Abstract: High tape acceleration rates are achieved in an unbuffered, capstanless tape drive system by a tape motion control apparatus employing separate drive motors for each reel of a reel-to-reel tape transport. Tape moves from one reel past a read/write head and a tape tension sensor to the other reel, there being no tachometer in the tape feed path. A tachometer on one reel shaft provides a large number of pulses per revolution which pulses are counted by a counter; and a tachometer on the other reel shaft provides only one pulse per revolution, which pulse gates out the count then accumulated in the counter for actuating means to provide motor acceleration currents of a magnitude corresponding to said accumulated count according to a predetermined servo algorithm for controlling rotation of both reels. A tape radius constant corresponding to the actual length and thickness of tape in the system is calculated during initial wrap of tape onto the takeup reel.