Download - A Report on Ballistic Missiles
A Report on Ballistic Missiles Deborah Joseph*1, Jayashree. S*2
#Department of Aeronautical Engineering, Anna University [email protected]
Abstract— This journal presents an analytical study on the various types of ballistic missiles and the basic missile systems. It compares
the different characteristics of each type with numerous examples and some factors such as ballistic coefficient that aids in obtaining an
accurate evaluation. It also includes a few basic MATLAB codes for simple mathematical computations which aid in evaluating the apt
trajectories of the ballistic missiles.
I. INTRODUCTION
The word missile comes from the Latin verb mittere, meaning “to send”. Missiles are greatly used in the
military both to defend and to attack. In the words of laymen, a missile is a body capable of being thrown or
journaled to strike a distant object. In scientific terms though, a missile is a self-propelled precision-guided
munition system, as opposed to an unguided self -propelled munition, referred to as a rocket. These are
categorized as ballistic missiles and cruise missiles. A cruise missile is a guided missile used against
terrestrial targets that remains in the atmosphere and flies the major portion of its flight path at
approximately constant speed. Cruise missiles are designed to deliver a large warhead over long distances
with high precision. Modern cruise missiles are capable of travelling at supersonic or high subsonic speeds,
are self-navigating, and are able to fly on a non-ballistic, extremely low-altitude trajectory. In this journal,
we are mainly concentrating on ballistic missiles. A ballistic is a missile that follows a ballistic trajectory
with the objective of one or more warheads to a predetermined target. A ballistic missile is only guided
during relatively brief periods of flight and most of its trajectory is unpowered and governed by gravity and
air resistance if in the atmosphere. This contrasts to a cruise missile, which is aerodynamically guided in
powered flight. Long range intercontinental ballistic missiles (ICBM) are launched on a sub-orbital flight
trajectory and spend most of their flight out of the atmosphere. The shorter- range ballistic missiles stay
within the earth’s atmosphere. MATLAB plays a major role in trajectory shaping for various ballistic
missiles and provides a ballistic target flight trajectory simulation which aids in evaluating its precision and
helps in making the required amendments in the missile systems. Numerous algorithms are used in
MATLAB in order to compute various values and obtain the perfect trajectory for a ballistic missile, which
is highly reliable.
II. Chapter-1- MISSILE SYSTEMS
A. Introduction
The invention of missiles was inspired by rockets which were used since A.D 1232 by the Chinese.
Rockets could be in other words called the “unguided missiles”. The early usage of rockets was as weapons
in wars and later on was developed to be used for communication or signals. The idea of creating guided
missiles was greatly influenced by aircrafts. The history of guided missiles dates back to the beginning of
World War I when the idea was born and implemented in World War II by the Germans (V1 and V2 series
of guided missiles). In the simplest of terms, Missile is an unmanned guided weapon. It is a precision-guided
munition that hits the specified target precisely with no collateral damage and maximum destruction of the
target (enemy’s assets). Basically missiles are categorized into Guided and Unguided missiles; but in this
chapter we will be discussing only about the guided missiles, its classifications, systems and properties.
Guided missiles are also known as homing missiles.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2248
Homing guidance is generally of active, semi-active, or passive type. Once the active missiles are
launched to the target they are capable of guiding themselves independently. These are also called launch-
and-leave missiles and are heavier than semi-active and passive missiles. The active guided missile have a
radiation source, this radiation from the interceptor missile radiates and strikes the target and is reflected
back. The missile then guides itself on this reflected radiation. In case of passive missiles, the radiation
originated by the target or some other source that is not a part of the overall weapon system is used. While a
semi-active missile uses a combination of both active and passive missiles, the source of radiation in these
types of missiles is at the launch point which radiates energy to the target. This energy is reflected back to
the missile and sensing the reflected radiation the missile homes on it.
B. Technology
Missiles basically have five major system components;
1. Targeting system
2. Guidance system
3. Flight System
4. Propulsion System/Engine
5. Warhead
Targeting systems
One of the most essential parts of Missiles is its targeting system. There are numerous ways in which
missiles can be targeted, the most common being the use of some type of radiation such as infrared, radio or
lasers to guide the missile onto its target. If the location of the target is known, then guidance system such
as Inertial Navigation System, Terrain Contour Matching or Satellite Guidance is used which calculates the
course between the missile and target when the location of both these components is known. This work also
can be done by a human operator who can visualize the target and the missile and guide it using either cable
or radio-based remote control or by an automatic system that can simultaneously track the target and the
missile.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2249
Guidance Systems
The three major parts of the guidance system of the missiles are navigation, guidance and control.
