E4B NEECAP at Offut
The US Strategic Command has got a plenty of airplanes to sustain reliable and redundante control of the nuclear triad (ICBM, SSBN and Bombers) in case of bolt out of blue attack in order to retaliate adversary: AF-1, NEECAP (E-4B), TACAMO (E-6 Mercury). During peacetime these airplanes are based in routine locations. For more see: https://en.wikipedia.org/wiki/Boeing_E-6_Mercury, https://en.wikipedia.org/wiki/Tinker_Air_Force_Base, https://en.wikipedia.org/wiki/Air_Force_One.
https://sketchfab.com/3d-models/747-100-f00ee8c4f587424898d5e405d0a44f27
library(sp)
library(leaflet)
Offut <- data.frame(latitude=41.12,longitude=-95.92,name="Offut, E-4B")
Andrews <- data.frame(latitude=38.80, longitude=-76.87,name="Andrews, AF-1")
Patuxent <- data.frame(latitude=38.3,longitude=-76.4,name="Patuxent, E-6")
Travis <- data.frame(latitude=38.27,longitude=-121.95,name="Travis, E-6")
Tinker <- data.frame(latitude=35.4,longitude=-97.38,name="Tinker, E-6")
df1 <- rbind(Offut,Andrews)
df2 <- rbind(Patuxent,Travis)
df <- rbind(df1,df2)
df <- rbind(df,Tinker)
coordinates(df) <- ~longitude+latitude
leaflet(df,width = 900,height = 600) %>% addCircleMarkers(radius = 10,color = "red",popup = df@data$name) %>% addTiles()%>%
addMiniMap() %>% addGraticule(interval = 10)The Boeing E-4 Advanced Airborne Command Post (AACP), the current “Nightwatch” aircraft, is a strategic command and control military aircraft operated by the United States Air Force (USAF). The E-4 series are specially modified from the Boeing 747-200B for the National Emergency Airborne Command Post (NEACP) program. The E-4 serves as a survivable mobile command post for the National Command Authority, namely the President of the United States, the Secretary of Defense, and successors. The four E-4Bs are operated by the 1st Airborne Command and Control Squadron of the 595th Command and Control Group located at Offutt Air Force Base, near Omaha, Nebraska. An E-4B when in action is denoted a “National Airborne Operations Center”.
For more see:
Though E4B jet or ‘doomsday plane’ has not got yet direct enemy attack record, some interesting facts can be unfolded about it’s survivability during natural disaster events for the past two years.
US Tornado Alley
On June 16, 2017, an EF-1 tornado – defined as a cyclone producing winds between 86 and 110 miles per hour and capable of flipping mobile homes and breaking windows – touched down at Offut, causing almost 20 million dollars in damage in total. This included a more than 8 million dollars bill just to repair both of the E-4Bs, also known as National Airborne Operations Centers (NAOC), which were at the base at the time, according to the Omaha World-Herald. The Air Force has four of the aircraft in total, and, as we reported at the time, Boeing was overhauling a third aircraft at its depot in San Antonio, Texas, leaving the fourth as the only one on active duty at a still undisclosed base.
For more see: https://www.thedrive.com/the-war-zone/18996/a-tornado-left-the-usaf-with-only-one-active-e-4b-doomsday-plane-for-months
NASA satellite image. River’s flooding into Offutt Air Base
The damage has crippled capabilities at an Air Force base considered essential to national security. Among its many roles, Offutt is home to the U.S. Strategic Command that oversees the Pentagon’s nuclear strategic deterrence and global strike capabilities.
The flooding submerged part of the runway and inundated dozens of buildings at one of the nation’s most important air bases. The calamity likely will cost many times more to repair than it would have cost to prevent.
That is why natural disaster respond plan is a milestone for the E4B survivability.
For more see: https://insideclimatenews.org/news/21032019/military-climate-change-flood-risk-offutt-air-force-base-army-corps-levee-failure
The primary task of NEECAP as NCA airborne backbone is to sustain reliable and seamless command chain between President of the USA (or one of his successors) as commander-in-chief and nuclear forces (ICBMs, SSBNs and bombers) under bolt-out-of-blue attack. E-4B jet is based in Offut on the constant high alert to take off for the doomsday flight and transmit EAM to the nuclear forces: commit or terminate some high priority actions with nuclear arsenal.
