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I'm certain there are several flight regimes where this could happen, and that the procedures should be different for each one. For instance, this is a very different question before lift off than it is at 100km. So, presuming that the SSMEs were burning and then all three cut out, what was the procedure at each regime, and what would have happened?

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Much of the time, you would die.

Refer to the 3 OUT BLACK ZONE chart from here

enter image description here

The heavy black lines show where the situation is not survivable (black zone).

Acronymology for the black zone charts:

  • alpha = Angle of attack
  • ALT = Altitude
  • c.g. = Center of gravity
  • EAS = Equivalent Air Speed
  • MECO = Main Engine Cutoff
  • MM602 - Major Mode 602, the onboard computer operations sequence that controls the gliding portion of an RTLS
  • PPA = Powered Pitch Around, the point in an RTLS where the vehicle flips over and starts flying backwards, thrusting away from the launch site to slow down
  • RTLS = Return to Launch Site (an abort selectable early in the ascent in which the vehicle lands back at Kennedy Space Center)
  • TAL = Trans-Atlantic Landing (an abort selectable later in the ascent in which the vehicle lands at a European airfield)
  • Vi = Inertial velocity
  • Vrel = Velocity relative to the launch site

The crew would select the appropriate abort procedure from this eye chart in the Ascent Checklist.

enter image description here

There's a lot going on here; I strongly suggest you read through the Contingency Abort document in my first link. One could literally write a book on this answer. Just as a taste, here are the definitions of the "color regions" for the three-engine out cases.

enter image description here

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    $\begingroup$ @Quietghost Also, the "uphill" in the first chart sounds very much like a "XKCD Thing Explainer" alternative to "ascent". $\endgroup$ – TooTea Nov 5 '19 at 8:13
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    $\begingroup$ For completeness, RTLS meant Return To Launch Site, TAL meant Transoceanic Abort Landing, AOA meant Abort Once Around, and ATO (not mentioned) meant Abort To Orbit. If the dire problem had happened early enough (but not too early) in the launch sequence, the Shuttle possibly could have returned to the launch site. After some amount of time, the Shuttle would have gained too much energy to return to the launch site, but it could have to have flown across the Atlantic to land in Spain. More energy yet would preclude TAL, leaving either Abort Once Around or Abort To Orbit as the only options. $\endgroup$ – David Hammen Nov 5 '19 at 8:53
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    $\begingroup$ @OrganicMarble Could you explain what any of the fancy color coded diagrams full of opaque acronyms and jargon in your post mean in your post, rather than referring to a document hosted somewhere else? $\endgroup$ – nick012000 Nov 5 '19 at 12:50
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    $\begingroup$ @nick012000 I added an explanation of the acronyms in the black zone charts. I don't feel it's practical for me to duplicate the contents of the contingency abort training manual that I linked; it's quite readable and does a concise job of explaining the material. $\endgroup$ – Organic Marble Nov 5 '19 at 13:25
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    $\begingroup$ Except when the link goes 404, this answer suddenly has 3 engines out. $\endgroup$ – Harper - Reinstate Monica Nov 5 '19 at 20:18

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