Write timing for RRO field in a constant density servo system

A storage device, comprising:

• a rotating constant-density storage medium on which servo data is written, the servo data including a repeatable run-out field representing a recurring contribution to position error;
• and
• circuitry for writing the repeatable run-out field, the circuitry comprising:
• a detector configured to locate a respective servo wedge on each respective track of the constant-density magnetic storage medium based on servo sync mark detection;
• and
• a controller configured to repeat, for each respective track at a respective radius of the constant-density magnetic storage medium:
• determining a respective track pattern frequency based on track location and desired data density,
• locating a position in a respective servo wedge of the respective track of the constant-density magnetic storage medium based on output of the detector,
• writing the repeatable run-out data to the respective servo wedge of the respective track of the constant-density magnetic storage medium at a time delay, from the location of the position in the respective servo wedge, that is inversely proportional to the respective radius, to achieve a predetermined offset, and
• repeating the determining, the locating and the writing for each servo wedge on the respective track of the constant-density magnetic storage medium.