above and the assumptions expressed above will yield a vessel THAT will maintain a substantially spherical shape. However, it can be shown that the assumptions are only good approximations and that A6,, and N, do vary over the surface of the sphere when under pressure. This variation is so small that all that results therefrom is that the ideal spherical shape of the vessel becomes somewhat altered when the vessel is pressurized, the alteration taking the form of the appearance of small peaks and valleys in the spherical surface, which peaks and valleys compensate for the actual variations arising from the design assumptions. Turning our attention now to the drawings in detail, the vessel to be formed by the present invention is preferably wound on a mandrel 10 having a radius a. The mandrel may be a hollow metal sphere or the like although preferably, in the present invention, the mandrel is a dissolvable mandrel such as a salt mandrel. As the vessel to be formed is a pressure vessel, it is obvious that it must have at least an inlet-outlet 12 although, as shown in FIGS. 1 and 3, the vessel has an inlet 12 and an outlet 14 of substantially identical configuration. As shown in the drawings, the inlet 12 and the outlet 14 are both cylindrical tubes and each is provided with a flange l6 and 18 of certain proportions to be described hereinafter in greater detail. Naturally other shapes of hardware may be employed. As here shown, and as is preferred, the surface of the mandrel 10 is contoured in order to render it complementary to the flanges 16 and 18 in order to present a substantially spherical outer surface for winding the vessel thereon. The contour cutouts or surface depressions for the flanges l6 and 18 are designated in FIG. 1 by the reference numerals 20 and 22. As already stated, each of the winding layers to be fonned to make the present vessel is to be in the form of a helix with each turn thereof following substantially a great circle of the sphere to be formed, the variation from a true great circle being the result of the pitch of the helix (FIG. 2). To form the first winding layer, which layer is designated by the reference numeral 1 in FIG. 3, it is preferred to pitch the layer so that the upper and lower edges thereof run tangent to the exterior of the tube 12. Thus

04,, that is the angle of inclination of the first layer to the vertical, is preferably determined by the physical dimensions of the inlet 12 and, if included, the outlet 14. Now, in view of the fact that winding number 1, which, as shown, is the winding which extends closest to the poles of the sphere, provides the sole resistance to meridianal force in the areagn the polar s id esofthe second layer, N must be equal to N which is an arbitrarily preselected value that preferably is equal to p x(a/2), wherein p is the maximum pressure to which the vessel will be subjected. Moreover, it is possible to fix the angle of the plane perpendicular to the polar axis at which winding 1 will afford the maximum resistance to meridianal force. This plane intersects the spherical surface at an angle 1; that will subsequently be assigned as the value of 01 The equation t o determine a is a sin"( 1/2 sin a Now equation (2) can be solved for N Once N is known, all of the parameters for the first winding are known. Therefore, a curve can be plotted to determine the contribution of winding 1 to resistance to meridianal force at various planes of contribution of winding 1 is less than the predetermined value of N Since no additional winding will be provided in the polar region between at and 01 means must be provided for yielding additional resistance to meridianal force. This means is the flanges 16 and 18 on the inlet 12 and the outlet 14, respectively. These flanges are preferably metal and are proportioned with respect to thickness and the nature of their material to provide additional N in the polar region to make sure that the polar region does not fail in meridianal stress. Turning our attention now to the second winding, that is winding 2, a is already established as above described. However, inorder to determine the number of turns in winding 2, that is N an assumption must be made with respect to the value of 01 That is to say, it is known that the third winding, winding number 3, will contribute no N at 01 Thus if equation (4) is solved where n is assumed to be a the value of N, can be calculated, as there are no other unknowns in the equation. Thus N45 is known as it has been preselected, N, is known as it has been previously calculated, 01 is known as determined above, and a is known. In order to select a to fulfill the final missing unknown in the equation save for the value of N itself, certain practical considerations must be taken into account. Thus, if a is too close in size to 01 then the number of windings to form the entire vessel will be