i

CERTIFICATION

SECOND YEAR PROJECT REPORT
on
Construction and Study of Miniature Trebuchet

By:













ii

ABSTRACT
Most of the inventions that have changed the world have originated from the military and war
background. The wars and battles in the past, not only caused devastation and demolition, but also led
to the foundation of new inventions which we are enjoying nowadays. The ancient war and battle
experts have brought a revolution in the world inventing new machines, intended primarily for military
purpose but later used for civil uses. A trebuchet is also an important invention in the history of mankind
that opened up new doors for new innovation.
A Trebuchet is a kind of catapult used in ancient war to throw the stones into the Castle walls and is
based on simple lever and sling mechanism. Our project is to construct a simple Mini Trebuchet that can
throw the projectile to a horizontal range of 15-20 m. The various physical and mathematical aspects of
the model are also studied and analyzed in this project. This report presents the methodology adopted
in constructing the model and experiments conducted on it. The Trebuchet could be used to analyze and
simulate the motion of projectile. The project will also provide us the opportunities to work in the field
of dynamics.

iii

ACKNOWLEDGEMENT
This academic project work has been completed with suggestion, guidance & help from many
individuals. Doing this project has been a rewarding experience for us. We are deeply indebted to those
who have contributed in this project.
We would like to thank Mr. Binaya K.C. for allowing us to conduct this project under his supervision, not
forgetting his thumping encouragements throughout the project schedules. Gratitude also due to Mr.
Krishna Prasad Shrestha for his aid in computer simulation and system analysis. Also, we extend our vote
of thanks to Mr. Ram Thapa Magar for his immense cooperation and valuable suggestions during lab
hours. We also thank all our friends and seniors for their valuable suggestions and support. Finally, we
are equally thankful to all the people who were directly or indirectly involved in our project.

iv

SYMBOLS AND UNITS USED

cm centimeter
cm
2
square centimeter
cm
3
cubic centimeter
g acceleration due to gravity (=9.81 m/s
2
)
gm gram
kg kilogram
m meter
s second

v

TABLE OF CONTENTS
CERTIFICATION ........................................................................................................................... i
ABSTRACT .................................................................................................................................... ii
ACKNOWLEDGEMENT ............................................................................................................. iii
SYMBOLS AND UNITS USED ................................................................................................... iv
CHAPTER 1 ................................................................................................................................... 1
INTRODUCTION .......................................................................................................................... 1
1.1 Background ........................................................................................................................... 1
1.2 Problem Statement ................................................................................................................ 1
1.3 Introduction ........................................................................................................................... 1
1.4 Objectives ............................................................................................................................. 1
1.5 System Overview .................................................................................................................. 2
1.6 Scope of the Project .............................................................................................................. 2
1.7 Limitations of the Project...................................................................................................... 2
1.8 Intended Output .................................................................................................................... 2
1.9 Methodology ......................................................................................................................... 3
1.10 Overview of Report............................................................................................................. 3
CHAPTER 2 ................................................................................................................................... 3
LITERATURE REVIEW ............................................................................................................... 3
2.1 HISTORY ............................................................................................................................. 3
2.2 Types of Trebuchet ............................................................................................................... 4
2.2.1 Traction trebuchet .......................................................................................................... 4
2.2.2 Hand-trebuchet ............................................................................................................... 5
2.2.3 Counterweight trebuchet ................................................................................................ 5
2.2.4 Modern recreational use type ......................................................................................... 7
2.2.5 Floating-arm trebuchet ................................................................................................... 7
2.2.6 King Arthur trebuchet .................................................................................................... 7
CHAPTER 3 ................................................................................................................................... 9
SYSTEM ANALYSIS .................................................................................................................... 9
3.1 Basic Working Principle ....................................................................................................... 9
3.2 Construction ........................................................................................................................ 10
vi

3.2.1 The Frame (Base) ......................................................................................................... 10
3.2.2 The Beam (Arm) .......................................................................................................... 10
3.2.3 Counter Weight ............................................................................................................ 10
3.2.4 Sling ............................................................................................................................. 10
3.2.5 The Projectile ............................................................................................................... 11
3.3 Mathematical Analysis........................................................................................................ 11
3.3.1 Trebuchet Geometry .................................................................................................... 11
3.3.2 Assumptions ................................................................................................................. 11
3.3.4 Elementary Analysis .................................................................................................... 11
3.3.5 Range and Energy Efficiency ...................................................................................... 12
3.3.6 Sling Release Mechanism ............................................................................................ 13
CHAPTER 4 ................................................................................................................................. 16
PROTOTYPE DESCRIPTION .................................................................................................... 16
4.1 Wooden Base ...................................................................................................................... 16
4.2 Beam ................................................................................................................................... 16
4.3 Counterweight ..................................................................................................................... 16
4.4 Sling and Pouch .................................................................................................................. 16
4.5 Projectile ............................................................................................................................. 16
4.6 Auto-lock Mechanism ......................................................................................................... 16
Cost Analysis ............................................................................................................................ 17
CHAPTER 5 ................................................................................................................................. 18
DESIGN ANALYSIS AND EXPERIMENTS ............................................................................. 18
5.1 Data and Observation .......................................................................................................... 18
5.1.1 For projectile of 53.5 gm ............................................................................................. 18
5.1.2 For projectile of 125.8 gm ........................................................................................... 19
5.2 Graphical Analysis .............................................................................................................. 19
5.3 Computer Simulation .......................................................................................................... 20
5.3.1 Assumptions ................................................................................................................. 20
5.3.2 Simulation .................................................................................................................... 20
5.3.3 Graphs .......................................................................................................................... 21
5.4 Basic Mathematical Analysis .............................................................................................. 23
vii

