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Eclipse Phase Space Warfare
Anders Sandberg
April 26, 2011
Abstract
noindent This essay analyses the physics of spacecraft and space
com-bat in Eclipse Phase. Based on the technological assumptions
explicitlyand implicitly made in the game together with known
physics, variousconstraints on space warfare can be concluded. In
general, the space bat-tlefield is extremely high-energy, high-loss
and dominated by the forcesthat can estimate the locations of enemy
assets accurately despite mas-sive interference. FTL quantum
entanglement communication provides abig but not decisive advantage
to forces able to afford it.
Contents
1 Introduction 31.1 Acknowledgements . . . . . . . . . . . . . .
. . . . . . . . . . . . 3
2 Ship performance 4
3 Energy requirements 43.1 Reactor sizes . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 63.2 Exhaust temperature . . . .
. . . . . . . . . . . . . . . . . . . . . 73.3 Cooling . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Detection 94.1 Sensors . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 94.2 Thermal emissions . . . . . . . . . .
. . . . . . . . . . . . . . . . 104.3 Exhaust emissions . . . . . .
. . . . . . . . . . . . . . . . . . . . 104.4 Sunlight . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 104.5 Sensor
sizes and sky scanning . . . . . . . . . . . . . . . . . . . .
114.6 Ship spectra and detectability distance . . . . . . . . . . .
. . . . 124.7 Scanning limitations . . . . . . . . . . . . . . . .
. . . . . . . . . 124.8 Particle emissions . . . . . . . . . . . .
. . . . . . . . . . . . . . . 144.9 Railgun projectiles . . . . . .
. . . . . . . . . . . . . . . . . . . . 144.10 Active sensors . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 144.11 Stealth
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
4.11.1 Anisotropic radiation . . . . . . . . . . . . . . . . . .
. . . 154.11.2 Cooling . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 15
4.12 Parallax . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 164.13 Hiding from many eyes . . . . . . . . . . . .
. . . . . . . . . . . . 164.14 Spoofing and jamming . . . . . . . .
. . . . . . . . . . . . . . . . 17
1
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5 Weapons 195.1 Independent weapon buses . . . . . . . . . . . .
. . . . . . . . . . 195.2 Lasers . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 19
5.2.1 Sources . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 195.2.2 Beam optics . . . . . . . . . . . . . . . . . . . . .
. . . . . 205.2.3 Heating beams . . . . . . . . . . . . . . . . . .
. . . . . . 215.2.4 Explosive beams . . . . . . . . . . . . . . . .
. . . . . . . 21
5.3 Railguns . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 215.4 Particle weapons . . . . . . . . . . . . . . . .
. . . . . . . . . . . 225.5 Missiles . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 22
5.5.1 Kinetic impactor rods . . . . . . . . . . . . . . . . . .
. . 225.5.2 Nukes and antimatter . . . . . . . . . . . . . . . . .
. . . 235.5.3 Rocks . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 245.5.4 Relativistic missiles . . . . . . . . . . . . . .
. . . . . . . 245.5.5 Leashes . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 245.5.6 Nanoweapons . . . . . . . . . . . . . . .
. . . . . . . . . . 24
5.6 Fighters . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 255.7 Networked warfare . . . . . . . . . . . . . . . .
. . . . . . . . . . 25
6 Armor 266.1 Kinetic impact . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 266.2 Beam impact . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 276.3 Conclusions . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 27
7 General strategy 28
8 Cloud combat 298.1 Weapons vs. sensors . . . . . . . . . . . .
. . . . . . . . . . . . . 29
9 Hitting a dodging enemy 30
10 Conclusions 3210.1 Deep space combat . . . . . . . . . . . .
. . . . . . . . . . . . . . 3210.2 Orbital warfare . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 33
List of Tables
1 Ship engine types . . . . . . . . . . . . . . . . . . . . . .
. . . . . 42 Ship properties . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 53 Energy storage . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 5
2
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1 Introduction
Eclipse Phase is a mostly hard SF role-playing game with a
setting stretchingacross the solar system (and some ex-oplanets).
Space travel is not uncom-mon and in the past there have
beenmilitary conflicts in space. While per-sonal combat is
described space com-bat is not; the game states that:
Spacecraft have few statsin Eclipse Phase, as theyare primarily
handled assetting rather than vehi-cles. Note also that nostats are
given for space-craft weaponry. It is highlyrecommended that
spacecombat be handled as aplot device rather than acombat scene,
given the ex-treme lethality and dangerinvolved.1
While this is sensible advice for aroleplaying game, it is a
direct chal-lenge for players who like to con-sider how space
combat might work,the strategies involved and how thesemight affect
the characters inside thegame. For example, is space com-bat
heavily stealth oriented or re-quires ships with massive armor
barg-ing through enemy point defenses?What are fighter craft (and
fighter pi-lots) useful for? How much of anadvantage does a space
habitat haveagainst an attacker?
In the following I will analyse whatfollows from the assumptions
made inthe game, as well as extrapolationsfrom known physics and
technology.
Technology in Eclipse Phase hasachieved dense energy sources
allow-ing fast spacecraft, fast optical pro-cessing running
human-level cognition,
and antimatter weaponry. But spacestrategy is limited by
lightspeed de-lays (somewhat modified thanks toquantum entanglement
FTL commu-nications), the limitations of materialsbased on
molecular bonds, high visi-bility of accelerating major crafts
andfinite reaction mass resources. Manytechnologies in the game are
close tothe limits set by physics, which simpli-fies analysis
somewhat.
1.1 Acknowledgements
This essay was inspired by past dis-cussions at the Eclipse
Phase Forum2,where many bright ideas were sug-gested.
The Atomic Rocket page3 andRocketpunk Manifesto4 have been
animportant source of inspiration, refer-ences and opinions
influencing this es-say.
The basic ship performance num-bers were kindly supplied by
JSnead.I would also like to thank him for hav-ing done proper
design calculations be-hind the scenes, simplifying this
workimmensely.
1Eclipse Phase core book, p.
346.2http://www.eclipsephase.com/forum3http://www.projectrho.com/rocket/index.html4http://www.rocketpunk-manifesto.com/
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Table 1: Ship engine types
Engine Acceleration G Acceleration m/s2 Isp sHydrogen-Oxygen
Rocket 4+ 39.3 450Metallic Hydrogen 3 29.5 1,600Plasma Rocket 0.01
0.1 20,000Fusion Rocket 0.05 0.5 100,000Anti-Matter 0.2 1.96
200,000Rocket Buggy 0.5 4.9
2 Ship performance
The key ability of spaceships is thatthey can accelerate long
and stronglyenough to reach high velocities orchange their velocity
(v) radically.This requires expelling reaction massat a high
velocity. A key value isthe specific impulse (Isp), how
muchmomentum each kilogram of reactionmass can impart on the ship.
Thefaster the reaction mass is emitted, thehigher the Isp. However,
this doesnot necessarily mean a higher acceler-ation. Available
engines typically havea high acceleration for low Isp and
viceversa: the high acceleration engines areless able to achieve
high v since theywaste much fuel, while high Isp enginescannot
produce high accelerations dueto energy limitations.
The achievable velocity change is
v = ve log
(m0m1
)where ve is the exhaust velocity (ve =
gIsp, g is the Earth surface gravity),m0 the initial total mass
of the space-craft and m1 the remaining payloadmass after all
reaction mass has beenused. Higher velocities require eitherhigher
exhaust velocities or exponen-tially more fuel.
Ships with v > 80 km/s typicallydo not have to worry about
launch win-dows, while slower ships need to plantheir trajectories
so that the origin anddestination are in the right alignment.
Ships are limited by how muchremaining reaction mass they
retainwhen making course corrections (es-pecially defensive ones)
en route. Iwill assume ships (especially warships)keep a fraction
of their reaction massbudget in reserve, giving them a frac-tion of
the total v for defensive oroffensive course changes5.
Table 1 describes the performanceof the basic ship engine types.
Table 2lists the basic Eclipse Phase spaceshipproperties.
3 Energy require-ments
Some estimates of the powers availablecan be gained from
considering space-
ship performance. A ship thruster re-quires P = (1/2)mv2e W of
power,where m is the mass flow in kilograms
5The Eclipse Phase core book (p. 283) suggests many ships burn a
quarter to a third ofthe reaction mass during the initial burn. In
practice this is rather costly, as reaction massnot used will make
the trip longer and require extra reaction mass for the
develeration burn.Saving this much fuel is rational only if drastic
course corrections may be needed, or the fuelvery cheap compared to
the cost of arriving later. Many commercial ships likely retain
verylow fuel margins, and may rely on tugships that help them slow
down at the destination.
