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On SpaceX's website, they make a claim that their rockets are the safest and most reliable in the industry. This is because apparently it can complete its mission even if up-to two of its engines fail during flight.

How is this possible? Wouldn't the lack of the engine thrust from two engines cause thrust imbalance and throw the rocket off course or destabilize it?

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    $\begingroup$ Decades ago, the Saturn V managed the failure of one engine in the second stage of Apollo 13 and also the failure of two engines of five J-2 engines of the second stage of Apollo 6. Handling two engine failures is even easier when there are 9 engines instead of 5. $\endgroup$ – Uwe Feb 21 '18 at 15:06
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    $\begingroup$ Also note that the Falcon's engines are very powerful. During the landing of the first stage booster, the falcon can't hover because even a single of the 9 engines provides enough thrust to lift the entire booster up at its lowest throttle setting. $\endgroup$ – Dragongeek Feb 21 '18 at 16:40
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    $\begingroup$ It is not a matter of very powerful engines, it is caused by the tyranny of the rocket equation. A nearly empty stage or booster' s weight should be much smaller than fully loaded with fuel. Structural weight should be very small compared with propellant weight to reach a delta v as high as possible. $\endgroup$ – Uwe Feb 21 '18 at 18:46
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    $\begingroup$ What's not been mentioned is that the other engines run longer to make up for the missing thrust (since they're all fed from the same tanks). $\endgroup$ – RonJohn Feb 21 '18 at 19:32
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The Falcon 9 can shut off a faulty engine, re-configure the remaining engines (change thrust levels, vector direction) and update its flight profile in real-time. This happened on the SpaceX CRS-1 flight (see also this article).

The Merlin engines can be gimbaled (change the direction of thrust), so on the Falcon 9 all engines can slightly change the thrust direction. This can be used to offset the lack of thrust from the failed engine.

Another way the Falcon 9 could compensate the thrust imbalance would be to switch off the engine opposite of the failed engine. That's what the infamous N-1 tried to do… but failed to implement properly.

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    $\begingroup$ Worth noting that almost all large liquid-fueled orbital launchers use gimbaled engines for steering/attitude control whether or not they have an engine out. $\endgroup$ – Russell Borogove Feb 21 '18 at 19:43
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    $\begingroup$ To be fair to the N-1 scientists, they were attempting to design an incredibly complicated rocket (30 engines vs Falcon 9's 9) and control system within the constraints of 1960s and 1970s technology - and they almost succeeded. $\endgroup$ – Ian Kemp Feb 22 '18 at 6:27
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    $\begingroup$ How are engine failures detected? $\endgroup$ – PoVa Feb 22 '18 at 7:37
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    $\begingroup$ @PoVa: There probably are several sensors in each engine to measure things like flow rate, temperature, pressure and other things. If these measurements are suddenly way off you can be sure something is wrong. In the article I've linked SpaceX is quoted: "We know the engine did not explode, because we continued to receive data from it." $\endgroup$ – DarkDust Feb 22 '18 at 7:41
  • $\begingroup$ Worth addressing the lack of thrust issue too? Is that down to the fact that the engines are not run at 100% for the launch? And can be throttled up in the event of an engine shutdown? Also, fuel wise I imagine they could use more fuel for additional thrust while sacrificing the ability to recover the first stage? Just guesses from me but would be interested to find out. $\endgroup$ – Fogmeister Feb 24 '18 at 12:26
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The engines can be vectored to manage this. They actually have had an engine failure and still made it to orbit in the CRS-1 mission. Note that there are some points in the mission that an engine failure is more likely to lead to a mission failure than others. It should be noted that while a 1 engine failure has been recovered from, a 2 engine failure has not been demonstrated, and would be significantly more difficult to recover from.

Most notably among these is the upper stage cannot fail. This is less likely than one of the lower stage failing, because it doesn't have to interact with other engines, but is still a risk.

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  • $\begingroup$ For example, the vacuum engine cannot fail. $\endgroup$ – Joshua Feb 21 '18 at 21:32
  • $\begingroup$ Are you sure the F9 can fly even with two adjacent engines failed? Wouldn't vectoring induce a substantial tilt? If this happens before Max-Q, it's going to be quite a side load. $\endgroup$ – uhoh Feb 22 '18 at 12:22
  • $\begingroup$ I am not sure. No doubt SpaceX has done simulations on this, but no results have been released to the public that I have seen. $\endgroup$ – PearsonArtPhoto Feb 22 '18 at 12:31
  • $\begingroup$ I'm wondering if "Falcon 9 can sustain up to two engine shutdowns during flight" means only one side engine actually fails, and they turn off the one opposite it to balance the force, rather than vectoring. If that were the case, this answer would be wrong, and the question itself would be flawed. $\endgroup$ – uhoh Feb 22 '18 at 12:37
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    $\begingroup$ @uhoh You might well be right. I didn't research the claim of two engines failing, and I was rather dubious about that myself. Added some text to indicate that. $\endgroup$ – PearsonArtPhoto Feb 22 '18 at 12:57
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Per the specs on the F9 page it has about a 1.4 to 1 thrust to weight ratio at takeoff and it goes up from there as the vehicle burns fuel getting lighter and the engines start to generate more thrust in the higher atmosphere. So theoretically if two engines failed right after lift off it would be down to ~1.1 thrust to weight ratio so it can still accelerate upwards and as others have mentioned the thrust can be vectored to compensate for the unbalanced thrust. Now it may not be able to handle any two engine out scenario so two engines right next to each other that stop right after take off might be too much. It might not be able to vector thrust enough to compensate while still keeping the thrust to weight ratio up enough to actually launch.

Another factor that hasn't really been mentioned is fuel reserves. Loosing an engine will mean lower performance which means with the same amount of fuel the first stage won't get the second stage going as fast because you spend more time fighting gravity. Normally this would mean the payload could make it to orbit but might not be in it's intended orbit. That would typically mean the payload would have to use more of it's own fuel to get to the correct orbit and would shorten it's useful life. The F9 for most launches has a pretty large reserve intended for landing the rocket but that could be used to ensure the payload gets to the intended orbit. Now even expendable launches typically have reserves that can be used to help cover for that and on some launches have even been used to be launched into super-synchronous orbits beyond what was required which ends up extending the life of the payload.

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