For more see: https://rstudio-pubs-static.s3.amazonaws.com/200551_499f1be280024d50b83916cf6b62e37e.html#probability-for-retaliation-strike
Here we assume that all four E-4B jets are based on the ground and are ready to take off with 95% probability. There are two possible options for surprise attack: no warning and warning on alert. What is the probability that at least one of four E-4B successfully take off - \(P_{E4B,1-4}\)?
20 hits distribution example
The original concept of CEP was based on a circular bivariate normal distribution (CBN) with CEP as a parameter of the CBN just as \(\mu\) and \(\sigma\) are parameters of the normal distribution \(N(\mu,\sigma)\). Munitions with this distribution behavior tend to cluster around the mean impact point, with most reasonably close, progressively fewer and fewer further away, and very few at long distance \(R\). That is, if CEP is \(n\) meters, 50% of rounds land within \(n\) i.e \(P(R\le{n})=0.5\) meters of the mean impact, 43.7% between \(n\) and \(2n\) i.e \(P({n}<R\le{2n})=0.437\), and 6.1% between \(2n\) and \(3n\) meters i.e \(P(2n<R\le{3n})=0.061\), and the proportion of rounds that land farther than three times the CEP from the mean is only 0.2% i.e \(P(R>3n)=0.002\). That is we have full probability of hit as \(0.5+0.437+0.061+.002=1\).
For more see: https://en.wikipedia.org/wiki/Circular_error_probable
Here we apply CEP concept to calculate single shot kill probability \(P_{SHKP}\) given \(R_{CEP}\) as CEP and \(R_{lethal}\) as lethal radius for the target to be destroyed.
\[P_{SHKP} = 1 - 0.5^{(R_{lethal}/R_{CEP})^2}\]
library(ggplot2)
#Single shot probability for RCEP and RLTH
PSHKP <- function(RCEP,RLTH) {
PA <-1-0.5^(RLTH/RCEP)^2
#PB <-1-0.437^(RLTH/(sqrt(3)*RCEP))^2
#PC <-1-0.061^(RLTH/(sqrt(5)*RCEP))^2
#return(PA+(1-PA)*(1-PC)*PB+(1-PA)*(1-PB)*PC)
return (PA)
}
#Lethal radius
LRM <- function(Y,H){
LRM1 <- 4540*(Y^(1/3))/(H^(1/3))
LRM2 <- (sqrt(1+2.79/H)+1.67/sqrt(H))^(2/3)
return(LRM1*LRM2)
}
RCEP <- c(250,500,1000) #CEP, meters
HH <- seq(from=1,to=60,by=1) #Hardness, psi
RLTHH <- LRM(0.15,HH)
RLT <- data.frame(
RLTHH,HH
)
ggplot(RLT,aes(x=HH,y=RLTHH)) +
geom_line() +
ggtitle(label="Lethal radius for Yield=0.15 MT")+
labs(x="Hardness,psi",y="Radius, meters",
caption = "based on “Strategic Command and Control.
Redefining the Nuclear Threat” by Bruice G.Blair")test_data_3 <-
data.frame(
RCEP,
TK1 = PSHKP(RCEP[1],RLTHH),
TK2 = PSHKP(RCEP[2],RLTHH),
TK3 = PSHKP(RCEP[3],RLTHH)
)
ggplot(test_data_3, aes(x=RLTHH)) +
geom_line(aes(y = TK1, colour = "250"))+
geom_line(aes(y = TK2, colour = "500"))+
geom_line(aes(y = TK3, colour = "1000"))+
ggtitle(label="Kill probability for Yield=0.15 MT")+
labs(x="Lethal radius, meters",y="Probability", colour="CEP, meters",
caption = "based on “Strategic Command and Control.
Redefining the Nuclear Threat” by Bruice G.Blair")“One Hundred Nuclear Wars: Stable Deterrence between the United States and Russia at Reduced Nuclear Force Levels Off Alert in the Presence of Limited Missile Defenses, Victor Esin, Matthew Mckinzie, Valery Yarynich, Pavel Zolotarev,”Science & Global Security 19, no. 3 (2011): 167-194.
