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I understand there in no air is space which is what allows an aircraft to fly a curved flight path. This is strictly a theoretical question given today's technology. Here are the conditions:

  1. There is an unlimited amount of fuel.

  2. There are many small reaction control system (RCS) thrusters placed strategically around the spacecraft, with near instantaneous gimbal reaction speed, to allow for very small and precise thrust firings to control trajectory.

  3. An advanced computer code allows for the firing of selected thrusters in very rapid (and repeated if necessary) succession to trace a relatively smooth arc. The spacecraft is not using air to curve the path but precisely directed, and timed, thrust firings from the RCS.

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    $\begingroup$ It may be helpful to edit in information on why you are asking this question. All space craft travel in curved orbits, and a low but continuous thrust with a slow rotation will get a steady curve. It is straight lines that would need the complex control system in your question. Is your interest a fictional craft that you want to move a certain way because plot, or are you trying to understand how a real world vessel flying over say the moon might travel? $\endgroup$ Commented May 31, 2022 at 8:13
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    $\begingroup$ My reading of the question leads me to think it is about "space dogfights" like we see in space movies where spacecraft "fly" as we expect to see them (nose always froward and course changes not caused by thrusters) rather than how they'd actually behave. $\endgroup$
    – BradV
    Commented May 31, 2022 at 14:12
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    $\begingroup$ Don't all moving vehicles turn in "a smooth, curved arc"? Bicycles, cars, airplanes, boats, and trains all follow what I'd describe as a smooth, curved arc whenever they turn while moving, and there's no reason why spaceships would be any different, unless I'm misunderstanding what you mean when you say "a smooth, curved arc." $\endgroup$ Commented May 31, 2022 at 16:50
  • $\begingroup$ The question it is related to fictional craft being able to perform "space dogfights" so much tighter turns, not long curve trajectories say if the ship was traveling from Earth to Mars. The supposition is that the possibility exists to perform such maneuvers if the technology exists as I've outlined in the three conditions, the most important point being there is an unlimited fuel source in this scenario. $\endgroup$
    – Steve
    Commented May 31, 2022 at 17:44
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    $\begingroup$ Fictional worlds that have space dogfights and take the time to explain the “atmosphere-like” flight characteristics of their fighters often use phrases like “etheric rudder” or “keeled in space-time” to explain their maneuverability. (i.e., they have a means of generating lift from the structure of their universe and exploit it, rather than simulating atmospheric flight via thrusters.) $\endgroup$
    – RLH
    Commented Jun 2, 2022 at 19:54

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Spacecraft have already flown a smooth, curved arc of a turn in space.

Shuttles undocking from the ISS performed a Twice Orbital Rate Flyaround to image the entire station.

enter image description here

Source: https://space.stackexchange.com/a/22053/6944

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  • $\begingroup$ That curved arc was only relative to a body traveling at the same speed in the same direction. For an outside observer standing on Earth, there was no "arc of a turn in space", it was just a very tiny wobble in its path. $\endgroup$
    – vsz
    Commented Jun 2, 2022 at 15:25
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    $\begingroup$ @vsz why this Earth-centric prejudice? To the ISS and shuttle crews it was an arc. $\endgroup$ Commented Jun 2, 2022 at 15:38
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Steve's question was clarified in the comment he made. He is asking about star wars & top gun type dogfight flying. With that in mind... here goes.

Possible? YES.

Practical? NO!!

  1. Sounds like you want unlimited thrust capabilities but magical-massless fuel/oxidizer. In order to be firing many thrusters so much and main engine with thrust vectoring you burn a lot of fuel. That fuel mass will be a major factor in not being able to change trajectory quickly. (Newton will not be ignored)
  2. RCS systems are mostly for making a craft spin about an axis (attitude control)… not so much major changes to trajectory. In the dogfight situation, think of it as turning a craft around so it is pointed backwards so that its main engine can fire to slow it down. Or, RCS spins craft 90 deg so main engine can fire cross trajectory causing ‘turn’. I think for primary trajectory control maneuvering you'd want 4 thrusters much more powerful than RCS, mounted mutually orthogonal at craft C.G. and nose (180 deg to main engine)
  3. Not such a big deal… fly-by-wire is already widely used, wouldn’t take too much effort apply to this. What would take a lot would be to get pilot to understand the complex and non-intuitive orbital mechanics the pilot is asking the flight control system to fight against to get the asked for flightpath.
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    $\begingroup$ To further emphasize this, while you could (theoretically) design a craft to travel in such a manner, its performance would be significantly worse than a purpose-built craft designed to fly in the vacuum of space, at it won't be limited by pretending to fly with 'atmospheric' maneuvers. $\endgroup$ Commented May 31, 2022 at 21:24
  • $\begingroup$ @Michael Richardson YES... absolutely no need for a 'space fighter' to look anything like we've come to expect by seeing pretty craft in movies. Also... no need always fly with 'front' forward. $\endgroup$
    – BradV
    Commented May 31, 2022 at 21:32
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    $\begingroup$ @Steve: In order to produce thrust a fusion reactor also needs reaction mass that it can expel at high velocity. Helium atoms don't have much mass. So don't you either need a lot of them or need to expel them at extremely high velocities? $\endgroup$ Commented Jun 1, 2022 at 15:52
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    $\begingroup$ @Steve sorry... I'm not thinking of propellant at all. For me this is all magical realm. The world building SE site may be a better source. $\endgroup$
    – BradV
    Commented Jun 1, 2022 at 16:41
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    $\begingroup$ @Steve even if it had an unending supply of propellant constantly being teleported to it from elsewhere, a craft that pretends it's in an atmosphere will not only be horribly inefficient, it'll be more predictable. In a fight, such a vehicle would be at a terrible disadvantage compared to vehicles that don't cripple their maneuverability. $\endgroup$ Commented Jun 2, 2022 at 12:45
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I choose Earth as reference frame and assume an Earth orbit.

