CROSS-REFERENCE TO RELATED APPLICATIONS 
     In this application, Applicants claim the right of priority under 35 U.S.C. § 119(a)-(d) based on patent application Ser. No. 99201677.4, filed May 27, 1999, in the European Patent Office; additionally, Applicants claim the benefit under 35 U.S.C. § 119(e) based on prior-filed, copending provisional application No. 60/136,761, filed May 28, 1999, in the U.S. Patent and Trademark Office. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a tire having minimized rolling resistance and to a mould for producing said type. 
     2. Description of the Related Art 
     Generally, a tire for a motor vehicle is made from a predetermined viscoelastic material and comprises at least one casing ply, right- and left-hand beads, a tread strip placed on the crown of said casing ply, and at least one belt strip interposed coaxially between said casing ply and said tread strip. The casing ply has a profile (plyline), in the plane of a meridian section, which has a central crown (or under-belt) portion and two sidewall portions, one on the right and one on the left. 
     The major source of energy dissipated by a tire when it rolls on a road surface consists of hysteresis losses due to the viscoelastic materials from which it is made. In particular, the energy dissipated by the various parts of a tire depends on the cyclical stresses and deformations to which it is subjected by the continual alternation of the inflated configuration (distant from the area of contact with the road or footprint) and of the flattened configuration (centre of the footprint area). 
     It is estimated that the hysteresis losses account for 90-95% of the total energy dispersed by a tire and that the remaining 5-10% is attributable to other dissipation mechanisms, such as the slip between the tire and the road, the aerodynamic losses due to the friction of the air, and the internal friction between the air and the tire. 
     Most of the energy is dissipated by the tread strip of the tire (≧50%). This energy dissipation is essentially due to the fact that the assembly consisting of the tread strip and the belt package (belt strips) of the tire undergoes a change of curvature in both the longitudinal direction (inflection due to the passage through the footprint) and the meridian direction (flattening of the tread strip). 
     This energy dissipation produces the rolling resistance of the tire, and therefore the term “rolling resistance” (R.R.) will be used in the course of the present description and in the claims to denote the power dissipated in one cycle as a result of the cyclical deformations of the viscoelastic materials of the tire in neutral, in other words when it is not subject to a torque. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to reduce the power dissipation of a tire when it rolls on a road surface, and consequently to reduce its rolling resistance. 
     The inventors have found that the power dissipated by a tire can be reduced by minimizing the deformations undergone by the assembly consisting of the tread strip and belt package of the tire, in such a way as to contain the quantity of power dissipated in these. They have also found that a reduction in dissipation can be obtained by shifting the power dissipation of the tread strip to the area of the sidewalls, in such a way as to reduce the ratio between the quantity of power dissipated in the tread and the quantity of power dissipated in the sidewall. 
     The inventors have also identified a mould which enables a tire to be produced with the desired characteristics. 
     A first aspect of the invention is a tire for a motor vehicle, made from a predetermined viscoelastic material, and comprising 
     a) at least one casing ply, 
     b) a tread strip placed on the crown of said casing ply, 
     c) at least one belt strip interposed coaxially between said casing ply and said tread strip, 
     d) right-hand and left-hand sidewalls, and 
     e) right-hand and left-hand beads, 
     f) said casing ply having a profile (plyline), in the plane of a meridian section, which has a central crown (under-belt) portion and two sidewall portions, one on the right and one on the left, 
     g) each of said sidewall profile portions being delimited by two points S and K, where the point S is located substantially at one edge of said at least one belt strip and the point K separates a sidewall from a bead, 
     h) said tire assuming, at the operating pressure and in the absence of a load, an inflated configuration having a predetermined outer profile which matches a predetermined enclosing rectangle, 
     i) said outer profile having a predetermined maximum chord {overscore (C)} and a predetermined maximum height {overscore (H)}, the ratio {overscore (H)}/{overscore (C)} lying in a range from 0.6 to 0.8, characterized in that, 
     j) in said inflated configuration, said crown profile portion has a radius of meridian curvature ρ c  lying in a range from 406 mm to 690 mm and each of said sidewall profile portions forms an angle α s  with the axis of rotation of the tire, at said point S, which lies in a range from 25° to 30°. 