increased and this will increase the complexity of the winding operations which is undesirable. However, if 01 is unduly large there will be substantial variations in the actual M between a and a as contrasted with the theoretical constant value throughout, and these variations at some practical point become undesirable. l have found that a practical number of windings to yield a desirable vessel falls somewhere in the range of 10 to 14 for most applications. Assuming as a first approximation that the difference in adjacent as is substantially uniform throughout, a reasonable approximation of a can be made. Once a; has been assumed or approximated as above described, equation (4) may be solved to determine N If the solution of the equation (4) for N yields a positive number, then the assumption for 04;, is a workable assumption and the calculation may be employed. If, however, the solution yields a negative number for N which solution would indicate that with the assumed value of angle a the second layer should have a negative number of turns in order to yield an N,,, equal to the desired value, then it becomes clear that the selection for a is wrong in that it is too small an angle and an adjustment in the assumption must be made to enlarge the assumed value of angle a whereupon the

calculation of N is repeated. Once the solution of equation (4) yields a positive value for N then the parameters for winding 2 are established in that the angle of inclination of the convolutions to the vertical (a is is determined, and the number of turns in the second winding (N is also determined. While the plotting of the curves of FIG. 4 are unnecessary to this analysis, if desired, the N,,, versus 1; curve can be plotted and it would appear as shown in FIG. 4 in dashed line. Turning our attention now to winding number 3, a similar procedure may be employed to determine the number of turns (N in winding number 3 as was employed above to determine the number of turns (N in winding number 2. Specifically, the summation form of the equation for N,,, above set forth as equation number (6), may be written where only three windings (l, 2 and 3) are present in accordance with the following equation: analyses, that is at various 1;, which curve is shown in solid lines in FIG. 4. It will be seen that the polar area between a, and 94 the N, Equation number (9) is presented with 1 already assumed to be 01 This assumption facilitates the calculation as it eliminates winding 4 from consideration in arriving at the parameters for winding 3 in the same way that 17 was selected to be 01;, in the solution of equation (4) for N Again, some arbitrary value for a, must be assigned prior to the solution of the equation (9) for N;;. The factors determining the selection of a, are the same as those set forth above with respect to a, and when a selection or first approximation for the value is made, equation (9) is readily solvable for N Again, if N;, should prove to be a positive number then the assumption as to the value of a is a useful and workable one and the calculations may be adhered to. Of course, with the assumption, if the value of N should prove to be negative, then it is obvious that a 4 has been chosen to be too close to the angle a and it must be enlarged. Again, as was true in the solution of N it will be seen that the solution of the equation for N is made by analyzing the sphere at a very convenient plane, namely the plane at which the contribution of winding 4, the next winding to be wound after winding 3, will be zero, whereby to enable the designer to ignore the contribution of winding 4 in calculating the number of turns in winding N The manner of determining the parameters of the remaining windings 4, 5, 6 save for the winding most remote from the poles, that is winding m, is precisely as that described above with respect to the second and third windings, and is a mere application of equation (6) presented above. The manner of solving the parameters of winding m will be described below. It should be noted that the sphere has been redesigned to yield constant N only at a preselected number of planes and no attempt has been made to determine whether the actual N at other analytical planes, that is at planes perpendicular to the polar axis which intersect the spherical surface at other angles 1 would be equal to the N chosen for the particular sphere. However, a review of the data and an observation of the results of the of the design method indicate that there is not substantial variation in M, over the entire surface of the sphere if the sphere is constructed in accordance with the method. Moreover, it should be noted that throughout the description to this point, no attempt has been made to determine whether N0, that is the hoop strength of the sphere, is constant throughout and whether

