A recent Eurasian Times article titled China Rapidly Expands “Carrier Killer” Missiles To Keep US Navy At Bay; A Look At Beijing’s Deadly ASMs(1) talks about a number of anti-ship missiles ranging from cruise missiles to the so-called Anti-Ship Ballistic Missiles (ASBMs) that ostensibly checkmate the superiority of American aircraft carrier groups in the South China Sea and the Pacific.

There has been breathless reporting on ASBMs for quite a while. The earliest enthusiastic, comprehensive reporting of this ‘wonder weapon’ has been by Professor Andrew Ericksson, whose eminently readable book, Chinese Anti-Ship Ballistic Missile (2) was picked up by the military academia and reproduced as articles  over the years. Professor Ericksson also appeared for Congressional hearing (3) on the subject. To add further flavor, eminent underwater weapons expert, HI Sutton through his imaginative MS paint drawings captivated the naval community with renderings of a ship launched ASBMs and air launched ASBMs (4).

The Chinese of course lapped it up and went to town with excellent graphics appearing on their military websites, state run media and an active ASBM program complete with ‘successful’ field trials. Not to be outdone, the Iranians too claim to have ASBMs which they have reportedly transferred to the Houthis (5). Not to be left behind, Pakistan too claims that they have a ASBM program up and running (6). With so much hype surrounding this ‘wonder weapon’ let us examine some basic FACTS to arrive at whether this class of weapon is a myth or a reality. At the outset, a disclaimer, the contents of this article are purely based on open-source information and no reference to any ‘privileged’ information has been made.

So, let’s start with the reality. Yes! The Chinese have developed and manufactured DF 21D, which they claim to be an ASBM of range 1500 to 2000 kms with ability to travel 10 times the speed of sound that can target American aircraft carriers to that range. We see photographs and videos of DF21Ds being exhibited at their various military parades.

Source: China Defence Observation at https://www.chinadefenseobservation.com/?p=1031

They have also ‘operationalized’ DF21D batteries for deployment from Chinese territories targeting specifically American aircraft carriers. All this is true. The US Navy on its part has also acknowledged the threat of ASBMs at various congressional hearings and statements from their senior naval hierarchy hint that they do take the threat seriously (7).

How do the Chinese envisage using this ‘wonder weapon’? Well for starters, the Chinese have let the world know that they have built a robust Anti Access Denial system also known as A2/AD that has three layers protecting the Chinese mainland from seaward threat. The inner most layer consist of coastal defence forces comprising of air, surface and subsurface assets up to 270nm. Second layer consists of air and subsurface assets deployed up to 540nm and the outermost layer consist of ASBMs and subsurface assets up to 1000nm from the Chinese coast. The entire area is serviced by a robust network of satellites, UAVs, long range aircraft, OTHT radars, all seamlessly passing information through a network. The satellites would pick up the position of American aircraft carriers beyond the outer layer and pass the information to the shore based ASBM batteries. On receiving the data, based on target parameters, the ASBM battery would launch the missiles which would get a mid-course update and then the missile would finally use terminal guidance to home on to the aircraft carrier. Sounds plausible? Believable? Sure, BUT let’s look at some FACTS.

This article will try and keep the ‘technical’ jargon to minimum but some recounting of high school physics and basic ballistic missile theory will be necessary.

When we term anything as ‘ballistic’ it means that after an initial push in the boost phase by using a propellant, the projectile, in this case a missile reaches a particular height, and then starts falling in a trajectory under the influence of gravity towards it target without any more external propellant. If an external propellant is used in any phase except the initial boost phase, it can no longer be called a ballistic missile. It becomes a powered missile, a cruise missile. Also, in terms of ballistic missiles,  they all necessarily leave the Earth’s atmosphere which is approximately 100km and then re-enter following a ballistic trajectory, which is usually a parabola. Now we need to delve a little into the works of Johannes Kepler (1571-1630) and Isaac Newton (1642-1726) to clear our understanding how ballistic missiles work. Yes! All fancy ballistic missiles are based on the findings written some 300 years ago. We will introduce a bit of Einstein later on to complete our understanding.

Kepler’s Law of Planetary Motion states that when a small heavenly body revolves around a larger heavenly body for example, Earth and moon, the orbit of the smaller body around the larger body is an ellipse whose one foci goes through the center of larger heavenly body. It is essentially a Two-body problem, very predictable unlike a three-body problem which can generate infinite solutions.

