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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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    $\begingroup$ Possibly unrelated: One big motivation for half-staging is that you can start all engines on the ground. Thus, if you notice any malfunction, you can shut it all down. Failure to ignite during staging in mid-air will most probably ruin your launch. While the Atlas drops some engines which feed from the same tank, the Soyus has independent liquid boosters, which are all ignited at launch. With 1950s tech, igniting all engines on the ground, and dropping some of them in mid-air was probably a prudent thing to do. $\endgroup$ Commented May 27, 2021 at 7:47

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The impact of the mass reduction on the payload can be determined using my Payload Calculator.

The Atlas D was the first operational version of the Atlas rocket. Based on the specifications here, 3.05 t was jettisoned with the booster engines.

The specifications also list a payload of 1.4t to a 300 km orbit. Using my payload calculator to scale it to a standard 200 km orbit, the payload increases to 1.48t. Without dropping the booster engines, the payload becomes negative - it is unable to reach orbit even with no payload.

However, this answer points out that the infrastructure to jettison the booster has a significant mass penalty. If we replace the 3.05 t mass for the booster engine assembly with the 1,286 kg mass for the 2 XLR89-5 engines, to simulate the engines being properly integrated into the rocket, we get a positive payload of 530 kg. This is just over 1/3rd of the original payload, so the booster engine jettison provides a large improvement in payload capacity despite more than doubling the mass of the booster engine assembly.

For the Atlas II mentioned in the title, the situation is different, due to it being a 2.5 stage launcher rather than a 1.5 stage launcher. The 1st stage only ends up on a suborbital trajectory with a much lower energy, so the impact on the payload mass from extra 1st stage dry mass is reduced (compared to the final stage, where there is a direct 1:1 relationship between dry mass and payload reduction).

The Atlas II specifications here list 4,187 kg for the booster engine assembly mass, and 6.58 t of payload to a 185 km orbit. Without dropping the booster engines, the payload is reduced to 6.3 t.

If we instead apply the same procedure of replacing the booster engine assembly with the 1.61 t of the 2x RS-56-OBA engines, the payload goes up to 6.74 t. Since this is higher than the original payload figure, it indicates that in this case the reduced dry mass is better than carrying the engines longer. There are a couple of possible reasons why this was not chosen for the Atlas II:

  • Even when integrated directly in the first stage without the option to jettison, the required mass is significantly higher than the engine mass alone, so in reality there's no improvement in payload mass
  • Integrating the booster engines into the 1st stage would require significant redevelopment, which is not worthwhile for only a ~2.5% payload increase.

When going to higher energy orbits than LEO, the differences in payload mass remain roughly constant: Graph of payload vs delta-v

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Atlas II's booster assembly, the MA-5A, massed about 4 tons. It was jettisoned at 172 seconds into flight.

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. $\endgroup$ Commented Nov 11, 2018 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. $\endgroup$ Commented Nov 11, 2018 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. $\endgroup$ Commented Nov 11, 2018 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. $\endgroup$ Commented Nov 11, 2018 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. $\endgroup$ Commented Nov 11, 2018 at 15:02