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What is the highest threshold speed of a space rocket traveling in an air pressure of 14psi with all of its stages if they where able to leave a solo at Mach 1 or more?

Related: What benefits can be gained from launching below ground?

https://metrouk2.files.wordpress.com/2018/03/russiamissile.gif

https://metro.co.uk/2018/03/30/russia-tests-4000mph-hypersonic-missile-near-impossible-to-shoot-down-7428694/

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closed as primarily opinion-based by Russell Borogove, Uwe, Jack, Muze the good Troll., Mark Omo Jul 19 '18 at 22:04

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Speaking strictly in terms of physics, that speed is that speed of light. However, obviously that's not achievable. It's going to drastically depend on geometry so it's going to be tough to give an answer at least in my mind $\endgroup$ – Gigaboggie Jul 19 '18 at 17:20
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Probably the historical highest was the Sprint missile which accelerated at 100 G and hit Mach 10 in 5 seconds, amazing speeds in the atmosphere. Obviously it had severe thermal issues. It was also a silo-launched popup missile which lit off after it left the silo.

In the video you can see the characteristic very low speed of the missile at which the engine ignites after emerging from the silo. It is hard to imagine that if there were a practical means of accelerating the missile out of the silo, it wouldn't have been done for this application. (Sprint's mission was to intercept incoming nuclear warheads that had made it through a higher altitude interception screen - it was all about getting to the target quickly)

enter image description here https://lasttechage.wordpress.com/2013/07/22/abm-under-the-dome-safeguard/

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  • $\begingroup$ beautiful..............Do that with the falcon1 or bigger? $\endgroup$ – Muze the good Troll. Jul 19 '18 at 18:12
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    $\begingroup$ From the wikipedia article: "Such a high velocity at relatively low altitudes created skin temperatures up to 6,200 °F (3,430 °C), requiring an ablative shield to dissipate the heat." What was the altitude when reaching Mach 10 after 5 seconds? $\endgroup$ – Uwe Jul 19 '18 at 18:13
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    $\begingroup$ @Uwe I couldn't find traj data. I'd love to see it. $\endgroup$ – Organic Marble Jul 19 '18 at 18:14
  • $\begingroup$ 5 seconds at constant acceleration of 100 g will result in 4.9 km/s speed. Mach 10 is 3.43 km/s. Height after 5 seconds at 100 g will be 12.25 km/s. But acceleration will not be constant for 5 seconds. $\endgroup$ – Uwe Jul 19 '18 at 18:34
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    $\begingroup$ The vehicle mass had to be dropping precipitously as all that prop was burned up. I imagine the 100 G is an average/ round number. The photo @Muze added shows 400 G (!!) on the booster, but that is HiBEX, not Sprint. $\endgroup$ – Organic Marble Jul 19 '18 at 18:42

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