At speeds near the speed of light, interstellar particles and gas may affect the movement of the ship, and microscopic particles may even badly damage the ship. Would not it make sense to make the shape aerodynamic so to reduce the damage and drag? Maybe the nose should even be armored?
Maybe the ships should even have wings so as to change course with less energy cost using interstellar hydrogen?
Interstellar gas isn't a continuous medium, it's individual particles, too far apart to interact significantly; hence there's no "aerodynamics" between the stars. In a ship at high relativistic speed, these particles will strike with the energy of small bombs. There may be some advantage to giving a ship a needle-like shape, to increase the effective thickness of the hull and shielding, but resistance to motion (aka drag) will depend on cross sectional area and speed, rather than shape. Adding wings merely increases both mass and radiation due to these collisions.
No. Whether you're talking about 0.10c (pretty fast) or 0.99c, there's no point in aerodynamic shapes. At those speeds any collision that is catastrophic will not be mitigated by angles that slope away from the center. For the sub-catastrophic collisions that cause ablation, that ablation can't be reduced by an aerodynamic shape.
The only real engineering concerns are having a spaceframe/hull sufficiently engineered to withstand the stresses of acceleration and deceleration.
On the other hand, of course, in the words of Doc Brown paraphrased poorly, if you're going to (time) travel, why not travel in style.
Aerodynamics is the study of gas flow around a rigid object. Zeiss explained that the density of interstellar gas is too low for this to be relevant. However, at velocities of just a few km/s, solid objects impacting a solid surface cause the impacted surface to behave as a liquid. That's 103-104 m/s. Recalling that $c$ is about 108 m/s, even traveling at a mere 0.1% of $c$ (about 105 m/s) will guarantee that you will impact some objects at well above the "liquefaction threshold". This is why there is no such thing as an "immovable object." No matter how big or dense you make something, there is something else which can be thrown at it with a velocity which will, at the least, cause the target object to dissociate. Black holes are the only exception (but throwing objects at them should cause them to move, nevertheless).
As others have noted, since you need to shield your ship in the direction of travel, you want to minimize the cross section. Since we presume the interior is pressurized for the survivability of the crew, a round-cross section provides the strongest containment shape (which is why airliners and submarines are mostly long round tubes). This is what leads us to a cylinder (not very sexy, I know). However, there is an important trade-off to be made. Tiny rocks in front of you are not the only hazard in space. The threat actually comes from all sides. Cosmic rays are also very dangerous to your crew, so you cannot simply make your ship a long, thin needle. There needs to be enough shielding mass on the sides to reduce cosmic radiation to a survivable level. So the ship should be long and narrow, but not too narrow.
The easiest way to change course is to turn off the main engine, rotate the ship to the desired vector, and turn on the main engine again. "But wings will save you from using RCS thruster fuel!" You actually don't need RCS thrusters to change orientation. You can do it purely mechanically, via gimballed gyroscopes, which is what the ISS does. There are limits to how much angular momentum can be altered, but since most of the time, your angular momentum should be zero (unless you are spinning for artificial gravity, in which case you have a whole bigger set of challenges), this accumulation should not normally be a problem. Even if you do need to make an attitude adjustment, the gyros should reduce your RCS fuel consumption dramatically.
Yes, the nose must be armored. But armor might not be enough. Star Trek has only a tenuous connection with real physics, but one concession to interstellar travel is the so-called navigational deflector. The closest thing you could make with real physics is a kind of internally generated magnetosphere. That would help divert charged particles, but wouldn't help so much with electrically/magnetically neutral ones. However, you could make everything charged by shooting everything in your path with a laser, producing enough energy to ionize everything about to hit you. It's questionable whether a ship could produce enough energy to actually deflect impactors at a significant fraction of $c$.
There was a relevant question about magnetic shields on the Space SE. But such a shield only protects against particles. The most dangerous threat is really gamma rays. The only reliable defense against these is a lot of mass. Theoretically, if you had a really good scintillator, you could down-convert the frequency of the gammas and harvest it as energy (to help power your magnetic shield, for instance). Possibly, the front armor plate could act as both a gamma scintillator and a particle shield for bits that make it through the magnetic shield, but it would probably need to be replaced periodically, because I think both uses will degrade it over time.