 A ballistic missile trajectory is a two-body problem where the trajectory is an ellipse, one foci being the apogee and the other passing through the center of the Earth. To keep our mathematical equations simple, we depict Earth as a perfect sphere and a reference sphere. Pictorially a ballistic missile trajectory is depicted below:-

Source: George M Siouris, Missile Guidance and Control Systems, Springer, NY, 2004, Fig 6.1, P 369

A little more high school physics is necessary even though the reader may find it boring.

Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In  high school we were taught that Force= mass X acceleration. Acceleration is also termed as rate of change of velocity. Now without delving into the actual derivation we will skip to the last part to express acceleration in terms of integration as

/a =   /v = /x (Lat & Long).

This is a very important for the reader to hoist. What it means is that if we know the acceleration exactly, we know our velocity exactly, we can arrive at our target position in terms of Lat & Long accurately.

But to know our acceleration accurately, we need to know our initial position accurately. To know our initial position accurately in  a three-dimensional space, we need to know our X, Y and Z coordinates accurately. In terms of ballistics, we refer to them as North, East and Down.

The accuracy of our position depends on how accurately we know the value of acceleration due to gravity at initial position and that depends on how accurately we know the Z component as also the center of the Earth.

Without confusing the lay reader any further, it suffices to say that the missile must know its initial position accurately. Ideally, the Z component should be exactly vertical with no tilt. Unfortunately, that is not possible due a variety of reasons and certain amount of tilt in the Z component always takes place which needs to be compensated. Since the position is a double integration, any error that creeps in the initial position grows quadratically with respect to time.  

In a ballistic missile, the guidance is done by an inertial navigation system that comprises of accelerometers and gyros. The accelerometer needs to be very accurate to reduce the error and the gyros too need to be accurate to reduce the drift, which we know by now increases quadratically with respect to time. No matter how accurate the accelerometer and gyros, the drift is significant in any ballistic missile that will always require a position update in its boost phase to reduce the error. This could be by means of a star sensor or by GPS.

For a standard ballistic missile trajectory, the powered flight is about 3 to five minutes and the missile reaches a velocity between 4 to 7 km per second till the burnout point. Thereafter the missile travels for about 25 minutes in a free fall till it reaches an apogee at 1200 km from there on the ballistic missile then starts falling towards the Earth and it enters the atmosphere at the high speed where the velocity of almost eight km per second and at this re-entry to the target point is about 2 minutes. The accuracy of the missile hitting the target depends to a very large extent on the accuracy of its initial position with respect to its position on the Earth.

Source: George M Siouris, Missile Guidance and Control Systems, Springer, NY, 2004, Fig 6.1, P 369

Now the biggest problem in ballistic missile theory is to find the position of where am I now? Since it is a three-dimensional space you have N,E and Down or X, Y and Z components in an orthogonal system. The calculations would have been very simple had the Earth been a perfect sphere and the value of acceleration due to gravity been constant. But unfortunately, the Earth is not a perfect sphere, it is an oblate spheroid. More so, when we view the Earth in terms of Gravity values, it is nowhere close to even an oblate spheroid, it is more like a misshapen potato.

Source: The European Space Agency Website at https://www.esa.int/ESA_Multimedia/Images/2005/04/The_Earth_s_gravity_field_geoid

This is so because  the Earth's mass is not evenly distributed. The measurement of gravity differs across the planet's surface which leads to something called as free air gravity anomalies which need to be mapped. The Earth Gravitational Model 2008 gives an approximate gravitational map of the Earth which is freely available as open source. Countries like the US have higher accuracy gravitation models of the Earth but those are classified as they have significant military purposes.  Now gravity at the equator is approximately 9.76 m/s2 and at the poles it is 9.832 m/s2 . The rotation rate is 23 hours 56 minutes, the speed of rotation is 465 m/s or 1669 km/hr. The Earth also tilts to 23.4 degrees and it oscillates between 22.1 to 24 .5 degrees.  We also have a Coriolis Force. Therefore, the missile guidance system needs to compute all this to reach its target for that we have an inertial navigation system on board which was briefly discussed earlier in the article. Further amplification on the inertial navigation systems is essential to clearly understand the subject.