CHAPTER 6 ................................................................................................................................. 25
CONCLUSION ............................................................................................................................. 25
6.1 Conclusion .......................................................................................................................... 25
APPENDIX I: ............................................................................................................................... 26
3-D VIEW OF THE MODEL ....................................................................................................... 26
APPENDIX II: .............................................................................................................................. 27
SIDE VIEW OF THE MODEL .................................................................................................... 27
APPENDIX III: ............................................................................................................................. 28
FRONT VIEW OF THE MODEL ................................................................................................ 28
APPENDIX IV.............................................................................................................................. 29
GANTT CHART .......................................................................................................................... 29
REFERENCES ............................................................................................................................. 30


viii

LIST OF FIGURES
TITLE PAGE NO.
Figure 1: Ancient Trebuchet ........................................................................................................... 4
Figure 2: Counterweight Trebuchet ................................................................................................ 5
Figure 3: Medieval Trebuchet ......................................................................................................... 6
Figure 4: How a Trebuchet Works? .............................................................................................. 10
Figure 5: Trebuchet Geometry ...................................................................................................... 11
Figure 6: The sling release mechanism in side and end views ..................................................... 13
Figure 7: Definition of the finger angle with respect to the beam ................................................ 14
Figure 8: The configuration of the sling during the throw, before release, showing the definition
of the angles and forces involved. ................................................................................................. 14
Figure 9: Graph of Counterweight Vs Range of Projectile........................................................... 19
Figure 10: Computer Simulation Diagram obtained and the corresponding data ........................ 20
Figure 11: Graphs Obtained from the Simulator( I) ..................................................................... 21
Figure 12: Graphs obtained from the Simulator (II) ..................................................................... 22
Figure 13: Graphs obtained from the simulator ( III) ................................................................... 23

LIST OF TABLES
Table 1: Data obtained for the projectile of 53.5 gm.................................18
Table 2: Data obtained for the projectile of 125.8 gm.19
1

CHAPTER 1
INTRODUCTION
1.1 Background
Ancient Engineering Inventions are one of the most remarkable achievements in the history of human
civilization. Humans have been using the naturally available resources for their benefit since their
existence in the world. The Greek, Chinese, Roman and Egyptian engineers in the past invented
marvelous equipments which aided them in building their civilization. These ancient inventions are the
base on which the modern day engineering is built on. Thus, the research into these ancient inventions
will certainly help us in advancing towards a better engineering prospect.
1.2 Problem Statement
Most of the students find it quite difficult to understand the basic theory of Newtonian Dynamics and
projectile motion. A lack of proper knowledge in this subject can prove fatal in their future career
(especially for Engineers). A possible solution to this problem could be to bring the physical principle
into practical application and study the results experimentally. A miniature trebuchet can be used as
such tool for the study of dynamics and motion.
1.3 Introduction
The war and battle in the past saw a gradual development of various weapons and artilleries. Trebuchet
is one of such wonderful creation of man. A Trebuchet is a counterweight siege engine that was used in
the middle ages to demolish the walls and castles during war. It is a type of catapult that works by using
the energy of a raised counterweight to throw the projectile. Man-powered trebuchets appeared in the
Greek world and China in about the 4
th
century BC and did not become obsolete until the 16
th
century,
well after the introduction of gunpowder. In fact, the Trebuchets were far more accurate than other
medieval catapults.
1.4 Objectives
- To construct a prototype of Hila Trebuchet used in ancient war that can hurl the projectile
of 50-100 gm to a horizontal distance of 15-20 metre.
- To investigate the effect on projectile motion due to different sizes of counter-weight,
length of sling, angle of release slot and the aerodynamics of projectile.
- To get knowledge about the medieval weapons of war.
- To apply the theoretical physics and statistics into practical application and study its
result.
- To learn the use computer programming and simulation in engineering practice.
2

1.5 System Overview
A Trebuchet is excellent ancient weapon artillery which can be used for the study of Projectile and
Newtonian Dynamics. It basically consists of counterweight, beam, sling and the projectile. The pivot is
more towards the shorter end than the other. The short end has a heavy counterweight and the other
end has a sling. When it's "cocked and locked", the counterweight is high and ready to drop. The
projectile sits in the pouch of the sling beneath the trebuchet, ready to be pulled along and flung. When
the trigger is released, the counterweight begins to drop due to gravity. This moves the other end of the
arm very quickly and the projectile in the sling is dragged along underneath the machine. As the weight
continues to drop and the arm continues to swing, eventually the projectile reaches the end of the base.
Centrifugal force holds the sling taunt as the sling swings out but the one end of the sling is still looped
over the hook. After travelling some angle, the projectile is finally thrown away.
1.6 Scope of the Project
Some of the chief areas of its application are:
- It can be used in physics experiments to study the aerodynamics of projectile through
computer programming and simulation.
- It was used to demolish the walls of castles during war.
- It can be used in parks, museums for recreational use.
- The trebuchet also finds its use in scientific research and investigation.
- It can also be used as a teaching tool for studying Newtonian Dynamics.
1.7 Limitations of the Project
Since we constructed a miniature model of trebuchet, it has certain limitations.
- The length of the arm of the trebuchet is fixed and cannot be varied.
- The machine is designed in order to study the projectile trajectory and dynamics of
motion which is totally different from the purpose of an actual trebuchet. Hence, it is not
as powerful as the actual trebuchet.
- It is intended to throw the projectile of light mass. It can effectively throw the projectile
of maximum mass 500 gm.
- The maximum weight that can be kept in the counterweight is 15 kg.
- It has a maximum horizontal range of 25 m.
1.8 Intended Output
Our project Construction and Study of A Miniature Trebuchet primarily intends to study the motion
and aerodynamics of projectile. We planned to hurl the projectile to maximum range and study its
motion. We also aimed to use the statistical and programming techniques to analyze the effect on
maximum range of the projectile due to variation in counterweight mass. Since the theoretical value
calculated is not exactly equal to the practical value, we intended to determine the fluctuation in this
value by doing experiment.
3

