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There were some famous accidents where rockets launched and just went up into flames. Many had something to do with leaking fuel in some sort.

I want to focus on aerodynamic stress however, like when a rocket deviates from its path or has a wrong angle of attack, what causes it to be destroyed? Purely drag force?

As an example: What mechanics were at work when an Ariane 5 was destroyed on June 4, 1996 due to an integer overflow? It just burst into flames!

Edit: Well, it seems like I may have been a little inaccurate. As many of you pointed out, fuel leaks are only a consequence of catastrophic failure. Additionally, most rockets explode only because they were told to do so to prevent damage to the vicinities.

What I actually meant was not what causes the explosion but why does the rocket break apart when not following the planned trajectory.

I thought it was because of the immense drag force when flying perpendicular to the velocity vector with high speed. In any case, thank you for your answers and comments, they gave me a much deeper insight in rocketry accidents.

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    $\begingroup$ That Ariane tried to fly sideways because its guidance system shut itself down due to a math error. Rockets are usually long flimsy columns full of propellants; they don't fly sideways well at all. I think you are mischaracterizing most failures as due to leaking fuel; that's like listing the cause of death as "heart failure". When a rocket's structure is torn apart, the fuel tends to leak out. $\endgroup$ – Organic Marble Sep 13 '18 at 12:55
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    $\begingroup$ I have good knowledge of the CRS-3/OrB-3 Antares failure. It had nothing to do with leaking fuel, but it didn't have anything to do with aerodynamics either. Would this be a useful answer to your question, or are you focused purely on aerodynamics? $\endgroup$ – Bear Sep 13 '18 at 12:56
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    $\begingroup$ Yep, most of failures end with leaking fuel+oxidizer and a big explosion. They usually start with something else that leads up to these. $\endgroup$ – SF. Sep 13 '18 at 13:17
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    $\begingroup$ In many cases, the cause of the explosion is the range safety officer doing the equivalent of pressing the BRB (big red button). The BRB is a fiction; it's actually two switches, both with plastic covers that need to be opened to protect against inadvertently toggling the switch. Every launch vehicle is outfitted with a flight termination system, a radio-activated explosive device. One switch enables sending a signal to the FTS. The other switch sends the signal, but only if the enable switch has already been thrown. Once enabled and activated, bye-bye, launch vehicle. $\endgroup$ – David Hammen Sep 13 '18 at 14:28
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    $\begingroup$ The range safety officer in the previously mentioned CRS-3/OrB-3 Antares failure was a bit slow on the draw. The signal was sent (and the launch vehicle did blow up), but the signal was sent too late to protect the launchpad. $\endgroup$ – David Hammen Sep 13 '18 at 14:30
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I want to focus on aerodynamic stress however, like when a rocket deviates from its path or has a wrong angle of attack, what causes it to be destroyed?

In many cases, it's not aerodynamic stress. Many launch vehicle explosions result because they are commanded to do so.

Every launch vehicle launched from the U.S., including the solid rocket boosters on the Space Shuttle, is equipped with a flight termination system (FTS). This includes an explosive device intentionally placed so that it will cause near-instant destruction of the vehicle if activated. For example, just outside the oxidizer tank works quite nicely on liquid propulsion vehicles.

The FTS also includes a mechanism that triggers this explosive device. Until recently, the triggering mechanism was a radio receiver that received an encrypted signal sent by the Range Safety Officer. The US Department of Defense and NASA have been working on an automated flight termination system, with the triggering mechanism sent instead by a dedicated computer on the launch vehicle.

The intent is to destroy a wayward vehicle before it causes damage to the launchpad or further downrange. This doesn't always work. The Range Safety Officer for the RS-3/OrB-3 Antares launch was a bit slow on the draw. The signal was sent when the rocket was obviously going awry, and the rocket did explode, but the signal was sent too late to prevent the rocket from damaging the launchpad.

In the case of the initial launch of the Ariane 5, that explosion was a result of an internally generated self-destruct command, followed shortly by a range safety officer command. The Ariane 5 was, and still is, designed to blow up when things go awry.