4
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Table 2: Ship propertiesShip1 Size (m) Cross-
section(m2)
FullyLoadedMass(tons)
EmptyMass(tons)
Enginetype
Total vkm/s
Maxaccel-eration(Gs)
Acceler.(m/s2)
Maxpower
Destroyer 150x50x50 7,500 40,000 25,000 AM 800 0.2 1.96 800
GW
FastCourier
75x13x13 975 1,000 300 AM 1,600 0.2 1.96 20 GW
BulkCarrier
150x25x252 3,750 90,000 4,500 Fusion 40 0.002 0.001964 9 GW
StandardTrans-port
150x25x253 3,750 /12,000
10,000 4,500 Fusion 400 0.02 0.01964 10 GW
Fighter 4.5x3x3 14 7 3 MH 11 3 29.46 16.8 MW
SCUMBarge
300x70x70 24,000 180,000 80,000 Plasma /fusion
80 / 400 0.003 /0.015
0.02946 /0.1473
5.4 GW /135 GW
LLOTVHO HI
25x16x16 400 450 26 HO 11 2 19.64 203 MW
LLOTVOHO LO
25x16x16 400 450 26 HO 7 2 19.64 203 MW
LLOTVMH HI
19x12.5x12.5 237.5 450 26 MH 17 2 19.64 720 MW
LLOTVMH LO
19x12.5x12.5 237.5 450 26 MH 8 2 19.64 720 MW
SLOTVHO HI
17x11x11 187 150 11 HO 11 2 19.64 67.5 MW
SLOTVHO LO
17x11x11 187 150 11 HO 7 2 19.64 67.5 MW
SLOTVMH HI
13x8.5x8.5 110.5 150 11 MH 17 2 19.64 240 MW
SLOTVMH LO
13x8.5x8.5 110.5 150 11 MH 8 2 19.64 240 MW
GeneralExplo-rationVehicle(GEV)
6x2.2x2 13.2 5.5 3 MH 3.6 0.1 0.982 0.44 MW
Missile4 1x0.1x0.1 0.1 0.02 0.002 MH 31 2005 1,964 3 GW1
Abbreviations: AM = Antimatter, HI = HIgh velocity configuration,
HO = Hydrogen-Oxygen chemical rocket, LLOTV = Large
Lander and Orbit Transfer Vehicle, LO = LOw velocity
configuration, MH = Metallic Hydrogen rocket, SLOTV = Small
Landerand Orbit Transfer Vehicle.
2 Plus externally mounted cargo pods.3 80 m wide and high with
rotating booms fully extended.4 Own design. Payload can be a small
( 1 kt) nuclear warhead, a 3 megaton antimatter warhead, kinetic
impactor projectiles or
attack nanotechnology.5 Short burst launch or evasion
acceleration.
Table 3: Energy storageEnergy source Specific power Power
density Specific energy Energy density
Fission 2.5 kW/kg 12.5 MW/m3
Fusion 200 kW/kg 1 GW/m3
Antimatter 372 kW/kg 1.86 GW/m3 4.5 PJ/kg 22.5 EJ/m3
Chemical fuels 10 MJ/kg 20 GJ/m3
Nuclear isomers 10 GJ/kg 100 TJ/m3
5
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per second and ve is the reaction massspeed. The thrust force F
= mveproduces an acceleration a = mve/Mon the spacecraft (of mass
M). Fora given acceleration and reaction massspeed the power is P =
(1/2)Mave.Expressed in terms of Isp, F = Ispm
g(where g 9.82 m/s2 is the gravita-tional acceleration at Earths
suface)a = gIspm
/M , m = aM/gIsp, andP = (1/2)gaMIsp.
This allows us to estimate thepower requirements of spacecraft
ifwe know their mass. Consider afusion-powered spacecraft. It has a
=0.05G 0.5 m/s2, Isp = 100, 000 s.A fully loaded bulk carrier with
totalmass 90 106 kg will hence require anoutput of 9 GW during full
thrust, anenergy output of 100 W per kg of shipmass. In practice
bulk carriers likelysacrifice exhaust velocity and powerfor
economy, so the output will be farbelow this level.
Antimatter-poweredships produce comparable energy out-puts (at
least in terms of propulsion,since the mechanism is relatively
simi-lar). The Destroyer, weighing 40,000tons, implies a reactor
power of 800GW.
As a comparision with existingtechnology, a Nimitz-class
aircraft car-rier produces 190 MW and a major nu-clear power plant
can reach 8 GW. Itis probably safe to assume that largeships have
reactors that can producepower up to the terawatt range Mostof this
energy is likely only availablefor propulsion rather than
poweringweapons due to the problems of con-verting it to
electricity. There are alsogoing to be efficiency losses leading
tolarge amounts of waste heat. Assum-ing 90% efficiency still
requires hun-dreds of gigawatts of cooling. Hencewarships are
unlikely to use their re-actors at full power during battle,
inorder to avoid having to unfold very
noticeable and vulnerable large radia-tor surfaces. The amount
of availableweapon power is still going to be verylarge.
As shown below, there are goodtactical reasons for wanting to
accel-erate quicker than allowed by fusionor antimatter drives.
This can beachieved by using high g-thrusters suchas metallic
hydrogen: while the mainengines aim at a very high exhaust
ve-locity to keep reaction mass require-ments down while achieving
a high v,these engines are intended to use lowvelocity reaction
mass to make a fewbrief but strong changes in ship veloc-ity. The
total v is negligble sincethey cannot be sustained for long,
butthey allow rapid evasive maneouvers.Also, main engines can in
some casesbe supplied with more reaction massthan normal to produce
short burstsof acceleration.
3.1 Reactor sizes
What is the size of capital ship re-actors? For fission reactors
the spe-cific mass is around 40 kg/kW, al-though advanced vapor
core reactorsmight go down to 0.4 kg/kW. Accord-ing to R.W.
Bussard6 the fusion reac-tor specific mass could be 0.05 kg/kW.For
the transports 10 GW reactor theweight would be 500 tons.
The destroyer is antimatter pow-ered, and assuming the whole
reactor isabout the size of the containment sys-tem we get a
specific mass of 0.0025kg/kW for antimatter power.
Assuming a density of the reactorto be about 5000 kg/m3 a 10 GW
fu-sion reactor would be 100 cubic meters,or a 4.6 4.6 4.6 cube. In
practicethe reactor will be far more extended,since these estimates
mainly deal withthe core. Containment, control, cool-ing systems
etc. will probably be at
6http://www.askmar.com/Fusion_files/FusionElectricPropulsion.pdf
6
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least ten times as large (but also oflower density). Similarly,
older reac-tors will also be much larger.
It should be noted that small vehi-cles like fighters and
missiles likely useother energy sources. An antimatter-powered 1
ton reactor could provide upto 370 MW of power, but for maxi-mal
acceleration various chemical fu-els (such as burning metallic
hydro-gen) would be more effective. Giventhe available technology
high energy-storage densities are possible, proba-bly on the order
of 10 MJ/kg (corre-sponding to computed explosives suchas
dinitroacetylene, octanitrocubaneand octaazacubane and still
smallerthan lithium-fluorine combustion). Foreven higher densities
nuclear isomerstorage might be possible.
This table sums up the above con-siderations. The specific power
ofchemical fuels and nuclear isomers de-pends on the rate of
reaction and canin principle become very high when re-leased
explosively.
3.2 Exhaust temperature
A sizeable fraction of the energy out-put is going to be present
as heat in theexpelled reaction mass. Rocket noz-zles of chemical
rockets can achieve 60-70% efficiency as heat engines convert-ing
heat into velocity. The remainingenergy will largely be carried
away byreaction mass. If the efficiency is andthe power is P , then
the exhaust willhave temperature
Texhaust (1 )P/Cm
where C denotes its specific heat ca-pacity in J/kg K.
For the Destroyer, expelling 40kg/s hydrogen at 60%
efficiencyTexhaust = 560, 000 K. This is a hardUV source and not
far from a particle
beam weapon. At distance d, assumingthe exhaust radiates
spherically, the in-cident energy is (1 )P/4pid2 W/m2.In this case
it is 25 MW/m2 at one kilo-meter distance, enough to vaporise
thesurface of steel7. This is why cooling isso essential for
accelerating spaceships.
Jons law: Any propulsion systempowerful enough to be
interesting, ispowerful enough to be a weapon.
3.3 Cooling
A key problem for all spacecraft withhigh power is cooling since
space is aperfect thermal insulator. While someengines (metallic
hydrogen, fusion, an-timatter) carry away a sizeable frac-tion of
the power as heat in the ex-haust, most ship power plants will
pro-duce vast amounts of waste heat thatmust be removed8. As a
rough ap-proximation, assuming 50% efficiency,the same amount of
power the reac-tor produces for the engines and otherforms of
usable work is also producedas waste heat. Radiators radiate
wasteheat into space but have an upper ac-ceptable temperature
Tmax. This re-quires a total radiator area larger thanArad =
P/T
4max where is the emis-
sivity (likely chosen close to 1) and = 5.67 108 W/m2K4 is
Stefan-Boltzmanns constant.
Using liquid lithium as a coolantgives Tmax = 1600 K. For P
=800GW Arad =2.15 million m
2, re-quiring multi-kilometer fins (or dropletradiators, where
sheets of droplets ofmolten metal are allowed to drift fromemitters
to collectors). The fighterrequires 45 m2 of radiators when us-ing
full power, not too different fromfighter plane wings. Using
thermalconduction in 3000 K tungsten thefighter can reduce the
radiator area to3.6 m2.
7http://panoptesv.com/SciFi/DamageAverage.html8There will also
be separate radiators for cooling low-temperature sections of the
ship such
as the life support system, but they are negligble compared to
the main radiators.
7
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In practice radiators of militaryships are foldable, fully used
onlywhen doing main accelerations andcompletely folded back when in
bat-tle mode for maximum protection andminimum emissions. Since
most bat-tles are very short this is usually justa minor problem,
but if the situationpersists overheating begins to becomean issue
(see section on cooling and in-ternal storage of heat). Damage
thatprevents full unfolding after a battleseverely limits course
changes.
Calculations by Nemtos9 for morerealistic tapering cooling fins
find thatthe total flux that can be radiated is(4/5)LT 4 where L is
the width ofthe fin. This gives a total mass ofL0/3, where 0 =
(8/5)L
2T 3/is the thickness of the central con-densing channel, is the
density and is the thermal conductivity of thefin material. Using
liquid potassiumas coolant (T = 1000 K), pyrolyticgraphite ( = 400
W/m, = 2200kg/m3) as a heat conductor and whiteceramic ( = 0.95) as
a surface mate-rial allows radiating away 43 kW/m2.Smaller fins
were much more efficientin terms of energy release per weightbut
require more extended pipe sys-tems since they need to be
extendedfurther out.
