Providing a stiffener in a tape reel hub to reduce tape dimensional stability errors

A tape cartridge comprising:

• a tape cartridge reel on which a tape medium is wound, comprising:
• an upper flange;
• a lower flange;
• a hollow cylinder hub between the upper flange and the lower flange, wherein the upper flange has an upper opening at an upper end of the hollow cylinder hub;
• and
• a hollow cylinder stiffener separate from the upper flange and positioned within the hollow cylinder hub between the upper flange and the lower flange, wherein an upper end of the hollow cylinder stiffener does not extend past the upper flange;
• and
• an inner surface formed within the hollow cylinder hub and the hollow cylinder stiffener and extending from the upper end of the hollow cylinder hub to a lower end of the hollow cylinder hub, wherein the inner surface forms a hollow space delimited by a surface of revolution with circular cross sections of different diameters, wherein an upper cross-section diameter of the hollow space at the upper end of the hollow cylinder hub comprises a smallest diameter of the hollow space.