a report on ballistic missiles

A Report on Ballistic Missiles Deborah Joseph*1, Jayashree. S*2

#Department of Aeronautical Engineering, Anna University [email protected]

[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

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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.



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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



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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



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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.



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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.



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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.



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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.



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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



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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



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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).



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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



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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



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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.



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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



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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.



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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



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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.



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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



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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.



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a report on ballistic missiles

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