1.9 Methodology
Methodology used for this project is described as follows:
- Defining the problem and setting the objectives
- Collection of relevant literature from various resource including magazines, individuals,
institutions and websites and their scrupulous study
- Design of the project to suit material availability cost and project funding
- Finalization of the drawing for manufacture
- Carrying out fabrication
- Conduction of workable tests at different stages and use of feedback for the modification
- Conduction of the final test.

1.10 Overview of Report
This report gives the overview to the works accomplished under the project and the methods we
applied in its completion. It closes up the report of completion of the system analysis that was intended
to finish by this time. Simplifying the report, it includes six chapters. Chapter 1 gives the introduction of
the project, which includes background, problem statement, introduction, objectives, system overview,
scopes, limitations and the intended output of the project. Chapter 2 provides the research and
literature survey done for the project. Chapter 3 includes the various calculations and system analysis
made. Chapter 4 includes the Prototype Description and Specifications and Chapter 5 contains the
system analysis and experiment conducted during the project testing phase. Chapter 6 concludes the
report. The appendices at the end give an overview to the mechanical design of the system.



CHAPTER 2
LITERATURE REVIEW
2.1 HISTORY
4

A trebuchet or trebucket (from the French: trbuchet) is a siege engine that was employed in the Middle
Ages. It is sometimes called a "counterweight trebuchet" or "counterpoise trebuchet" in order to
distinguish it from an earlier weapon that has come to be called the "traction trebuchet", the original
version with pulling men instead of a counterweight. Man-powered trebuchets appeared in the Greek
world and China in about the 4th century BC.
The counterweight trebuchet appeared in both Christian and
Muslim lands around the Mediterranean in the twelfth century. It
could fling projectiles of up to three hundred and fifty pounds (140
kg) at high speeds into enemy fortifications. Occasionally, disease-
infected corpses were flung into cities in an attempt to infect and
terrorize the people under siege, a medieval form of biological
warfare. The trebuchet did not become obsolete until the 16th
century, well after the introduction of gunpowder. Trebuchets were
far more accurate than other medieval catapults.
2.2 Types of Trebuchet
2.2.1 Traction trebuchet
The trebuchet derives from the ancient sling. A variation of the sling, called staff sling (Latin: fustibalus),
contained a short piece of wood to extend the arm and provide greater leverage. This evolved into the
traction trebuchet in which a number of people pull on ropes attached to the short arm of a lever that
has a sling on the long arm. This type of trebuchet is smaller and has a shorter range, but is a more
portable machine and has a faster rate of fire than larger, counterweight-powered types. The smallest
traction trebuchets could be powered by the weight and pulling strength of one person using a single
rope, but most were designed and sized for between 15 and 45 men, generally two per rope. These
teams would sometimes be local citizens helping in the siege or in the defense of their town. Traction
trebuchets had a range of 100 to 200 feet when casting weights up to 250 pounds. It is believed that the
first traction trebuchets were used by the Mohists in China as early as in the 5th century BC, descriptions
of which can be found in the Mojing (compiled in the 4th century BC). The Chinese named the later
counterweight trebuchet Huihui Pao (Muslim Weapons, "huihui" means Muslim) or Xiangyang Pao (
), where Pao means bombard.
The traction trebuchet next appeared in Byzantium. The Strategikon of Emperor Maurice, composed in
the late 6th century, calls for "ballistae revolving in both directions," (
), probably traction trebuchets (Dennis 1998, p. 99). The Miracles of St. Demetrius,
composed by John I, archbishop of Thessalonike, clearly describe traction trebuchets in the Avaro-Slav
artillery: "Hanging from the back sides of these pieces of timber were slings and from the front strong
Figure 1: Ancient Trebuchet
*source: www.wikipedia.org
5

