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The question Would there be any advantages for a rocket with two “half stages”? begins with:

A "half stage" is a rocket stage which separates with its engines, but not fuel tanks. Common examples include Atlas (1.5 stages), Atlas-Agena (2.5 stages), and Atlas-Centaur (2.5 stages).

Wikipedia says:

Atlas is a family of American missiles and space launch vehicles. The original Atlas missile was designed in the late 1950s and produced by the Convair Division of General Dynamics,[2] to be used as an intercontinental ballistic missile (ICBM). It was a liquid propellant rocket burning liquid oxygen and RP-1 fuel in three engines configured in an unusual "stage-and-a-half" or "Parallel Staging" design: its two outboard booster engines were jettisoned during ascent, while its center sustainer engine, propellant tanks and other structural elements were retained through orbital insertion (for orbital flights).

Other weight-saving techniques used in some designs included leaving off the paint and making the wall so thin it needed to be inflated with pressurized nitrogen when not fully fueled and pressurized to avoid collapse.

How much mass was dropped, at what point in the flight, and how much did engine-mass-dropping increase maximum payload mass to LEO?

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Atlas II’s booster assembly, called MA-5A massed about 4 tons. It was jettisoned at 172 seconds into flight. https://en.m.wikipedia.org/wiki/MA-5A

The launcher’s payload to LEO is about 6.8 tons; if the booster engines were shut down at the same point but retained rather than dropped, it could only lift 2.8 tons payload. Keeping the engines burning a little longer could improve the payload slightly, but the longitudinal acceleration would get quite severe.

The original Atlas launcher could lift only around a ton (depending on version) to LEO, by dropping its 3-ton booster section; without the half-staging it would not reach LEO at all.

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  • $\begingroup$ I see, the trick is to ignore everything that happens before jettison time, then the problem then becomes trivial. It seems I'd overthunk it. $\endgroup$ – uhoh Nov 11 '18 at 7:30
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    $\begingroup$ Well, that provides a lower bound on performance — if you keep the engine, you can use the engine, shortening time to orbit and reducing gravity losses, but (a) those losses are more significant early in the flight and (b) Atlas Original Flavor, at least, was already a brutal accelerator with an ascent time half that of most orbital launchers. $\endgroup$ – Russell Borogove Nov 11 '18 at 7:35
  • $\begingroup$ I see; in that case I'll hold off to see if someone would like to post an answer beyond by 6.8 - 4 = 2.8 that addresses part of the question. $\endgroup$ – uhoh Nov 11 '18 at 8:17
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    $\begingroup$ Another factor is that a permanently attached set of engines can be lighter than a section that has to cleanly separate in flight, for the same performance. $\endgroup$ – Russell Borogove Nov 11 '18 at 14:57
  • $\begingroup$ That's true as well. For that though, I tried to work around it with careful wording of the question, asking only how the specific act of "engine-mass-dropping" increased payload mass to orbit, not the design. $\endgroup$ – uhoh Nov 11 '18 at 15:02

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