Liquid droplet radiators were es-timated to require about 50% of
thecooling fin mass. Since the dropletsloose energy faster when
they are hotit is more effective to build compactradiators with a
flight time around asecond. Given some of the limitationsof
droplets screening each other it wasconcluded that it could radiate
away20 kW/m2 when using liquid tin atT = 1000 K. Droplet radiators
arehence preferable over cooling fins whenmass budgets are an
issue, such as insmall ships.
Another cooling method is to heatcoolant and dump it into space.
Us-ing hydrogen 14.30 103 J per kilogramand Kelvin can be
removed10. Heatingmetallic hydrogen to 10,000 K wouldremove 143 MJ
per kilogram. As anexample, the 800 GW Destroyer wouldneed to
vaporize 2,797 kg/s for cool-ing. This is impractical for
normalcooling, but acceptable during combatwhere radiators are not
available (andthe detectable coolant emissions areovershadowed by
the main engines).The fighter requires 0.06 kg/s (assum-ing 50%
efficiency). It only got about4 tons of MH fuel, so it gets just
18hours of cooling even if it doesnt useany hydrogen for
propulsion.
Cooling through expelling coolantsis particularly useful for
cooling lasersand railgun weapons during battle, es-pecially if
they are disposable. It isworth remembering that if you need
XJoules to harm your enemys ship youwill have to dissipate X(1)
Joule ofheat at home, where is the conversionefficiency of the
weapon.
9http://nemtos.ouvaton.org/techfiles/Cooling_Systems.pdf10I am
ignoring the complications of different thermal capacity at
different temperature
here.
8
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4 Detection
Detection of enemy spacecraft and as-sets is of central
importance. Unlikeon a planet there is no intervening ma-terial
that blocks radiation emissions,but the sheer volume of space
compli-cates things. There are often tradeoffsbetween how wide part
of the sky canbe scanned, how exact positions can bedetermined and
the time it takes.
4.1 Sensors
Passive sensor systems collect energyfrom particular directions,
sum the to-tal energy and try to tell whether thereis a
statistically significant differencefrom the background.
The signal to noise ratio (S/N) fora sensor collecting photons
such as aCCD sensor is
S/N =Ft
(Ft+Bnpt+Btnp +Dnpt+R2np
where F is the average photon fluxfrom the source (photons per
secondper square meter), t is the time inter-val of the
measurement, B is the fluxper pixel per second from the sky
back-ground, Bt is the flux per pixel fromthe telescope itself, D
is the dark cur-rent flux (due to the CCD array itself),R is the
readout noise per pixel and npis the number of pixels11.
Typicallyuseful observations begin to be possi-ble at S/N > 5,
although guessing thatsomething might be there is possible atS/N =
2 or 3 (but estimates of energyand other properties will have 50%
er-rors). In Eclipse Phase sensors can beassumed to be nearly
perfect - B,Bt,D,and R are small, and every photon iscaught and
turned into a measurableelectron.
For sensors with very low noise,a dark sky background and a
rela-tively bright source the S/N ratio isFt. The time needed to
reach a use-
ful S/N is on the order of 1/F sec-onds. If the sensor looks for
pho-tons of wavelengths in an interval (its bandwidth), has a
collecting ra-dius r and the source has a flux ofFs photons/m
2/ m/s then the timeis on the order of 1/piFsr
2. As rincreases the sensor can tell whetherthere is something
there faster.
As an example, for infrared light = 1 m (most sensitive to a
3000K body), a bandwidth of = 1 m(a broadband sensor) and radius r
= 1m the sensor needs about 300,000 pho-tons in order to detect the
target in onesecond.
If the sky background is significantcompared to detector noise,
then thetime needed scales as Bnp/F
2. Thistends to scale as 1/r2 for large tar-gets and 1/r4 for
targets so small theyare limited by diffraction: larger pho-ton
collectors are significantly faster.Typical backround sky fluxes in
the so-lar system are between 109 106Watt/m2 per steradian in the
mi-crowave to UV range of interest tospacecraft detection12. For
lukewarm(300 K) objects the heat radiation inthe zodiacal light is
the main confusingfactor, while hotter (3,000 K) objectsare
confused by the background of re-flected sublight, faint stars and
galacticcirrus. In order to be visible againstthe backround the
flux density fromthe target needs to be above 12,000 -3 108 photons
per square meter at thedetector. [develop!]
The time it takes to achieve a given
11http://www.physics.mq.edu.au/current/undergraduate/units/ASTR278/10_ASTR278_
JL_5_Sensitivity.pdf See also The Design and Construction of
Large Optical Telescopes,ed. Pierre Y. Bely, Springer 2003
12Ch. Leinert, S. Bowyer et. al. The 1997 reference of diffuse
night sky brightness, Astron.Astrophys. Suppl. Ser. 127, 1-99
(1998)
9
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S/N is
tdetect = (S/N)2 1
F
(1 +
B
F
)The Planck radiation law gives that aspherical object of radius
r and tem-perature T at distance R will producea spectral flux
of
F =2pic
4(ehc/kT 1)( rR
)2
wavelength photons per square me-ter (here I assume is small
enough;for broadband detectors F needs tobe integrated over all
sampled wave-lengths). If there are several partsof the object of
different temperaturetheir spectral fluxes can be added to-gether.
Note that for best performancethe detector needs to look at a
smallangle of the sky, since the backgroundflux will grow with the
angle.
In order to calculate whether detec-tion is possible we need
some estimatesof the thermal emissions of spaceships.
4.2 Thermal emissions
A spacecraft or other object radiat-ing at power P uniformly in
all di-rections will produce a total flux ofFtot = P/4pid
2 W/m2 at distance d.A ship of temperature T and surfacearea A
will radiate AT 4 W of ther-mal radiation, or Ftot = AT
4/4pid2.Typically a ship on full power will
have extended radiators at tempera-ture Tmax (and enough area to
handlethe power). For reasonable Tmax be-tween 1,000 and 3,000 K
the peak fluxis between 1-3 m IR radiation.
A ship that is merely coasting willhave an energy output much
belowthese levels, but still significant. Eachbiomorph onboard
produces around100 W, not to mention life support. Arough guess at
the energy dissipationis about 1 kW per crew member. Thiswould put
the Destroyer minimal en-ergy dissipation at 9 104 W and the
fighter at 1 kW. These limits can prob-ably be pushed for short
spans, espe-cially by using heating internal coolingreserves (see
below). The internal en-vironment will also be maintained ata
temperature around 300 K throughheating or cooling, and this will
likelycontribute to a harder to shield surfacetemperature.
4.3 Exhaust emissions
An accelerating ship will be leaving along trail of energetic
hydrogen, chem-ical exhaust or plasma behind it, andthis will have
detectable black-body ra-diation. Even if the ship itself is
per-fectly caumoflaged the thermal emis-sion (and its doppler
shift, allowing acalculation of relative velocity to theobserver)
will be detectable.
Exhaust temperatures go down as
Te(t) =1
3
3A(t C)/K
where t is the time, A is the area ofa one second parcel of
exhaust, K isthe thermal capacity of it (J/K kg)and C = K/AT 30 is
a constant setso that at time 0 the temperature isthe initial
exhaust temperature T0. Forhigh temperature exhaust it is a
goodapproximation to treat it as releasingnearly all its energy
instantly at tem-perature T0. This tends to dominateother radiation
sources, especially forshort-wavelength emissions.
4.4 Sunlight
Internal heat becomes dominantroughly around the orbit of
jupiter.Inside that orbit reflected sunlight is asignificant source
of radiation of totalpower P = SA/R2 W at solar distanceof R AU,
sunward ship area A and so-lar constant S = 1.366 103 W. If theship
or object has albedo it will re-flect Preflect = SA/R
2 W, which is
10
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can be very visible. The reflected sun-light might however be
made highlydirectional, for example by placing aplane mirror in
front of the object.
The absorbed sunlight, Pabsorb =(1 )SA/R2 kW, will turn into
heatthat is emitted largely homogeneously.The resulting temperature
due to theabsorbtion (assuming equilibrium anda spherical object of
radius r) will be
T =
[S(1 )4R2
]1/4where is the emissivity (typicallyclose to 1 for dark bodies
and down to0.02 for polished silver). In Earth orbitfor a high
reflectivity object with =0.9999 with low emissivity = 0.02
theequilibrium temperature is 74 K. For ashiny metal object with =
0.75 and = 0.9 T = 168 K.
Inner system civilian spaceshipsand equipment are often made
white orreflective to keep solar heating down,while outer system
ships can be anycolor they like. Military ships will havereflective
mirrors and dark, absorbentcoloring in order to be stealthy
duringcertain phases of battle.
4.5 Sensor sizes and skyscanning
Ideally sensors should cover the entiresky and watch
continously, but theyare limited by the conflicting demandsof
having large apertures that cancollect many photons (a large
lightbucket), a narrow angular field ofview to avoid too much
backgroundnoise and the physical practicalities ofwhere to attach
sensors to spacecraft.For habitats and defense systems it
ispossible to put large numbers of bigsensors in place covering
most of thesky, but a spacecraft and in particulara mobile asset
such as a missile will nothave much space.
As an example, the WMAP satel-lite has a 52.8 arcminute beam
sizefrom its 2.24 m2 sensors: this corre-sponds to 1 part in 67,827
of the entiresky. If it were to make a quick one sec-ond scan of
each part it would need 18hours to do a full sky scan.