ropes, by which, pulling down and releasing the sling, they propel the stones up high and with a loud
noise." (John I 597 1:154, ed. Lemerle 1979)
They were also used with great effect by the Islamic armies during the Muslim conquests. A surviving
Arab technical treatise on these machines is Kitab Aniq fi al-Manajaniq ( , An
Elegant Book on Trebuchets), written in 1462 by Yusuf ibn Urunbugha al-Zaradkash. It provides detailed
construction and operating information.
There is some doubt as to the exact period in which traction trebuchets, or knowledge of them, reached
Scandinavia. The Vikings may have known of them at a very early stage, as the monk Abbo de St.
Germain reports on the siege of Paris in his epic De bello Parisiaco dated about 890 that engines of war
were used. Another source mentions that Nordic people or "the Norsemen" used engines of war at the
siege of Angers as early as 873.
2.2.2 Hand-trebuchet
The hand-trebuchet (Greek: cheiromangana) was a staff sling mounted on a pole using a lever
mechanism to propel projectiles. Basically a portable trebuchet which could be operated by a single
man, it was used by emperor Nikephoros II Phokas around 965 to disrupt enemy formations in the open
field. It was also mentioned in the Taktika of general Nikephoros Ouranos (ca. 1000), and listed in the
Anonymus De obsidione toleranda as a form of artillery.
2.2.3 Counterweight trebuchet
The earliest written record of the counterweight
trebuchet, much more powerful than the traction version,
appears in the work of the 12th century Byzantine
historian Niketas Choniates. Niketas describes a trebuchet
used by Andronikos I Komnenos, future Byzantine
emperor, at the siege of Zevgminon in 1165 which was
equipped with a windlass, an apparatus which was
required neither for traction nor hybrid trebuchets to
launch missiles. Chevedden dates the invention of the new
artillery type back to the Siege of Nicaea in 1097 when the
Byzantine emperor Alexios I Komnenos, an ally of the
besieging crusaders, was reported to have invented new
pieces of heavy artillery which deviated from the conventional design and made a deep impression on
everyone.
The dramatic increase in military performance is for the first time reflected in historical records on the
occasion of the second siege of Tyre in 1124, when the crusaders reportedly made use of "great
trebuchets". By the 112030s, the counterweight trebuchet had diffused not only to the crusaders
states, but probably also westwards to the Normans of Sicily and eastwards to the Great Seljuqs. The
military use of the new gravity-powered artillery culminated in the 12th century during the Siege of Acre
Figure 2: Counterweight Trebuchet
*Source: www.wikipedia.org
6

(118991) which saw the kings Richard I of England and Philip II of France wrestle for control of the city
with Saladin's forces.
The only pictorial evidence of a counterweight trebuchet in the 12th century comes from an Islamic
scholar, Mardi bin Ali al-Tarsusi, who wrote a military manual for Saladin circa 1187 based on
information collected from an Armenian weapon expert in Muslim service. He describes a hybrid
trebuchet that he said had the same hurling power as a traction machine pulled by fifty men due to "the
constant force [of gravity], whereas men differ in their pulling force."
(Showing his mechanical proficiency, Tarsusi designed his trebuchet
so that as it was fired it cocked a supplementary crossbow, probably
to protect the engineers from attack). He allegedly wrote
"Trebuchets are machines invented by unbelieving devils." (Al-
Tarsusi, Bodleian MS 264). This suggests that by the time of Saladin,
Muslims were acquainted with counterweight engines, but did not
believe that they had invented these machines.
During the Crusades, Philip II of France named two of the trebuchets
he used in the Siege of Acre in 1191 "God's Stone-Thrower" and "Bad
Neighbor."[11] During a siege of Stirling Castle in 1304, Edward
Longshanks ordered his engineers to make a giant trebuchet for the
English army, named "Warwolf". Range and size of the weapons
varied. In 1421 the future Charles VII of France commissioned a
trebuchet (coyllar) that could shoot a stone of 800 kg, while in 1188
at Ashyun, rocks up to 1,500 kg were used. Average weight of the
projectiles was probably around 50100 kg, with a range of ca. 300
meters. Rate of fire could be noteworthy: at the siege of Lisbon (1147), two engines were capable of
launching a stone every 15 seconds. Also human corpses could be used in special occasion: in 1422
Prince Korybut, for example, in the siege of Karltejn Castle shot men and manure within the enemy
walls, apparently managing to spread infection among the defenders. The largest trebuchets needed
exceptional quantities of timber: at the Siege of Damietta, in 1249, Louis IX of France was able to build a
stockade for the whole Crusade camp with the wood from 24 captured Egyptian trebuchets.
Counterweight trebuchets do not appear with certainty in Chinese historical records until about 1268,
when the Mongols laid siege to Fancheng and Xiangyang. At the Siege of Fancheng and Xiangyang, the
Mongol army, unable to capture the cities despite besieging the Song defenders for years, brought in
two Persian engineers who built hinged counterweight trebuchets and soon reduced the cities to rubble,
forcing the surrender of the garrison. These engines were called by the Chinese historians the Huihui
Pao ()("huihui" means Muslim) or Xiangyang Pao (), because they were first encountered
in that battle. Recent research by Paul E. Chevedden indicates that the hui-hui pao was actually a
European design, a double-counterweight engine that had been introduced to the Levant by Holy
Roman Emperor Frederick II (12101250) only shortly before.[12] The Muslim historian Rashid-al-Din
Hamadani (1247?1318) refers in his universal history to the Mongol trebuchets used at the Song cities
as "Frankish" or "European trebuchets" ("manjaniq ifranji" or "manjaniq firanji"):
Figure 3: Medieval Trebuchet
*Source: www.medievalweapons.com
7