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    $\begingroup$ For reference also look up some videos of russian launch failures. They don't believe in self destruct. $\endgroup$ – xyious Sep 13 '18 at 15:37
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    $\begingroup$ @MagicOctopusUrn xyious seems to be quoting EverydayAstronaut. $\endgroup$ – leftaroundabout Sep 13 '18 at 16:09
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    $\begingroup$ @fooot Ariane 5 is a European rocket and launches from French Guiana, so not affected by the US's timetables. $\endgroup$ – hobbs Sep 13 '18 at 20:20
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    $\begingroup$ Perhaps an even better object lesson in how bad things can get if an out-of-control rocket doesn't explode quickly enough would be the Intelsat 708 launch in 1996, which crashed on a Chinese village and killed several (at least six, possibly many more) people there. It's not on the video that @leftaroundabout linked to because that one only includes incidents with no loss of life; I was going to write that there's also no video of it, but apparently there is. $\endgroup$ – Ilmari Karonen Sep 13 '18 at 20:40
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    $\begingroup$ @IlmariKaronen - Another example was the 1947 launch of a V-2 from White Sands, New Mexico. Instead of going north, it veered south and shortly thereafter crashed a mile and a half south of Jaurez, Mexico, and very close to an ammunition dump where Mexican mining companies stored powder and dynamite. That it's not a good idea to spark international incidents with wayward rockets is something the US learned very early in its development of space exploration technologies. $\endgroup$ – David Hammen Sep 14 '18 at 14:33
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This Proton M launch in 2013 was caused by a serious problem with the guidance system (some parts were connected back to front apparently). If you watch the video you can see that the vehicle reaches an "impossible" angle (for a rocket) and then the top is torn away due to air resistance before the tanks start rupturing causing a fire (hypergolic propellants) just before it hits the ground. I don't know if the Russians have FTS or not but if they do then it didn't work in this case. Perhaps the rocket "thought" everything was fine as the guidance system was totally confused.

Bit like the whale from hitchhikers guide to the Galaxy "what's this thing coming toward me very fast? So big and flat and round, it needs a big wide sounding name like 'Ow', 'Ownge', 'Round', 'Ground'! That's it! Ground! Ha! I wonder if it'll be friends with me? Hello, Ground!"

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  • $\begingroup$ Russians don't believe in FTS, instead they try putting their rockets in the middle of no-man's land, where they can't hurt anyone. Also, like in many authoritarian-ish societies, the value of human life is not necessarily the same as in, say, Central Europe. Makes for spectacular pictures, though! $\endgroup$ – Jörg W Mittag Sep 14 '18 at 1:17
  • $\begingroup$ Some of the angular velocity sensors were installed upside-down. Naturally this inverted the information sent to the control system causing the rocket to amplify deviations from its trajectory rather than to correct for them. $\endgroup$ – J... Sep 14 '18 at 12:13
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    $\begingroup$ @JörgWMittag - that claim needs sources. Soyuz has a self-destruct system. The N-1 too. And that's just the first 2 launchers I looked into. $\endgroup$ – Hobbes Sep 15 '18 at 17:42
  • $\begingroup$ IIRC Proton has a FTS but it just shuts off the engines. Spaceflight 101 confirms the presence but not how it works. spaceflight101.net/proton-m-briz-m.html $\endgroup$ – Organic Marble Sep 16 '18 at 0:57
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During the Space Shuttle Challenger accident the actual orbiter was destroyed due to aerodynamic loads. It is often described as an "explosion" but most of what was visible was actually just venting hydrogen and oxygen. The Rogers Commission Report says:

19 Chapter III: The Accident Flight of the Space Shuttle Challenger on Mission 51L began at 11:38 a.m. Eastern Standard Time on January 28, 1986. It ended 73 seconds later in an explosive burn of hydrogen and oxygen propellants that destroyed the External Tank and exposed the Orbiter to severe aerodynamic loads that caused complete structural breakup.

And

All fractures and material failures examined on the Orbiter, with the exception of the main engines, were the result of overload forces, and they exhibited no evidence of internal burn damage or exposure to explosive forces. This indicated that the destruction of the Orbiter occurred predominantly from aerodynamic and inertial forces that exceeded design limits.

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Rockets don't explode as a consequence of failure. As discussed in other answers, the visible explosions are usually the deflagration of released propellants subsequent to either a commanded self-destruct, or a structural break-up. In the first case, the self-destruct is designed to open up the propellant tanks in order to disperse their contents so that the whole thing doesn't fall to the ground together; it seems almost inevitable that dispersed fuel and oxidizer will meet somewhere hot, or maybe there are hypergolics in the mix; either way, there is combustion and big smoke and flame. In the second case, if some structural part fails, the consequence is usually that some other structure gets overloaded and fails too, leading to a progression of failures inevitably involving the propellant tanks, and again the result is a big deflagration.

For an interesting twist on this, look at this youtube. This was a test flight of the Apollo launch escape tower using a Little Joe rocket. The objective was to test the system at high altitude, replicating the velocity/altitude conditions of a real Apollo launch. What actually happens is that by about the 17:13 mark in the video, the Little Joe booster has malfunctioned and begun an out-of-control roll. The roll gets so severe that at about the 17:35 mark, it has begun to undergo progressive structural failure. What's interesting about this, is that the failure prematurely triggers the escape system (it was deemed a successful test despite the malfunction); you don't really see an explosion of the failed stage, just bits and pieces flying off and a few big puffs of what appears to be smoke or perhaps aerosolized propellants.

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