-- module Nuke (main) -- where -- TODO: work in radiation deaths. import Pcheck import Test.QuickCheck import Monad (liftM3) {- For many equations and results, it is nonsensical to have negative results, but we don't want to use solely natural numbers because then we lose precision. So we define a PosReal type which tries to define the subset of real numbers which are 0 or positive; this way the type system checks for negative results instead of every other function having conditionals checking for negative input or output. -} newtype PosReal = MakePosReal Float deriving (Show, Eq, Ord) -- Basic numerical operations on positive reals instance Num PosReal where fromInteger = toPosReal . fromInteger x + y = MakePosReal (fromPosReal x + fromPosReal y) x - y = toPosReal ((fromPosReal x) - (fromPosReal y)) x * y = MakePosReal (fromPosReal x * fromPosReal y) abs x | x >= 0 = x | otherwise = x * (-1) signum x | x >= 0 = 1 | otherwise = (-1) -- Define division on PosReals instance Fractional PosReal where x / y = toPosReal ((fromPosReal x) / (fromPosReal y)) fromRational x = MakePosReal (fromRational x) -- Positive reals are truncated at 0 toPosReal :: Float -> PosReal toPosReal x | x < 0 = MakePosReal 0 | otherwise = MakePosReal x fromPosReal :: PosReal -> Float fromPosReal (MakePosReal i) = i -- Define an instance to allow QuickCheck operations instance Arbitrary PosReal where arbitrary = liftM3 fraction arbitrary arbitrary arbitrary where fraction :: Integer -> Integer -> Integer -> PosReal fraction a b c = fromInteger a + (fromInteger b / (abs (fromInteger c) + 1)) -- coarbitrary x = coarbitrary (x, x) type KiloPascal = PosReal type PSI = PosReal type Meters = PosReal type W = PosReal -- Note w is always in kilotons. type Joule = PosReal type Time = PosReal -- Characterizes the output of a nuclear weapon data Output = Output { heat :: PosReal, blast :: PosReal, nuclear_radiation :: PosReal } deriving (Show, Eq) main :: IO () main = do bool <- parTest [kpaTest, psiTest, energyTest, thermalMaxTest, timeMaxTest] if bool then print "Success" else print "Failure" -- Units kpaTest :: IO Bool kpaTest = parCheck (\s -> kpa s >= 0) 1000 kpa :: KiloPascal -> PSI kpa a | (a > 0) = 0.145 * a | otherwise = 0 psiTest :: IO Bool psiTest = parCheck (\s -> psi s >= s) 100 psi :: PSI -> KiloPascal psi = (6.895 *) meter :: PosReal -> PosReal meter = (3.281 *) foot :: PosReal -> PosReal foot = (0.3048 *) -- Find ideal height for an air burst. height :: W -> Float --height w = 60 * (1 / (w * w * w)) -- w^3 height w = 60 * ((fromPosReal w)**(1/3)) {- Calculate total energy of a given kilotonnage. Answer in joules. This works because critical mass gives a lower kilotonnage bound for fission bombs. -} energyTest :: IO Bool energyTest = parCheck (\s -> energy s == 0 || energy s >= 2.0929999e12) 100 energy :: W -> Joule energy s | s >= 0.5 = 4.186 * joule * s | otherwise = 0 where joule = 1000000000000 :: PosReal -- 10^12 regularNuke :: W -> Output regularNuke w = Output { heat=(0.35 * energy w), -- 35% heat blast=(0.50 * energy w), -- 50% kinetic energy nuclear_radiation=(0.15 * energy w) -- 15% non-thermal radiation } {- A radiation weapon trades off a decreased thermal and blast energy against a considerably increased radiation yield. It is defined in terms of regularNuke because it just modifies it. -} radiationNuke :: W -> Output radiationNuke w = Output { -- regularNuke w heat=(0.35 * energy (0.50 * w)), blast=(0.50 * energy (0.50 * w)), nuclear_radiation=(0.15 * energy (10.0 * w)) } -- 10x non-thermal radiation! {- Answer in joules /m^2. r = distance from impact/radius; t = correction factor (1.5^2 for snow & high clouds, 1.5 for singly either). This is how many joules of heat per square inch at a given distance for given kilotonnage (weather included). -} totalPointImpact :: W -> Meters -> PosReal -> PosReal -> Joule totalPointImpact w r clouds snow | r /= 0 = (0.35 * (weatherMultiplier snow clouds) * (energy w)) / (4.0 * reducedPrecisionPi * r) | otherwise = energy w -- If 0, then at ground zero and no diminution b/c of distance where weatherMultiplier :: PosReal -> PosReal -> PosReal weatherMultiplier a b | a*b > 0 = (a * b) | a + b > 0 = (a `max` b) | otherwise = 1 reducedPrecisionPi = 3.141592653589793 :: PosReal -- Results in kPA peakOverPressureUnderWater :: W -> Meters -> Joule peakOverPressureUnderWater w r = 1.07e7 * (1 / (w / 0.37)) * (1 / (r / (-1.18))) -- = 1.07e7 * w^(0.37) * r^(-1.18) -- thermal deaths - pmax = kJ/m^2 --thermalMax = 270 -- incapacitation thermalMaxTest :: IO Bool thermalMaxTest = parCheck (\s -> (thermalMax s s s s) >= 0) 100 thermalMax :: Meters -> Joule -> Joule -> Joule -> Joule thermalMax w r clouds snow = (0.38 * (totalPointImpact w r clouds snow)) / timeMax w timeMaxTest :: IO Bool timeMaxTest = parCheck (\s -> timeMax s >= 0) 100 timeMax :: W -> Time timeMax w = 0.0417 * (1 / (w / 0.44)) -- TODO: add a test pressureKilledPerson :: Meters -> Joule -> Joule -> Joule -> Bool pressureKilledPerson w r clouds snow | thermalMax w r clouds snow >= 270 = True | otherwise = False --radiationDeaths = dose-rate * exposure-time -- radiationKilled = undefined -- centigray is 1/10 a gray --gray joule kg = joule / kg --450 centigray = 50% fatalities -- We'll assume the following scales linearly -- at 10 r, 3billion / 1million major defects 1stgen (1/3000th), /10million (1/300th) cumulative total -- 3billion / 10million (1/300th) early mortalities 1stgen, /200million (1/15th) cumulative total {- weapon vital statistics -- icbms -- minuteman II # 450 11 300 1 W56 minuteman III # 200 13 000 3 W62 minuteman III (MK12A) # 300 13 000 3 W78 mx 50 11 000 10 W87 -- slbm -- poseidon 224 4 600 10 w68 trident I 384 7 400 8 w76 -- bombers -- B-1B 97 9 800 22 FB-111A 59 4 700 6 B-52G/H 193 16 000 b052h/g model: 20 SRAM or b-52h: 20 ALCM b-52g: 12 ALCM and 6 bombs f-4 C/D/E 2 250 1060-2400 3 F-15 A/C 5 W25 or genies F-16 A/B/C/D 5 B43 or B57 F-111 A/D/E/F 3 b43|b57|b61|b83 -- Missiles -- pershing II 111 1 790 1 W85 GLCM 250 2 500 1 W84 Pershing IA 72 740 1 W50 lance 100 125 1 W70 nike hercules 27 160 1 W31 tomahawk 200 2 500 1 W80-0 -- bombs -- W31 75 1-20kt W56 450 1.2MT W50 100 60-400 W62 600 170kt W70 1 282 1-100kt W78 900 335kt W87 500 300kt W68 2 240 40kt w76 3 072 100kt w80-0 200 5-150kt w85 125 .3-80 w84 325 .2-150kt b28 b28RE b43 b57 b61 b83 "genie" "b-52G/H 20 SRAM" B-52G B-52H -} {- A list of possible scenarios. US first strike USSR first strike NATO / Warsaw Pact Far East strategy US USSR escalation Middle East war USSR - China attack India Pakistan war Mediterranean war Hong Kong variant SEATO decapitating Cuban provocation Inadvertent Atlantic heavy Cuban paramilitary Nicaraguan preemptive Pacific territorial Burmese theatre-wide Turkish decoy NATO first strike Argentina escalation Iceland maximum Arabian theatre-wide U.S. subversion Australian maneuver Iranian diversion ...? limited Sudan surprise NATO territorial Zaire alliance Iceland incident English escalation Zaire sudden Egypt paramilitary Middle East heavy Mexican takeover Chad alert Saudi maneuver African territorial Ethiopian escalation Canadian ...? Turkish heavy NATO incursion U.S. defense Cambodian heavy Pact medium Arctic minimal Mexican domestic Taiwan theatre-wide Pacific maneuver Portugal revolution Albanian decoy Palestinian local Moroccan minimal Hungarian diversion Czech option French alliance Arabian clandestine Gabon rebellion Northern maximum Syrian surprise ...?sh paramilitary SEATO takeover Hawaiian escalation Iranian maneuver NATO containment Swiss incident Cuban minimal Chad alert Iceland escalation Vietnamese retaliation Syrian provocation Libyan local Gabon takeover Romanian war Middle East offensive Denmark massive Chile confrontation S.African subversion USSR alert Nicaraguan thrust Greenland domestic Iceland heavy Kenya option Pacific defense Uganda maximum Thai subversion Romanian strike Pakistan sovereignty Afghan misdirection Thai variation Northern territorial Polish paramilitary S.African offensive Panama misdirection Scandinavian domestic Jordan preemptive English thrust Burmese maneuver Spain counter Arabian offensive Chad interdiction Taiwan misdirection Bangladesh theatre-wide Ethiopian local Italian takeover Vietnamese incident English preemptive Denmark alternate Thai confrontation Taiwan surprise Brazilian strike Venezuela sudden Malaysian alert Israel discretionary Libyan action Palestinian tactical NATO alternate Cyprus maneuver Egypt misdirection Bangladesh thrust Kenya defense Bangladesh containment Vietnamese strike Albanian containment Gabon surprise Iraq sovereignty Vietnamese sudden Lebanon interdiction Taiwan domestic Algerian sovereignty Arabian strike Atlantic sudden Mongolian thrust Polish decoy Alaskan discretionary Canadian thrust Arabian light S.African domestic Tunisian incident Malaysian maneuver Jamaica decoy Malaysian minimal Russian sovereignty Chad option Bangladesh war Burmese containment Asian theatre-wide Bulgarian clandestine Greenland incursion Egypt surgical Czech heavy Taiwan confrontation Greenland maximum Uganda offensive Caspian defense -}