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My question is: How do we control a Reentering Capsule in the denser part of the atmosphere? How does the aerodynamics of the Reentry vehicle workout?

In other words, how does a reentry module maneuver once it is in the denser part of the atmosphere? Do most of them follow a blind descent (since mostly they either make a splashdown in ocean or a 'soft landing' in desert) or do they use RCS or even perhaps grid fin like structures to steer?

Searching in google led me to this image of Apollo CM. I see they are giving the direction of a lift vector (I thought there is only Drag during reentry! + I see no airfoils!)

enter image description here

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    $\begingroup$ I adjusted the wording of your question a bit so that it fit the site's style a bit better, have a look to make sure it's still the question you'd like to ask, and feel free to fine tune it further. $\endgroup$ – uhoh Apr 28 at 15:48
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    $\begingroup$ @uhoh yes it's ok and even better! $\endgroup$ – Navoneel Karmakar Apr 28 at 15:51
  • $\begingroup$ Can you clarify "the dense atmosphere" you mean, for this question? The answers are likely very different if you are talking the early vs. later stages of reentry $\endgroup$ – costrom Apr 29 at 18:31
  • $\begingroup$ @costrom I am referring to the lower atmosphere where we have aerodynamic control over the capsule/vehicle. I guess you referred to it as later stages of re-entry. $\endgroup$ – Navoneel Karmakar Apr 29 at 18:34
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The entry vehicle for the Apollo missions is the command module (CM), which has a symmetric body with an offset center of gravity (c.g.). This offset c.g. causes the CM to trim aerodynamically at an angle of attack with a resulting lift force as illustrated in figure 1. The magnitude of the lift force is not controllable; therefore, trajectory control is provided by modulating the direction of the lift-force vector.The direction is modulated by rolling the CM, and hence the lift-force vector, about the relative-wind-velocity vector.

enter image description here

Mission Planning for Apollo Entry p. 232 of pdf

The command module also had a reaction control system which was usable for entry and in fact was used to roll the lift vector.

enter image description here

Apollo Operations Handbook, Reaction Control System

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For Gemini, Apollo, and Soyuz capsules, lift is achieved by offsetting the center of gravity of the reentry module from the center line of the craft. This is represented in your diagram by the "location of heavy equipment" callout, and results in the tilt of the capsule relative to the flight trajectory shown. The tilt causes the body of the spacecraft itself to act as an airfoil, giving the lift vector shown. By rolling the spacecraft from side to side with the RCS, the direction of the lift vector can be adjusted. With the lift axis more vertical, the spacecraft will fly longer and further. Rolling side to side causes the lift force to be applied sideways, trading off downrange distance for crossrange. With positive vertical lift, the spacecraft stays in less dense air for longer, reducing the peak g-force sustained by the crew. The Mercury capsule, having a zero-lift profile, took about 11g on reentry, while the Apollos did 6-7g.

It would be possible to add body-flap control surfaces to such a capsule for finer control, but since the initial conditions of reentry are quite well controlled, and the landing point doesn't need to be ultra-precise, it hasn't been done for this type of capsule.

The US Space Shuttle, of course, had much more complex aerodynamic control surfaces.

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    $\begingroup$ What about the Mercury capsule? $\endgroup$ – Uwe Apr 28 at 18:10
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    $\begingroup$ Mercury had CG on the centerline, so reentry was purely ballistic, zero-lift, and consequently a lot rougher in terms of pilot G-load. Theoretically RCS could be used to pitch the craft during reentry to tilt and lift, but there was not enough RCS propellant to significantly steer the craft; once it started to bite air there was no way to control the splashdown point. $\endgroup$ – Russell Borogove Apr 28 at 18:19
  • $\begingroup$ meh... attitude is achieved by offsetting the CoG, the attitude achieves the lift $\endgroup$ – JCRM Apr 29 at 13:58

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