Does space ship acceleration scale with size?

[Yora]

In science fiction, we often see smaller ships being much faster than larger ones, under the assumptions that they accelerate faster because they have less mass to move. But at the same time, larger ships also have much larger engines.

Do these factors cancel each other out, or are the other aspects that would make a difference. Since we're in space and there is no drag, 10 small ships should accelerate exactly the same way as 10 identical small ships taped together into a bundle with 10 times the mass and 10 engines. But what about engines itself? Do they become more or less efficient when they get scaled up?

Can a larger ship with proportionally the same amount of steering thrusters turn just as fast and with the same forces? With a ship that has all numbers doubled, the front and back end would be further from the center of mass providing longer leavers to turn. Does that scale proportionally with the mass that needs to be turned?

I really don't understand the physics of forces to move objects at all. Are there any generalizations that can be made about how larger and smaller space ships would fly?

[hamishspence]

I think it works as follows.

Mass scales as the cube of length/width, but area of rocket nozzle scales as the square of width - and the thrust is determined by the area of the hole all the reaction mass is coming out of.

The velocity of the reaction mass is fixed. The acceleration relates to the velocity of the reaction mass.

As such, the bigger Rocket B is, assuming it's shaped exactly the same way as Rocket A, the lower its acceleration will be.

So, big spaceships that are exactly the same shape as small spaceships, will accelerate more slowly.

10x size = 1000 x mass, but only 100x area (for engine nozzle).

So, you need a lot more nozzles, to accelerate the big ship at the same rate as the small ship.

For a real-life example, look at the Saturn V accelerating Apollo, compared to the Titan accelerating Gemini. The Saturn is much bigger at the bottom than the top - like a pyramid - but the Titan is cylindrical. Big rockets have huge "bottom-ends" - small rockets don't.


However - big rockets can accelerate for longer (unless they have more nozzles than small rockets).


So - it would work something like this (in hard vacuum, with no nearby gravity, with rockets that are identical in shape).

Rocket A (1/10 as long as rocket B, 1/1000 the mass) accelerates 10x as fast, but only for 1/10 the time of rocket B - so rocket A and Rocket B achieve the same velocity.

[Yora]

Another thing I noticed is that even when the mass of a ship's structural frame scales cubically just like the mass of the ship, the cross section of each beam only scales quadratically. Which means they are weaker to deformation and fracturing. That would mean larger ships need more mass in their structural frame, even if everything else scales proportionally. That would make them slower.

[hamishspence]

Sounds about right- bigger ships need to be more sturdily built to survive the same accelerations as smaller ships. Given the limitations on this, then that would be another reason why big ships will tend to have lower accelerations overall.

[Yora]

I believe regardless of how fast you can spin a smaller or larger ship around, changing direction in space should come down almost entirely to acceleration and deceleration.
In an extreme case of doing a full turn to fly back to where you started, a ship first needs to lose all its velocity away from the starting point, and then begin accelerating back from 0 (ignoring orbits for now).

Going with the idea that large ships have less rear surface to put engines on and thrust relative to their mass, and can't convert their fuel to trust as quickly as a smaller ship, the smaller one with less inertia can slow down much faster and then gain speed in the opposite direction much quicker than a more massive ship.

Even if we don't have to complete cancel the original vector velocity or only want to add sideways velocity, the principle becomes still a factor. Which means the smaller ships would have much smaller turn radiuses. Even when we ignore how fast we could actually turn the nose of a big ship into a new direction without crumpling it.

So when we have the same thrust force per unit of fuel, and the same ratio of fuel to ship mass, we get the same final velocity once all the fuel is used up. So in terms of "speed" size would make no difference.
But smaller ships would have a clear advantage in pursuits? If both the large ship and the small ship reach the same final velocity (assuming they use both half their fuel) the small ship should have a big lead, and then can increase that lead by being able to coast at top speed for longer before having to hit the breaks. And it would easily outmaneuver the larger ship.