     Preferably, each of said sidewall profile portions forms an angle α k  with the axis of rotation of the tire, at said point K, which is ≧45°. 
     Advantageously, said crown profile portion is substantially flat. 
     In the inflated configuration, the tire according to the invention has, for given overall dimensions, extremely flat belts in the meridian plane, so that in the flattened state, when the belts pass through the footprint, their deformation in this plane is virtually zero. 
     Moreover, the median casing profile has a more erect (vertical) inflated configuration in the lower area of the sidewall than a conventional tire, and consequently the deformations in the upper parts of the sidewalls are greater than those in a conventional tire. 
     In the tire according to the invention, therefore, the power dissipation has an optimized distribution among the various parts because it is more balanced than that of a conventional tire. This makes it possible to reduce the total power dissipation and minimize the rolling resistance of the tire. 
     The shape of the tire in the inflated state having the structural characteristics indicated above is obtained by means of a special geometry of a mould used for forming it. 
     A second aspect of the invention is a mould for producing a tire made from a predetermined viscoelastic material, said mould having 
     A) a crown formed by radially movable sectors for moulding a tread strip and shoulders of said tire, and 
     B) cheeks for moulding sidewalls and beads of said tire, 
     C) said mould having a profile, in the plane of the meridian section, which has a predetermined maximum chord C, a predetermined maximum height H and a fitting line I, and is formed centrally by a base profile of one sector and laterally by profiles of said cheeks, 
     D) said base profile of the sector having a central portion flanked by two connecting portions, which in turn are flanked by two lateral portions, 
     E) each cheek profile having a total height H g  and having a first portion with a first radius of curvature R fs  and a second portion with a second radius of curvature R fi , characterized in that 
     F) the ratio between said first and second radius of curvature R fs /R fi  ranges from 0.45 to 0.56. 
     Preferably, the ratio between said first and second radius of curvature R fs /R fi  is approximately 0.5. 
     Advantageously, the centres of said first and second radius of curvature R fs  and R fi  lie on said maximum chord C and said maximum chord C is located at a distance H lc  from said fitting line I equal to approximately ⅔ of said height of the cheek profile H g . 
     In one embodiment, said central portion of said base profile of the sector is substantially flat and has a radius of meridian curvature R≧500 mm, and each of said connecting portions has, at the point of junction with one of said lateral portions, an angle α 0  with respect to the longitudinal axis of the mould which is ≧42°. 
     Preferably, said base profile of the sector, comprising said central portion and said flanking connecting portions, has a camber f of ≦7.5 mm. 
     A third aspect of the invention is a mould for producing a tire from a predetermined viscoelastic material, said mould having 
     i. a crown formed by radially movable sectors for moulding a tread strip and shoulders of said tire, and 
     ii. cheeks for moulding sidewalls and beads of said tire, 
     iii. said mould having a profile, in the plane of the meridian section, which has a predetermined maximum chord C, a predetermined maximum height H and a fitting line I, and is formed centrally by a base profile of one sector and laterally by profiles of said cheeks, 
     iv. said base profile of the sector having a central portion flanked by two connecting portions, which in turn are flanked by two lateral portions, characterized in that 
     v. said central portion of said base profile of the sector is substantially flat and has a radius of meridian curvature R≧500 mm, and 
     vi. each of said connecting portions has, at the point of junction with one of said lateral portions, an angle α 0  with respect to the longitudinal axis of the mould which is ≧42°. 
     Preferably, said base profile of the sector, comprising said central portion and said flanking connecting portions, has a camber which has the value indicated above. 