There are two types of inertial navigation systems -  autonomous and assisted. These can be either gimballed or strap down. The earlier systems were gimballed, mechanical because the technology of the day had not evolved sufficiently. They were bulky and were super expensive to manufacture being mechanical systems. The advantage was that there was no need to compensate for the motion of the missile. A strapdown system requires complex algorithms to compensate as the system is physically fixed to the body of the missile.  The inertial navigation system on board a missile necessarily has to be small in size and is called as Inertial Measurement Unit (IMU). The IMU has various grades depending on the type of usage. It ranges from instrumentation, tactical, navigation, and strategic. For a strategic missile, the accelerometer bias needs to be less than 1µg and the gyroscopic bias needs to be less than 0.0001 degree per hour (8). These are horribly expensive to manufacture and very few countries have the capability to make such strategic grade IMUs. Even if they do make them, the high cost and frequent replacements limit their utilization to strategic nuclear missiles. It is doubtful that any country would use such high-grade systems on a conventional ballistic missile. The  ‘highly accurate’ IMU peddled by various companies have an accuracy of tactical grade at the best and all of them require positional updates or else the drift rate errors are too high to be of any use.

Now let us look at the frames of references that a missile uses for it to accurately hit the target. Firstly, it has the inertial frame which is fixed in space. Secondly, is the earth centred frame which rotates with the earth. Thirdly is the Earth's surface frame. Fourthly, it is the missile local frame. The equations of motion computed within these frames of reference are six Degree of Freedom (6DoF) equations because you have the three axes -X,Y and Z, and roll pitch and yaw. Computing 6DoF equations and controlling translation errors amongst the frames of references is no easy task.

More so, the accuracy of targeting is time dependent. GPS or Baidu if used integral to the system loosely coupled or tightly coupled suffers from numerous errors; those that originate at the satellite namely the satellite clocks, the selected availability and the accuracy of ephemeris data. GPS errors also originate in signal propagation or atmospheric refraction causing atmospheric delays.  Then there are errors that originate at the receiver namely multipath and receiver clock accuracy. At this point a bit of Einsteinian relativity also comes into play. Various effects that make a difference are gravitational red shift, time dilation, Sagnac effect, inter satellite links, earth oblateness, curvature delay, Shapiro delay, tidal potential and the Lense-Thirring effect. All these add to GPS errors. So next time you think GPS is very accurate, it is not, especially when it comes to ballistic missile targeting.

If we were to summarize the sources of ballistic missile errors it could be clubbed under ; navigation, accelerometer, gyroscope and miscellaneous. There are 24 basic errors that actually translates into computing over 300 global parameters. Majority of these calculations are completed prior launch of the missile and the balance while in flight.

Now let us come to the re-entry phase. According to open-source information and those fabulous YouTube videos that you would have seen; a ballistic missile warhead enters the atmosphere and starts revolving at 2 revolutions per second. The missile acceleration reaches 120 G, the missile velocity is eight km per second and the re-entry time is two minutes.  The videos would have you believe that the cone shaped warhead revolves exactly and hits the target with pin point accuracy. Not true.

On entry, a warhead is subjected to intense heat due to atmospheric friction. To protect the warhead and the guidance system, the warhead needs a protective shield. In the olden days, the heat shield was a heat sink, a heavy layer of aluminium, steel or beryllium alloy which due to aerodynamics, were blunt shaped and these wobbled on the way down as described by Graham Spinardi in his wonderful book, From Polaris to Trident (9)  resulting in a large Circular Error Probable (CEP). Now, all ballistic missile warheads have a carbon-carbon ablative shield that burns off . Though the weave pattern does control the wobble to a large extent, weather encountered on the way down still induces a certain amount of wobble and error in hitting the target (10). The errors however are manageable as the target is a stationery fixed target. The launch position is also a fixed position. A moving launch platform such as a ship, a submarine or an aircraft introduces even more complication as now the 6DoF equations of motion of the platform also need to be calculated.

The earliest successful missile in this class was the Pershing II that saw deployment by the Americans in the period 1983-1991. The Pershing II was a two-stage solid fuel missile, with an 80-kilo tonne warhead, range of 1700 kilometres with re-entry velocity of Mach 8. It had vector control fins for guidance. It had inertial guidance and radar guidance in the terminal stage and the CEP was reportedly 30 metres(11). The ballistic trajectory was deliberately made manoeuvrable so that Anti-Ballistic missile systems would have a hard time destroying it. As per open source, the Pershing II on entering the Earth's atmosphere would do a ‘pull up’ manoeuvre and thereafter scan the surface using its built- in radar and home onto the target  with the help of the control fins. In any pull up manoeuvre, the velocity reduces. Calculations show that a Mach 8 ballistic missile entering the Earth’s atmosphere on doing a pull up manoeuvre would have the velocity reduced to just about Mach 2. The Pershing II was designed specifically to hit stationery targets. It was abolished as part of ratification of Intermediate  Range Nuclear Forces Treaty in May 1988. The Chinese extensively studied the Pershing II and the DF-21D  was born. 