Navigation tracks the existing location of the missile; guidance directs the missile in the accurate direction
of the target by taking navigation data and the target information as input. On the grounds of the profile of
the target, guidance system is classified into Go-onto-target (GOT) and Go- Onto- Location-in- space
(GOLIS). GOT is highly efficient on both stationary and moving targets while GOLIS is mostly successful
in cases with stationary or almost stationary targets. Line of sights system, pure pursuit and proportional
navigation are the most used Guidance Systems.
Flight Systems
The Flight system uses the data from the targeting or guidance system to maneuver the missile in
flight, allowing it to convert inaccuracies in the missile or to follow a moving target.
There are two main systems:
1. Vectored thrust- enables the missile to manipulate the direction of thrust in order to gain control over the
attitude or the angular velocity of the missile.
2. Aerodynamic maneuvering- since missiles do not posses conventional control surfaces, they employ
aerodynamic control surfaces in order to maneuver the missile in the desired direction.
Engine
Missiles are obviously powered by rockets engines. Rockets are generally of the solid propellant type
for ease of maintenance and fast deployment, although some larger ballistic missiles use liquid-propellant
rockets. Long-range missile may have multiple engine stages, particularly in those launched from the surface.
These stages may all be of similar types or may include a mix of engine types. For example, Surface-
launched cruise missiles often have a rocket booster for launching and a jet engine for sustained flight.
Some missiles may have additional propulsion from another source at launch; for example, the MGM-51 S
Shillelagh was fired out of a tank gun.
Warhead
Missiles generally have one or more explosive warheads, which provide primary destructive
power to the missile and also sometimes provide extensive secondary destructive power due to the high
kinetic energy of the weapon and unburnt fuel that may be on board. Warheads are most commonly of the
high explosive type, often employing shaped charges to exploit the accuracy of a guided weapon to destroy
hardened targets. There are some types of warhead used in missiles are sub munitions, incendiaries, nuclear
weapons, chemical, biological or radiological weapons or kinetic energy penetrators. Without warhead
missile cannot be constructed, the warheadless missiles are often used for testing and training purposes.
C. Types of Missiles
Missiles are generally categorized by their launch platform and intended target. In broadest terms there
will either be surface i.e ground or water, and then sub-categorized by range and the target type. Missiles
require some modification in order to be launched from the air or surface, such as adding boosters to the
surface-launched version.
1. Surface-to-surface missile
2. Air-to-surface missile
3. Surface –to-air missile
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2250
4. Air-to-air missile
5. Anti- satellite weapons
Figure 2.1The various types of missiles
Surface-to-surface missiles
Figure 2.2 Surface-to-Surface Missile- Prithvi II-Range of 205- 350 km
A surface -to-surface missile (SSM) or ground -to-ground missile (GGM) is a missile designed
to be launched from the ground or the sea and strike targets on land or at sea. They may be fired from hand-
held or vehicle mounted devices. They are often powered by a rocket engine or sometimes fired by an
explosive charge. It’s having fins or wings which provide lift and stability. The V-1 flying bomb was the
first operational surface-to- surface missile.
Some surface-to-surface missiles examples are given below;
Prithvi- I SRBM- India- Range of 150km
Prithvi- II SRBM - India- Range of 205-350km
Prithvi- III SRBM - India- Range of 350-600km
Agni-I MRBM- India- Range of 700-900km
Agni- II MRBM- India- Range of 2,000- 3,500 km
Agni- III IRBM-India- Range of 3,500-5,000km
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2251
Agni-IV IRBM- India- Range of 4,000km
Agni- V ICBM- India- Range of 5,000-8,000km
Agni- VI Four stage ICBM- India- Range of 8,000-10,000km
Dhanush-Naval variant of Prithvi II- India- Range of 350km
Shaurya- Hypersonic, Canister launched- India- Range of 700-1900km
Types
Surface-surface missiles are usually broken down into a number of categories:
Ballistic missiles:- travel in a high trajectory, motor burns out partway through flight
Tactical ballistic missile:- Range between about 150km and 300km
Battlefield range ballistic missile (BRBM):- Range less than 200 km
Theatre ballistic missile (TBM):- range between 300 km and 3500 km
Short-range ballistic missile (SRBM):- Range 1000km or less
Medium –range ballistic missile (MRBM):- Range between 1000 km and 3500 km
Intermediate-range ballistic missile (IRBM) or Long-range ballistic missile (LRBM):- Range between 3500
km and 5500 km
Intercontinental ballistic missile (ICBM): - Range greater than 5500km
Submarine-launched ballistic missile (SLBM):- Launched from ballistic missile submarines (SSBNs), all
current designs have intercontinental range.