[Mechalich]

But smaller ships would have a clear advantage in pursuits? If both the large ship and the small ship reach the same final velocity (assuming they use both half their fuel) the small ship should have a big lead, and then can increase that lead by being able to coast at top speed for longer before having to hit the breaks. And it would easily outmaneuver the larger ship.

Depending on what maximum velocity is and what defensive systems ships have, a vessel may be able to coast at their maximum velocity effectively forever. After all, our extremely fragile Voyager space probes have been coasting at their max velocity for decades. So it may make sense to have defensive ships, or even just weapons platforms, positioned in strategic orbits around the location they are intended to protect and moving at their max velocity in perpetuity.

Also, it's important to recognize that the smallest 'ship' is actually a big missile (this is already true on Earth) and unmanned missiles have the ability to bypass the pesky limits on acceleration imposed by having a living being onboard (unless you cheat by using 'inertial dampers' or some other handwavium).

[Excession]

Small ships are cheap, almost throwaways. Just the one pilot too. Big ships are a much bigger investment, and contain hundreds of crew. That means the big ships end up with something really heavy added to them that small ships don't have: armour.

This is similar to surface navies IRL, which a lot of sci-fi is inspired by.

With real physics it's all power to weight, the amount of fuel on board, and the specific impulse of the engine. The smaller ship that's all engine and fuel will still be "faster" I'm general, but not in ways that look as fun on screen.

[Yora]

Armor only goes on the outside, making it fall under the square cube law. If the thickness of the armor remains the same, then larger ships require a smaller fraction of their total weight for that armor. If the ratio of armor weight to other weight remains the same, then bigger ships simply have stronger armor.

[GeoffWatson]

How do the engines in your story work?
You can choose whatever you want in science fiction.

[Brother Oni]

The velocity of the reaction mass is fixed. The acceleration relates to the velocity of the reaction mass.

As such, the bigger Rocket B is, assuming it's shaped exactly the same way as Rocket A, the lower its acceleration will be.

I think these two points are critical for the assumptions here - larger ships are just scaled up smaller ships.

If the larger ships were not just scaled up smaller ships but instead took advantage of their increased size to use alternate propulsion that threw the reaction mass faster out the back end (say, a ram scoop that ran the length of the ship and hence accelerated the reaction mass for longer), they would be faster.

You can see this to a degree in wet navy ships; the USS Gerald R. Ford (CVN-65) has a top speed of 56kmph with a displacement of 100 kilotonnes and is 337 m long. In comparison, the USS Iowa (BB-61) had a top speed of 61 kmph, with a displacement of 45.7 kilotonnes and 270 m long.

So a nuclear powered ship with a steam turbine engines can push a vessel over twice the mass and 1.25 times the length at the same approximate speed as something coal oil powered.

This observation of different accelerations but same top speed is also reflected in Age of Sail vessels as larger ships of the line had more sail, so could make more use of available wind. The first rate ship of the line HMS Victory had a top speed of around 10-11 knots, while HMS Audacious (a third rate) had a top speed of 12 knots, despite being around half the weight.
It's only when ships are designed for completely different purposes that the speeds are notably different - clipper ships (fast merchant vessels) range from 16 knots to 22 knots (achieved by the Sovereign of the Seas), much faster than the aforementioned warships.

[Storm_Of_Snow]

A smaller vessel is more likely to be dedicated to a single role (be it a fighter, or something up to a destroyer type hull), while a larger vessel may have to fulfill multiple roles, with extra equipment that takes up volume and adds mass without improving the performance of the vessel.

[sktarq]

Science fiction seems a bit all over the place on this topic (see the escape from Tatoine in SW episode IV for both strong chase ability and impressive roll acceleration of a large ship)

Basically if you have a question of how does engine thrust scale with size? This will vary depending on tech/handwavium being applied
If there is a say a reaction volume (of say a chamber in the engine that warps space) then it will make no difference as the engine scales
If thruster mouth area is a limiting factor the above issue of the square/cube will be a good reason to have slower acceleration in large ships.
If length (of say an acceleration track for the trust mass) is a determinant factor then large ships will have better acceleration than small ones.