For a large ship in Eclipse Phase af-fixing a few square meter
size sensorsdoes not appear to be a major problem;assuming 1% of
the ship surface is usedfor sensors would allow the Destroyerto
have 75 m2 sensors and the fighter0.14 m2. If we assume 8 sensors
onthe Destroyer (one scanning each oc-tant of sky) they would have
a 9.4 m2
area each. These would be the highsensitivity deep scan sensors:
in directbattle more numerous, disposable sen-sors would be
deployed for point de-fense control against incoming missiles.
Full sky scans at long distance donot have to be instant.
Assuming a fullsky scan takes an hour, standard trans-ports can
move 1,400,000 km, destroy-ers 2,900,000 km, fighters 40,000
km,fast couriers 5,800,000 km and missiles110,000 km. This is more
than enoughto detect them before they can getclose. Once detected
sensors can trackthem more intently, estimating theirtrue speed,
course and other proper-ties.
A sensor covering one octant of thesky in one hour will watch
0.000436steradians of sky per second, a field ofview of about 1.2
degrees side.
One issue is detecting that some-thing is an interesting target
and notjust random debris, a space habitat ora remote star. A first
step is to com-pare the position with a detailed ob-ject catalogue,
which allows the sensorto ignore all known objects. The nextstep is
to compare the spectrum to pos-sible ship profiles. Active
spaceshipshave different emissions from debris -infrared from
internal energy produc-tion, short wavelength emissions fromthe
drive, hot radiators, doppler effect
11
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from high velocity etc. The scannerwill distribute its scanning
time be-tween investigating objects of interestat length and
jumping past empty orblocked directions.
4.6 Ship spectra and de-tectability distance
Putting the above considerations to-gether, we get the following
approxi-mate fluxes from the ships of EclipsePhase.
I here assume the target ship is 1AU from the sun, 1 AU from the
detec-tor, has albedo 0.5, that the radiatorsare fully extended and
the ship is accel-erating maximally. The emissions con-sist of
thermal emissions from the radi-ators, emissions from the ship
(largelydue to absorbed sunlight), emissionsfrom the exhaust and
reflected sun-light. The sensor is assumed to be a0.000436
steradian sensor with 1 m2
area, bandwidth 1 and desired S/N =5. Background noise is
assumed to be106 W/m2 sr.
Manned ships can be detected overinterplanetary distances using
an IRsky scan that takes one hour. Typi-cally ships have a
characteristic multi-temperature spectrum: one peak forthe hot
engine exhaust, one for the ra-diators, one for the reflected
sunlight.
Reflected sunlight and the radia-tors are the biggest
contributions: aship that has folded most of the radia-tors,
reflects away sunlight with a mir-ror, powered down to a minimal
leveland cooled the surface to a few Kelvinis significantly harder
to detect. TheDestroyer is just barely detectable at0.09 AU
distance (13,000,000 km) inthis case, and the fighter at 60,000
km.This means that stealth can be prof-itable, at least in the
light of cloudcombat: a silent approach allows asurprise launch of
attack assets in acloud large enough to be hard to evadefor the
enemy. The fighter is notquite stealthy enough to reach a
targetwithout being discovered, but it has achance to close to a
very short rangeand launch a barrage of missiles.
4.7 Scanning limitations
These estimates assume overload-freesurroundings. As soon as the
bul-lets start to fly any sensors this sensi-tive will be blinded
(quite possibly de-stroyed) if they look anywhere close
todetonations.
Note that not all directions areavailable for scanning: thermal
sensorspointing at the sun or nearby plan-ets will be blinded. In
deep spacethis is a minor problem, but in thevicinity of planets
distributed sensorsare necessary to keep watch over localspace. The
number of objects is alsofar larger, turning scanning into moreof a
pattern recognition problem thana detection problem.
A ship that is accelerating is mostly
blind backwards due to the exhaustcloud. The blind angle is
determinedby how fast hot particles from the ex-haust spread
laterally relative to howfast they move backwards. It is afew
times13 = 2 arctan(
kT/mv2e)
where T is the exhaust temperature, mthe mass of the exhaust
particles andve the average exhaust speed. For fora hydrogen-oxygen
engine at 3000 Kwith ve = 450, 000 m/s 0.3 whilefor an antimatter
rocket with a millionK hydrogen plasma moving back at 108
m/s 0.1. Hence the blind angleis a few degrees across.
Sensors must also be placed so theyare not blinded by unfolded
radiatorfins. These cover a far larger partof the sky but can be
avoided by for
13Since the Maxwell-Boltzmann distribution extends beyond its
average value.
12
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Figure 1: Quanta received by a 1 m2 sensor at 1 AU from
different ship types atfull acceleration. The red line is the
zodiacal light background, giving a roughestimate of the noise.
Figure 2: Time until a 1 m2 sensor at 1 AU can confidently
detect different shiptypes at full acceleration. The red line is 1
second scanning time.
13
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example placing sensors at their ends(gaining parallax
information in addi-tion).
4.8 Particle emissions
Antimatter annihilation does not justproduce the desired gamma
photons,they also produce pions and muonsthat decay while radiating
neutrinos.Fusion reactors also produce neutrinosfor some fusion
reactions (pure helium3 reactions avoid it, but reactions
withhydrogen may release neutrinos). Thismeans that even if a ship
hides itsplasma tail it will radiate a neutrinosignature. Given
Eclipse Phase tech-nology such as emergency farcasters weknow that
neutrinos can be detectedover interplanetary distances. How-ever,
it may be hard to get a good posi-tion from neutrinos, so the enemy
willjust know there is an active antimatterreactor somewhere. Note
that muondetectors would be effective at detect-ing active
antimatter annihilation overdistances of a few kilometers,
helpingmissiles to zoom in on active antimat-ter reactors.
4.9 Railgun projectiles
Railgun projectiles can in principlebe detected by their heat
emissions.When accelerating a projectile to ve-locity v, (1/2)mv2 J
of work is done.A fraction f ( 1 but > 0) of thiswill turn into
heat. The temperaturebecomes T = (1/2)fv2/C, where C isspecific
heat capacity ( 500 J/kg Kfor metal). If f = 1% and v = 10km/s, the
result is bright 1,000 K pro-jectiles. For v = 100 km/s f mustbe
much less, since otherwise the pro-jectile would be a vaporized
mess. Iff = 104 the faster projectile will also
be 1,000 K.
The only thing making them hardto see is their small area.
Assumingthe visible area is 10x10 cm, thenthey can be detected
4,487,940 km [check, update - old equation insteadgives
13.4*0.1*500 = 670 km away.That gives you 67, 6.7 or 0.67 secondsto
point defence them. At least forprojectiles slower than 100 km/s
thisis pretty OK for the defender. ]
current railguns have plasmaflashes 23,000-35,000 K, blackbody
ra-diation 1.6-8.1 MW/cm2
4.10 Active sensors
Active sensors are a dead give-awayof where you are (unless they
man-age to mimic natural EM activity),but the sensors can be put on
an ex-pendable buoy (and triangulation oftargets from dispersed
sensors is sig-nificantly more accurate). Stealthingagainst
radar/twave/lidar/Xdar on allwavelengths is not going to be
practi-cal.
Unfortunately active sensors havea shorter range than passive
sensorssince the radiation emitted decreasesas the square of the
distance and thenthe reflected radiation also decreaseswith the
square of the distance, giv-ing a return signal that scales
like1/d4. In order to double the range thepower has to be increased
16-fold. Theradar equation describes the limitingdistance where an
active sensor can de-tect a target:
dradar =
[PSG
22
64pi3Pm
]1/4where PS is the power emitted, G isthe antenna gain, is the
wavelengthused, is the radar cross section of the
14A way around this is to use bistatic radar, where the signal
emitter and receivers are indifferent locations: sensors close to
the target will receive a stronger signal. This requires thatthe
sensor cloud is at least as large as the basic radar range to
work.
15http://www.fas.org/spp/military/program/track/pavepaws.htm
14
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target and Pm is the minimum receivedpower that can be
detected14.
A current missile and satellitetracking system like PAVE
PAWS15
uses a peak power of 582 kW, a fre-quency of 420 Mhz ( = 1.4 m)
andhas a range of 5500 km. Scaling itup to a 1 GW radar would
increase therange about 6-fold, to 35,000 km. Notethat shorter
wavelengths have shorterranges: a teraherz version would havea
range of just 113 km, while one using30 kHz would have a range of
650,000km.
While having a long range may ap-pear useful, it also includes
more po-tential targets and more clutter. Ina space battle active
sensors are moreuseful for pinpointing nearby incomingprojectiles
and direct defensive fire onthem.
There is also a trade-off betweenrange and resolution. The
angular res-olution is 1.22/L, making the kHzradar useless for
detecting direction.The range resolution is c/2B whereB is the
signal bandwidth, 1/.Shorter, more high frequency pulseshave higher
bandwidth; a radar with 1m range resolution needs a frequencyin the
150MHz band. Point defenseradar needs very accurate position
andDoppler measurements and will hencehave a short range.
4.11 Stealth
Reducing the profile of a ship or assetrequires reducing
emissions that can beseen with passive sensors, and prevent-ing
signals from active sensors frombouncing back with revealing
informa-tion.
Stealthing against active sensorsworks if you can absorb the
signalwell enough or reflect it in a safe di-rection, reducing the
radar cross sec-tion. Thanks to metamaterials and ad-vanced
materials science this is oftenpossible - for particular
frequencies.
It is generally not possible to stealthagainst all frequencies,
so if the en-emy uses the wrong sensors the invis-ible object will
be obvious. Some mil-itary ships can reconfigure the
surfacemetamaterials to adapt to expectedopponent strategies but
the process isnot instantaneous, taking minutes tohours.