     The mould according to the invention can be used to produce a tire with the desired inflated configuration, as a result of the fact that the base profile of each sector, in other words the envelope line at the base of its projections and grooves, has at its sides an angle of inclination with respect to the axis of rotation of the tire which is very small, or in any case is smaller than that of a conventional mould. The base profile of the sectors is therefore flatter and has a more open outlet than a conventional mould. In turn, the cheeks of the mould have radii of curvature R fi  and R fs  which have a characteristic ratio R fs /R fi  in the range from 0.45 to 0.56, and preferably ≅0.5, and their centre line is located at a height H lc  equal to approximately ⅔ of the height of the cheek H g . Additionally, the cheeks have a maximum chord C which is wider, and a width at the rim E which is greater than in a conventional mould, to prevent the beads of the tire from being moulded in a configuration which is too “inset”, in other words too inclined with respect to the axis of rotation of the tire, and therefore from having a low rigidity in the inflated state. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Characteristics and advantages of the invention will now be illustrated in greater detail with reference to an embodiment shown by way of example, without restriction, in the attached drawings, in which 
     FIG. 1 is a partial sectional view, in a meridian plane, of an inflated tire, made according to the invention; 
     FIG. 2 shows the tire of FIG. 1 in the inflated and flattened configurations; 
     FIG. 3 is a partial sectional view, in a meridian plane, of a conventional inflated tire; 
     FIG. 4 shows the tire of FIG. 3 in the inflated and flattened configurations; 
     FIG. 5 shows for the purpose of comparison the flattened configurations of the tire according to the invention shown in FIGS. 1 and 2 and of the conventional tire shown in FIGS. 3 and 4; 
     FIG. 6 is a graph showing how the flattening of the tire of FIGS. 1 and 2 and that of FIGS. 3 and 4 varies as the load on the tire varies; 
     FIG. 7 is a partial sectional view, in a meridian plane, of a mould for forming the tire of, FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 shows a tire  1  according to the invention in the inflated configuration, in the absence of a load. The tire  1  is classed as 195/65 R  15  and is of the radial type. The tire  1  comprises a casing  2 , belt strips  3 ,  4  and  5 , a tread strip  6  and bead cores  7 . FIG. 1 shows a shoulder  8 , a sidewall  9 , a bead  10  and a bead filler  11 , which are located to the right of an equatorial plane  13 . Those located to the left of the equatorial plane  13  are not shown, because the tire  1  is symmetrical about this plane. The tire  1  has an air-tight inner layer (liner)  12 . The casing  2  is formed from a rubberized fabric ply, reinforced with textile cords lying in meridian (radial) planes and wrapped around bead cores  7 . 
     The belt strips  3 ,  4  and  5  and the tread strip  6  are placed on the crown of the casing  2  and extend circumferentially around it. The belt strips  3  and  4  are formed from rubberized fabric plies, reinforced with corresponding metal cords, crossing each other symmetrically with respect to the equatorial plane  13 . The belt strip  5 , placed on top of the belt strips  3  and  4 , is formed from a rubberized fabric ply, reinforced with textile cords, orientated circumferentially (0° belt). The tread strip  6  is provided with projections, blocks and grooves (not shown) which, during operation, come into contact with a road surface. 
     The outer profile of the tire  1  has a maximum chord {overscore (C)} of 200.8 mm and a maximum height {overscore (H)} of 128.1 mm. The ratio {overscore (H)}/{overscore (C)} is 0.63 and lies in a range from 0.6 to 0.8. 
     The casing ply  2  of the tire  1  has a meridian profile (plyline)  14 , represented by a broken line, comprising a central crown portion (under-belt)  15  and two sidewall portions  16 , one on the right and one on the left. FIG. 1 shows only half of the crown portion  15  and the sidewall portion  16  which are located to the right of the equatorial plane  13 . Those located to the left are mirror images. Each sidewall portion  16  is delimited by two terminal points, S and K. The point S is located at one edge of the belt package  3 ,  4  and  5 , and forms the point of separation between the crown portion  15  and the sidewall portion  16 . The point K forms the point of separation between the sidewall portion  16  and a bead portion  17 . The crown portion  15  of the meridian profile  14  has a radius of curvature ρ c . The sidewall profile  16  forms an angle α s  with the axis of rotation of the tire at the point S, and forms an angle α k  with the axis of rotation of the tire at the point K. The tread  6  has a width  1 . 
     In the tire  1 , the angle α s  advantageously ranges from 25° to 30° as the radius of curvature ρ c  varies in a range from 406 mm to 690 mm. 
     The angle α k  lies in a range from 45° to 50°. 
     In particular, in the tire  1  the radius of curvature ρ c =689.8 mm; the angle α s =29.6°; the angle α k =45.8°; and the width 1=74.6 mm. 
     In the tire  1 , the variations of curvature between the inflated and flattened states of the belt package  3 ,  4  and  5  and the tread strip  6  are minimized by making these have an extremely flat shape in the inflated configuration. 
     This is demonstrated by the formula discovered by the inventors, which relates the variation of equatorial curvature ΔC due to the passage through the footprint to the characteristic parameters of the tire: 
     
