GrandMasterTerwynn wrote:
Sikon wrote:
There is a tendency to assume a large space warship must be far slower than a smaller ship. That is invalid.
A heavily armored space warship can be almost as fast as a smaller unarmored one. The performance of an engine can be described as its combination of specific impulse ("fuel efficiency") and thrust to mass ratio. These characteristics mainly depend upon the engine type rather than the size of the spaceship. For example, if a ship has 1 million sec Isp and an initial propellant mass fraction of 50%, the rocket equation gives the same final velocity whether it is 10 tons, 10000 tons, or 1 million tons. As a different example, if a warship's mass is increased 50% by adding armor, there is not an order of magnitude reduction in obtainable acceleration but just a 33% reduction.
This is a simple matter of physics. In order to propel a given mass to a given velocity requires an input of at least 0.5*m*Vf^2 (non-relativistic, assuming 100% efficiency) units of energy. Joules being the most common unit used. So to drive a given rocket to, say 1% the speed of light (too much more than this and the relativistic KE equation comes into play,) and one gets the following numbers:
10 tons = 4.94E+16 J
10000 tons = 4.494E+19 J
1000000 tons = 4.494E+21 J
Thus, one has to do more two orders of magnitude more work to get a megaton battleship up to 1%
c than they would a 10 kiloton destroyer. This is just the KE of the vehicle, and doesn't include the total energy expended in getting there, which is quite a bit higher.
Yes, a ship 100 times as massive requires 100 times the energy to reach a given speed, but it also would tend to have 100 times the fuel and 100 times the power output.
If for some reason the larger ship had much lower power to mass ratio, then it would be much slower, but there is no reason that has to be the case. Whether chemical, nuclear, or antimatter, engines based on real-world physics tend to have specific impulse performance primarily independent of mass. The specific impulse is the exhaust velocity and hence corresponds to the energy given per unit mass of fuel.
Take your examples. For the 10 ton rocket ship to obtain 4.9 E+16 J means that it must have fuel giving substantially more than 4.9 E+15 J per ton. Yet if the 10000 ton rocket ship has the same fuel, then proportionally it should obtain the 3 orders of magnitude higher energy needed.
Take my arbitrary example with a spaceship having 50% of initial mass propellant and 1 million sec Isp. As derived in detail at
this website, the ideal rocket equation is
delta u = V_eq ln (m_f / m_e)
which is stating that the change in velocity (u) from a rocket engine firing is the exhaust velocity Veq (corresponding to the specific impulse of the fuel) times the natural logarithm (ln) of (m_f / m_e), where m_f is mass fueled and m_e is mass empty. In my example, m_f / m_e equals 2. As V_eq = 9.8 E+6 m/s, delta u = 6.8 million m/s. The change in velocity is usually called delta v instead of delta u.
In my example, all three ships reach 6.8 million m/s velocity.
Some high-performance forms of propulsion like nuclear engines can in fact be hard to scale down to a low size.
For example:
Covenant wrote:
A ship made out of orion pusher-plates [...]
Like Covenant, the opening poster of the thread, I like the Orion concept for warship propulsion. It has a rare combination of real-world plausibility, high specific impulse, and good thrust-to-weight ratio. The Orion nuclear pulse propulsion designs tended towards higher obtainable velocity with greater size. A concept like antiproton-initiated microfission/fusion might make smaller variants more practical, but a bigger ship can still reach as high velocity as a smaller ship.
GrandMasterTerwynn wrote:
So, for the brick versus needle, which are orders of magnitude apart, one will be orders of magnitude slower on the helm than the other.
A ship orders of magnitude more massive would be orders of magnitude slower than a small ship IF both had same mass engine/fuel. Sure, one could have a 1000-ton ship with a 500-ton propulsion system, then have a 100,000-ton ship with the same 500 tons of engine and fuel mass. However, they wouldn't if I was designing them. I don't think a future military would do so either. If the 100,000-ton ship instead has a 50,000-ton propulsion system, it would not be orders of magnitude slower.