4.11.1 Anisotropic radiation
Averaged over time the total power ra-diated by an object must
equal the to-tal power generated. It is possible tocool a ship
surface (at an energy cost)and radiate the heat into particular
di-rections, and to store heat into tanksfor a while. However,
these stealthmethods have serious limitations.
A ship of power P that emits itspower as a blackbody will have a
sur-face temperature T = [P/A]1/4 whereA is the total surface area.
Usingonly a fraction f of this area increasesthe temperature of the
hot surface byf1/4 and the flux will be P/f W/m2.
[extend]
4.11.2 Cooling
Cooling the surface using a cold reser-voir at temperature TC
has maximumtheoretical efficiency = T/(T TC).The amount of work
needed to reducethe heat of the surface is W = Qwhere W is the work
if the heatpump and Q = KT is the changeof heat in the surface (K
is the ther-mal capacity). Putting this togetherthe energy cost of
cooling from Thot toTcool is
W = K
ThotTcool
T/(T TC)dT
= K
[TC ln
(Thot TCTcold TC)
)+ Thot Tcold
]A typical spacecraft temperature in
Earth orbit varies between 173 K and
15
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393 K depending on light and shadow.Using an average of Thot =
283 Kand cooling to Tcool = 3 K using areservoir at TC = 1 K would
takeW = K[2.15+280] J of energy. Assum-ing a radius 20 meter
spherical shipwith specific thermal capacity around1 kJ/kgK,
density 1.2 g/cm3 and thatonly the top cm need to be cooled, Kis
about 60,000 and the total energycost for cooling down to stealth
tem-perature is 17 MJ.
During stealth mode the power hasto be fed directly to the
cooling tank.It will last for KCM/P seconds beforeincreasing in
temperature by 1 Kelvin(where KC is the specific thermal ca-pacity
of the cooling substance, M thetank mass). Since TC is so low it
willbe enough for a few Kelvins of increaseto get above the desired
stealth tem-perature Tcold (and the efficiency ofcooling
drastically decreases). Usinghydrogen, which has the best
specificheat capacity KC 12 kJ/(gK) andP = 30 kW (power of a
one-man he-licopter), the ship uses up 2.5 kg ofcoolant per second.
A one hour stealthepisode would require 1,440 kg (21 m3)of coolant.
Assuming a more energeticship of P = 140 MW (Boeing 747) therate is
12,000 kg/s, and the above ra-dius 20 ship would at most
(assumingit to be entirely filled with coolant) last187
seconds.
[cooling lasers are too inefficient- compare heat capacities.
Electro-magentic thermal radiation has ef-fective volumetric heat
capacity of32pi5k4T 3/15(hc)3. ]
4.12 Parallax
Determining the position of somethingin space will be dependent
on resolv-ing its location. The resolving powerof a telescope is =
1.22/D where is the wavelength and D the diame-ter of the
telescope. Parallax distanceerrors are d /2. For the ideal
case of a target at orthogonal distanced to a spaceship of
length L with twotelescopes at the sides, 2L/d andwe get d
0.305d2/DL2.
For a baseline of 100 m, looking at = 105 (300 K blackbody
radiation),D = 1 m and d = 10 km the uncer-tainty in distance is
about 3 mm. Atarget at 1000 km distance will how-ever have
uncertainty of 300 metersand at 10,000 km the uncertainty ismore
than 30 km - far too much for anyuseful targeting of even a
ship-sized ob-ject.
Turning the formula around, as-suming umax to be the
maximumacceptable distance uncertainty, themaximum range where
targets can behit is
dparallax = LDumax/0.305
Note that increasing L increasesdmax proportionally: having
sepa-rate sensors imaging the same targetfrom widely separated
vantage pointsgreatly extends the range from which itcould be hit.
By using multiple sensorsand data fusion this range can be
im-proved further to some degree. Largertelescopes and shorter
wavelengths aremuch less effective.
4.13 Hiding from manyeyes
If the enemy is known to be watch-ing from a particular
direction it mightbe possible to reduce detection prob-ability by
carefully aligning a mirrorto hide the emissions of the ship
(andavoid reflecting other bright sources),avoid accelerations and
use stealthingagainst active sensors. Similarly it issometimes
possible to approach (or de-part) from an observer along the
direc-tion towards the sun, planets, stars oreven hiding in the
zodiacal light (as-suming very low emissions; it has apower around
0.0005 W/m2).
16
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However, as the parallax sectionshows, there is a great
advantage inhaving multiple sensors scattered overa long distance.
If the sensors are adistance L apart and the angular di-ameter of
the background object is ,then the hiding ship must be more
dis-tant than
dhide = (L/2) tan(pi/2 /2)to hide from both. In the case of
theSun in Earth orbit, for L = 100mdhide =10.7 km, while a 10 km
base-line forces a hiding distance of morethan 1,000 km. At Jovian
distancethe distances are about 5.2 times largerand at Saturn 9.2
(as a rule of thumb,just multiply by the distance to thesun in AU).
Hiding in planetary lightis harder: using Venus or Jupiter tomask
an approach near Earth has adhide 300 km for 100 m baseline anda
30,000 km distance for a 10 km base-line. Using red giant stars
will notwork within 400,000 km even for near-sighted L = 100 m
spaceships16.
Multisensor detection depends notjust on failure to keep away
from back-grounds that produce contrast, butalso whether the sensor
network candetect a discrepancy and flag it as in-teresting. The
larger the number ofsensors the higher chance one of themwill
detect something interesting, butat the same time the amount of
datato be processed and the number of er-rors will increase. If
there are N sen-sors and each has a probability p persecond of
generating a false positive(crying wolf) the probability persecond
of avoiding false alarms will bejust (1 p)N . In practice very
sophis-ticated data fusion algorithms can beused to get robust
estimates, handlingfaulty or even suborned sensors (c.f.
the Brooks-Iyengar algorithm, whichworks up to N/3 faulty
sensors). How-ever, the best algorithms also requiresignificant
network bandwidth as eachsensor needs to communicate with ev-ery
other.
[fake blackbodies] [metamaterials][occultation probability]
[directionalradiation] [changing direction]
4.14 Spoofing and jamming
While correctly imitating the exhaustplume from an accelerating
spacecraftis hard (the luminosity, spectrum anddoppler shift need
to match the orig-inal, and this requires essentially thesame
engine and performance as theoriginal) in the high-noise
environmentof a space battle it is likely possible toproduce
distracting or apparently sim-ilar phenomena. This might
misleadsensors, targeting systems or point de-fenses.
[spoofing doppler] [spoofing back-ground] [confusing
sensors]
It is easy to clutter radar and IRby releasing chaff that
reflects signalsstrongly or in the right wavelengths.Exactly how
well chaff works dependson the signal processing abilities of
theenemy.
In particular, sensors are easilyblinded by bright detonations
or de-liberate scorch attacks with beamweapons. This either
permanentlydamages them or leaves them blind un-til they recover.
Having replacementsensors that can be opened when thecurrent one
are down will be necessary,but still introduces a short delay of
ob-servation. Assuming a fully functionalC3I system one side can
time closingsensor ports with the arrival of en-ergy from their own
detonations, giv-
16Of course, the ship or object has to have an angular diameter
much less than the back-ground for this trick to have a chance.
17As a simplistic example, sensors could be watching during even
seconds and attacks timedto occur during odd seconds. In practice
the pattern would have to be pseudorandom andtake lightspeed delays
into account.
17
-
ing itself an advantage. This is easierwith QE signalling, but
even withoutit some synchronization is possible17.
[overwhelming point defenses withlarge clouds of objects
If point defenses can drill X me-ters of object per second, then
attack-ing with more than that (per second)will allow a hit on the
ship. ]
18
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5 Weapons
The forms of weapons available forranged space battle are
lasers, railguns,particle weapons, missiles and
fighters.Nanoweapons can be included in rail-gun and missile
payloads.
5.1 Independent weaponbuses
Weapons can either be placed on theship, or on free-flying
weapon buses.Placing offensive assets outside theship has the
advantage of allowingshots at closer range and without riskto the
main ship, but also limits theamount of energy they can
providesince they are too small to contain re-actors.
Chemically stored energy is on theorder of 20 MJ/kg (20 GJ/m3)
whilenuclear isomers could reach 10 GJ/kg(100 TJ/m3). A volume V
weaponwith energy density and efficiency (likely < 0.5) will be
able to fireN = V/Eattack attacks of energyEattack. The remaining
(1 )V en-ergy becomes waste heat; the resultingtemperature (T = (1
)/C whereC is the heat capacity in J/m3) of theweapon will scale
proportional to theenergy density of storage. Using largeamounts of
energy makes the weaponheat up significantly, making it hard tohide
(in addition to energy release fromorientation thrusters). Most
weaponsare hence intended to fire just a singleburst attack and
then coast away onthe recoil.
Missile buses also have this disad-vantage, but to a lesser
degree: mis-siles can be launched quietly from astealthed bus using
springs or cold gas
and their engines activated at a dis-tance from the bus. The
main useof a missile bus rather than individ-ually drifting
missiles is that the buscan be equipped with maximal
stealth,hopefully drifting close to a tacticallyimportant volume
before releasing themissiles18 (at the price of risking los-ing all
missiles to an unexpected at-tack: some bus designs have an
emer-gency eject function that releases themissiles prematurely if
the bus comesunder attack).