it is equal to the meridianal strength of the sphere in order to yield a substantially 100 percent efficient vessel. The reason for the absence of such calculations is the assumption previously mentioned that when the vessel is designed for a constant N a substantially constant Nml ,rssuln dflN'a, willbesah i t all jgua to Na.l-lowever, in order to insure that the hoop strengt of the sphere does meet the design requirements for a highly efficient vessel, the winding with the maximum a, that is the winding m, is preferably designed to satisfy the requirements of equation (7) and not of equation (6). That is to say equation is r r tten as +1; Nm 01 2311.". A i 711 1" J ln solving equation (1) for N,,,, n will be chosen to be 90 in order to determine that the hoop strength at the diametral plane of the vessel is equal to N is equal to Na, Thus in equation (10) the value of sin n will be 1. It will be obvious that between the expression in the equation beginning with N and the expression in the equation beginning with N,,, may appear a number of additional expressions similar to those already presented but for the other windings in the vessel. However, all of the parameters for these windings will be known (having been arrived at by the previously described procedure) and the entire equation 10) is readily solvable for N,,, in order to yield a winging m which will yield the proper hoop strength for thevessel in the equatorial area. This gives' added assurance that the vessel will be a highly efficient one. Utilizing the design procedures above described, a highly satisfactory pressure vessel has been wound in accordance with the present invention to yield a vessel with a radius (a) of 6.75 inches and the ability to withstand a pressure of 6,530 psi. Such a vessel was formed of Owens Corning 8-994 fiberglass prepreged with US. Polymeric E790 epoxy resin The winding layers were wound one at a time and after the complete vessel had been formed it was subjected to the curing temperature for the epoxy resin carried by the prepreged fiber glass to cause the resin to form a substantially continuous rigid matrix for the filament winding. After the resin had been set or cured, water was introduced into the interior of the vessel through the inlet 12 to dissolve and flush out the salt mandrel whereby to yield the desired vessel. It will be obvious that the plastic need not be incorporated in the vessel being formed as a coating on the filament winding although this is highly desirable. Thus uncoated reinforcing filament such as fiber glass could be employed and after the winding layers are formed, the winding layers could be impregnated with liquid polymeric material as by spraying or brushing, and thereafter the plastic could be cured. Moreover, as is well known in the art, it is not necessary that the plastic be epoxy, although this is desirable. For example, any rigid or semi-rigid thermoplastic or thermosetting plastic material such as, for example, ABS (acrylonitrile, butadiene, styrene) plastic; acrylic plastic such as polymethyl methacrylate; polystyrene; vinyl plastics, urea-formaldehyde condensates; phenol-formaldehyde condensates; polyoxymethylene plastics; or polyolefins; etc., may be employed. The epoxy resin used in the specific example is a condensate of epichlorhydrin and bis phenol A, although other epoxies could be employed. While fiberglass is the preferred reinforcement due to its high tensile strength, it will be obvious to anyone skilled in the art that other types of reinforcing filaments can be employed within the present invention. Thus, any of the well known continuous filaments, whether synthetic or natural, may be employed, including, by way of example, polyamides, such as polyhexamethylene adipamide and

polycaproamide; polyesters, such as ethylene terephthalate polymers and copolymers; acrylic polymers and copolymers such as polyacrylonitrile; vinyl polymers such as polyvinyl alcohol, polyvinyl chloride and polyvinylidene chloride; fluorinated ethylene polymers such as polytetrafluoroethylene and polytrifiuoromonochloroethylene; polyhydrocarbons such as linear polyethylene, linear polypropylene and copolymers of ethylene with other polymerizable monomers; regenerated cellulose; cellulose acetate; polyurethanes; and the like. In addition, biconstituent filaments made up of polyamid and polyester, e.g., nylon polyester or the like, may be employed. Such biconstituent filaments are produced commercially, for example, by Allied Chemical under the trade name BF-121. (Frequently such biconstituent filaments of nylonpolyester are referred to as merged filaments) Generally, these filaments are obtained by the simple expedient of melt mixing polyamide and polyester, e.g., nylon and polyethylene Lastly, if desired, metal fibers and such naturalfibers as silk, may be employed. While in the preferred method above described all of the layers save the layer N are designedby