Before that there had not been any large Frankish catapult in Cathay [i.e. China], but Talib, a catapult-
maker from this land, had gone to Baalbek and Damascus, and his sons Abubakr, Ibrahim, and
Muhammad, and his employees made seven large catapults and set out to conquer the city [Sayan Fu or
Hsiang-yang fu = modern Xiangfan].[13]
With the introduction of gunpowder, the trebuchet lost its place as the siege engine of choice to the
cannon. Trebuchets were used both at the siege of Burgos (14751476) and siege of Rhodes (1480). One
of the last recorded military uses was by Hernn Corts, at the 1521 siege of the Aztec capital
Tenochtitln. Accounts of the attack note that its use was motivated by the limited supply of
gunpowder. The attempt was reportedly unsuccessful: the first projectile landed on the trebuchet itself,
destroying it. In 1779, British forces defending Gibraltar, finding that their cannons were unable to fire
far enough for some purposes, constructed a trebuchet. It is unknown how successful this was: the
Spanish attackers were eventually defeated, but this was largely due to a sortie.
2.2.4 Modern recreational use type
Trebuchets are popular in modern times in a number of contexts. In particular, traditional models are
constructed by historical re-enactment and living history enthusiasts, and others use the trebuchet as an
engineering challenge. Trebuchets are used to throw pumpkins at the annual pumpkin chunking contest
held in Sussex County, Delaware. The record-holder in that contest for trebuchets is the Yankee Siege,
which at the 2009 Championship tossed a pumpkin 2034 feet. The 51 foot tall, 55,000 pound trebuchet
fires 810 pound pumpkins. Modern engineering thought and materials have come up with several non-
traditional designs, in particular, several with "floating arms" to increase efficiency.
2.2.5 Floating-arm trebuchet
A floating-arm trebuchet is an efficient modern variant. Rather than having an axle fixed to the frame, it
is mounted on wheels that roll on a track parallel to the ground, and the counterweight is constrained to
fall in a direct path downwards upon the release. This increases the proportion of energy transferred to
the projectile.
2.2.6 King Arthur trebuchet
The King Arthur is often regarded as the most efficient trebuchet design, invented by Chris Gerow in
2001 in his efforts to compete in the Pumpkin Chunking championship. In this design, the arm is locked
with the hanger when cocked. The arm points nearly straight down, and the hanger points nearly up.
When the hanger is released, then when it reaches the optimum point, the secondary trigger is pulled,
releasing the arm.

8










9

CHAPTER 3
SYSTEM ANALYSIS
3.1 Basic Working Principle
The trebuchet is a counterweight siege engine. It basically consists of a lever and a sling.
1. The Lever
A lever is a simple machine that gives a mechanical advantage when given a fulcrum, or pivot point. It is
often used to move heavy loads with less effort. The trebuchet is a First Class lever. In the First Class
lever, the force is applied to one end, the load is on the other end and the fulcrum sits between the two.
The playground see-saw is a First Class lever. For the trebuchet, the force is very large and the load is
very small. The fulcrum is placed towards the force end so that the other end will move further.
2. The Sling
The sling is the oldest projectile weapon. There is a pouch to hold the projectile and two long strings.
Both ends of the string are held in one hand and the sling is swung around and around. Then, at the
proper moment, one end of the sling is let go with the other end is still held by the hand. The pouch can
no longer hold the projectile and the projectile continues on its way. For the trebuchet, this release is
done with a nearly straight hook so that the sling swings out and eventually slips off the hook, releasing
the projectile.
3. The Trebuchet
So, putting it all together, the trebuchet starts with a long arm. The axle (fulcrum) is more towards one
end than the other. The short end has a heavy counterweight and the other end has a sling. When it's
"cocked and locked", the counterweight is high and ready to drop. The projectile sits in the pouch of the
sling beneath the trebuchet, ready to be pulled along and flung.
When the trigger is released, the counterweight begins to drop. This moves the other end of the arm
very quickly and the projectile in the sling is dragged along underneath the machine. As the weight
continues to drop and the arm continues to swing, eventually the projectile reaches the end of the base.
Centrificial force holds the sling taunt as the sling swings out but the one end of the sling is still looped
over the hook.
Forces try to straighten out the sling and eventually the loop on one end slips off the hook. The
projectile is no longer held in the pouch and so continues on its way down range.

10


Figure 4: How a Trebuchet Works?
*Source: http://tasigh.org/ingenium/physics.html

3.2 Construction
The basic parts of a trebuchet include
3.2.1 The Frame (Base)
The frame is the body (base) of the trebuchet which is used to support the beam (arm) and the counter
weight. It is usually made of wood and sometimes, it also consists of wheels which is believed to
improve the efficiency of transfer of energy from the counterweight to the projectile.
3.2.2 The Beam (Arm)
It is a long slender rod which acts as the main part. It has counterweight at one end and the projectile
connected at the other end with ropes. The fulcrum is placed near the counterweigh to throw the
projectile at a larger distance.
3.2.3 Counter Weight
The counter weight is a large mass that hangs on the short arm of the beam. On older models, a person
would pull down on the arm to throw the projectile and this would make the person pulling down the
arm the counterweight. In order to vary the counter weight, a basket may be constructed into which
varying weights may be placed.
3.2.4 Sling
The sling is a sack used to hold the projectile until there is enough energy to launch it. It may be a piece
of cloth or leather with the ropes to connect it with the beam. It is used to double the power of
trebuchet causing the projectile to go twice as far as it would without it.
11

3.2.5 The Projectile
It is the object that is to be thrown away.
3.3 Mathematical Analysis
3.3.1 Trebuchet Geometry


Figure 5: Trebuchet Geometry
Let us assume
Pivot be the origin
m1 = mass of counterweight
m2 = mass of projectile
l1 = length of short arm of beam
l2 = length of long arm of beam
l3 = length of the sling
l4 = distance between the end of short arm and counterweight
and the angles as shown above in figure 5.
3.3.2 Assumptions
- The trebuchet is rigid.
- The joints rotate perfectly around points.
- The pouch and sling has negligible mass.
- The trebuchet remains stationary on the ground during launch.
- There is no air resistance and other frictions are also absent (unless otherwise stated).
3.3.4 Elementary Analysis
Consider a projectile fired on a horizontal plane that has a velocity vo at an angle o with
respect to the horizontal. It will have a range given by
R =