[railguns in space can be made long][snap open phased arrays -
since
disposable device, little need keep lowprofile after firing]
5.2 Lasers
[Expand, update]Laser weapons work by either heat-
ing a target to an unsustainable tem-perature (which requires a
long lockon the same spot providing more than108 W/m2 over a second
or more), arapid energy impulse causing a localplasma detonation
(requires on the or-der of 1013 1014 W/m2) or drillingthrough the
outer shell (requires an en-ergy density of LEeap W/m
2 where Lis the desired drilling distance per sec-ond and Evap
is the energy needed forvaporisation per cubic meter).
5.2.1 Sources
Laser beams can be generated usingsingle laser cavities or
phased arrays.Laser cavities contain a gain mediumwhere atoms,
molecules or free elec-trons are placed in an excited energystate
and then stimulated to decay toa lower energy state, releasing
electro-magnetic waves that trigger other de-
18There is some potential for game theory in whether to launch
all missiles or leave oneas a surprise later launch. A revealed
missile bus is easy to hit and hence has little valueto store a
surprise in, but in a situation where long-range defenses are busy
(since there areapproaching missiles) it would be a low priority
target. This leads to a mixed strategy equilib-rium where the
missile side randomly leaves surprise missiles and the defender
side randomlydecides whether to shoot at the worthless target.
19
-
cays and shoots out as a beam. Thisis relatively simple but has
the prob-lem that to function the cavity needsto be resonant: the
waves must beable to bounce between the front andback to produce a
resonance, and thismeans the cavity itself will need to re-sist the
laser power. Worse, puttingthe medium into an excited state
in-volve big energy losses that also heatsthe medium. Hence large
amounts ofcooling are needed.
Phased arrays make use of manysmaller lasers or antennas,
producing abeam by combining many small com-ponents accurately. For
lasers phasedarrays need to be manufactured usingnanotech
metamaterials.
5.2.2 Beam optics
(Gaussian) laser beams have a diver-gence angle of /piw0 where
is thewavelength and w0 its smallest width.If the laser is produced
by a lensof width L it will produce a spotsize at distance d w =
d/2piL andwith intensity piPL2/2d2 W/m2 ifP is the total beam
power. Short-wavelength lasers remain sharp overlonger distances
than long-wavelengthlasers, and in space it is possible to goall
the way down the the vacuum fre-quencies of UV around 108 m thatare
strongly absorbed by air and othermatter. Large lenses allow
tightly fo-cused beams. However, with the nan-otechnology available
in Eclipse Phasephased array lasers are possible: manysmall
elements producing parts of thebeam, possibly focusing it closer to
thesource if needed (this also allows higherpower densities at the
target than atthe source, always a nice thing for aweapon). With a
size L array focusedon the distance d target the focal widthis w0 =
2d/piL and the length of thefocal region is L2/42.
[example, showing that the regionis usually long]
When firing a laser the ideal beamwidth at the target is wopt =
2(v)d/c,the uncertainty in target lateral veloc-ity v times the
lightspeed delay be-tween the target and laser (if there
areQE-linked sensors shortening the de-lay this is reduced further
down to aminimum of (v)d/c). If the velocitymeasurement is perfect
there is still av < 2ad/c due to unknown accelera-tions since
last observations (with QEthe factor 2 approaches 1). So the
op-timal beam width will be
wopt = 2(v)d/c+ 4ad2/c2
However, close to the laser theactual beam width will be
limitedby the focal width of the beam,giving a beam width at the
tar-get of min(wopt, 2d/piL. The dis-tance beyond which velocity
uncer-taity dominates is d = (c2/2piaL) (c(v)/2a). Typically this
dependson the beam wavelength, with IRlasers being
uncertainty-limited andUV lasers diffraction-limited over com-bat
distances.
Now, this suggests another reasonyou dont want to fight close to
planets:stationary defence stations can easilyset up pretty big
phase array lasers,and then they can blast you very well.Ships
could in principle unfold big ar-rays too, but I expect it is hard
to bothpower them and keep them accuratelypointed while dodging
incoming lasers,projectiles and missiles.
This kind of laser arrays still havethe problem that if you are
uncertainof exactly where the enemy is (and weare talking about
meters here) you willmiss him. So my previous calculationsstill
apply - the Titan moon lasers canvaporize nearly anything, but if
youare more than a few thousand kilome-tres from a sensor that
pinpoints youand flying evasively, they will not beable to hit
you.
[Energy requirements, size require-ments, range]
20
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[calc neergy needed for 1 m pene-tration - kills smaller ships,
scale up10 to hurt big ships]
[cycling time] [flash cooling]
5.2.3 Heating beams
A beam pulse of length tp that has acircular radial spread at
the target rarrives after a delay td from observa-tion. During this
time the target hasaccelerated with acceleration a, hav-ing an
unknown relative velocity atd,which will have become a(td + tp)
atthe end of the pulse. Assuming thebeam hits, it will move across
the sur-face since the firing system is not prop-erly taking the
unknown componentsof target motion into account. The to-tal area
heated will be pir2 + 2ra(td +tp).
The velocity smear will reduce theheating, and preclude damage
if thearea is more than K times the in-tended. This gives the
requirement
td + tp < (K 1)pir/2a.
An 1 m2 object that of mass Mand specific thermal capacity K
that isheated by power P Watt/s for tp sec-onds will reach
temperature Ptp/MKif it cannot radiate away the heat.The time
needed to reach a damag-ing temperature Tdam is roughly tp
=MKTdam/P shorter pulse lengths re-quire proportionally higher
power, upto the limits set by the firing array.
In reality the target will reach anequilibrium temperature where
the in-flux equals the thermal radiation. P =T 4 Teq = [P/]
1/4 If Teq is too lowthere will not be any real damage.
Therequired power is P > Tdam
4 (persquare meter).
A rough calculation of the timeneeded to reach this temperature
isTeq = Ptp/MK tp = MK[1/P
3]1/4
tp needs to be shorter than this in or-der to avoid large energy
losses.
If the vaporization energy per kgis Evap, in time tp it can
vaporize to adepth z = Ptp/pir
2rhoEvap (assuminga tdtp tp[P/pirhoEvapz]
Diagram of r tp plane for fixedintensity r must be larger than
diffrac-tion limit r must be smaller than limitof damaging power tp
limited by heat-ing of array - too fast gets too hot tplimited by
equilibrium temperature
r2 tp[P/pirhoEvapz] - able toget to damage depth
constraint due to targeting
5.2.4 Explosive beams
A very high power does damage not byheating the target but by
vaporisingthe surface layer, creating a pressurewave fed by the
beam.
5.3 Railguns
Rick Robinsons First Law of SpaceCombat: An object impacting at
3km/sec delivers kinetic energy equal toits mass in TNT.
Railgun projectile speeds: cur-rently a few kilometers per
second,comparable to normal inter-spacecraftvelocity differences
(even running intoa stationary pebble will do signif-icant damage
to a ship). It is plausi-ble that in Eclipse Phase
ship-launchedrailgun projectiles will be significantlyfaster,
between 10 and 1000 km/s.Railgun projectiles need to be tens
orhundreds of km/s in order to hit flee-ing ships, but can often
move moreleisurely.
The kinetic energy from a 10 km/s1 kg impact is 50 MJ. At this
point thekinetic energy starts to become biggerthan any
(chemically) explosive forcethat can put in the projectile. 100
21
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km/s is 5 GJ (about one ton of TNT)and 1000 km/s projectiles
release 500GJ (100 tons of TNT).
A railgun projectile of massmmov-ing at speed v takes (1/2)mv2/
J tolaunch at efficiency . Conversely, withan energy E the
projectile gets velocityv =
2E/m.
multi-barrel railguns can be madeshorter 6 km/s, 20000 G accel,
100kg projectile 90 m, 4 barrels, tempera-ture increase 450 K
sleeve thickness 10mm, sleve radius 0.09 m, outside ra-dius
0.07m
They will penetrate to a distanceabout equal to the projectile
lengthtimes the ratio of projectile to armourdensity (Newtons
penetration law).This is actually a problem: the at-tacker wants to
deposit all the energyinside the ship, so they must tune
theprojectile length to the target armour.Too heavy projectiles
will go straightthrough the ship. Sometimes havingno armour at all
is the optimal strat-egy (just hope they do not hit any an-timatter
containers). Too light projec-tiles and all energy gets deposited
out-side the armour. [Merge with armorsection discussing this?]
[Energy requirements, size require-ments, range]
5.4 Particle weapons
Particle weapons produce beams ofheavy relativistic particles.
Giventhe existence of personal particlebeams and fusion engines
(which areessentially propelling proton-electronplasma in a beam)
larger particle beamweapons are plausible. The advan-tage of
particle beams is that theydeposit their energy deeper into
thetarget, producing a stronger detona-tion and depositing
Bremsstrahlungand secondary particles into
sensitivenanosystems.
Unlike lasers they are hard to fo-cus and will tend to disperse
over longdistances. Beam divergence angles areon the order of = 4.5
108T/Zwhere T is the beam temperature andZ is the atomic number of
the beamparticles19. If a beam power P andinitial radius r is
directed at a tar-get at distance d the intensity will be P/4pi(r+
kT/Z)2 PZ/4pik2Td2W/m2. The halving distance (wherethe energy per
square meter has de-clined to half) for a proton beam (Z =1) is 280
km, for a mercury ion beam2,500 km.