utilizing equation (6) with an eye to maintaining M constant at preselected planes at angles a a etc., and only the last winding, that is the m winding is designed utilizing equation (7) for hoop strength, a satisfactory vessel can be designed by aiming for a substantially constant N at the various planes of analysis determined by the angles 11 ,01 etc., by utilizing eaQUATlON (7), and a similarly efficient vessel can be obtained. If such a procedure is elected, however, the layer closest to the polar regions, that is winding 1, should nevertheless be designed in order to yield an appropriate meridianal strength at the angle a, in order to insure that the vessel is reasonably efficient in the meridianal direction as well as in the hoop direction. Thus, as a generalization, it can be said that winding number 1, that is the winding closest to the polar region of the vessel, must be designed in accordance with the equation (6) to yield a desirable meridianal strength for the vessel in the polar region, and winding number m closest to the equatorial region of the vessel must be designed in accordance with equation number (7) to yield a vessel having a desirable hoop strength. The windings in between the first winding and the m winding may be designed in accordance with either equation (6) or equation (7) utilizing, of course, the assumptions and procedures above described. However, it will be obvious that to facilitate calculations, all of the windings between winding 2 and winding m-l are preferably designed with respect to the same equation, that is either with respect to equation (6) or with respect to equation (7). One exception to the above statement may be that if desired the first two windings closest to the polar region of the vessel, that is winding 1 and winding 2 may be both designed utilizing equation (6) to yield a substantially constant meridianal strength and the two windings most remote from the polar regions, that is windings m and m-l may both be designed by the utilization of equation number (7), that is to yield in the equatorial region substantially constant hoop strength for the vessel. In such a method, thewindings 3 through m-Z may be designed in accordance with either equation (6) or equation (7) or any combination thereof, although, as already mentioned above, it is more desirable to utilize the same equation throughout the intermediate layers or windings.

Once the calculations for all of the windings are completed in accordance with any of the above embodiments of the invention, the mandrel is set with the bosses 12 and 14, placed as shown in FIG. 1, and layer 1 is wound at an angle of inclination of a, and with a number of turns of N as calculated. The winding may be wound by hand although it is preferred that it be wound by machine as conventional winding machines will maintain more uniform spacing of the adjacent turns in the particular winding. During winding a mild tension is applied to the filaments in order that they lay snugly on the mandrel but this tension is relieved almost immediately after removal of the mandrel if it is a dissolvable mandrel such as a salt mandrel. If the mandrel 10 happens to be a metal sphere, the amount of tension applied to the windings is of such small amount that it leaves the metal sphere forming the mandrel substantially unstressed. After winding 1 is completed, the machine is readjusted to wind the second winding pattern at an angle and with a number of turns N Thereafter the machine is reset for each additional winding through winding m. In view of the fact that a number of resetting's must be made, and each of these takes time in fabrication, it is desirable to keep the number m relatively small, always, of course, taking into account the requirement for a substantially uniform N and N9, throughout the surface of the vessel. As already noted, if the number of windings, that is if the number m, is between about l0 and about 14, satisfactory results with a pra namb r ofr pes ac i 7 It will be obvious that upon completion of winding and the curing of the plastic resin, the mandrel, if removable as would be true of a salt mandrel, is dissolved by flushing water into the interior of the vessel through inlet 12 Naturally, if a metal liner is employed in the mandrel, the metal liner will remain as an integral part of the vessel. As already indicated, the completed sphere is spherical under no stress, but when it is subject to its intended operating pressures, it will not maintain a truly' spherical shape. Instead, a vessel made in accordance with the present method will under pressure deform to exhibit small peaks and valleys in its surface that are not readilyv visible to the naked eye. The appearance of the small peaks and valleys is the adjustment of the vessel itself to compensate for variations in N and N over the surface of the vessel arising as a result