       
         Δ C=K   r *s/( T/p )= K   r * s /(1-2*ρ s * α s )= K   r * s /(1*(1-ρ s /ρ c )) 
       
     
     where ρ c , α s  and α k  represent the parameters indicated above; 
     ρ s =radius of meridian curvature in the area of the point S; 
     K r =radial rigidity of the sidewall; 
     s=flattening; 
     T=total pull on the belt package in the circumferential direction; 
     p=air pressure inside the tire. 
     From the above relation it may be seen that ΔC decreases with a decrease in α s  and with a decrease in the ratio ρ s /ρ c , in other words with an increase in ρ c . 
     In the tire  1 , the radius of curvature ρ c  has a much higher value than in a conventional tire, as will be illustrated in greater detail below. The meridian profile  14  of the tire  1  therefore has a smaller ratio ρ s /ρ c  Additionally, the lower area of the sidewall  16  has a more upright shape than that of a conventional tire. When the tire is flattened, this shape of the sidewall tends to cause the deformations due to the meridian inflection to be concentrated in the area of the sidewall lying between the maximum chord and the edge of the belt package. 
     The configuration adopted for the meridian profile meets the conditions of the enclosing rectangle in the inflated state and enables the casing profile to be joined to the bead filler while avoiding points of discontinuity in the sidewall portion of said profile. 
     FIG. 2 shows the tire  1  in the inflated configuration  1 G, with an operating pressure p=2.2 bar, and in the flattened configuration  1 S, under a load Q=493 kg. 
     FIG. 3 shows a conventional tire  21 , having the classification 195/65 R 15 and identified by the symbol NP6. 
     The tire  21  comprises a casing  22  formed by a ply folded around bead cores  27 , belt strips  23 ,  24  and  25 , and a tread strip  26 . A shoulder  28 , a sidewall  29 , a bead  30  and a bead filler  31  of the tire  21  are shown. An air-tight inner layer  32  is also shown. 
     The casing ply  2  of the tire  21  has a meridian profile (plyline)  34  comprising a central crown portion (under-belt)  35  and two sidewall portions  36 , one on the right and one on the left. 
     The tire  21  has a radius of curvature ρ c =357.1 mm; angle α s =31.4°; angle α k =42.2°; and width 1=75.8 mm. 
     When FIG. 1 is compared with FIG. 3, it is clear that the belt package  3 ,  4  and  5  and the tread strip  6  of the tire  1  have a flatter shape than the belt package  23 ,  24  and  25  and the tread strip  26  of the tire  21  so that their deformation in the meridian plane is smaller when they pass through the footprint. 
     FIG. 4 shows the tire  21  in the inflated configuration  21 G, with an operating pressure p=2.2 bar, and in the flattened configuration  21 S, under a load Q=493 kg. 
     When FIG. 4 is compared with FIG. 2 it may be noted that the upper mid-point of the sidewall  9  of the tire  1  (near the tread strip  6 ) is more markedly deformed in the flattened state than the lower mid-point of the sidewall (near the bead  10 ), while the upper and lower areas of the sidewall  29  of the tire  21  are deformed in a more uniform way in the flattened state. 
     In FIG. 5, the flattened configuration  1 S of the tire  1  according to the invention and the flattened configurations  21 S of the conventional tire  21 , found with the same load of 493 kg, are compared. 
     The graph in FIG. 6 shows the variation in the flattening with a variation in the load for the tire  1  (line a) and for the tire  21  (line b). The tire  1  is found to undergo a greater flattening than the tire  21  for the same load. This is due to the fact that the upper area of the sidewall is more deformable than that of the tire  21 . 
     Two tires having mixtures with the following characteristics were used to evaluate the rolling resistance of the tire  1  with respect to the tire  21 : 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 Elastic modulus 
                 tan δ 
               