Large ships will always have the issue of needing proportionally larger frames (due to cross section of a bracing member having to deal with the square/cube law) Which could effect density.

but it basically whatever you want in the story.

[Telok]

As a massive over-simplification: you're looking at the ratio of force (in whatever form you measure it) to mass. The higher the ratio, the more acceleration.

You can do this with toy rubber band cars. Get a big car, a little car, and a bunch of rubber bands. Put the same band on each car and the big one is slower, but the big one can have more bands or stronger ones which can make it go faster or longer (or both).

[Drogorn]

It depends entirely on what the spacecraft is using for an engine. Not all rocket engines scale down efficiently; you cannot, for example, mount a nuclear pulse propulsion engine on something the size of a fighter and expect it to work well. However, what you can have is a situation where a drone carrier with an extremely efficient engine like a magnetoplasmadynamic thruster(yes, that’s a real engine, not made up) launches drones that use powerful and lightweight but inefficient chemical rockets for thrust. You end up with the same carrier-strikecraft dynamic. It’s not what I think will happen because the lack of horizon makes beam weapons so unstoppable, but it’s a conceivable future at least for situations where annihilating the target is undesirable.

[Chronos]

There are a lot of things that we flatlanders take for granted that don't apply in space. For instance, the assumption that large ships will have a smaller cross-sectional area per volume than small ships. Why? Why can't a large ship be just a big slab, flying face-on through space? Then it could have exactly as much cross-section-per-volume as a small ship. Or the assumption that mass is proportional to volume: That's only if all ships have the same density. But maybe a big ship is just a big empty space, or filled with a lightweight honeycomb structure, so almost all of the mass is in the surface.

Ultimately, I think, you have to start by asking why large ships and small ships exist. If large ships exist because economies of scale let them mount more effective engines, then the large ships will have more acceleration. If there's a desire for especially speedy or maneuverable ships, then they might have very large engines, but everything else made as small as possible, while a ship that doesn't need much acceleration might be very large overall but with small engines. If the enemy has weapons that can blast a 30-meter hole through even a hardened target, but with a slow rate of fire, then warships should be flocks of very small ships, so each hit only destroys one, and the rest can swarm the enemy before it can shoot again. If the enemy weapons are weak, but cover a very large area, then you might want a ship large enough to be able to efficiently carry the armor thick enough to stop those weapons. All of these details feed into each other.

[Trafalgar]

Look at a real world example. Ocean going ship size started growing in the 1800s with improvements in steel strength and the development of more powerful steam and internal combustion engines. That trend continued until a supertanker named the Seawise Giant was built in 1979. Since then, no one has built a bigger ship.

There are several reasons for this. But a big one I think is that it reached a limit to how big you can effectively build something out of steel. You have to use higher and higher strength steel alloys which are more expensive to manufacture, mill, and weld on. Another is the fact that a longer ship has larger forces placed on the midships area. It is possible for these ships to break in half due to repeated stress.

[Storm_Of_Snow]

Ultimately, I think, you have to start by asking why large ships and small ships exist. If large ships exist because economies of scale let them mount more effective engines, then the large ships will have more acceleration. If there's a desire for especially speedy or maneuverable ships, then they might have very large engines, but everything else made as small as possible, while a ship that doesn't need much acceleration might be very large overall but with small engines. If the enemy has weapons that can blast a 30-meter hole through even a hardened target, but with a slow rate of fire, then warships should be flocks of very small ships, so each hit only destroys one, and the rest can swarm the enemy before it can shoot again. If the enemy weapons are weak, but cover a very large area, then you might want a ship large enough to be able to efficiently carry the armor thick enough to stop those weapons. All of these details feed into each other.

Well, there's always going to be a limiting resource - whether that's the materials involved in making the vessel, the fuel required to get it from point a to point b or simply the availability of crew you need to run it.