The Lethal Radius (LR) is defined as the distance from the point of the nuclear explosion that the warhead will be able to destroy its target. The formula for LR (in meters) as a function of Yield (Y–in Megatons) and silo hardness (H –in overpressure pounds per square inch or psi) is given by:
Lethal Radius im meters
Nuclear blast overpressure
The Effects of Nuclear Weapons Samuel Glasstone and Philip J. Dolan, Third edition, 1977
The height of burst and energy yield of the nuclear explosion are important factors in determining the extent of damage at the surface.
Here we apply data from Samuel Glasstone, Philip J.Dolan “The Effects of Nuclear Weapons, 1977 Third Edition” to estimate damage produced by peak overpressure of an air nuclear blast to the E4B aircraft based on the land.
Samuel Glasstone, Philip J.Dolan “The Effects of Nuclear Weapons, 1977 Third Edition”
Samuel Glasstone, Philip J.Dolan “The Effects of Nuclear Weapons, 1977 Third Edition”
For E4B airplane we can assume 3 psi overpressure as preliminary estimate for severe damage (see Table 5.153). On the other hand, 86-110 mph wind by EF-1 tornado on June 16, 2017 that had damaged E4B at Offut airbase, proves our estimate too (see Table 3.97 below). All in all we can assume 3.5 psi overpressure as 95% confident estimate.
Suppose some undetected submarine would launch missile with three MIRV 150 kT each on suppressed trajectory giving \(P_{SLBM}=0.95\) arrival probability to the target and no time for the warning. Then the probability that no less than one of four E-4B jets would take off after attack looks like:
\[P_{E4B,1-4,NW}=1-[1-(1-P_{SLBM}P_{SSK})^3]^4\]
# E4B positioned in garage
PSSK <- PSHKP(RCEP = 1000,RLTH = LRM(Y = 0.15,H = 30))
PSSK3 <- 1-(1-0.95*PSSK)^3
E4BGAR <-1 - (PSSK3)^4
E4BGAR## [1] 0.5365508
# E4B positioned outdoors on the run way
PSSK <- PSHKP(RCEP = 1000,RLTH = LRM(Y = 0.15,H = 3.5))
PSSK3 <- 1-(1-0.95*PSSK)^3
E4BOUT <-1 - (PSSK3)^4
E4BOUT## [1] 0.0006928961
This option assumes enough time for implementing all procedures necessary to take off safely.
\[P_{E4B,1-4,WA}=1-(1-0.95)^4=0.9999\] To be confident we should estimate runaway distance for E4B airplane after receiving warning as \(X=V_0t + at^2/2\) or putting \(a=(V-V_0)/t\) we get \(X=(V_0+V)t/2\) where \(t\) - time for takeoff and runaway. Given 1 minute for detecting SLBM launch and 2 minutes for NCA decision as well as time of RV arrival \(t_{RV}=(L_{SLBM}cos(\beta))/V_{SLBM}\) sec.
V0 <- 275 #E4B takeoff speed, km/h
V <- 875 #E4B cruise speed, km/h
L_SLBM <- 3000 # distance from SLBM start to E4B at Offut airbase
beta <- 15 # angle in degrees for SLBM suppressed trajectory
V_SLBM <- 6 # km/sec
t_RV <-3000*cos(beta*pi/180)/V_SLBM
t <- t_RV/60 - 1 -2
t # 5 minutes ## [1] 5.049382
t <- t/60 # as hour
X <- (V0+V)*t/2 #E4B runaway distance
cat("E4B runaway distance =",round(X,1), "km")## E4B runaway distance = 48.4 km
Applying Lethal Radius for nuclear blast wave formula and E4B runaway distance we can estimate probability of E4B kill by SLBM even with three RV by 1 MT each as
RLTH = LRM(Y = 1,H = 3.5)
RLTH## [1] 5108.835
1-(1-PSHKP(X,RLTH/1000))^3## [1] 0.02291171
As we see E4B airplane is safe enough to run away from SLBM given warning.