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Previous answers state that the Shuttle launch roll program occurred as soon as practical after tower clear and was achieved by SRB thrust vector control. Can we get a more precise answer on the conditions that triggered the Shuttle rollover?

(NASA seems to call it a roll program, even though all three axes are involved.)

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The Single Axis Rotation (SAR) maneuver started when the computed relative velocity of the stack exceeded the value stored in a reconfigurable flight software variable called PPOLY(2). The nominal value of PPOLY(2) was 118.45 ft/sec. This was nominally achieved at ~ T + 8 seconds and and altitude of ~376 feet.

Source - Ascent Nominal I-Loads Definition and Verification (not online)

There's a great view of it here from an SRB cam and an MET clock in the upper right corner of the video.

See also What event determined the transfer of control from Kennedy Space Center to Houston?

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