[check this, compare destroyer en-gine]
[Energy requirements, size require-ments, range]
5.5 Missiles
Missiles can presumably accelerate atleast a few 100 G.
missiles that burst into clouds ofshrapnel as they approach or
if hurt[calc velocity needed to cover target]
number of fragments that can bezapped on approach
[calc saturation with how manymeters laser point defenses can
burnthrough - indicates how many missilescan be shot down per
second and whatthe overwhelming number is]
can act as vector denial system
[Energy requirements, size require-ments, range]
5.5.1 Kinetic impactor rods
Kinetic missiles are little more thanmines, making use of ship
delta vrather than their own acceleration.Missiles typically have
small delta v (afew km/s), but this is enough to do se-rious
damage.
either straight - armor piercingsideways - higher imact area,
good for
19http://www.projectrho.com/rocket/rocket3x1.html#particle
22
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weakly armored targets usually built sothat a hit disperses
rods
5.5.2 Nukes and antimatter
Both nuclear warheads and antimatterhave roughly the same
effect: a mas-sive release of gamma rays (and someparticles,
especially from enhanced ra-diation warheads), with a small
ex-panding cloud of plasma. The kineticimpact, heat blast and EMP
that oc-curs in planetary environments is ab-sent making the kill
radius small, onthe order of kilometers. A high preci-sion hit is
hence required.
An x kt detonation provides an en-ergy of 4.19 1012x/4pid2 W/m2
at dis-tance d in about a microsecond. In or-der to produce
impulsive shock dam-age (the vaporisation of material movesfaster
than the speed of sound in thematerial) on the order of 1013 to
1014
W/m2 is required, producing a minus-cule kinetic kill distance
of
dkkill = 5.77x
meters. The most likely effect is tomelt part of the facing
surfaces, pos-sibly vaporising a thin layer. This mayor may not be
disabling.
However, the amount of particlesis likely enough to kill
biomorphs andsensitive nanotechnology at a longerdistance. Using
the loose estimates inNuclear Rocket20 a conventional nu-clear
weapon produce an X-ray flu-ence of 2.6 1027x/d2 and neutron
flu-ence of 1.8 1023x/d2, and a unshieldedbiomorph will receive a
dose of 1.78 109x/d2 Grays acute x-ray dosage and7.2108x/d2 Grays
of neutron dosage21.
In order to exceed 20 Grays (immedi-ate disorientation) the ship
needs to becloser than
drkill = 9433x
m. This does not take radiation pro-tection from the spaceship
into ac-count: if the ship armor absorbs afraction fX of x-rays and
fn of neu-trons the distance changes to drkill =max(9433
fxx, 6000
fnx) m. For a
ship with 5 cm of steel and 5 cm car-bon in the hull fx 0.62 and
fn 0.8522, giving drkill = 7428
x (still
dominated by the x-ray damage in thiscase).
Using nuclear shaped charges(Casaba-Howitzer) jets of
plasmatravelling at 10,000 km/s can be gen-erated, transmitting up
to 5% of thetotal energy of the detonation as ki-netic energy in a
cone with half-angle0.1 radians23. Assuming it can be di-rected
accurately at the target, thiswould have a
dkkill = 667x
meters and (unshielded) radiation killout to
drkill = 21, 000x
m. Since the beam diameter is 0.2d m,it has a fairly broad
cross-section forhitting a spaceship.
Nuclear warheads have the advan-tage of guaranteed stability,
but anti-matter packs significantly more punchper weight.
Theoretical limits on fu-sion warhead mass are 1 kg per kilo-ton
(current warheads closer to 500 kgper kiloton). A warhead requires
a 45
20http://www.projectrho.com/rocket/rocket3x1.html#nuke21Antimatter
weapons would instead deliver nearly all energy as gamma rays.22f
2
i ti/vi , where the sum is over all materials, each with
thickness ti and half-value
thickness vi for the relevant kind of radiation. This is at best
an approximation since itignores the effects of secondary
radiation, Bremsstrahlung from charged particles and
othercomplications.
23Winterberg, Thermonuclear Physics, p.41,
122.24http://www.projectrho.com/rocket/rocket3x1.html#nuke
23
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kg/kt missile with a volume of 0.036xm3/kt (based on
extrapolations fromthe US trident missile24). Antimatterwarheads
have 43 megaton yield per kgof mass, requiring 10 times the
amountof shielding. Using previous numbersimplies a missile mass of
0.01 kg/ktand 8 106 m3/kt. So small chemi-cal missiles are likely
not possible, butsmall antimatter candles might bepossible.
Given the stability risks of antimat-ter thermonuclear devices
are likelypreferred on ships not using antimatterengines and not
expecting significantcombat. Antimatter warheads how-ever have the
advantage that if pointdefenses destroy them at close rangethey
will go off anyway, doing damagethe less volatile nuclear warheads
willnot do.
http://www.5596.org/cgi-bin/
nuke.php has a nuclear effect calcula-tor.
5.5.3 Rocks
It is entirely feasible to boost small as-teroids into orbits
that will impact tar-gets. The upside is that the mass canbe
significant, the damage enormous,and the asteroid is hard to stop
(es-pecially if equipped with some pointdefenses). The downside
that the im-pact can usually be predicted weeksor months ahead.
Rocks represent arelatively minor threat to space habi-tats and
aerostats, which can be movedout of the way. They represent a
sig-nificant threat to planetary or aster-oid habitats that are not
defended bydefense arrays. However, since theywould tie up the
defense array (andproduce fragments) as they get withinrange they
also provide an ideal timefor a conventional attack.
5.5.4 Relativistic missiles
More of a strategic weapon than a re-alistic space battlefield
weapon, rel-ativistic missiles attempt to hit tar-gets at long
distance using projectileswith a sizeable relativistic mass.
Theirmain benefit is the impossibility of pro-tecting oneself from
them, since theywould not be detectable from the tar-get until
shortly before impact andthere is no way of stopping a verylarge
mass moving fast (it would passthrough armor as per Newtons
impactlaw, and any effect that splinters it willnot be able to make
the fragments de-viate very far before it hits).
Fortunately, given the energy re-quirements of launching
relativisticmissiles launch is very visibile, and QEallows
monitoring of possible launchsites giving information long before
themissile reaches its target. There arealso some doubts on whether
relativis-tic missiles are feasible or not in EclipsePhase.
5.5.5 Leashes
A leash is a warhead that is attachedto the hull of the enemy
ship, readyto explode on command or if tam-pered with. In principle
just placinga missile with a functioning warheadon or near the ship
works, but in prac-tice the extra reassurance from tam-perproofed
antimatter containment ispreferred. Actually leashing a ship
isquite a coup, and allows the leasher todictate terms to the
leashed.
5.5.6 Nanoweapons
Nanomachines encased in diamondoidshells can resist
accelerations up to108 1010 G, making delivery by highvelocity
impactors possible if they canbe slowed just before impact. This
canfor example be done by placing themfar back in a penetrating
warheadorhaving an explosive charge accelerate
24
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them in the opposite direction just be-fore impact. The main
problem withnanoeweapons is that the amount thatcan be transfered
is relatively smallcompared to the amount of defensivenanosystems
onboard (see section 7)and that hives generally cannot
surviveimpacts. This makes direct attacksusing disassemblers weak.
The mainnanoweapon payloads tend to be sab-otage nanites or
proteans constructinga position tracking transmitter.
5.6 Fighters
essentially a roving missile bus
5.7 Networked warfare
Generally, I expect space battles toinvolve extended networks of
decoys,drones, munitions, sensors and what-not. The communications
issues areserious: I expect it to be worth themoney to use FTL
quantum com-munication to keep everything linked,untraceable, fast
and unjammable.Qubits are a very strategic resource(incidentally, I
doubt they can bestored without some very good nano- bad news for
the Jovians, who proba-bly have to break a few rules to get
it).Primitive forces that have lightspeed-limited networks are at a
serious dis-advantage, and must also ensure thatthe enemy cannot
detect *where* thecloud sends its messages (OTP en-crypted neutrino
broadcasts in all di-rections instead?)
Burnsides Zeroth Law of spacecombat: Science fiction fans
relatemore to human beings than to siliconchips. While the polities
of the so-lar system have very good reasons notto like AIs, AGIs
and infomorphs con-trolling weapon systems the militarybenefits
often outweigh these consider-ations. On the strategic level there
isa tension between avoiding developing
systems similar to the ones implied inthe Fall and keeping a
military edge.
25
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6 Armor
If we assume that the cost of drive sys-tems is large compared
to the cost ofweapon systems, then it is clear thatwarships will
tend to be as protected aspossible. This can be achieved
throughheavy armoring or making them ableto evade (through stealth,
maneouver-abilityor point defenses) attacks.
Armor needs to be able to han-dle hypervelocity impacts and
beamweapons.
6.1 Kinetic impact
Any impacts faster than a few km/swill produce inertial stresses
muchlarger than the material strength (evenfor extremely hard
materials like dia-mond): for all practical purposes thearmor
behaves like a liquid. This isnot just a military problem but
alsoan issue for any ship moving at orbitalvelocity, since impacts
with microme-teorites and other debris is potentiallydangerous (at
speeds of 800 km/s 1gram impacts correspond to explosionsof 76 kg
of TNT).
One way to handle this is Whippleshields: a relatively thin
outer bumpershield placed a distance from the wallof the
spacecraft. The incoming par-ticle will be shocked and may
disin-tegrate, spreading its energy across alarger area of the
inner wall. Shieldscan be stacked, further dispersing theenergy,
and the space between themfilled with shock or radiation absorb-ing
material. They are light but in-crease the spacecraft size; some
shipsuse unfoldable Whipple shields. Theouter shields tend to be
damaged bymicrometeors and conflict, but are ex-pendable and can be
cheaply repairedafterwards.
Newtons law of impact depth
states that a projectile of length Lwith density P impacting a
targetwith density A will penetrate to adepth L(P /A). This is
applicablefor hypervelocity impacts where mate-rial cohesion can be
ignored. Whilehigh density projectiles are possible(osmium achieves
22610 kg/m3, 2.9times steel) just extending the projec-tile into a
spear guarantees deep pen-etration. This will also tend to
pene-trate Whipple shields, since the desin-tegrating parts will
just make way formore incoming spear.