If the spacecraft has much thrust and smooth throttling from 0 to 100 % it could fly a smooth curved arc. But only very small changes of direction are possible. The amount of propellants needed for a 90° or 180° turn is huge. Reversing a low Earth orbit would require a much bigger rocket than that needed to launch the spacecraft from ground. A rocket with four instead of two stages.

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    $\begingroup$ And launching that four-stage monster into LEO in the first place would require two more humongous stages. $\endgroup$ Commented May 31, 2022 at 16:05
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    $\begingroup$ This is only true if you choose Earth as your reference frame (and assume the spacecraft is in orbit of Earth - the question doesn't specify.) If you choose a point/object in space comoving with the spacecraft at T=0 as your reference frame, all sorts of velocity direction changes in that frame are possible with minimal energy. This is how we often choose to view docking maneuvers. $\endgroup$
    – Willa
    Commented May 31, 2022 at 19:29
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    $\begingroup$ It surely did not require 4 stages for the SST to fly a loop around the ISS as mentioned by Organic Marble!!! $\endgroup$ Commented May 31, 2022 at 20:12
  • $\begingroup$ @LawnmowerMan But it was almost stationary compared to the station, by having the same orbital speed. From an observer standing on the Earth, there was barely any change in its orbit. $\endgroup$
    – vsz
    Commented Jun 2, 2022 at 15:22
  • $\begingroup$ @vsz the question doesn't say anything about the Earth frame or orbits, does it? $\endgroup$ Commented Jun 2, 2022 at 20:07
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The system in your question is plausible, and it's absolutely possible to follow smoothly curving trajectories in space — in fact, don't we usually? But there are limits on those trajectories; the tighter we want the curves to be, the more instantaneous thrust we need to be able to develop in a given direction. Smart computer control means we can adjust thrust quickly, but it still needs to physically come from somewhere.

Thrusters are generally small and used for attitude control for a reason; with enough of them we can thrust in any direction we want (plus keep the noise pointing in the "right" direction for the sake of the viewers at home) but doing that while making them large enough to do aerobatic-looking stuff would have serious problems with power-to-weight ratio, and the result would look more like a pinecone than a fighter.

Or we could have one big high-thrust "main engine" on the back, and use the thrusters for attitude control, which is overall more reasonable, but the tightest turns would require the craft to change orientation by up to 180° nearly instantly (to get the engine pointing the right way) while under high thrust, which again, demands oversized thrusters (or oversized momentum wheels) and extraordinarily heavy body construction — and would be uncomfortable for any occupants.

The advantage airplanes have is multi-facted: they get to push off of something (air) that they don't have to carry with them; aerodynamic forces (lift and drag) generally increase with higher speed; and those forces are more efficiently distributed over the surface of the craft. These add up to make it easy for aircraft to do what is extremely impractical for spacecraft. Good computers and bottomless gas tanks aren't enough to close the gap without additional magic technology.

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There is not really a problem with this. It's confusing because things are already moving really fast (relative to the earth) when they are orbiting the earth. But let's imagine you are really far from anything except a small space station for reference. If the spacecraft is moving 50 mph past the station and wants to smoothly curve, all it has to do is turn on a thruster perpendicular to the direction of motion. As long as the thruster is on with a fixed thrust, the craft will move in a circular arc.

If you want it to bank like a plane, you can pick an arbitrary "down" direction, and have a ball of outward thrusters that always come on when they are pointing "up" to simulate the force of gravity. You would have another thruster that comes out of where the wheels would be on a plane that is always on simulating the lift of the wings. You could have thrusters pointing forward to simulate drag, and of course ones pointing backwards to simulate thrust in an atmosphere. And finally you could have thrusters where the control surfaces would be to simulate the ailerons, rudder, and elevator. This would work until you ran out of propellant.

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More or less realistic space battle, even under the favorable condition of a powerful drive that needs only limited amounts of reaction mass ("my name is Solomon Epstein, and I changed everything"), is shown in the Expanse TV series. There are many videos out there celebrating the Expanse for realism, I more or less randomly looked at this one.

One thing Alan says in the video is very relevant here: The maneuvers are limited by the g-forces the human body can sustain. Interestingly, we have to throttle down even our comparatively stone-age spaceships when the tanks are near-empty and acceleration is highest in order to protect the fragile people in them.

Dog fights in airplanes already go to the physical limit of the pilots; the problem in space is that your delta-v is 10 times or more than that in air. You cannot do dog fights in manned vehicles at 10 km/s. What you will have is strategical placement, intercept courses, adjustments, kinetic and guided weapons, possibly evasive maneuvers for long range weapons — but no close combat with dog fights. In essence you will typically have very short, high-speed encounters on trajectories whose general direction cannot be changed unless there is a slingshot possibility available. Unmanned vehicles, like heat-seeking rocket-propelled missiles, will be able to do much crazier maneuvers though, as they do already in air fights. They are also disposable: They don't need to return anywhere and can spend all their fuel and reaction mass in the hit attempt.

The second issue is indeed the reaction mass. The Expanse fandom wiki estimates an exhaust velocity of a few percent of light speed which to me seems entirely unrealistic. With lower velocity comes, unfortunately, a larger reaction mass requirement which would make the ships look much more like ours: Large stacks of fuel with tiny payloads on top. Even less maneuverable.

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