A Constellation of Warships II

Here, we will continue the discussion on space fleet composition and formations.

As mentioned in Part 1, one of the most important determinants of fleet composition and formation is the technologies in use. Spaceships will be designed to exploit the advantages offered by certain technologies, while mitigating side-effects and weaknesses.

The Grand Fleet at the Battle of Jutland

However, all that matters in practice is the difference in effectiveness of the technologies between the combatants, in other words, it's the relative strengths that matter.

An example would be propulsion technology. In a sufficiently advanced setting, a wide variety of nuclear, chemical and electric rocket engines might be available to mount on warships. The choice would affect the rate of travel, the effective range of fleets and more.

Isp vs deltaV

However, all warships will likely mount the drive best suited for combat, and what will matter then is the relatively minor differences in performance that result from equipment designed and built by different groups, instead of the huge differences between the various options. 

We'll now go down a list of various factors that will affect fleet compositions and formations:

Pixel-formations

As established in a previous series of posts, stealth in space is a non-negligible possibility. Its importance increases the closer a setting is to modern-day technology.

In the default scifi setting, spaceships put out incredible amounts of power to move around quickly. This does not mean that stealth is not a factor. A pixel-formation is recommended.

A 'perfect' or single-pixel-formation is a close arrangement of spaceships, made so that all of the fleet's detectable emissions lie within a single pixel of the sensors you are trying to evade. A pixel-formation is two-dimensional, as the depth of the formation has no effect on the detectability, at extreme ranges. 

The perfect pixel-formation allows the number of spaceships inside a fleet to be obscured from the enemy. Since exhaust plumes cannot be distinguished, it can even help prevent the enemy from knowing the mass and performance of the spaceships in formation. 

A pixel-formation is possible thanks to the finite angular resolution of a sensor. This formula gives the maximum separation of spaceships within a pixel formation at which they cannot be distinguished:

• Pixel width: Distance * tan(69.9 * Wavelength /Diameter)

Distance is the separation between sensor and fleet. Wavelength is that of the Diameter is that of your sensor array. A single sensor is limited to the radius of its mirror, in the handful of meters, but an array can create a 'virtual telescope' of radius equal to their separation. 

ALMA links with other observatories to create an Earth-sized Virtual Telescope

We can quickly see that this is only useful against individual spaceships or at interstellar distances. Sensors can easily be placed at opposite sides of an orbit to create a virtual telescope thousands of kilometers across, able to pinpoint the location of a spaceship down to the millimeter. In combat, doing so might not be so simple.

If multiple spacecraft maintain a separation within two pixel-widths, then their signal will form a large, uniform spot on the sensor. This is a more practical application of the pixel formation, but with reduced effectiveness: unlike a single pixel formation, your enemy will know that multiple spacecraft are present, even if the exact number cannot be determined. 

Closely Distributed Signals

In situations where detection of spacecraft is not a foregone conclusion, it would be sensible to reduce the opponent's ability to detect spacecraft using distributed signals.

As mentioned in Stealth in Space, the difference in the ranges at which a sensor can detect a spaceship when it is under power or drifting cold is great. In the examples, calculated, it was the difference between being spotted across the Solar System (several hundred million km) or staying undetected a day away from your opponents (one million km or less).  

This leads to a situation where, for spacecraft that do not continuously accelerate and have non-negligible travel times, they are only detected when the engines are running. Switching the engine on and off would be seen by a sensor as a lightbulb appearing and disappearing from sight. 

Like twinkling stars...

Due to the way motion works in space, you cannot change your trajectory without producing thrust. As noted, producing thrust makes you detectable. The immediate conclusion is that your trajectory while undetected can easily be deduced from your motion at the end of your engine burn. It can be as simple as connecting the dots and following the vector they trace.

However, a fleet in space can defeat an opponent's ability to predict their motion in this manner. The first method relies on distributed signals. Closely distributed signals are the result of spaceships in very close formation, alternating the firing of their engines in a random manner. They would be seen as a cluster of signals appearing and disappearing in an unpredictable manner. This alone is not enough to prevent their trajectory from being predicted. 

Explanation of the effect of closely distributed signals

The figure above explains how closely distributed signals can throw off predictions on a fleet's trajectory. This method can be combined with 'cold engines' that are used to re-position spaceships within a fleet, a task well suited to their low efficiency.

Closely distributed signals is very effective in defeating missiles with low deltaV, so unable to catch up to spaceships if shot onto an intercept course far from their target's actual trajectory. It is also essential in evading 'stealth' projectiles that cannot be detected until very close, but cannot alter their trajectory either. 

Remotely Distributed Signals. 

Here, we rely on the fact that sensor platforms cannot cover the sky with very sensitive narrow-angle sensors, the sky cannot be scanned instantly and all data cannot be correlated confidently within a short span of time.

1 degree FoV is quite large by today's standards

To exploit these limitations, the fleet's individual spaceships attempt to depart on very different trajectories, converging on their target only by the end of their trip. Maximal separation puts them millions, if not hundreds of millions of kilometers apart, with their emissions literally coming from all corners of the sky. This 'maximum remoteness' technique might be able to prevent your target from even recognizing the signals as belonging to an attack, but it will cost your fleet much more deltaV to perform, and your total trip time will have to be very rigidly defined so that all spaceships meet at the same point.

Mid-Remote Distributed Signals. 