Heavy armor needs to be thickerthan spear projectiles unless it
is signif-icantly denser. This is hard to achieveacross a whole
ship since the mass be-comes prohibitive: even a heavily ar-mored
ship will just armor vital sys-tems (reactor, cooling, antimatter
con-finement, possibly crew battlestations)and rely on redundant or
repairablesystems elsewhere. Another approachis to use thick
low-density shieldingin the form of water or reaction masstanks
that would anyway be present.A hit will destroy the compartment
butdissipate the energy.
Another approach is to have verylight armor and allow
projectiles topass through, relying on redundantship systems to
survive the damageand nanoswarms to repair it. How-ever, high
velocity impacts turn intorapidly expanding clouds of shrapnel.A
velocity v impactor of mass m willrelease 0.5mv2 J of kinetic
energy. Ifall of it turns into kinetic energy offragments (and
assuming them to havea Maxwell-Boltzmann distribution25)the average
lateral velocity of the frag-ments will be v/
2, corresponding to
a approx35 cone. Hence this strat-egy works best for very long
and thinships, where little of the volume can be
25There are m/mf fragments, where mf is the fragment mass. Each
gets E = 0.5mfv2
kinetic energy if it is divided evenly. The average speed in the
lateral direction isE/mf ,
producing the above formula.
26
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affected.
6.2 Beam impact
[ Flash damage, impulse kill, drillingThe energy needed to drill
through anobject is within a factor 2 of the heat ofvaporisation of
the object best vapor-ization energy for mass carbon, 29.6kJ/g
(boron even better) des 5 g/cm2(increase density?), burning a
1cm2hole requires 148 kJ and 20 millisec-onds combat conditions
need largerspot to remain focused - 10 cm2 spotsaccepts uncertainty
velocity 5 m/s ]
6.3 Conclusions
One approach is to add maximal ar-mor, making the target hard to
dam-age. [how handle laser effects?]
Self-repair using nanomachines canrestore Whipple shields fairly
rapidlyafter a battle, but is too slow to mat-ter during a
battle.
27
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7 General strategy
The conflict between different mili-tary assets can be described
using theLanchester (square26) model:
Let B represent the number of as-sets of side blue and kb is the
de-struction efficiency, how many enemyassets one blue asset can
neutralize perunit of time. Let R and kr representthe red side. The
both sides will suf-fer attrition like
B = krRR = kbB
Blue will win by attrition (i.e. reduceR to 0) if kbB
2 > krR2. There is a size-
able advantage in having more offen-sive assets, bigger than
merely lethalassets. Concentrating forces so theycan focus their
fire gives a big advan-tage (but the concentration needs to
bediffuse enough so that no volume effectweapons can strike at
them, somethingthe model does not include). The sidewith fewer
assets still have a chanceof winning if they can make strikesthat
disrupt the command and controlstructure of the other side, for
exampletaking out the main communicationslinks (again outside the
basic attritionmodel).
In practice the Lanchester equa-tions will be just a crude
approxima-tion, since there exist weapons that de-stroy groups of
enemies, some weaponshave synergistic effects (detonationsthat
temporarily blind enemy sensorsyet provide active sensor
informationabout enemy asset locations), there aresensors and other
assets that do not at-tack yet are valid targets, and there
aredifferent kinds of weapons that work
differently well against different tar-gets. The key point
likely remains: theside that can manage to rapidly reducethe enemy
assets early on has a largeadvantage.
In traditional warfare the sidewith smaller numbers can improve
itschances if it splits up into hard-to-findunits and make local
raids where ithas numerical superiority27. This ishard to do in
deep space combat, sincevisibility is high, but an approxima-tion
is to use missile buses and fightersto rapidly deploy local
superior forcewhen needed. In orbital warfare it iseasier to do
guerilla tactics, mak-ing surprise ambushes and retreats
intounmonitored volumes.
26The name comes from the square in the winning criterion, the
equations themselves arelinear. Ironically there are also the
linear Lanchester model that describes conflicts wherethe loss rate
is proportional to the product of the force sizes (and hence forms
a pair of nonlin-ear equations). This model describes situations
where combat occurs between pairs of units,and here the advantage
in number is reduced to a linear relation.
27S.J. Deitchman, A Lanchester model of guerilla warfare,
Operations Research 10:6, 818-827
28
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8 Cloud combat
Much of deep space battles occursbetween distributed assets
driftingthrough space, forming two (or more)clouds passing through
each other atmultikilometer per second speed. Iffriendly assets
have not cleared enoughenemy assets ahead of the ship, it
willlikely be hit.
Assets can be made very low-emission by cooling before
launch,mechanical low-energy launching(springs, slow railguns, even
bolalaunching), internal heat storage, lowemission electronics,
being folded to-gether and equipped with stealth cov-ering. This
can also cause a hard-todetect change in ship velocity thatcould
grow into positional uncertaintybefore the battle.
A cloud launched at time T beforecombat at velocity vs will have
radiusvsT . The passage through the cloudof a ship of velocity v
takes 2vsT/vseconds. vs is presumably restrictedto less than 1 km/s
if silent launch isused. If v = 10km/s and T = 1 daythe passage
takes 4.8 hours, while forv = 100km/s passage takes 29 minutesand
for v = 400 km/s just 7 minutes.
However, after the first side haslaunched their cloud the other
side canchoose to do a maneouver with v >vs, avoiding the cloud
and being ableto launch a cloud of protective assets.Obviously the
first side can themselveschange the velocity to make this
cloudworthless, and so on. If continued thisturns it into a pure
ship-to-ship bat-tle. This is the preferred strategy fora side with
limited spaceborne assetsand plenty of v to burn.
If a ship moving with velocity vtowards another ship launches an
as-set cloud spreading with velocity vswhen at distance d, the
cloud willhave radius vsd/v when it reaches theother ship. To evade
it, the shipneeds to change its velocity by at
least vs (favoring rapid, possibly de-tectable launches).
However, the den-sity of assets in a wide cloud willbe lower. If
assets have a ranger and N assets are launched in thecloud, on
average a ship will be withinrange of 3Nr2v2/4v2sd
2 assets if pass-ing straight through the cloud. Thisfavors a
late and slower launch, pro-ducing a denser cloud. If M
assetswithin range are needed to achieve awin, they should be
launched withindistance
3N/4M(rv/rs), but if the
enemy is expected to have a highenough v budget earlier and
sub-optimal launches are needed - muchhinges on accurately
estimating howmuch fuel the enemy can spend on eva-sion and the
performance of their en-gines.
8.1 Weapons vs. sensors
A cloud of density has average dis-tance to the nearest asset
< d >=k1/3, where k 0.5622.
If there is resources C to produceassets per unit volume, and
sensorscost 1 and weapons x, C = s + xwwhere s is the sensor
density and wis the weapon density. Assumine afraction f of the
resources are used tomake weapons, w = fC and s =((1 f)/x)C. The
average delay be-tween a sensor detecting a target anda weapon has
a chance to hit it is:
t = k
[1/3s +
1/3w
c+1/3w
v
]where v is the weapon velocity. Themiddle term represents a
delay as in-formation is transmitted at lightspeedto the nearest
weapon. If a QE link ispresent it is zero.
t = kC1/3[x1/3(1 f)1/3 + f1/3
c+f1/3
v
]To minimize t the expression in thebracket has to be minimal,
leading to
29
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the optimal weapons allocation
f =1
1 + (1 + c/v)3/4x1/4
If x is very low (cheap weapons)most assets should be weapons.
Forweapons as costly as sensors 50%should be weapons if v c while
62% if they are lasers: a railgun ormissile-based system will tend
to havenumerous weapons, hoping to be closeto a detected target.
For more expen-sive weapons a smaller fraction is opti-mal.
[check QE term, check other case]
9 Hitting a dodgingenemy
Suppose a vessel observes another ves-sel at distance d and
known velocityand fires immediately with a projectilewith velocity
v (v = c for a laser)28.The time it will take for light from
theenemy to reach the vessel and for theprojectile to reach the
vicinity of theenemy is
t = d(1/c+ 1/v)
During this time the enemy will be ac-celerating with
acceleration a < amaxin a random direction to escape a hit.After
time t it has moved up to
rmax = (1/2)amaxt2
and will be within a sphere of radiusrmax around the position it
would havehad if it had not accelerated. The at-tacking vessel does
not know where in
the sphere the enemy is, but we willassume it knows rmax (for
example byobservations of past accelerations andship type).
A projectile will hit anything alongits path through the sphere
within itseffective cross section (this includesthe area A of the
ship and the radius rpof the projectile, A+2piArp; if Nshots are
optimally fired is multipliedby N). This is equivalent to
selectinga point on the cross-sectional disk seenby the launching
ship: the area of thedisk is pir2max, and an area will be
af-fected. The evading ship will attemptto distribute its
probability across thedisk uniformly29), so the probability
ofhitting will be
phit = /pir2max =
4
pia2maxd4(1/c+ 1/v)4
When phit 1 the evader has a goodchance of avoiding a hit. While
a highacceleration ability is useful, increasingdistance has a far
greater effect.
The critical distance devasion wherephit approaches unity is
devasion =
[4
pi
]1/41
amax(1/c+ 1/v)
Inside this distance the probability ofhitting is large. The
first term variesslowly with and is of the order unity.For = 1 m2
it is 1.06, for = 100m2 it is 3.36 and for = 1000 m2 5.97.
As an approximation, the enemyis possible to hit if d <
devasion v/amax for projectiles and if d