And then there's the missions the vessels going to be carrying out - if you're running a few documents from one place to another, the space going equivalent of a bike courier's going to be a lot more efficient than dedicating a bulk liquid carrier to it. Larger warships have the intimidation factor and can be used to "show the flag", while smaller vessels can patrol or conduct spoiling raids, or be first on the scene and provide aid if there's some kind of a disaster.

[Drogorn]

Well, there's always going to be a limiting resource - whether that's the materials involved in making the vessel, the fuel required to get it from point a to point b or simply the availability of crew you need to run it.

And then there's the missions the vessels going to be carrying out - if you're running a few documents from one place to another, the space going equivalent of a bike courier's going to be a lot more efficient than dedicating a bulk liquid carrier to it. Larger warships have the intimidation factor and can be used to "show the flag", while smaller vessels can patrol or conduct spoiling raids, or be first on the scene and provide aid if there's some kind of a disaster.

Building off this, it's worth noting that there are some weapons that need to be big to be effective. An ultra-relativistic electron beam weapon, for example, needs to be 3-4 kilometers long. That gets you a death ray that can damage things on Pluto from Earth orbit. (not science fiction, this is something we'll probably be able to build with no new science.)

[Rockphed]

I think these two points are critical for the assumptions here - larger ships are just scaled up smaller ships.

If the larger ships were not just scaled up smaller ships but instead took advantage of their increased size to use alternate propulsion that threw the reaction mass faster out the back end (say, a ram scoop that ran the length of the ship and hence accelerated the reaction mass for longer), they would be faster.

You can see this to a degree in wet navy ships; the USS Gerald R. Ford (CVN-65) has a top speed of 56kmph with a displacement of 100 kilotonnes and is 337 m long. In comparison, the USS Iowa (BB-61) had a top speed of 61 kmph, with a displacement of 45.7 kilotonnes and 270 m long.

So a nuclear powered ship with a steam turbine engines can push a vessel over twice the mass and 1.25 times the length at the same approximate speed as something coal oil powered.

This observation of different accelerations but same top speed is also reflected in Age of Sail vessels as larger ships of the line had more sail, so could make more use of available wind. The first rate ship of the line HMS Victory had a top speed of around 10-11 knots, while HMS Audacious (a third rate) had a top speed of 12 knots, despite being around half the weight.
It's only when ships are designed for completely different purposes that the speeds are notably different - clipper ships (fast merchant vessels) range from 16 knots to 22 knots (achieved by the Sovereign of the Seas), much faster than the aforementioned warships.

The top speed of a surface vessel is partially determined by its waterline and partially by its cross section and mass. I suspect that fast battleships had more engine power to mass and more waterline to cross section than a nuclear carrier.

[pendell]

There's other reasons to build bigger ships than bigger engines I can think of.

One reason is bigger weapon and ammunition capacity. Another reason is a bigger crew; if you're going to deploy the spacecraft for months on end it might be a good idea to include enough of a crew to repair and maintain it if things go wrong, rather than putting it all in the hands of one pilot who has to be able to maintain a nuclear reactor, plot a course, troubleshoot the computer, and deal with any of the other problems that might go wrong on a complex piece of machinery all by zirself millions of kilometers from the nearest repair bay.

Coupled with that is sheer capacity to support a lengthy deployment ; storage space for food, water, medicine, a sickbay.

The reason we can build aircraft with a crew of one or two people is because they are never more than a few hours away from an airfield or carrier, where a dedicated support staff of hundreds of people is waiting to rearm, refuel, repair the craft itself as well as provide medical help and other necessities to the pilot. But if you're going on a deep space mission it may be months or years from that kind of support or any kind of dockyard; that means you need to bring all the necessities along with you, same as they did during the age of sail. That means a crew which might go up into the hundreds of people, and a ship size to match.

Respectfully,

Brian P.

[farothel]

A lot also depends on what you need the ship for. A large merchant ship probably doesn't need a lot of acceleration, taking longer to get to top speed (or efficient speed, which is not the same) and taking longer to break as they want more space for cargo instead of big engines. A warship or a small courier needs more acceleration due to their mission. The same is true today. Nuclear aircraft carriers are of a similar size as merchant ships (there are bigger merchants, but a lot are in the same general size). Merchants are not often going above 20-22 knots (some can, but they don't often do it). A carrier goes routinely above 30 knots and actually it's escort ships have a very similar top speed.