of the fact that the procedure for designing and making the vessel is based on assumptions that are good approximations but not perfect ones. The desirability of the method is that it yields a vessel which through these minute distortions in shape adjusts itself to correct for these variations. While the description presented with respect to FIGS. 1 and 3 was with respect to a vessel having an inlet 12 and an outlet 14, a similar method may be employed where the vessel has only one portal to the interior thereof which serves at various times as an inlet and outlet. The hardware for such a vessel is shown in FIG. 5, wherein the boss 12 with its flange 16 set in a depression 20 in the surface of a salt mandrel 10 identical to the mandrel 10 of FIG. 1. However, in view of the fact that the vessel to be formed on mandrel 10 of FIG. 5 is to have only one opening, a problem arises with respect to the opposite polar regions. If symmetry is to be maintained in the winding, and this is highly desirable for practicing the present method, there would be an opening at the opposite polar region but this would render the vessel useless. There are various ways of avoiding this problem and one of them is illustrated in FIG. 5 wherein asolid concave plate 114 having a diameter and curvature equal to the diameter and curvature of flange 16 is set in the opposite polar region to the hardware 12. If desired,

the central polar part designated by the reference character 116 may be slightly thickened whereas the annular remainder 118 may have precisely the same dimensions and properties as the flange 16 above. The purpose for the slight recess between the portions 116 and 118 is to provide a guide or shoulder for the first winding, that is winding 1. However, it will be obvious that such a shoulder is not necessary to practicing the present method. It will also be obvious that such a solid disc need not be employed. In lieu thereof, if there is to be only one inlet outlet, the vessel may nevertheless be formed with two as in FIG. 1 and then one of them may be closed as by a metal plug or the like. However, it is important in considering the present method to realize that there is no fibre in the immediate vicinity of the poles of the vessel and some form of insert to provide the necessary meridianal and hoop strength in the polar regions must be included in order to yield a useable vessel. Throughout this description it has been assumed that the first layer to be wound on to the mandrel is winding 1 that extends closest to the poles of the sphere. It has further been assumed that each successive winding 10 be wound on to the mandrel is the one extending next closest to the poles and that the final winding to be placed on the mandrel is the winding m which is most remote from the polar regions. While this is the preferred method of laying down the windings, it is not the only method embodying the invention. For example, the order of laying down the windings, once the calculations have been made, could be reversed. In the alternative a relatively random selection of layers to be wound'could be employed such as, for example, winding 3, winding 7, winding 5, winding 9, winding 1, etc. However, such a pattern would require more adjustment of a winding machine and would therefore not be as desirable as the preferred order described or the reverse thereof. With the method of the type herein described, a highly efficierit, fibre reinforced, spherical plastic vessel can be formed. What is claimed is: 1. A substantially spherical filament reinforced plastic pressure vessel wherein said vessel is to withstand a preselected meridianal force of M pounds per inch and a preselected hoop force of Na, pounds per inch, said vessel including means for permitting defonnation of said vessel upon pressurization thereof to exhibit throughout the entire vessel an ability at all planes perpendicular to the polar axis to withstand a substantially constant meridianal force of M and at all planes parallel to said polar axis to withstand a substantiallY constant hoop force of N9, said last mentioned means comprising a plurality (m) of lielically wound layers of filament, the convolutions of which follow substantially great circle paths, each winding layer being composed of windings disposed in planes which intersect the center of the polar axis of said sphere at an angle of inclination (a), that is different from said angle of inclination of the windingsof the other of said layers, said winding layers being designated progressively from 1 to in in accordance with their respective angles of inclination, said winding layer 1 satisfying the equation Ni Vsin 1 sina at 1; 90; and windings (2) through (m-l) satisfying together with the windings of more acute angles of inclination, one of said two equations at analytical planes intersecting the surface of said sphere at 1 a t-l.

