A spacing drum comprising: a segment receiving drum section capable of receiving a predetermined number of segments per revolution of the drum from a procession of segments approaching the segment receiving drum section at a segment-feed spacing and a segment-feed speed; a segment releasing drum section capable of releasing the predetermined number of segments at a segment-release spacing and a segment-release speed; and a radial profile flight comprising a continuous arc segment extending across at least portions of the segment receiving drum section and the segment releasing drum section. Associated methods are also provided, including method of changing pitch along a spacing drum progressively with a radial profile flight.