Cruise missiles:- travel low to the ground ,motor burns during entire flight, typical range 2,500km
Anti-tank guided missiles:- travel low to the ground, may or may not burn motor throughout flight typical
range 5km (3mi)
Anti-ship missiles:- travel low over the ground and sea, and often pop up or link before striking the target
ship: typical range 130km (80mi).
Air-to-surface missiles
An air-to-air missile (ASM) or air-to-ground missile (AGM or ATMG) is a missile designed
to be launched from military aircraft at targets on land or sea. There are also unpowered guided glide bombs
not considered missiles. The two most common propulsion systems for air-to-surface missiles are rocket
motors, usually with shorter range, and slower, longer-range jet engines. Some Soviet-designed air-to-
surface missiles are powered by ramjets, giving them both long range and high speed.
Guidance for air-to-surface missiles is typically via laser guidance, infrared guidance, and optical
guidance or via satellite guidance signals. The type of guidance depends on the type of target. Ships, for
example, may be detected via passive radar or active radar homing, less effective against multiple, small,
fast-moving land targets.
There is some cross-over between air-to-surface missiles and surface-to-surface missiles. For
example, there was an air-launched version of the Tomahawk missile, superseded by the AGM-86 ALCM.
A major advantage of air-to-surface missiles for ground attack by aircraft is the standoff distance they
provide: missiles can be launched from a distance without coming within range of the target’s air defense.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2252
Figure 2.3 Air-to-Surface Missile- BrahMos- Range of 400km
Most air-to-surface missiles are fire-and-forget from a standoff distance, allowing the attacker to
withdraw without approaching further after launch. Some missiles typically cruise missiles or anti-ship
missiles have long enough range to be launched over the horizon, finding the target autonomously. Few of
the many examples are listed below:
Nag – India- Range of 7-10km
Helina- India – Range of 7-8km
BrahMos- India and Russia- Range of 400km
AGM-114 Hellfire- USA – Range of 500-8km
AGM- 84 Harpoon- USA- Range of 124m
AGM- 65 Maverick-USA- Range of 22km
Types
Air-to-surface missiles are classified as follows;
Ballistic missile (DF-26—China)
Air-launched anti-tank guided missiles (AS-25k – Argentina)
Air-launched cruise missiles (AGM-86 – USA)
Air-launched anti-ship missiles (AGM-84 Harpoon – USA)
Surface-to-air missiles
These are generally radar or infrared guided missiles fired from ground position to destroy the
aircrafts of the foes. SAMs were developed to defend the ground positions from hostile air attacks especially
from the high altitude bombers flying beyond the range of the ‘anti-aircraft artillery’. These missiles are
used to demolish the enemy’s aircrafts as well as other missiles. It requires extreme precision to hit the
target accurately.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2253
Figure 2.4 Surface-to-Air Missile- Akash- Range of 30 km
Thus SAMs are still being developed to gain high accuracy by using various guidance methods. The most
common examples of SAMs used by the Indian Defense are:
Akash – India- Range of 30km
Barak 8 – India- Range of 90km
Maitri – India- Range of 25-30km (under development)
Trishul- India- Range of 9km
RIM-7 Sea Sparrow- USA- Range of 19km
FIM- 92 Stinger- USA- Range of 8km
RIM-116 Rolling Airframe Missile- USA- Range of 9km
Air-to-air missiles
Figure 2.5 Air-to-Air Missile- Astra- Range of 80- 110 km
Air- to- air missiles are powered by rocket motors to hit the intended targets that are aircrafts or
missiles in air. AAMs are broadly classified into two types, SRAAMs or WVRAAMs i.e., short- range air-
to-air missiles or within visual range air-to-air missiles and MRAAMs or LRAAMs i.e., medium range
missiles or long range missiles.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2254
SRAAMs infrared guidance and are known by the name ‘heat seeking missiles’ while MRAAMs and
LRAAMs use the inertial guidance. Various other guidance systems are used under these categories
depending upon the requirement and the accuracy is acquired accordingly. Since the First World War there
have been numerous developments in the AAMs. We have two Air-to-Air missiles manufacture in India:
Astra Mk.I- India- Range of 80-110km
AIM-7 Sparrow- USA- Range of 11-70km
AIM-9 Sidewinder- USA- Range of 1-35.4km
AIM-120 AMRAAM- USA- Range of 55-180km
Anti Satellite Weapons
In the recent past space has been highly used as a medium for war. The military potential of the
satellite is diverse, such as, signal intelligence, early-warning systems, navigation and most importantly
communication. The side which gets the upper hand in dealing with the satellite defiantly has an advantage
and will dominate over the other side when it comes to war. Once the satellite is used in war, everything that
the enemies do is monitored and can even be controlled. The Air Force describes space superiority as “the
ability to maintain freedom of action in, from, and to space, sufficient to sustain mission assurance.” Once
the satellite is detected, the missile is launched into orbit close to the targeted satellite. It takes 90 to 200
minutes (or one to two orbits) for the missile interceptor to get close enough to its target. The missile is
guided by onboard radar. The interceptor, which weighs 1400 kg, may be effective up to one kilometer from
a target. Few examples of Anti-Satellite are listed below:
ASM-135 ASAT- USA- Range of 648 km
SC-19 ASAT- China- Range of 865km
RIM-161 (SM 3)- USA- Range of 700km
Figure 2.6 Anti- Satellite Missile – SM 3 ASAT Missile
III. Chapter-2- BALLISTIC MISSILE
A. Introduction
In case of Ballistic Missiles, the targets are predetermined and the missile follows a ballistic
trajectory most of its flight path with the objective to hit the intended target, for terminal stage ballistic
missiles fall under the influence of gravity and air resistance if in the atmosphere. Most of the modern
ballistic missiles have more than just one warhead thus making it more effective in destroying the target.
