How many engines are restarted for landing the falcon boosters
$begingroup$
For landing the boosters, it is clear that SpaceX is using the center engine, but I suspect that igniting one engine will not be helpful.
If they aren't igniting all the 9 engines, how are they managing to overcome the backflow of exhaust plumes into the adjacent engines.
spacex falcon-9 landing
$endgroup$
add a comment |
$begingroup$
For landing the boosters, it is clear that SpaceX is using the center engine, but I suspect that igniting one engine will not be helpful.
If they aren't igniting all the 9 engines, how are they managing to overcome the backflow of exhaust plumes into the adjacent engines.
spacex falcon-9 landing
$endgroup$
add a comment |
$begingroup$
For landing the boosters, it is clear that SpaceX is using the center engine, but I suspect that igniting one engine will not be helpful.
If they aren't igniting all the 9 engines, how are they managing to overcome the backflow of exhaust plumes into the adjacent engines.
spacex falcon-9 landing
$endgroup$
For landing the boosters, it is clear that SpaceX is using the center engine, but I suspect that igniting one engine will not be helpful.
If they aren't igniting all the 9 engines, how are they managing to overcome the backflow of exhaust plumes into the adjacent engines.
spacex falcon-9 landing
spacex falcon-9 landing
asked Dec 17 '18 at 10:12
Vasanth CVasanth C
50212
50212
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.
$endgroup$
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
add a comment |
$begingroup$
From basic physics, I'd expect backflow not to be an issue.
- the engines are an enclosed volume with only 1 exit at the bottom. Air flowing into the engine bell will 'fill' the engine bell. When the air pressure inside the engine reaches a threshold (at ~local air pressure), airflow can't force more air into the engine and the air will start to flow around the engine instead. All you have is some turbulence in the engine.
- the turbopumps are designed to pump propellants into the combustion chamber at a much higher pressure than is reached by point 1. The ignition system is already designed to ignite the firehose of propellant coming out of the purbopumps, the combustion caused by the airflow will be small compared to this.
$endgroup$
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
add a comment |
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2 Answers
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2 Answers
2
active
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$begingroup$
There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.
$endgroup$
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
add a comment |
$begingroup$
There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.
$endgroup$
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
add a comment |
$begingroup$
There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.
$endgroup$
There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.
answered Dec 17 '18 at 11:09
geoffcgeoffc
55k9160306
55k9160306
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
add a comment |
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Consider adding some links to some of the excellent previous answers as well? This isn't the first, or second time this has been explained.
$endgroup$
– uhoh
Dec 17 '18 at 11:35
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
Got any demonstrations of anything except 1-3-1 or 1 engine burns? I've only seen the 1-3-1 sequence, and believed it was necessary to a) ensure stability during engine startup & b) reduce G force and provide more precision in the final moments of nearly empty booster landing burn.
$endgroup$
– Saiboogu
Dec 17 '18 at 15:45
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
I remember a 1-3-3 but not which flight.
$endgroup$
– geoffc
Dec 17 '18 at 17:03
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
IMO, your comparison of a 3 engine vs. a 1 engine burn doesn't clarify that the booster would be allowed to fall for a (slightly) longer time, building up more velocity, until the 3 engine burn is fired, at a lower altitude than the 1 engine burn starts. The 3 engine burn results in traveling the same distance and ending with the same velocity, as the 1 engine burn, but the travel is done over a shorter time than would be required for the single engine burn, which results in the total velocity gained from gravity being lower and thus less fuel expended to counter that velocity.
$endgroup$
– Makyen
Dec 17 '18 at 21:13
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
$begingroup$
Most of the engines are only provided enough TEA-TEB for a single ignition, but they are all ignited the same way, with a slug of that fluid injected into the propellant lines. Ignition by ground equipment would require a whole new ignition method for those engines, and i'm not sure that it's even possible with RP-1 fuel (expendable RP-1 rockets generally use pyro ignitors as far as I'm aware).
$endgroup$
– Christopher James Huff
Dec 17 '18 at 22:20
add a comment |
$begingroup$
From basic physics, I'd expect backflow not to be an issue.
- the engines are an enclosed volume with only 1 exit at the bottom. Air flowing into the engine bell will 'fill' the engine bell. When the air pressure inside the engine reaches a threshold (at ~local air pressure), airflow can't force more air into the engine and the air will start to flow around the engine instead. All you have is some turbulence in the engine.
- the turbopumps are designed to pump propellants into the combustion chamber at a much higher pressure than is reached by point 1. The ignition system is already designed to ignite the firehose of propellant coming out of the purbopumps, the combustion caused by the airflow will be small compared to this.
$endgroup$
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
add a comment |
$begingroup$
From basic physics, I'd expect backflow not to be an issue.
- the engines are an enclosed volume with only 1 exit at the bottom. Air flowing into the engine bell will 'fill' the engine bell. When the air pressure inside the engine reaches a threshold (at ~local air pressure), airflow can't force more air into the engine and the air will start to flow around the engine instead. All you have is some turbulence in the engine.
- the turbopumps are designed to pump propellants into the combustion chamber at a much higher pressure than is reached by point 1. The ignition system is already designed to ignite the firehose of propellant coming out of the purbopumps, the combustion caused by the airflow will be small compared to this.
$endgroup$
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
add a comment |
$begingroup$
From basic physics, I'd expect backflow not to be an issue.
- the engines are an enclosed volume with only 1 exit at the bottom. Air flowing into the engine bell will 'fill' the engine bell. When the air pressure inside the engine reaches a threshold (at ~local air pressure), airflow can't force more air into the engine and the air will start to flow around the engine instead. All you have is some turbulence in the engine.
- the turbopumps are designed to pump propellants into the combustion chamber at a much higher pressure than is reached by point 1. The ignition system is already designed to ignite the firehose of propellant coming out of the purbopumps, the combustion caused by the airflow will be small compared to this.
$endgroup$
From basic physics, I'd expect backflow not to be an issue.
- the engines are an enclosed volume with only 1 exit at the bottom. Air flowing into the engine bell will 'fill' the engine bell. When the air pressure inside the engine reaches a threshold (at ~local air pressure), airflow can't force more air into the engine and the air will start to flow around the engine instead. All you have is some turbulence in the engine.
- the turbopumps are designed to pump propellants into the combustion chamber at a much higher pressure than is reached by point 1. The ignition system is already designed to ignite the firehose of propellant coming out of the purbopumps, the combustion caused by the airflow will be small compared to this.
answered Dec 17 '18 at 17:02
HobbesHobbes
88.3k2250398
88.3k2250398
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
add a comment |
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
$begingroup$
Agreed, The backflow will not be an issue while the ascent, as the flow, is supersonic. Does the exhaust flow is supersonic? while landing? My question is how are they preventing exhaust plumes of one engine damaging the adjacent engines while landing.
$endgroup$
– Vasanth C
Dec 18 '18 at 6:29
add a comment |
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