Let us now discuss the Chinese ASBM ‘kill chain’ as it is depicted on various Chinese websites. A brief description was provided at introduction but now a slightly detailed look is needed.

Source: https://blogos.com/article/35397/

According to the depiction, satellites would pick up the position of advancing American aircraft carriers. They would relay the data to aircraft or UAVs also. The position would be relayed to the ASBM launchers ashore and the missile would be launched based on the information received.

So let us look at the vital components of this ‘kill chain’. Firstly, the satellite data flow. If there is a satellite in polar orbit travelling at speeds 7 to 8 km per second, it has a 10-minute window to pass data to the ground station. The raw data reaches the ground station and is processed. The processing time depends on the sophistication and processing power deployed. It could  days, an hour or maybe even minutes. Let us give the Chinese the benefit of doubt that they have reduced the processing time lag to minutes. Thereafter the user then retransmits this data to the  launchers, the aircraft or UAVs deployed. If you increase the number of satellites then the data flow can be reduced to as much as 6 to 7 minutes. These are theoretical calculations. Nobody knows what the truth is. The satellites have their own internal errors in tracking the target, its own position with respect to the frames of references and transmission losses during data transfer. The air assets data flow whether  using drones or fixed wing aircraft, their speeds, coverage, numbers deployed and associated data link issues on account of use of HF/VHF/UHF or satellite link, all have significant errors.

Another red herring which we often come across on the Internet is that the Chinese are using Over the Horizon Targeting B (OTH B) radars for initial tracking of the aircraft carriers. Let us look at the basic physics of an OTHB radar. The frequency range is from 3 to 30 megahertz. The wavelength is 100 to 10 metres. The range resolution is 20 to 40 kilometres. The bearing resolution is between two to four kilometres. The system is heavily dependent on an accurate climatological model which has to be updated on an hourly basis. Even after doing that the position that you get can be off by tens of kilometres. OTH B radars primary use is for detecting ballistic missile launch and aircraft detection not warships. Simply not practicable.  The other variation, OTH Surface wave radar which is used for detection of warships is limited by physics to a range of about 180nm and therefore would not fit the template.

Let us  now look at the actual interception calculations.

Source: https://www.popularmechanics.com/military/weapons/a12366/how-it-works-china-antiship-ballistic-missile/

As per open-source information, the DF-21D supposedly has a range of 1500 to 2000 kilometers. On being launched its boost phase time is about 70 secs where it attains a velocity of 4km/s. Target update has to happen in this boost phase before the burnout. Thereafter the missile has a mid-course of 400 secs and it reaches an apogee of about 400km. No maneuvering is possible in this phase. Thereafter it enters the atmosphere with a velocity of Mach 8 and time to target is 67 secs. The missile is designed to do a pull up maneuver like the Pershing II and open its guidance to home on to the target. At this point, the missile velocity would drop to 0.6 km/s or Mach 2. Any Aegis SM-3 equipped warship can easily destroy the warhead as the SM-3 system can intercept a 3 to 5 km/s missile with ease. More so, an aircraft carrier at speed of 24knots after 60 secs would have moved off by 740 meters based on simple vector analysis. The chances of hitting a moving target are absolutely slim, if at all. 

So, what is the proof that DF-21D works? on 26 August 20, approx. four missiles, DF 26 and DF-21 D were reportedly launched into the South China Sea. According to Taiwanese reports these were unsuccessful. Out of which, one of them landed ashore! Then we also have satellite photographs of Chinese ASBM tests in the Xinjiang desert wherein an aircraft carrier model on a railway track is shown. Then we have another set of satellite photos showing that the missile has hit a destroyer sized target in the desert (12). Calculating the trajectory of a missile to hit a target which is moving in a linear fashion on a rail track is quite different from targeting a moving target at sea which can move anywhere in any direction. We all have read the reports on the subpar performance of standard American weapons in the Ukraine Russia war (13).

Here we have an untested, unknown, futuristic weapon which  claims to hit aircraft carriers out at sea. So far there is no evidence. Theoretically, ASBMs can hit a moving target. But the actual mechanization of the physics, the need for flawless and seamless performance of each and every equipment in the entire network makes it an extremely difficult proposition to succeed in the real world.

About the author:

Rear Admiral Ajay V Bhave (Retd) is a Navigation and Direction specialist. In his over 37 years naval career, he has held important appointments such as the Principal Director Strategy, Concepts and Transformation, NA Moscow, Chief Staff Officer (Sea Vector) Strategic Forces Command, DG Varsha and Flag Officer Doctrines and Concepts in addition to his over 18 years at sea. The views expressed in this article are those of the author and are based solely on open-source information.