These are long range surface-to-surface missiles with a range of over 5,500 km. The shorter ranged ballistic
missiles do not leave the Earth’s atmosphere.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2255
The path of motion of ballistic missiles is very similar to the motion of a ball thrown in air; which to some
extent travels in air due to the force with which it was thrown and then falls down due to gravity. Ballistic
missiles are categorized according to their range, the maximum distance measured along the surface of the
Earth’s ellipsoid from the point of lunch of the ballistic missile to the point of impact of the last elements of
its payload. The course of the ballistic missiles are pre-set, thus cannot be altered after the missile has
burned its fuel unless a warhead maneuvers independently or some form of terminal guidance is provided.
They also closely follow the a pre-established azimuth (the direction of a celestial object from the observer,
expressed as the angular distance from the north or south point of the horizon to the point at which a vertical
circle passing through the objects intersects the horizon) from launch point to target. It is extremely difficult
to counter act Ballistic missiles because during impact they reach hypersonic speeds of Mach 10 to Mach 30.
B. Components
A ballistic Missile basically has two major components-
1. Payload
2. Booster
Ballistic missiles are extremely destructive and difficult to defend against. They traverse distance
rapidly; a long-range ballistic missile can travel to the other side of the world in less than 30 minutes. Since
they are extremely fast and give less or no advance warning before delivering small but fast moving
payloads they have the potential to demolish entire cities together.
1) C. Payload
Payload is basically a package in ballistic missile that contains the guidance systems and the explosives
which include one or many warheads and is called MIRV (Multiple Independently Targetable Re-entry
Vehicle) system. The missiles that bear MIRV are said to be MIRVed the first of which was developed in
USA in the year 1970. Generally only long-range ballistic missiles are MIRVed. It may -possess a low
power propulsion system that enables it to impart slightly different velocities to each of its warheads, which
it releases at different times. The nuclear warheads mounted on modern long-range ballistic missiles are
usually thermonuclear warheads having yields in several hundred kilotons to several megatons (one kilotons
is equal to the explosive power of one thousand tons of the chemical explosive TNT; thus one megaton is
equivalent to a million tons of TNT). The regional or approximate targeting for each warhead is attained by
bus maneuvering and release timing during cruise phase. And during the descent phase the warhead may
steer itself towards the target by means of inertial guidance, radar guidance or a combination of two.
Inertial guidance can be best explained with the example of aiming a basket in the game of basket ball; when
a player releases the ball the intent is to give the ball the trajectory that would make the ball fall straight into
the basket.
However once the ball is released the shooter has no control over it. Sometimes when the aim is wrong or
the ball does not follow the trajectory due to some reason it is possible for some other person to push it back
to the right course so that it lands inside the basket. In this case, the
second person plays the role of providing the required guidance. Similarly, the inertial guidance system
supplies the intermediate push to get the missile back on the proper trajectory. MARVs may also refine their
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2256
final course by consulting the Global Positioning System or by using radar to guide themselves during final
approach.
D. Boosters
Booster is the name used for the rocket inside the missile that lofts the payload into the upper
atmosphere or into space. In the earlier days, the booster rockets were powered by liquid fuels. A liquid-fuel
rocket consists of fuel (hydrazine, liquid hydrogen, or other) and liquid oxygen in tanks. Pressurized steams
of fuel and oxygen are mixed and ignited at the top of a bell- shaped chamber. The hot gases expand and
rush out of the small opening in t he bell, giving the required momentum to the rocket in the opposite
direction. One major disadvantage of liquid-fuel rocket is that they require frequent maintenance. Thus since
the late 1950’s solid- fuel boosters are used instead as they require less maintenance, launch preparation
time and are more reliable because they consist of fewer moving parts. Solid-fuel rockets contain long,
hollow –core casts of a fuel mixture that, once ignited, burn from the inside out in an orderly way, forcing
gases out the rear of the rocket. There are various stages of solid-fuel booster. Stages are independent
rockets that are stacked to from a single, combined rocket.