If you have a deflector laser for ionizing rocks, then the nose of your ship will be quite busy. The shield/scintillator will need to be opaque to gamma rays, but transparent to whatever frequency your deflector laser runs at (UV? you don't want the deflector to be too high-frequency, or it will go through the rocks instead of ionizing them). Some real-life gamma scintillators are transparent organic crystals. So it would be pretty cool if the nose of your ship was a big thick glass-looking crystal with a laser battery and PV array behind it. Food for thought.
Alastair Reynolds covered this in his novel "Pushing Ice".
Basically, any contact with any particle will result is significant energy transfer.
His answer was to have interstellar ships push a two kilometer (or longer) tube of ice in front of the ship to act as ablative armor.
Very interesting question!
I would say yes, but not necessarily for the same reasons you are thinking about. With an increasing number of satellites in LEO, predicting their drag accurately becomes more and more important. The flow regime for objects in space is usually characterized by a very high Knudsen number:
$Kn = \frac{\lambda}{L}$,
where $\lambda$ is the mean free path length of the molecules in the flow and $L$ is a characteristic length scale, say the max size of your satellite. A numerical tool used for this is the Direct Simulation Monte Carlo method (DSMC).
So if you write a relativistic version of such a DSMC code you can use it to minimize/maximize the drag of your spaceship due to free-molecular flow. However, I don't know if you will end up with a shape that is aerodynamic in the colloquial sense.
On the other hand, radiative heating is a big issue in hypersonic flow and becomes more and more important the faster you go. Radiation in general also seems to be a big issue for relativistic spacecraft. Now radiative heating is directly proportional to the local radius of curvature $R$ of your spaceship hull (see Anderson: Hypersonic and High-Temperature Gas Dynamics). So it makes sense to try and minimize $R$. What does this mean? Your spaceship will be as slender as possible, very similar to Alastair Reynold's lighthuggers.
Of course this is all speculation and there may be other effects at play that are much more dominant than "aerodynamic" drag.
On the one hand, if you can generate a force field, you don't need solid control surfaces... you can project them as needed. A craft could be whatever was most efficient to house its components (including field emitter[s]) and then could project up whatever shape it needed in atmosphere. The visibility/opacity/color and control of same would be at the author's whim. Just because Star Trek/Wars shields are invisible doesn't mean yours have to be.
And does it bother anyone else that invisible shields from those franchises are blocking beams of light that really ought to pass right through them unobstructed?
On the other hand, if you want your ship to "look aerodynamic" you could hand-wave up something about how the field emitters that charge and repel incoming stellar dust need that shape because optimal polarity inversion technobabble.
Don't forget the advantage of sloped armor. The further from perpendicular an impact is, the more force is deflected instead of absorbed. Also, in the above hand-waving, the more time a given particle will spend in proximity to the ship and therefore have more force applied to push it away and avoid the impact entirely.
This would also produce an "equal and opposite reaction" that might feel remarkably like aerodynamics. I'm not sure I'd try for any control beyond 'uniform distribution', flaps and ailerons seem like they'd be a hard sell, but hey, it's your story.
This craft would have a charged particle "wake" that would be detectable, an "ion trail" if you will... though a craft could exert even more power to balance the charge of its wake back out again, given the correct hardware.
Aerodynamics has no effect in space, the relative velocities are too high for particle interactions to be anything other than "impacts".
The nose must be armoured, but the armour is, by design, the opposite of aerodynamic. The best bet for hyper-velocity armour is bulky multi layered whipple shields. The main concern for these shields is the lifespan of each layer: each spot can only take a single hyper-velocity impact so you are far better orienting it squarely as the impact area increases with the sin of the angle.
Wings won't work, the increase in profile would have serious drawbacks. The only design that uses a profile increase with a plausible benefit is the extremely large intake on a bussard ramjet.
Everything around spaceships for harder scifi settings has completely different design paradigms to any known engineering, spaceships are not planes.
Eh, yes, and no..
A interstellar vehicle might not need to be aerodynamically shaped- but it might be in dire need of drones that take particle hits ahead of it and deflect the debris and energy out of the path / scout out really large objects (flung out planets etc.).
How one catapult those drones ahead, keep them stationary realtive to ones course and how to shape those drones to basically blast yourself away between the stars.. that i can not answer.
It actually won't make any difference if the ship is aerodynamic or not outside an atmosphere. A particle hitting the ship's hull with enough force, even if it is just as small as a mustard seed, will deal a lot of damage. A ship traveling at near light speed will hit a pebble as if the pebble was the one traveling at near light speed. That said, if you want the ship to be designed aerodynamically there is also no harm in doing so, especially if the ship is also meant to fly into an atmosphere.