2. The pressure vessel of claim 1, wherein N is substanilfl Y/QQL QLI JYH i H 3. The pressure 'vessel of claim 2, wherein saidwindings (2) .t ir l..) waist!thesame qua isa. 4. The pressure vessel of claim 3, wherein said same equation is said first presented equation. 5. The pressure vessel of claim 2, wherein said winding (2) satisfies together with winding (1) the first presented equation at n a said winding (ml satisfies together with windings (1) through (m-2) the second presented equation at 11 a and the windings (3) through (m-2), together with the windings of more acute angles of inclination, satisfies one of said two equations at analytical planes intersecting the surface of said sphere at 1 a 6. The pressure vessel of claim 1, wherein said filament is fiber glass. 7. The pressure vessel of claim 4, wherein said filament is fiber glass. 8. The pressure vessel of claim 7, wherein (m) is between 10 and 14. 9. The pressure vessel of claim 1, wherein said plastic is a substantially continuous matrix for said winding layers and is at least semi-rigid. 10. The pressure vessel of claim 7, wherein said plastic is rigid or semi-rigid and is a substantially continuous matrix for said winding layers. 11. The pressure vessel of claim 1, further comprising a flanged boss disposed at one of the poles of said sphere, said boss having a radius of, a sina,, said flange having a radius of a slna 12. The pressure vessel of claim 11, further comprising a second flanged boss disposed at the other of the poles of said sphere, said second boss having a radius of a sinoq, the flange of said second boss having a radius of a sina 13. The pressure vessel of claim 11, further comprising a concave imperforate disc disposed at the other of said poles of said sphere and having a radius of a sina 14. The pressure vessel of claim 10, further comprising a flanged boss disposed at one of the poles of said sphere, said boss having a radius of a sina said flange having a radius of a sma 15. The pressure vessel of claim 14, further comprising a second flanged boss disposed at the other of the poles of said sphere, said second boss having a radius of a sina the flange of said second boss having a radius of a sina 16. The pressure vessel of claim 14, further comprising a concave imperforate disc disposed at the other of said poles of said sphere and having a radius of a sina 17. The pressure vessel of claim 14, wherein (m) is between 10 and 14.

DESCRIPTION DETAILED DESCRIPTION The entire polymerization reaction is preferably carried out in the polymerization zone defined by an essentially spherical wall. In fact, the inventors have found that by carrying out the polymerization reaction under the conditions of the process according to the present invention, it is possible to obtain, in a reproducible manner and using a single agitator, polymers and copolymers based on vinyl chloride which after screening possess interesting characteristics in terms of high apparent density, mean particle diameters adjustable to need and a low weight percentage of fine particles, despite the fact that the reaction mixture successively has four different states from the beginning to the end of the polymerization reaction; liquid state, suspension of solid particles in a liquid, pasty state, and powdered state, and its consistency changes considerably. According to the present invention, it is possible to vary the speed of rotation of the blade-type turbine assembly as a function of the state of the reaction mixture and its consistency, the desired mean particle diameter of the polymer or copolymer or any other parameter of the processor the quality of the resins to be prepared. The speed of rotation of the blade-type turbine assembly is generally reduced between the beginning andthe end of the polymerization reaction to a value lower than one-third the initial value and to as low as one-fourth the initial value. Also according to the present invention, the polymerization reaction may bestarted in the polymerization zone defined by an essentially spherical wallwith a very small initial volume of reaction mixture, which makes it possible to carry out polymerization operations in which part of the monomer or monomers and/or part of the polymerization initiator or polymerization initiators and/or at least part of any other additive can be introduced into the said polymerization zone during the polymerization or the degassing of the polymer obtained. According to a first variant o the process according to the present invention, the polymerization reaction is carried out in two steps, which are carried out in different devices, carrying out a prepolymerization operation with a monomer composition based on vinyl chloride in the first step and a final polymerization operation in the second step, the said first step being carried out in the polymerization zone defined by the essentially spherical wall. According to an embodiment of the first variant of the process according tothe present invention, the prepolymerization operation is carried out in the polymerization zone defined by the essentially spherical wall until the degree of conversion of the monomer composition reaches 3% to 15%, a supplementary monomer composition based on vinyl chloride, which is identical to or different from that used during the first step, is added to the reaction mixture if desired, after which the final polymerization operation is carried out with the reaction mixture thus formed while stirring slowly. According to this embodiment, the final polymerization step can be carried out, e.g., in a polymerizer of the conventional type as described, e.g., in French Patent No. 1,382,072

