I'm going to interpret safely as meaning successfully.
Ejections mean safety has gone out the window - literally.
There was a case in the Vietnam War where a pilot continued to fly his heavily damaged F-4 after his RIO (back seat radar operator) ejected.
He managed to keep it together long enough to get back over friendly territory before ejecting himself.
Note, this was an interview I saw some years ago, I haven't been able to find a link to post.
In this case the airplane had been hit badly enough that landing was not going to happen, however if the RIO had ejected accidentally or the airplane less damaged then a safe landing would have been possible.
So yes, flying has been done and landing is entirely possible after someone has ejected.
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The first test with ejection seats were performed in 1942 in Sweden with a Saab 17 and in Germany in 1941 with a Junkers 87 and in 1943 with a Heinkel 219 and Heinkel's pneumatic seat.
Of course, then it was not the pilot who ejected but his back seater, but the aircraft did not need much modification for the tests.
In each case, the pilot performed an uneventful landing after the test flight.
Saab 17 (above, source ) and Heinkel 219 (below, source ) during ejection seat trials.
To enable someone to fly the aircraft home after an ejection requires two conditions: The second seat must be equipped with flight controls
The ejection sequencing is switched off, so the seats can be activated independently.
Normally, triggering the sequence from either seat will eject all occupants.
It is exceedingly rare that both conditions are true in a modern combat aircraft.
There have been a few cases where a crew member flew an aircraft to a successful landing after the pilot bailed out, but I know only a single case where the bail-out was done by ejection seat.
It was a Boeing B-47 , and the YouTube link is to a re-enactment of this B-47 flight in which one observer, who was also a trained pilot, took over after the crew had bailed out due to a fire in the electrical installation.
Read the last of the stories from this page for one accident in which everyone but the pilot ejected from an S-3 with a stuck nose wheel, and the pilot later performed a safe landing.
I guess you are concerned about the damage done by an ejection.
The firing of the rockets happens in the rear part of the now very well ventilated cockpit and is a very brief event, so the flight controls and instrumentation should be in working order after an ejection.
However, after the event nobody will be there to take over, and there is no way another crew member will be able to take over unless he/
she has his/her own set of controls.
There have been cases of inadvertent ejection seat activations by mechanics on the ground.
When this happens, a new ejection seat is needed, the shear pins and in most cases the canopy need replacement.
After that, the cockpit area needs to be checked and cleared.
But the airplane will return to service.
Fun fact:
The XB-70 had ejection capsules to make ejection at supersonic speed possible and to protect the pilots in case of pressure loss.
Life support systems and a minimum set of flight controls were duplicated inside the capsule, and the pilot could continue to fly the aircraft down to a safer altitude after initiating the encapsulation sequence.
Only then he would trigger the ejection.
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The fighter can remain airworthy (in the technical sense not in the regulatory sense) after ejecting.
For example the cornfield bomber made a belly landing onto a field after the pilot ejected.
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Martin Baker uses (or used, it may have been retired)
a modified Gloster Meteor to test ejection seats.
The aircraft is piloted, with the seat being in a separate area behind the cockpit.
This aircraft is definitely reusable, it's been used to test ejection systems many times.
So yes, it is possible to design an aircraft in such a way that it can be flown after an ejection of (one of) its ejection seat.
Of course in case of operational ejections these are usually done after the aircraft has sustained enough damage that it can't be flown anyway, so having it flyable after ejection isn't a high priority.
And without the crew on board it becomes even less of a priority, as the crew are the ones flying it in the first place.
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There was a case when Soviet MiG-23 was flying for more than 500 miles after ejection of pilot.
https://en.wikipedia.org/wiki/1989_Belgian_MiG-23_crash
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What kind of damage does the ejection process do to the inside of a cockpit or to the aircraft in general?   If ejection were accidentally triggered on the ground (i.e. the ejection wouldn't be followed by a hull damaging/destroying crash), would the damage be minimal enough that it could be flown again by simply installing a new seat and canopy, or would it have to go through a major inspection to ensure no additional damage was done to instruments, wiring, etc?
Can an aircraft be controlled after an ejection?
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<ejection-seat>
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The fighter can remain airworthy (in the technical sense not in the regulatory sense) after ejecting. The flight controls and instrumentation should be working after an ejection and there have been recorded incidents of planes continuing to fly after an ejection, notably in the Vietnam War and a Soviet MiG-23.  The aircraft should still be operational after an ejection, and there are known examples of planes continuing to fly after an ejection.
There are known examples of planes continuing to fly after an ejection. The aircraft should still be operational after an ejection.