Mid-remote distributed signals is more situational. It is to be used against an opposing fleet, with a limited number of sensors. Narrow-angle sensors only cover a small section of the sky. The objective then is to distribute the fleet's spaceships over an area larger than that covered by a single narrow-angle sensor. 

Kepler's CCD

Your opponent will be forced to scan the entire section of the sky your spaceships are possibly in. This means that the sensors cannot continuously cover your spaceships' likely positions. For example, if a 0.5 degree FOV sensor was looking at targets approximately 10 million km away, then it can only cover a section of the sky 87260 by 87260km across. If the spaceships in a fleet are distributed over an area 150000km in radius, then the sensor can only ever see 10.8% of the fleet at any one time. If the sensor wishes to pick up details 10m across, then it requires 76 trillion pixels, or a CCD plate 8.7 meters wide, consisting of 1 micron sized pixels.

Twice the performance, thrice the efficiency of the previous Titan X

A 10 GPU stack of Nvidia's GTX1080 can handle 100GB/s. The CCD will produce 152 TB images of its FOV. Therefore, full scans of the fleet's mid-remote distributed signals area will be completed every four hours ... and this is without any further analysis of the data. Entire insertion burns can go unseen. Even a gentle 0.01G acceleration for 4 hours will push a spaceship to 1412m/s. If it is travelling at a closing velocity of 20km/s, and it performs no other burns, by the time it is detected by wide-angle sensors at a distance of 1 million km, it would be out of position by 635000km. It would evade any pre-positioned kinetics, and would attack at a 32.4 degree angle.

In return, your opponents will be forced to massively increase processing bandwidth, accept lower details or reduce the scanned area and take the risk of being surprised at much shorter ranges, where wide-angle sensors start picking up cold spaceships. 

In return, you will focus on higher acceleration spaceships that perform their burns in shorter periods of time, and on 'spoofer' spaceships that are able to distance themselves from the fleet stealthily, perform a visible burn, then slowly cancel the velocity gained with 'cold engines'. This will massively increase the area sensors will have to cover.   

Lasers and angles

Kosmos 2499 feared to be a laser-equipped satellite

The most mass-efficient configuration for a spaceship is one where all armor is concentrated in the likely direction of the threat will be. In other words, the front. This design philosophy is most prominent in tank design. 

Taken to its extreme, front-loaded armor will end up forming a 'faceplate'; a thick plate on the front of the spaceship. However, the freedom of movement in space precludes this from being a viable design.

The reason is that in a setting where lasers are an effective weapon, opponents can position themselves far from the Hohmann corridor or other likely trajectories, and fire lasers at an angle.

Firing at an angle by-passes front-loaded armor. The only way to counter this for certain is to extend the armor past the front of the spaceship and over the sides. However, increasing the surface area covered by armor translates into a greater mass penalty. This has to be compensated for by reducing the thickness of side armor, reducing the mass of the frontal armor through sloping, going for an 'all-or-nothing' armor scheme where voluminous propellant tanks are not protected, accepting lower deltaV to use denser propellants with lower volumes, ect...

There has to be a balance between the angles of attack your armor protects from, and the percentage of your payload you are willing to dedicate to armor. The balance point is determined mostly by where you expect your enemy to be. 

In practice, spacecraft will be very well defended against attacks directly from the front, thanks to sloping. Against a small arc to the front, the full thickness of frontal armor will be put to use. A wide angle to the sides is covered by thinner armor. The rear is unarmored, as it would be prohibitive to cover the propellant tanks and it leaves room for radiators and nozzle openings.

Arcs defined by armor coverage

The frontal arc is mostly defined by the likely positions of targets the warship will be able to detect and orient itself towards them, before an engagement. This will correlate with the field of view of narrow-angle sensors.

The lateral arc is mostly defined by the rocket engine's performance, as a more efficient engine will allow the spaceship to mount more armor while still reaching the same deltaV targets. The rear arc is open to space and contains sacrificial, expendable and unprotectable equipment. 

The objective of an attacking warship becomes its positioning at an angle from the target's nose large enough for it to negate sloping, or even better, attack the side armor. If it can catch the rear arc, then the target was grossly out of line and would have been defeated, with or without armor protecting it.

With this objective in mind, fleets will arrange themselves into offensive or defensive formations. There are infinite variations possible.

Each vertex is a spaceship.

One example of an offensive formation is a pyramid with one target spaceship from the opposite fleet, singled out, at its tip, and the attacking craft forming the base. The target cannot point its armor at any of the attacking craft without exposing its sides to another. 

An example of a defensive formation is the shield-stack. Spaceships arrange themselves into very close formation, closing off the innermost ships from attack from all angles, and reducing the fleet's exposure to only the outermost ships. Depending on the numbers involved, it can be a simple 4-ship diamond, up to a thousand-ship sphere with optimal exposed-to-protected ratios. 

The laser angling objective can be approached temporally as well as spatially. If a cluster of spaceships opens fire on the target from one direction, forcing it to point towards them, this creates an opening for a spaceship that escaped detection using distributed signal techniques to perform a flank attack at a very favorable angle. 

Not necessary to have fun

The battle should be dynamic, and opposing fleets will change their strategies and formations to defeat those employed by the enemy. A shield-stack must evolve into a 'puffer-fish' formation to defeat undetected stealth craft, and in return becomes vulnerable to missiles as it cannot manoeuvre effectively. Once dispersed, individual spaceships will focused by a pyramid, requiring a reverse-pyramid counter-attack to even the odds, and so on...

We will continue in part III.