               
                   
                 Material 
                 E′ (N/mm 2 ) 
                 (Loss factor) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Tread 
                 6.975 
                 0.1486 
               
               
                   
                 Sidewall 
                 3.768 
                 0.0856 
               
               
                   
                 Abrasion-resistant 
                 9.7 
                 0.217 
               
               
                   
                 material 
               
               
                   
                 Bead filler 
                 57.35 
                 0.204 
               
               
                   
                 Liner 
                 3.318 
                 0.269 
               
               
                   
                 Casing 
                 3.925 
                 0.09596 
               
               
                   
                 Belts 
                 9.234 
                 0.108 
               
               
                   
                 Zero-degree belts 
                 6.42 
                 0.1025 
               
               
                   
                   
               
             
          
         
       
     
     Tests were carried out with a vertical load of 493 kg, a speed of 100 km/hr and a mixture temperature of 70° C. 
     The following values were found for the tire  1 : 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Power 
                 Proportion 
                   
               
               
                 Tyre 1 
                 Area 
                 dissipated 
                 of total 
                 Ratio 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R.R. = 5.93926 
                 Tread 
                 409818.28 
                 51.4 
                 4.3 
               
               
                 (thou.) 
                 Sidewall 
                 94287.94 
                 11.8 
               
               
                   
               
             
          
         
       
     
     R.R. indicates the coefficient of rolling resistance, expressed in thousandths of the value of the ratio between the vertical load applied to the tire and the tractive force required to move the tire. The power dissipated is expressed in N*mm/s. The “Ratio” column shows the ratio between the power dissipated in the tread mixture and the power dissipated in the sidewall mixture. 
     The following values were found for the comparative Tyre  21 : 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Power 
                 Proportion 
                   
               
               
                 Tyre 21 
                 Area 
                 dissipated 
                 of total 
                 Ratio 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R.R. = 6.24967 
                 Tread 
                 425859.08 
                 50.7 
                 7.0 
               
               
                 (thou.) 
                 Sidewall 
                 61035.40 
                 7.3 
               
               
                   
               
             
          
         
       
     
     It is found that the ratio between the power dissipated in the tread mixture and the power dissipated in the sidewall mixture is smaller in the tire  1  than in the tire  21 . The tire  1  therefore has a power dissipation distribution which is more balanced between its parts than that of the tire  21 . 
     FIG. 7 shows a vulcanization mould  40  of the centripetal type, suitable for tire production. The mould  40  comprises a central crown  41 , formed by a plurality of radially movable sectors  44 , for moulding the pattern of the tread strip and the shoulders of the tire. The projections and grooves of the sectors  44  are not shown. The mould  40  also comprises two cheeks  42  and  43  which are mirror images of each other and are axially opposed, for moulding the sidewalls and beads of the tire, and an inner bladder, not shown, which can be inflated by means of a pressurized fluid. The sectors  44  are moved radially in both directions (centripetal and centrifugal), perpendicularly to the longitudinal axis of the mould, by an operating ring which is not shown. The cheeks  42  and  43  are movable axially and reciprocally with respect to each other. 
     In the plane of the meridian section, the mould  40  has an inner profile  45 , formed centrally by a base profile  46  of a sector and laterally by two profiles  47  and  48  of the cheeks. The base profile  46  has a central portion  46   c  flanked by two connecting portions  46   r  which in turn are flanked by two shoulder portions  46   s . Each of the cheek profiles  47  and  48  is formed by two portions,  47   s ,  47   i  and  48   s ,  48   i  respectively. 
     FIG. 7 shows the following dimensional parameters of the mould  40 : C=chord of tire; L S =width of sectors; C b =chord of tread; R=radius of tread on crown; R l =radius of crown-shoulder joint; R S =radius of shoulder; α° angle of shoulder with respect to a longitudinal axis  50 ; R fs =radius of upper sidewall; R fi =radius of lower sidewall; f=camber of tread; H s =height of sectors; H=height of section; H g =height of cheeks; H lc =height of maximum chord point; E=width of mould rim. 
     In the mould  40 , the angle α° lies in a range from 42° to 43°, and the radius of meridian curvature R lies in a range from 500 mm to 619 mm. In turn, the radii of curvature R fs  and R fi  of the portions  47   s ,  47   i  and  48   s ,  48   i  of the cheek profiles have a ratio R fs /R fi  equal to approximately 0.5 and the centres of the radii of curvature R fs  and R fi  are located at a height H lc  which is equal to approximately 2/3 of the height of the cheek H g . 
     In particular, the mould  40  for producing the tire  1  has the following dimensions: 
     C=209.4 mm; L s =183.0 mm; C b =142.6 mm; R=619.0 mm; R l =129.0 mm; R s =30.0 mm; α°=42.6°; R fs =47.4 mm; R fi =105.0 mm; f=7.5 mm; H s =29.5 mm; H=127.75 mm; H g =98.25 mm; H lc =65.46 mm; E=174.0 mm.
A mould for producing a tire includes a crown and at least two cheeks. The crown includes radially-movable sectors. A first cheek is axially opposite a second cheek. The mould includes a main profile in a plane of a meridian section. The main profile includes a maximum chord, a maximum height measured from a fitting line, a profile of the first and second cheeks, and a base profile of a sector. The base profile includes first and second lateral portions, first and second connecting portions, and a central portion. The first lateral and connecting portions are axially opposite the second lateral and connecting portions. Each cheek profile includes first and second portions including first and second radii of curvature, where a ratio of the first radius of curvature to the second radius of curvature is greater than or equal to 0.45:1 and less than or equal to 0.56:1.