A papermaking machine for making a paper product using a through air drying process. A headbox supplies an aqueous furnish. A structuring fabric has a surface with a contact area and (i) receives the furnish from the headbox on the surface to thereby form a cellulosic web from the furnish and (ii) non-compactively dewaters the cellulosic web. At least one through air drier dries the cellulosic web on the structuring fabric. A portion of the structuring fabric on which the cellulosic web is formed has an adjusted planar volumetric index of at least about 27.