and its above-referenced Certificates of Addition; in French Patent No. 73 05537, published as Nos. 2,218,350 and No. 75 32124, published as No. 2,328,722 and in French Patent No. 85 05429, published as No. 2,580,192. According to a second variant of the process according to the present invention, the polymerization reaction is carried out in two steps, which are carried out in different devices, carrying out a prepolymerization operation in the first step with a monomer composition based on vinyl chloride and a final polymerization operation in the second step, the second step being carried out in the polymerization zone defined by an essentially spherical wall. According to an embodiment of the second variant of the process according to the present invention, the prepolymerization operation is carried out with highly turbulizing agitation until the degree of conversion of the monomer composition reaches 3% to 15%, a supplementary monomer compositionbased on vinyl chloride, which is identical to or different from that used during the first step, is added to the reaction mixture if desired, after which the final polymerization operation is carried out with the reaction mixture thus formed in the polymerization zone defined by an essentially spherical wall. According to this embodiment, the prepolymerization step can be carried out, e.g., in a prepolymerizer of the convention type as described, e.g., in French Patent No. 1,382,072. The inventors have also found that if the process according to the present invention is employed either by carrying out the entire polymerization reaction in the polymerization zone defined by an essentially spherical wall or by carrying out the polymerization reaction in two steps, which are performed in different devices, the second step being carried out in the polymerization zone defined by an essentially spherical wall, the duration of the degassing treatment is noticeably reduced under otherwise identical conditions. In practice, the space between the blades and the wall of the spherical polymerization zone of the reactor, in which the process according to the present invention is carried out, is advantageously between 2 mm and 50 mm. The length of the blades of the turbine assembly is such that the distance between their tips and the lowest point of the spherical wall, measured vertically, is at least equal to one-tenth the diameter of the sphere, in which case the diameter of the circle described by their tips during rotation is at least equal; with regard to the play, to threefifths the diameter of the sphere, which means that the said blades pass by in the vicinity of the spherical wall over at least 10% of the surface. The blades may pass by in the vicinity of the sherical wall such that they reach an equatorial plane, in which case the diameter of the circle described by their tips during rotation is equal; without regard tothe play, to the diameter of the sphere. The blades may also extend slightly beyond the equatorial plane perpendicular to the axis of rotation. The turbine assembly generally comprises one to six blades, especially three blades, which are preferably disposed regularly around the axis of rotation and are advantageously profiled so as to facilitate intensive mixing. In addition, the reactor may be, but does not need to be, equipped with an additional scraping system consisting of one or several rotated members inthe part of the spherical polymerization

zone not occupied by the turbine assembly. The shape of the industrial reactions which are suitable for usefor the process according to the present invention is not necessarily that of a complete integral sphere. According to the present invention, the only important thing is that the polymerization zone be defined by an essentially spherical wall. However, the spherical shape of the reactor may be interrupted by various tubes, pipe connections or openings. Thus, for the convenience of use and especially cleaning, the reactor may comprise openings of sufficient size to permit access to the inside and, e.g., the entry of a person in the case of large reactors. The reactor maybe, e.g., of the type described in French Patent No. 1 22425, published as No. 2,517,313. The descriptions illustrating the embodiments of the process according to the present invention will be described below in an illustrative rather than a limitative manner with reference to FIGS. 1a through 1d of sheet 1 of the appended drawings, and a reactor suitable for use for carrying out the process according to the present invention will be described with reference to FIGS. 2 and 3 of the drawings. FIG. 1a shows a closed polymerization zone Z.sub.1 defined by a spherical wall S.sub.1. A turbine assembly T.sub.1, provided with blades disposed regularly around a pivot B essentially located in the bottom point of the sphere, is mounted to rotate around the said pivot. A motor M drives the turbine T.sub.1. In this example, the tips of the blades of the turbine assembly T.sub.1 extend beyond the equatorial plane (line E--E) perpendicular to the axis of rotation (which is essentially vertical in the case of FIG. 1a) and pass by in the vicinity of the internal sphericalwall over 60% of the surface of the sphere. FIG. 1b shows a closed polymerization zone Z.sub.2 defined by a spherical wall S.sub.2. A turbine assembly T.sub.1, mounted to rotate around a pivotB, is driven by a motor M in the same manner as shown in FIG. 1a. In this example, the tips of the blades of the turbine assembly T.sub.2 describe acircle whose diameter is at least equal; without regard to the play, to threefifths the diameter of the sphere S.sub.2. FIG. 1c shows a diagram analogous to FIGS. 1a an 1b showing a polymerization zone Z.sub.3 defined by a sphere S.sub.3. The turbine assembly T.sub.3, driven by the motor M, rotates around a pivot B which isshifted relative to the bottom point of the sphere. In this example, the axis of rotation of the turbine T.sub.3 is not vertical. The equatorial plane (line E--E), perpendicular to this axis of rotation, is oblique. Thetips of the blades of the turbine T.sub.3 describe a circle whose diameter is equal; without regard to the play, to that of the sphere S.sub.3. FIG. 1d illustrates an essentially spherical polymerization zone Z.sub.4 defined by a spherical wall S.sub.4 and by a cylindrical extension C.sub.4which can serve as a screen or permits access to zone Z.sub.4. The turbine T.sub.4, which is driven by the motor M to rotate around a pivot B, is mounted in the same manner as in FIG. 1c.