[Imbalance]

Wouldn't it need to? Wouldn't the increased mass be more susceptible to gravity in a vacuum as well as having its own? Nevermind surface landing or the vessel's purpose, near-planetary orbit would exert greater pull on a more massive vehicle that it would have to work harder to overcome than a smaller one, right?

[Rockphed]

Wouldn't it need to? Wouldn't the increased mass be more susceptible to gravity in a vacuum as well as having its own? Nevermind surface landing or the vessel's purpose, near-planetary orbit would exert greater pull on a more massive vehicle that it would have to work harder to overcome than a smaller one, right?

If you are in orbit already you can use whatever drive you want to get the delta-v to get into a different orbit. Different drives just change how much reaction mass, time, and energy you need.

[Quizatzhaderac]

Rocketry tactical maneuverability
Smaller vessel can have a higher acceleration, but that's probably only helpful for missiles.

With the space shuttle, the limit of acceleration is the human crew; a fighter sized vessel couldn't accelerate any faster. A 200-300 ft long ship could still manage to reach 5G with today's technology.

A ship much bigger than a modern warship would be slower.

Rocketry operational maneuverability
Since space is big, acceleration is usually pretty irrelevant in determining where you can go and how fast you can get there. Delta-v stays constant with changes in scale.

Ion thrusters
The exhaust requires very, very little area, so one could basically have serval rows deep of ion engines, with little gaps to allow the deeper engine's ions to pass through. Constant with scale.

Unlike rocketry, acceleration may be tens thousands of times less, so acceleration might actually be the limit on getting somewhere quickly.

Warping space
This one should actually improve with scale. The cost is proportional to the area between the volume of warped space and regular space. So one might expect to see bigger ships with "deeper" warps as the transition area is thicker.

[Storm_Of_Snow]

Rocketry tactical maneuverability
Smaller vessel can have a higher acceleration, but that's probably only helpful for missiles.

With the space shuttle, the limit of acceleration is the human crew; a fighter sized vessel couldn't accelerate any faster. A 200-300 ft long ship could still manage to reach 5G with today's technology.

Technology could work around that - fighter pilots for instance have flight suits that compress their legs in high-g manuevers to prevent blood from being pulled from the head, you've got the inertial dampening fields in Star Trek, and I'm sure there's bio-modifications you could start to add in to the crew if you wanted to go down that route - from auxilary blood pumps and flow baffles in veins, to full brain in a jar.

Warping space
This one should actually improve with scale. The cost is proportional to the area between the volume of warped space and regular space. So one might expect to see bigger ships with "deeper" warps as the transition area is thicker.

Depends on the rules of your warping tech - a straight foward Star Trek warp drive then yes, something like Stutterwarp from Traveller 2300AD is dependant on both the amount of power you can provide to the drive and the amount of mass you're moving, and hyperspace style drives may either make no difference, or larger vessels may be limited to certain wide and slow paths in that environment while smaller vessels can slip down narrower, faster streams (I'm thinking 40k's warp space here).

[Rakaydos]

A lot also depends on what you need the ship for. A large merchant ship probably doesn't need a lot of acceleration, taking longer to get to top speed (or efficient speed, which is not the same) and taking longer to break as they want more space for cargo instead of big engines. A warship or a small courier needs more acceleration due to their mission. The same is true today. Nuclear aircraft carriers are of a similar size as merchant ships (there are bigger merchants, but a lot are in the same general size). Merchants are not often going above 20-22 knots (some can, but they don't often do it). A carrier goes routinely above 30 knots and actually it's escort ships have a very similar top speed.

Also context. A single tie fighter during the battle of endor is nothing. A single tie fighter (variant) at the end of Mando Season 1, when noone has anti-vehical weapons, is much scarier.