Figure 3.1 Components of a Ballistic Missile
E. Types of Ballistic Missiles
Ballistic Missiles are generally categorized by their range. Different countries use different schemes to
categorize the range of ballistic missiles.
The United Sates divides missiles into four range classes
1. Intercontinental Ballistic Missile ICBM over 5500km
2. Intermediate-Range Ballistic Missile IRBM 3000-5000km
3. Medium-Range Ballistic Missile MRBM 1000-3000km
4. Short-Range Ballistic Missile SRBM up to 1000km
The Soviet and Russian Military developed a system of five range classes
1. Strategic over 1000km
2. Operational – Strategic 500-1000km
3. Operational 300-500km
4. Operational- Tactical up to 50km
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2257
Intercontinental Ballistic Missile
Intercontinental Ballistic Missiles have a minimum range of 5,500 kilometers. Most of the
modern missiles support MIVRs which enables it to carry several warheads, each of which can strike
different targets. ICBMs have three different flight phases:
Boost phase- This phase lasts for around 3 to 5 minutes. It is actually shorter for a solid-fuel rocket than for
a liquid-propellant rocket. Depending upon the trajectory chosen, the typical burnout speed varies between
4km/s to 7.8 km/s. at the end of the phase the altitude reached by the missile is around 150 to 400 km.
Midcourse phase- This lasts for approximately 25 minutes. The journalile of the flight path
on the surface of the Earth is close to a big circle, slightly displaced due to Earth’s rotation during the time
of flight.
Reentry/Terminal phase- This phase starts at an altitude of 100km and its impact is at a speed
of up to 7km/s.
Figure 3.2 A Soviet R-36M (SS-18 Satan)- Range of 10,200- 16,000km, the largest ICBM in history
After the launch of the ICBM, a booster pushes the missile and then falls away. Most modern
boosters are solid-fueled rocket motors, which can be stored easily for long periods of time. Once the
booster falls away, the remaining bus releases several warheads each of which continues on its own
unpowered ballistic trajectory. The warhead is encased in a cone-shaped reentry vehicle and is difficult to
detect in this phase of flight as there is no rocket exhaust or other emissions to mark its position to
defenders. The high speeds of the warheads make them difficult to intercept and allow for little warning,
striking targets many thousands of kilometers away from the launch within approximately 30 minutes. As
the nuclear warhead reenters the Earth's atmosphere its high speed causes compression of the air, leading to
a dramatic rise in temperature which would destroy it if it were not shielded in some way. As a result,
warhead components are contained within an aluminum honeycomb substructure, sheathed in a pyrolytic
carbon-epoxy synthetic resin composite material heat shield. Warheads are also often radiation-hardened (to
protect against nuclear-tipped ABMs or the nearby detonation of friendly warheads).
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2258
Figure 3.3 A Pictorial representation of a three stage ICBM
Listed below are the two specific ICBMs:
Land-Based ICBMs-
Russia, the United States, China, North Korea and India are the only countries currently known to
possess land-based ICBMs, Israel has also tested ICBMs but is not open about actual deployment. As the
name suggests these missiles are launched from the land. Currently the United States operates around 405
ICMs in three USAF bases, the Russians Strategic Rocket Forces have 286 ICMBs able to deliver 958
nuclear warheads, China on the other hand has developed various long-range ICMBs over the years and
even has a mysterious underground ICMS carrier system called the “Underground Great Wall Journal” and
India has a series of ballistic missiles called Agni. On 19 April 2012, India successfully test fired its first
Agni-V, a three-stage solid fuelled missile, with a strike range of more than 7,500 km (4,700 mi). The
missile was test-fired for the second time on 15 September 2013.[13] On 31 January 2015, India conducted a
third successful test flight of the Agni-V from the Wheeler Island facility. The test used a canisterised
version of the missile, mounted over a Tatra truck.
Figure 3.4 A U.S Peacemaker missile – Range of 14,000 km launched from a silo
A few examples of Land-Based Ballistic Missiles are listed below:
DF-5 – China—Range of 12,000-15,000 km
DF-41—China—Range of 12,000-15,000 km
Hwasong-14 – North Korean – Range of 6,700- 10,000 km
Hwasong-15 – North Korean – Range of up to 13,000 km
LGM-30 Minuteman III—USA—Range of 13,000 km
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2259
RT-2UTTH “Topol M” – Russia – Range up to 11,000 km
R-36 – Soviet Union—Range of 10,200- 16,000 km
Agni V—India—Range of 5,000-8,000 km
Submarine-Based ICBMs-
A Submarine based ICBM is a ballistic missile capable of being launched from submarines.