The spherical reactor 1 shown in FIG. 2 comprises two hemispheres, an upperhemisphere 2 and a lower hemisphere 3. The hemispheres 2 and 3 are assembled and maintained by bolts 4 distributed in a diametrical plane over the respective flanges 5 and 6 and the hemispheres 2 and 3. A synthetic rubber gasket 7 ensures tight sealing between the two hemispheres. The reactor 1 is equipped with a magnetically operated drive assembly 8 driving a shaft 9 disposed vertically along one diameter of the reactor 1,with insertion of a coupling 10. The shaft is sealed by a polytetrafluoroethylene packing 11. A turbine assembly carried b a projection 12 mounted in the bottom point of the lower hemisphere 3 comprises three blades 13 connected to the base 14 which is rigidly attached to the shaft 9. The turbine assembly is mounted so that the blades pass by in the vicinity of the internal wall of the lower hemisphere 3 and extend to the level of the equatorial plane (line E--E) of the reactor 1. The reactor 1 is surrounded by two jackets 15 and 16 which are fastened to the hemispheres 2 and 3, respectively, in which a heat exchange fluid circulates, entering via the tubes 17 and 18 and leaving via the tubes 19 and 20. In its upper part, the reactor 1 comprises a tube 21 for feeding in the monomers, the polymerization initiators and any other additive used, as well as a tube 22 for discharging the nonreacted monomer composition. In its lower part, the reactor 1 comprises a tube 23 controlled by a valve 24for discharging the polymer. Any polymerization initiator which can be used to prepare polymers and copolymers based on vinyl chloride by mass polymerization and which generally form free radicals is suitable for use in the process according to the present invention, such as organic peroxides, e.g., lauroyl peroxide, acetyl cyclohexanesulfonyl peroxide, isobutyroyl peroxide, dichloroacetyl peroxide, trichloroacetyl peroxide; peroxydicarbonates, such as ethyl peroxydicarbonate, ethyl hexyl peroxydicarbonate, isopropyl peroxydicarbonate, isobutyl peroxydicarbonate, cetyl peroxydicarbonate, cyclohexyl peroxydicarbonate, tert.-butyl cyclohexyl peroxydicarbonate; tert.-butyl perneodecanoate, cumyl perneodecanoate; tert.-butyl permethoxyacetate; tert.-butyl perethoxyacetate; tert.-butyl perphenoxy-2-propionate; 2,4,4-trimethyl pentyl perphenoxy-2-acetate; and azo compounds such as 2,2'-azo-bis-(2,4-dimethylvaleronitrile). The polymerization initiator or polymerization initiators are used, in general, in amounts of 0.001 wt. % to 0.006 wt. %; expressed as active oxygen, relative to the total weight of the monomer composition used. The polymerization temperature is, in general, between 10 100 The invention will be further described in connection with the following examples which are set forth for purposes of illustration only.

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