,
where g is the acceleration due to gravity. This has a maximum range for o = 45 which
12

is
Rm =

The kinetic energy in the projectile,
having a mass m2, at the start of the
trajectory is then
KEproj =

A counterweight mass m
1
at a height h above a reference plane has a potential energy given by
PEcw = m
1
g h.
The most efficient mechanism for a trebuchet would, clearly, be able to transform all of the initial
potential energy into kinetic energy of the projectile. Assume that there is a perfectly efficient
mechanism that can do this. Thus, if the mass of the counterweight is initially at a height h above its
lowest point, the maximum possible range that could be attained is obtained by equating the initial
potential energy in the counterweight with the kinetic energy in the projectile at the start of the
trajectory, yielding
Rm = 2

h .
This theoretical maximum range is easily seen to be reasonable--it is larger for heavier counterweights
and lighter projectiles. It is linear in the initial height of the counterweight. Perhaps surprisingly,
depending upon one's mechanical intuitions, it is independent of the acceleration of gravity--it would
throw just as far on the moon!

This simple equation can be very useful in the preliminary design of any trebuchet. However, a real
trebuchet will not, of course, attain this theoretical maximum range because of various factors such as
the friction at the axle, the slide, the air resistance on the projectile, rotational energy of the beam, and
unutilized kinetic energy remaining in the swinging CW after the projectile is fired. It is mathematically
found that, for a real trebuchet, in order to increase the efficiency, the sling length should be equal to
the length of the long arm of the beam, and the beam should be set at a 45 angle with respect to the
horizontal.
3.3.5 Range and Energy Efficiency
The efficiency of a real trebuchet can be reasonably defined in at least two ways. The first, and arguably
the most useful of the two, is the ratio of the range actually attained by an actualized treb to the range
of the theoretical ideal trebuchet. This is termed as range efficiency, c
R
.

The range efficiency of the
model with no air resistance is given by

where h is the distance the counterweight can drop and is the angle that the projectile makes with the
horizontal at the start of its flight after leaving the trebuchet.
13

Another possible useful definition of an efficiency for a trebuchet will be the fraction of potential energy
in the counterweight that is actually deposited as kinetic energy in the projectile. Lets call this energy
efficiency, c
E
.

The energy efficiency is always greater than zero and therefore not equivalent to the range efficiency
given above. The relationship between the two measures is readily seen to be

Thus, when = 45,

And the two efficiencies are equal. The optimum release point for the projectile to achieve a maximum
range is seldom exactly 45, so there is usually a small difference between the two efficienciesthe
range efficiency is generally slightly smaller than the energy efficiency.
3.3.6 Sling Release Mechanism
The mechanism that is used to
release the sling is critical, of
course, to the proper and efficient
functioning of the trebuchet. The
usual arrangement for the release
is to have a fixed projection from
the beam (a hook, prong or a peg)
over which a loop of the sling or a
ring tied to one end of the sling
slides freely. We will refer to the
peg as finger". The other end of
the sling is permanently attached
to the beam so it does not go
flying off with the projectile.
When the beam is horizontal and
not moving, it would look something like that
shown in Fig. 6.
The finger can be mounted on the top surface
of the beam by some means, or for smaller
trebuchets it can be simply screwed into the
Figure 6: The sling release mechanism in side and end views

14

end of the beam. In general the finger is placed at some angle with respect to the beam. It is useful to
define this angle, o, with respect to the extension of the beam (so that it is an acute angle). A closer view
of this is shown in Fig. 7.
First of all, it should be clear that in the absence of any friction, the ring will start to slide as soon as the
angle between the finger and the sling
decreases below 90. In the limiting case in
which the finger is very short, and friction is neglected, one could set the finger angle to be o = r - 90,
where r is the sling/beam angle given as the optimal release condition from the simulation. When
friction cannot be neglected, the release will be sometime after the sling/finger angle, is greater than
90, and o should be set to a smaller angle than this.
The influence of the static force of friction between the ring and the finger is rather easy to be taken
into account, and is worth looking at, and can give a better approximation of what value o should be set
to.
The configuration of the sling during the motion of the beam, with the angle , used previously, and its
relationship with o is shown in Fig. 8.
Since the sling is made out of string or rope, it can only exert a tension force along itself, in the direction
shown--the rotating projectile exerts a force, Fs, on the ring, tending to pull the ring along the finger. In
principle, this force depends on (t). It can be resolved into a force normal to the finger, Fn, and one
along the finger, Fp. The force tending to hold the ring fixed relative to the finger, resisting the pull Fp, is
the force of friction, Ff = Fn, where is the static coefficient of friction between the ring and the
finger. From the geometry shown, it can be seen that
Figure 7: Definition of the finger angle with respect to the beam

Figure 8: The configuration of the sling during the throw, before release, showing the definition of the angles and forces
involved.
15

Ff = Fn = Fs sin(o )
where
o = o+t
The force exerted along the finger by the projectile, through the sling, is
Fp = Fs cos(o ).
The ring just begins to slide when Fp = Ff. That is,
Fs cos(o ) = Fs sin(o )
or, cot(o ) =
or, cot(t+o) =
which leads to the final result, that the ring will begin to slide when
= t + o - arc cot ,
where, of course, the angles are expressed in radians.