Modern day submarine-launched ballistic missiles have a range of over 5,500 km.
Figure 3.5 A UGM- 96 Trident I- Range of 7,400 km clears the water after launch from a US Navy submarine
Listed below are a few examples of Submarine-launched ICBMs:
UGM-133 Trident II (D5LE)—USA—Range of 12,000 km
RSM-54 R-29RMU2 “Layner”—USA—Range of 8,300-12,000 km
M51—France—Range of 8,000-10,000 km
JL-2—China—Range of 7,400- 8,000 km
K-5 – India—Range up to 6,000 km
Pukkuksong-1/KN-11—North Korean – Range of 500- 6,700 km
Intermediate Range Ballistic Missile
Figure 3.6 Successful test fire of Agni- IV – Range of 4,000 km
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2260
Intermediate -range ballistic missile can also be called strategic weapon, which has a range of 3,000-
5,000 km. As intermediate-range ballistic missiles range is lesser than Intercontinental ballistic missile, it
can hit the target more accurately compared to Intercontinental ballistic missile. At present Intermediate –
range ballistic missile are operated by only few country namely China, India, Israel, North Korea, United
States, USSR, United Kingdom, and France were former operators of this missile.
A few specific IRBMS examples are listed below:
PGM-17 Thor – United states, United Kingdom – Range of 1,850-3,700 km
DF-3A –China –Range of 4,000-5,000 km
Agni-III –India –Range of 3,500-5,000 km
Agni-IV –India –Range of 4,000 km
Hwasong-12/KN-17 –North Korea –Range of 3,700-6,000 km
Medium- Range Ballistic Missile
Figure 3.7 Shaheen- III- Range of 2750 km
A Medium-Range ballistic missile is a part of theatre ballistic missile , having a range between
1,000-3,000km.
A few example of specific Medium-Range ballistic missiles are listed below:
Agni II –India –Range of 2,200 km
Ashoura –Iran –Range of 2,000-3,000 km
Blue Streak –Range of 3,700km
Hwagson-10/RD-B Musudan –North Korea –Range of 2,500-4,000 km
Shaheen-III –Pakistan –Range of 2,750 km
Shaheen-II –Pakistan –Range of 2,500km
Short- Range Ballistic Missile
A Short –Range ballistic missile has a range of about 1,000 km or less. Mainly these kinds of ballistic
missiles carry nuclear weapons. Its relative low cost and ease of configuration makes it suitable for using
whenever there is a need to hit a nearby opponent country in short distances. Like the above two types this
ballistic missile is also a part of theatre ballistic missile.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2261
Figure 3.8 Redstone No. CC-56 – Range of 92.5- 323 km
A few examples of SRBM are listed below:
Al- Hussein—Iraq—Range up to 400 km
Hwasong-7—North Korea—Range of 700-995 km
PGM-11 Redstone—U.S—Range of 92-323 km
Hyunmoo-2—South Korea—Range of 300-800 km
Sky Spear – Taiwan—Range of 120-300 km
F. Ballistic Coefficient
Ballistic Coefficient of a body is a measure of its ability to overcome air resistance in flight. It is
inversely proportional to the negative acceleration; a high number indicates a low negative acceleration that
is the drag on the journalile is small in proportion to its mass. In simple words it is often put as “the ability
of the body (here missile) to maintain velocity, in comparison to a standard journalile”. By definition it is
the weight of the object divided by the product of the coefficient of drag and the journaled area, in kilograms
per square meter.
Ballistic coefficient enables the trajectory of the missile to be easily figured out even before
the missile is launched. This aids in resolving the necessary amendments required which prevents various
defaults from affecting the missile path of motion when in air.
General formula-
BC= M/(Cd * A)
Where,
M- Mass
A- Area
Cd- Drag coefficient
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2262
Ballistics Formula-
BC= m/(d2 * i)
Where,
m- mass of the missile
d- measured cross section (diameter)
i- Coefficient of form
i= (2/n)* √((4n-1)/n)
n- number of calibers of the journalile’s ogine. In ballistics or aerodynamics, an ogive is a pointed, curved
surface mainly used to form the approximately streamlined nose of a missile, reducing air resistance or the
drag of air.
