Various tire constructions have been devised over the years which enable a tire to run in an underinflated or non-inflated condition, such as after receiving a puncture and loss of air, for extended periods of time and at relatively high speeds, to enable the vehicle operator to safely drive the vehicle to an appropriate location for repair or replacement of the punctured tire.  Certain of these safety tires, referred to as "run flat tires", have been successful for certain applications and embody various types of tire constructions.  Many such run flat tires achieve their run flat property by the placement of reinforcing layers or members of relatively stiff elastomeric material in the sidewall areas of the tire where they enable the tire to support the vehicle weight even with the complete loss of internal air pressure. 
Examples of various prior art run flat tire constructions are set forth in the following patents:
U.S. Pat.  No.  3,911,987 discloses a low profile motorcycle tire which has an elastomeric internal reinforcement that enables the tire to stay inflated for a short duration with little or no air pressure.  This reinforcing layer has a Shore A hardness of at least 45, preferably within the range of 60 to 90, and is positioned either outwardly of two tire body carcass plies or between the two carcass plies.  This elastic reinforcement is constructed with varying thicknesses, and is cross-sectioned to eliminate abrupt changes of effective hardness of the sidewall and reinforcing layer. 
U.S. Pat.  No.  3,949,798 discloses another run flat tire construction for a low profile tire having reinforcing rubber insert strips located between the inner strips located between the inner liner and body ply carcass of the tire sidewall. 
U.S. Pat.  No.  3,954,131 discloses a safety tire which has elastomeric internal reinforcements in the sidewalls which permit the tire to be used for short durations with little or no air pressure within the tire.  The elastomeric side reinforcements are of varying thicknesses and are positioned outwardly of the tire carcass. 
U.S. Pat.  No.  4,067,372 discloses a pneumatic radial tire having internal reinforcements in its sidewalls which are formed of hard rubber and are used in combination with the body carcass plies and tire bead rubber inserts to give additional stiffness to the supple portions of the tire.  The body carcass plies are located outwardly of the rubber inserts and are made from several cord fabric radial plies, and extend completely to the bead area of the tire. 
U.S. Pat.  No.  4,202,393 discloses a low profile motorcycle tire that has sidewall reinforcements to allow for a run flat condition in which the reinforcements are composed of an elastic filler with a reinforcing ply positioned completely around the elastic filler. 
U.S. Pat.  No.  4,2023,481 discloses a run flat tire construction having reinforcing inserts made from a high modulus, low hysteresis rubber compound, which are located inwardly of the reinforcing carcass plies of the tire. 
U.S. Pat.  No.  4,261,405 shows another run flat tire construction for a low profile tire having a specially constructed rubber insert mounted between the inner liner and body ply carcass in the sidewall of the tire, in order to achieve the required rigidity for supporting the vehicle in an uninflated condition. 
U.S. Pat.  No.  4,287,924 discloses another run flat safety tire with sidewall reinforcing members.  These members are comprised of two components, one of which is more flexible than the other, having a hardness rating greater than 70 and the other having a hardness rating of between 80 and 95.  These reinforcing members are encased in the carcass plies of the tire and have a heat conducting layer positioned between the two components of the supporting members to alleviate heating problems in the thickest portions of the supporting members. 
U.S. Pat.  No.  4,365,659 discloses a run flat safety tire which has sidewall reinforcements made from low heat build up rubber which are positioned between an inner protective layer and the outer carcass plies of the tire. 
U.S. Pat.  No.  4,917,164 discloses the use of crescent-shaped reinforcing layers in the sidewalls of the tire to allow the tire to run for short durations with little or no air pressure.  The reinforcing layers are of varying thickness and have a Shore A hardness of between 65 and 85, and are positioned between the innerliner and carcass plies of the tire.  The wall thickness of the reinforcing members is between 1 and 12 millimeters. 
Although many of these run flat tire constructions set forth in the above-referenced patents, have proven to be successful for certain applications, all these constructions pertain to low profile tires, that is a tire having a section height less than 5 inches and are of the type usually found on high performance vehicles (such as racing cars) or motorcycles, and rely almost entirely on the stiffness of the elastomeric insert to provide the support for the uninflated tire.  Furthermore, these high performance and motorcycle tires carry relatively smaller loads when compared to the higher weights carried by the larger cars using the higher section height tires. 
Heretofore, providing a run flat tire with a high profile tire construction, that is, a run flat tire having a section height of 5 inches or greater, has not proved successful due to the relatively large sidewall reinforcement members which would be required to adequately support the tire in an uninflated condition to enable the tire to run for a relatively long distance at a high rate of speed.  The relatively large rubber inserts required would increase the weight of the tire to an unacceptable limit and would materially detract from its ride characteristic.  If the amount of or type of material in these relatively large sidewall inserts were reduced or changed in order to lessen the weight of the tire and improve its ride characteristics, excessive heat would be generated within the inserts during a run flat operation, resulting in the rapid destruction of the tire, thus preventing the desired run flat conditions from being achieved at usual highway speeds for satisfactory use on such tires on most passenger vehicles. 
Patents have also addressed the addition of metal salts of organic acids to rubbers compositions.  U.S. Pat.  No.  4,076,255, for instance discloses a golf ball having a central core comprising a cis-polybutadiene elastomer, and a monomer capable of grafting with the elastomer and comprising a metal salt of an unsaturated carboxylic acid and a polyol ester or anhydride of a polybasic unsaturated carboxylic acid. 
U.S. Pat.  No.  4,824,899 discloses rubber compositions suitable for use in a bead filler of a tire which composition contains a metal salt of an acrylic acid with no mention of the latter being grafted to the rubber which is either natural or a blend with a synthetic diene rubber. 
U.S. Pat.  No.  4,929,684 discloses a sidewall for pneumatic tires comprising natural rubber, addition polymerized synthetic rubber and blends thereof, with zinc dimethacrylate.  No mention of grafting is provided as the metal salt is only employed as a reinforcing filler to increase the static tensile modulus of the rubber stock.  Alternative additives for this purpose disclosed by the patent include chopped cellulose and styrene acrylonitrile resin. 
Nevertheless, a sulfur-vulcanizable rubber compound having sufficiently high modulus for use in tire components or structural elements so as to allow the resulting tire to have run flat characteristics is not described in the foregoing art.  The need has existed for a rubber compound for use in components such as sidewall inserts for high profile pneumatic safety or run flat tires.  This need has not been met by known rubber compounds.