16

CHAPTER 4
PROTOTYPE DESCRIPTION
The Miniature Trebuchet Model that we designed has following parts and specification:
4.1 Wooden Base
It is the main base on which the whole trebuchet is built. It has dimension of 75 x 40 cm
2
and has got
two pillar of 6 x 6 x 60 cm
3
embedded at the edge of its middle portion on each side with a joint. These
pillars are supported by two triangular planks of 2 x 30 x 30 cm
3
on each side (refer to Appendix).
4.2 Beam
It is a wooden arm which can rotate about the fixed axis. It is 100 x 6 x 4 cm
3
and has got a long arm and
a short arm. The long arm is 70 cm long and carries the sling with the projectile at its end while the short
arm has counterweight hanging at its end.
4.3 Counterweight
It is a wooden basket on which the counterweights can be placed. The basket has a volume of 20 x 22
x16 cm
3
. It is hinged to the short arm of the beam with the help of two iron arm of 13 cm.
4.4 Sling and Pouch
The sling is made of rope and is 140 cm long and its length can also be varied. It has a pouch of rubber at
its middle on which the projectile that is to be hurled is placed.
4.5 Projectile
The projectile is a tennis ball which has mass of 53.5 gm. The other projectile is of 125.8 gm.
4.6 Auto-lock Mechanism
The auto-lock is made up of a rectangular iron chamber, which consists of iron rod with a square profile
inside it with spring coiled around it. Thus, when the beam is brought back to the original position, the
rod moves inwards and due to the spring action the rod is pushed outwards and hence the beam is
locked.

17

Cost Analysis

S.N. Particulars Quantity Rate Amount
1 Mild steel rod 2.00 kg Rs. 95.00 Rs. 190.00
2 Rope 2.00 m Rs. 15.00 Rs. 30.00
3. Wooden Plank 30*150 cm
2
------- Rs. 1000.00
4. Wheels 4 Rs. 100.00 Rs. 400.00
5 Paint 0.5 Ltr Rs 500.00 Rs.250.00
6 Adhesive Glue 100 gm Rs. 200 Rs. 200.00
7 Dia 10 Nut & Bolt 10 piece Rs. 8.00 Rs. 80.00
8 Dia. 5 nut & bolt 10 Piece Rs. 6.00 Rs. 60.00
9 Wooden Beam
1 piece (100*6*4
cm
3
)
Rs. 250.00 Rs. 250.00
10 Bearing Set 2 set Rs. 150.00 Rs. 300.00
11 Wooden Pillars (60*6*6 cm
3
)*4 Rs. 200.00 Rs. 800.00
12 Iron Nails 2 kg Rs. 30.00 Rs. 60.00
13 Spring 1 piece Rs. 35.00 Rs. 35.00
14 Miscellaneous - - Rs. 400.00

Total - - Rs. 4055.00


18

S.N. Counterweight (gm) distance(x1) distance(x2) distance(x3) distance(x4) distance(x5) mean
1 3435.4 3.6 3.75 4.2 4.2 4.1 4.025
2 3617 4.2 3.85 3.75 3.9 3.8 3.9125
3 4612.4 7 6.9 7 7 7.1 7.025
4 5735.4 10 10.3 10.4 10.6 10.2 10.3
5 6862.5 13.9 14 13.4 13.6 13.5 13.6
6 7889.4 14.2 14.2 14.7 14.5 14.2 14.4
7 9016.9 15.8 16.2 16.3 16.2 16.5 16.2
8 9256.1 15.8 17.1 17.5 17.5 17.4 17.05
9 10383.6 18.2 18.9 17.6 18.5 18.4 18.175
10 11286.1 19.3 19.8 17.8 19.5 19.1 18.925
CHAPTER 5
DESIGN ANALYSIS AND EXPERIMENTS
5.1 Data and Observation
The following data are obtained from the experiment.
Mass of counterweight basket (when empty) = 1.4631 kg
Mass of projectile =53.5 gm, 125.8 gm
Arm density = 800 kg/m
3
Finger ring mass = 2 gm
Length of finger = 2 cm
Length of short arm = 25 cm
Length of long arm = 70 cm
Total length of beam = 100 cm
Length of arm support = 55 cm
Sling length = 140 cm
Mass of sling = 83.8 gm
Length of counterweight support = 13 cm
5.1.1 For projectile of 53.5 gm
The following data table is obtained:
Table 1: Data obtained for projectile of mass 53.5 gm
19

5.1.2 For projectile of 125.8 gm
The following data table is obtained:

Table 2: Data obtained for the projectile of 125.8 gm
5.2 Graphical Analysis
On drawing the graph of counterweight mass and range of projectile, we get the following graph:
In the above graph, the solid line represents the projectile of 53.5 gm and the dotted line represents the
projectile of 125.8gm. From the above graph, we see that when the mass of counterweight is less than
2.5kg, the trebuchet does not work i.e. it doesnt throw the projectile. On increasing the mass of
S.N. Counterweight (gm) distance(x1) distance(x2) distance(x3) distance(x4) distance(x5) mean
1 3463.1 1 1.3 1.2 1 0.9 1.025
2 4586.1 4 4.35 4.4 4.2 4.3 4.225
3 5735.4 6.73 7 7.2 7.3 7.2 7.1075
4 6740.1 10.5 9.5 9.45 9.6 9.4 9.7375
5 7889.4 12.6 12.2 11.4 11.6 11.9 11.875
6 9016.9 14.6 14.7 13.8 13.7 14.2 14.075
7 9256.1 15.8 15.2 15.3 15.8 15.7 15.65
8 10383.6 17 17.6 16.9 16.8 17.3 17
9 11286.1 19.7 20 20 20.1 19.8 19.9
10 12896.4 21.7 21.9 20.4 21 21.6 21.175
Figure 9: Graph of Counterweight Vs Range of Projectile
20

