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Since unlike the Shuttle, the Buran did not carry the main engines, why was it not mounted on top of the external tank equivalent - Energia's core stage?

And even better, why wasn't Energia's second stage also mounted in series with its first stage?

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Putting those big Buran wings on top of the rocket would have actually made it nearly impossible to control. That would move the center of pressure (that is, the point the rocket "feels" all the drag as coming from) far forward of the center of gravity, which would make the rocket inherently unstable and require precise control to maintain orientation during launch.

Note that this is exactly what SpaceX's Starship is doing -- even though its little winglets are fairly small, the Starship/Superheavy stack is unstable and requires constant computer action to keep it pointy-end up, flamey-end down.

If the CP is aft of the CG, the rocket is inherently stable; the drag from the airstream acts to keep it pointed into the wind, like a weathervane -- that's why a lot of older rockets have tail-fins; it helps push the CP rearward. If the CP is very far aft of the CG, it might even make the rocket too stable, to the point that it's hard to steer.

If you reverse the two points, then the rocket becomes unstable as the drag pressure tries to flip the rocket around, and if it gets even a little off-center, the increased drag becomes an even stronger force trying to turn it backward. Imagine a weathervane with the fins at the front, and I think you can easily intuit what's going to happen.

Putting the big wings on the side of the stack should keep the CP further back, near the CG if not behind it. (I'm not sure of the exact locations of those points on Energia.) Keeping the boosters on the sides instead of underneath is for the same reason, you want to keep the wings as near to the tail-end of the stack as you can. It's much easier to deal with slightly off-center drag than to manage a highly unstable rocket, both because it takes less force to counteract, and because if you plan things right, you don't even want to counteract it that much. Ultimately the rocket's launch path is supposed to lean it over as it launches, to go from pointing straight up at the pad to pointing more or less at the horizon as it attains orbital altitude. The Space Shuttle always rolled after launch to put the orbiter on the 'inside' of the intended turn, so the off-center drag would just try to make it do what they wanted to do anyway.

As a secondary issue, I don't remember off the top of my head whether the Energia core stage fired on the ground and ran at low power until booster separation, or if it was designed to light up while in-flight. Some rockets light the main stage on the ground even though it's not actually needed until several minutes later because ground-lighting is (or at least was) simply more reliable than an igniter or hypergolic slug.

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    $\begingroup$ This same drag issue is why the X-37, the Space Force's "mini-shuttle", is always launched inside a payload fairing. $\endgroup$
    – Mark
    Commented Apr 22, 2023 at 22:13
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    $\begingroup$ @Mark and why the crew version of Dream Chaser (which can't launch in fairings due to launch escape requirements) is not just a straightforward development of the cargo version. $\endgroup$ Commented Apr 23, 2023 at 0:53
  • $\begingroup$ It's been almost done more recently (didn't go all the way to orbit) but I think it was made possible by only the very latest in aerodynamic simulation and numerical control technology not available at the time. See ISRO's space plane on top of of a rocket - how unstable was it? and its answer(s). $\endgroup$
    – uhoh
    Commented Apr 23, 2023 at 19:37
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    $\begingroup$ @uhoh Yes, today we're pushing the boundaries, but it requires the extremely fast microprocessors we have, which weren't really an option in the 80s. (And there's a pretty strong argument that it's still a bad idea to launch something that insanely unstable no matter how good the control system is!) $\endgroup$ Commented Apr 24, 2023 at 0:49

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