You said slower on the helm, so you might be referring instead to the speed at which the ship can be rotated. A ship 3 orders of magnitude more massive would tend to be 1 order of magnitude longer than a smaller ship, so, yes, it would rotate slower. A question is how much is that a disadvantage. See a later part of this post.
GrandMasterTerwynn wrote:
Sure they might have the same final velocity, but the a smaller ship will be able to get to its final velocity much faster than a larger ship. This means that over the timeframes of a space battle (assuming similar initial velocities,) the smaller ship will, in fact, be noticably faster than the larger one. Even if the difference in accelerations is only 30%.
Not necessarily. See above. There are some material limits that would come into play at extreme sizes, not directly limiting velocity but limiting acceleration. However, whether 10 meters, 100 meters, or 300 meters in length, the ships are not so astronomically huge for structural strength to be the probable limit on acceleration. More likely, for hard science fiction engine performance, the limit will be either the thrust-to-weight ratio of the engines, the fuel supply for prolonged acceleration, or the acceleration tolerance of the crew.
GrandMasterTerwynn wrote:
The problem being, of course, that a long cylinder tends to be hard to turn, especially if you're concentrating more of its mass at its ends. Sure its nose may laugh off your high-energy lasers, but if you can't keep your heavily armored bow between your enemy and your vital bits, then that armor isn't going to mean much when he jams lasers into your less-protected broadside.
Engagement ranges are going to tend to be at least thousands or million of kilometers. A realistic hard science fiction battle would be nothing like Star Trek or Star Wars. There will be no ships zooming around dogfighting at a few kilometers range, as any ships trying that would be destroyed long before they were that close. The tendency will be for it to take either minutes, hours, or days for ships to close their distance, while the elongated warship can turn in a matter of seconds.
For my sample 10000-ton ship, it was 110 meters long if I recall correctly. To turn it in a matter of seconds requires no more than tens of m/s velocity. Have an appropriate set of thrusters mounted on rotating mounts at each end under computer control. Rotating a ship at tens of m/s is trivial compared to having engines capable of accelerating it at multiple-g's to many thousands or even millions of m/s.
Frankly, I am no more sure the warship should have 10:1 length to diameter ratio than for it to have 20:1 or 5:1. That was an arbitrary example. It depends upon assumptions like whether the enemy will usually come from multiple directions, the relative effectiveness of direct-fire weapons (i.e. lasers) versus weapons able to curve around to hit the sides (missiles), etc.. However, I am sure some elongation will be helpful to allow extremely thick frontal armor.
GrandMasterTerwynn wrote:
I'll address the second half of this post later today.
Okay. I enjoy debate. Just to be clear, the big example is using arbitrary figures to illustrate its point. It uses implausibly powerful lasers. The range figures are arbitrary. I am sure combat ranges will be thousands of km at a minimum, but the 100,000 km is just a random example.
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Regarding larger ships versus smaller ships:
The main potential disadvantage of a larger ship is simply cost. A 1-million ton ship may cost as much as a large number of 10,000-ton ships. This is complicated. There is sometimes a certain economy of scale from making large ships. There may be fewer parts per unit mass, reducing the expense per unit mass.
An extreme example is illustrated by present-day rockets, where the difficulty of extreme miniaturization can make a small rocket sometimes cost as much as large one:
Quote:
This went against conventional wisdom and common sense, but at Aerojet Truax collected enough facts and figures to prove its truth beyond doubt. Indeed, he'd been assembling the necessary data from the time he'd been in the navy, where he'd had access to all sorts of cost information.
Take Agena versus Thor, for example. These two rockets were identical in every way: each had one engine, one set of propellant tanks, and so forth; the only significant difference between them was size. The Thor was far bigger than the Agena, but the surprise was that the *bigger* rocket had cost *less* to develop.
"I was shocked to discover the Agena cost more than the Thor," Truax said later. "The Thor was between five and ten times as big!
source
On the other hand, the above quote is obviously only illustrating an unusual case. Alternatively, smaller ships might be more easily mass-produced, and sometimes nothing is more effective than mass-production at dropping costs.
I don't know the optimal warship size. However, if small warships are the best choice, it will be despite having no orders-of-magnitude advantage in obtainable velocity.