counterweight the range increases rapidly for sometime and then the growth becomes gradual. As
depicted on the graph, we find that for the same counterweight mass the horizontal range of projectile
for less mass is greater than that for larger mass.
5.3 Computer Simulation
We used a simulating software EngiCalcTrebuchet Simulator v3.1 in order to study the dynamics of the
trebuchet. With the help of the simulator, we predicted the results, and those predicted results were
compared to the results obtained through experiments.
5.3.1 Assumptions
- Air friction is neglected.
- Effects of aerodynamics on projectile and counterweight are neglected.
- The masses of counterweight link and sling pouch are neglected.
- Frictions in pivots are assumed to be function of diameter.
- Friction coefficient is taken as 0.3.
- Counterweight is assumed to be rotating type.
5.3.2 Simulation
The data supplied to the simulator and the simulation obtained is shown in the figure below. For the
projectile of mass 53.3 gm, we obtained the range 18.2 m from the simulator when the counterweight
mass was 9.2561 kg. Similarly, from the experiment for the same data we obtained the range 17.05m.
Thus, the difference between two results is 1.15 m. This difference in the results can be accounted to
the air friction, environmental condition, aerodynamics and random errors.
Figure 10: Computer Simulation Diagram obtained and the corresponding data
21

5.3.3 Graphs

Figure 11: Graphs Obtained from the Simulator( I)
The first graph shows the relationship between the time and the velocity of projectile. The velocity
increases along with time and obtains its maximum value right before the release. Then the velocity
changes as shown in the graph.
The second graph shows the relationship between the time and the acceleration of the projectile. The
acceleration increases along with the time, obtains maximum value and starts decreasing, after the
release, the projectile continues its motion with constant acceleration.
The third graph shows the trajectory of the projectile
The fourth graph shows variation in sling tension with time. The sling tension is maximum during
release.
22


Figure 12: Graphs obtained from the Simulator (II)

The first graph shows the maximum and minimum bending moments, and the second graph shows the
maximum and minimum stresses. The third graph shows the relationship between the time and finger
load and the The fourth graph shows the relationship between the time and energy balance.
23


Figure 13: Graphs obtained from the simulator ( III)
The first graph shows the relationship between the time and counterweight angle. The second graph
shows the variation in counterweight velocity with time. The third graph gives the trajectory of the
counterweight and the fourth graph shows the relationship between the time and pivot load.
5.4 Basic Mathematical Analysis
For the projectile of mass 53.5 gm and the counterweight 9.2561 kg, we can get the theoretical range as
Rm = 2

h
Where,
m1= mass of counterweight
m2 = mass of projectile
h= initial height of the counterweight from the reference = 40 cm (approx.)
Thus, we get the theoretical maximum range as
R
m
= 138.4 m
However, a real trebuchet did not, of course, attain this theoretical maximum range because of various
factors such as the friction at the axle, the slide, the air resistance on the projectile, rotational energy of
the beam, and unutilized kinetic energy remaining in the swinging CW after the projectile is fired.

24

Range and Energy Efficiency
The range efficiency of the real trebuchet when air resistance is neglected, is given by

From simulation, we obtain o= 39.3. Thus, we get
c
R
=0.123
Similarly, the energy efficiency is given by

From simulation, we have v
0
= 13 m/s (approx)
Thus,
c
E
= 0.124
So, we have

c
R
/c
E
=0.991
which is almost equal to 1, the condition for maximum efficiency.




25

CHAPTER 6
CONCLUSION
6.1 Conclusion
The mystery surrounding the original designs of trebuchets provides a wonderful historical context in
which the relatively modern conservation principles can be studied. There is enough physics in the
operation of the trebuchet to engage students at both the introductory and advanced level in mechanics
courses. Construction of a model trebuchet is inexpensive and straightforward, as is the analysis of its
motion. It can be used for the study of aerodynamics of projectile, Newtonian Dynamics and even in
recreational use.
In addition to these benefits, this project will certainly add up to our fabrication experience and
experimental analysis technique. It will be the straightforward tool to understand the physical laws that
we studied in class. With the constant help from our supervisor and seniors, we hope to complete the
project on time and obtain the desired output.

26

APPENDIX I:
3-D VIEW OF THE MODEL


27

APPENDIX II:
SIDE VIEW OF THE MODEL

28

APPENDIX III:
FRONT VIEW OF THE MODEL

29

APPENDIX IV
GANTT CHART



30

REFERENCES
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- Campbell, W. The Hila Trebuchet. Retrieved on Sept. 24, 2010 from
http://hila.webcentre.ca/projects/trebuchet/.
- Engineering Calculation Simulator. Retrieved on March 25, 2011 from
http://www.engicalc.com/simulators
- Hadingham, E. Ready, Aim, Fire!, Smithsonian Magazine, January 2000.
- How does a trebuchet works? (2009). Retrieved on Sept 23, 2010 from
www.youtube.com.
- Leonardos Catapult (2009). Retrieved on Oct 11, 2010 from
http://members.iinet.net.au/~rmine/Leonardo.html.
- Trebuchet (2010). Retrieved on Oct 11, 2010 from
http://library.thinkquest.org/05aug/00627/phy.html.
- Trebuchet Physics (2010). Retrieved on Oct 11, 2010 from http://www.real-world-
physics-problems.com.