n= ((4*l2 +1)/4)
l- length of the head in number of calibers
Cd= 8/ (p*v2*π*d2)
v- journalile velocity at range
Satellites in Low Earth Orbit (LEO) with high ballistic coefficients experience smaller perturbations to their
orbits due to atmospheric drag. The ballistic coefficient of an atmospheric reentry vehicle has a significant
effect on its behavior. A very high ballistic coefficient vehicle would lose velocity very slowly and would
impact the Earth's surface at higher speeds. In contrast a low ballistic coefficient would reach subsonic
speeds before reaching the ground. In general, reentry vehicles that carry human beings back to Earth from
space have high drag and a correspondingly low ballistic coefficient. Vehicles that carry nuclear weapons
launched by an intercontinental ballistic missile (ICBM), by contrast, have a high ballistic coefficient, which
enables them to travel rapidly from space to a target on land. That makes the weapon less affected by
crosswinds or other weather phenomena, and harder to track, intercept, or otherwise defend against.
G. Standard Atmospheric Model
The International Standard Atmosphere (ISA) is an atmospheric model of how the pressure,
temperature, viscosity and density of the Earth’s atmosphere vary over a wide range of altitudes or
elevations. The ISA aids in providing a common reference for temperature and pressure at various altitudes
and also has a set of formulae to derive these values. The defense operations i.e., detection, discrimination
and interception of ballistic missiles take place within the atmosphere t rather high altitudes. Interception
takes place at altitude ranging above 20-30 km sometimes reaching up to a 100 km. Analyses normally
require one to use a model of the atmosphere that gives the atmospheric density and temperature as a
function of altitude, with emphasis on altitudes above 100 km where the density is low and the principal
variation is solar activity rather than latitude and season. Currently over 30 different model atmospheres are
in use, each model atmosphere depicts the atmospheric density and temperature at some specific time and
place. The availability of so many model atmospheres can make inter-comparison between simulation
analyses difficult and can obscure instances where real atmospheric effects are critical. For instance, for
ICBM targeting the difference between summer and winter atmospheres on a given path can amount to a 40-
km difference in range, which is obviously critical. Comparable effects arise due to varying winds, day/night
density variation, short-time dynamic perturbations, and the effects of a non-spherical earth.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2263
Winds and densities--in particular in the lower atmosphere--affect ballistic missile accuracy significantly.
For a high-performance ICBM the most important effects come from low-altitude variations in wind and
density. His calculations show that for 5-km layers centered at 5 and 10 km, a 1-percent change in density or
0.3-m/sec change in wind speed leads to perhaps a 200-m target error. This is a basic analysis that ought to
underlie any of the more sophisticated treatments that can be employed nowadays. (In fact, newer and more
sophisticated calculations of density effects frequently do not include the effects of winds.)
Figure 3.8 gives a frequency distribution of (scalar) winds with altitude at a specific location. It is
presented here to point out that the effects of wind and of its variability must be considered, to be sure that
they are not significant for a particular application. As one example, the difference between the 50th and the
75th percentile of wind speed at 6 km is 9 r/sec. In the following Table the ballistic missile range error due
to a 9-m/sec wind and a 15-percent change in density, both in the 5-10 km altitude range, for various values
of missile ballistic coefficient β= W/CD*A, for both ICBM and IRBM conditions is shown. The range
error is proportional to the wind speed as well as to the transit time through the region in which the wind is
blowing. The table shows that the effect of wind speed can be significant for some applications. Ballistic
missile targeting is affected both by details of the atmosphere and by the precise shape of the earth. The
effective range of an ICBM varies by some 20-40 km with season, purely as a consequence of the different
atmosphere. The large ICBM used in this analysis travels farther in summer and winter than in spring or fall.
Altitude
(km)
Percentile (Wind Speed)
50 75 90 95 99
1 7 10 13 15 19
6 20 29 36 41 50
10 31 43 53 60 73
11 32 44 55 62 79
12 32 44 55 62 79
20 6 10 14 17 26
23 6 10 14 17 26
40 55 67 82 90 105
50 79 96 111 120 132
58 83 107 128 140 164
60 83 107 128 140 164
75 50 65 87 98 118
Figure 3.9 Scalar Wind Speed Distribution
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2264
Engagement models simulate the flight of a ballistic missile attack from launch to interception. This
engagement takes place in the earth's atmosphere and requires the use of a unified description of
atmospheric density and temperature as a function of altitude, i.e., a model atmosphere. For BMD (Ballistic
Missile Defense) simulations it is important to use a single model atmosphere to minimize confusion in the
inter-comparison of different tactical schemes for system applications. To determine how large the effects of
atmospheric variability are on a particular application, it is recommended to run the simulation using the
US-62 model and then repeating the run with the US-76 model. The difference between these two models is
about as large a variability as one finds between any two model atmospheres. If there is a difference in the
output for the two models, this indicates the need for closer examination of the physics of the particular
problem.
