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In this youtube video, it talks about steering Soyuz by changing lift. Why does roll rotation help in changing lift and also helping in cross range steering?

I am looking for an answer from aerodynamics and structural point of view.

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By itself the roll doesn't generate lift. But the Soyuz descent module (DM) enters with a non-axial center of mass that results in a non-zero angle of attack, and hence some lift. Several spacecraft, including the Apollo Command Module, have used this offset-mass approach to generate lift, thus achieving some measure of control over the atmospheric flight path.

In a spacecraft-centered coordinate frame that lift vector is always in the same direction. To achieve controllability the spacecraft is rolled to point the lift vector in the desired direction—up, down, to one side or the other. If the entry trajectory is a bit too steep, or the trajectory design calls for shallowing the flight path angle, the spacecraft is rolled to point the lift vector upward. To get some cross-track steering, the spacecraft rolls to point the lift vector to one side or the other. Of course, intermediate roll angles are also possible, giving both vertical and cross-track steering simultaneously.

What do you do if the trajectory is where you want it and you don't want any steering, either vertical or horizontal? You spin the spacecraft around the roll axis. The net impulse from one full rotation sums to zero, so it's like you aren't generating lift at all. This is why the "ballistic entry" in the video has the DM spinning: it's cancelling the lift effects.

For the optimal entry the lift vector is pointed mostly upward, shallowing the flight path angle to yield lower inertial loads ("g forces") and lower heat shield temperatures and pressures. If the flight path gets too shallow they'll turn that lift vector downward. You can also steer toward an intended landing location. If you appear to be landing "long", you can turn the lift vector downward, steepening your descent, and getting you more quickly into denser air so you decelerate faster. If you're off to one side a bit, turning the lift vector toward the other side can get you back on track.

This kind of steering—termed "bank angle modulation" (BAM) by the community—is one of the techniques proposed for use in aerocapture. (My review paper, with a bunch of co-authors, in the Journal of Spacecraft and Rockets is here; it covers the main maneuvering techniques proposed so far). Without such controllability aerocapture would be essentially impossible. BAM is also a useful technique for skip-entry (also called "boost-glide").

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