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Did Apollo 11 climb vertically upwards i.e. radially outwards, or "normal" to earth surface till it separated its first stage (approximately 38 Miles/60 Km or so..), or did it tilt at or before that altitude?

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This plot shows the pitch profile for a Saturn V from launch to Earth Parking Orbit and it's described like this:

The vehicle rises nearly vertically from the pad, for approximately 450 feet, to clear the tower. During this period, a yaw maneuver is executed to provide tower clearance in the event of adverse wind conditions, deviation from nominal flight and/or engine failure.

(See figure 2-1 for start and stop times for this and other maneuvers and events).

After clearing the tower, a tilt and roll maneuver is initiated to achieve the flight attitude and proper orientation for the selected flight azimuth. Launch azimuth is 90 degrees; flight azimuth may vary between 72 and 108 degrees. The actual flight azimuth within this range is computed just prior to launch from a launch-day-dependent polynomial of launch azimuth as a function of launch time. From the end of the tilt maneuver to tilt-arrest, the pitch program provides a near-zero-lift trajectory that satisfies vehicle performance, heating and loads requirements. Tilt-arrest freezes the pitch attitude to dampen out pitch rates prior to S-IC/S-II separation. The pitch attitude remains constant until initiation of the Iterative Guidance Mode (IGM) which occurs during the S-II stage flight.

enter image description here

From SA-507 Flight Manual

.. the first figure gives you the best indication of those pitches, on page 2-4, which looks like basically from 90° to 30° for the duration of the first stage burn. Then it appears to hold that pitch for 30-45 seconds while the second stage ignited and then the interstage was jettisoned. From there, looks like it pitched down at a pretty regular rate and hit about 0° by the time the second stage burnt out. Then it looks like during the third stage to achieve parking orbit it burnt at a negative pitch to maintain apogee while raising perigee to the right altitude.

from here, emphasis mine

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