The following points should be noted:
1. The most critical atmospheric parameter is normally density, which falls off drastically with
altitude; for targeting and other high-precision applications, a non-zero density may need to be considered
up to 150-180 km where the density is on the order of 10-9 of its value at sea level.
2. It must be recognized that the atmosphere varies with latitude, season, time of day, and solar
activity. Above 100-200 km the variation of density with solar activity is often the largest single effect, so
that the difference between US-62 and US-76 models may well be the largest single measure of variability.
3. In addition to these effects, there are other factors, such as wind, the non-spherical shape of the
earth, and a variety of short-term phenomena, that may be critical for specific BMD applications.
H. Journalile Motion
Journalile motion is the term used to describe the form of motion that an object when thrown in air
experiences and moves along a curved path due to the action of gravity on that object.
Figure 3.10 Journalile Motion
Journalile motion is very closely related to ballistic missile, as the study of this type of motion is
called ballistics and such a trajectory is known as ballistic trajectory. This curved path was given the name
parabola by Galileo. The only force of significance that acts on the object is gravity, which acts downward,
thus imparting to the object a downward acceleration. Because of the object's inertia, no external horizontal
force is needed to maintain the horizontal velocity component of the object.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2265
Objects that are journaled from and land on the same horizontal surface will have a vertically
symmetrical path. The time it takes from an object to be journaled and land is called the time of flight. This
depends on the initial velocity of the journalile and the angle of journalion. When the journalile reaches a
vertical velocity of zero, this is the maximum height of the journalile and then gravity will take over and
accelerate the object downward. The horizontal displacement of the journalile is called the range of the
journalile and depends on the initial velocity of the object. When an object is in a journalile motion it moves
in a bilaterally symmetrical, parabolic path. Journalile motion only occurs when there is one force applied at
the beginning on the trajectory, after which the only interference is from the gravity.
The behavior of journalile is greatly affected by air resistance and analyzing this effect is
extremely complex. In most of the instances on Earth, a journalile motion is subjected to both the forces but
in any case if an artificial vacuum has been created then it will only be subjected to the force of gravity. The
acceleration due to gravity is 32 ft (9.8 m)/sec2, usually expressed as "per second squared." This means that
as every second passes, the speed of a falling object is increasing by 32 ft/sec (9.8 m). Where there is no air
resistance, a ball will drop at a velocity of 32 feet per second after one second, 64 ft (19.5 m) per second
after two seconds, 96 ft (29.4 m) per second after three seconds, and so on. When an object experiences the
ordinary acceleration due to gravity, this figure is rendered in shorthand as g. Actually, the figure of 32 ft
(9.8 m) per second squared applies at sea level, but since the value of g changes little with altitude (it only
decreases by 5% at a height of 16km) it is safe to use this number.
Missiles are as of now the most complex form of journalile. The trajectories of the missile
vary in accordance with the initial velocity and air resistance, also known as drag. The figure 3.10 shows a
graph of how it varies with respect to these two factors.
Figure 3.11 Trajectories of a journalile with air drag and varying initial velocities
Some of the basic formulae used to analyze the various factor related to the journalile motion of a body are
listed below:
Initial Velocity
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2266
ux = ucosθ
uy = usinθ
Time Flight
T= (2uy)/g
Acceleration
ax= -g
Velocity
ux = usinθ - gt u= ux2 + uy
2
Figure 3.12 The Parabolic trajectory of a journalile
Displacement
x= utsinθ - 12gt2
Parabolic Trajectory
y= xtanθ - x2g2u2cos2θ
Maximum Height
h= (u2sin2θ)/2g
Range
R= (u2sin2θ)/ g
IV. CONCLUSION
In this world where the strength of a nation is determined by the strength of its defense
forces, missiles play a prominent role. Ballistic missiles in general are extremely hard to defend against.
Ballistic missile attacks are extremely deadly and destructive. Currently ballistic missiles are among the
most expensive of single –use weapons, up to several million dollars. The only challenge faced while
manufacturing ballistic missile is the high accuracy required for intercepting the targets which demands
proper guidance system. India began the development of the ballistic missile defense system in 1999. The
development was planned in two stages. The first phase was challenging due to the complex technologies
and indigenous mission systems employed in the mission. After 8 years of development the first missile test
was conducted in November 2006. The Prithvi-II Missile was successfully intercepted by the PAD in the
endo- atmosphere at an altitude of 48 km. Today, India is one amongst the top few countries that own the
most effective ballistic missiles.
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2267
JASC: Journal of Applied Science and Computations
Volume V, Issue XII, December/2018
ISSN NO: 1076-5131
Page No:2268