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Simulation on Motion of a Trebuchet
Karthik Baburao Mulamuttal
1(&)
, Komal Kattigenahally Nagaraj
1
,
Gangadharan V. Kalluvalappil
2
, Pruthvi Raj
2
,
Narasimhamurthy Kyathsandra Chandrashekar
1
,
and Suchitra Vankalkunti
1
1
Siddaganga Institute of Technology, Tumkur, India
{kcnmurthy,suchitrav}@sit.ac.in
2
National Institute of Technology Karnataka, Suratkal, India
Abstract. In this paper, an innovative approach to analyze the performance of
one of the basic mechanical system “Trebuchet”is discussed. An efficient sim-
ulation approach is developed for ‘The motion of a Trebuchet’analysis. The
developed simulation tool provides the access for all possible parametric varia-
tions so that the theoretical concepts are visualized easily by very simple simu-
lation process. The process of development of the simulator is briefed in this
paper. Simulations can be efficiently used to analyze the behavior of a Trebuchet
system. For diverse patterns of control parameters, the system design can be
tested using simulations and the most efficient system can be implemented in real
time. Likewise, this paper explains in detail how the motion of a trebuchet is
effectively analyzed using simulation by giving extreme conditional parameters.
HTML, CSS and JavaScript tools are used to develop this simulation.
Keywords: Simulation Trebuchet Experiential learning
1 Introduction
Engineering requires the scientific understanding of nature and then applying it to
innovate. The rapid advancements in technology have made available different tools for
potential understanding and learning of engineering principles. To design a system it is
necessary to have prior knowledge on the system control parameters and its behavior
under different parametric conditions. Also, a user friendly and simulation tool with
many parametric variations create interest in the subject matter and motivates
users/students to learn the course with more confidence [1–4].
Using simulations is helpful in the following scenarios: i) when a new system is
being designed and major developments in the physical layout have been demanded. ii)
When a large investment is being considered for an existing developed system. iii)
Simulations with animations are a very effective tool for training and educating where
the animation can be the only source of understanding the complete system working.
iv) Simulations have the added advantage of the ability of designing even the worst
case systems, without any risk that would predict its abrupt behavior before it could be
implemented in real time. v) It can be used to perform an experiment or develop
designs repetitively, any number of times required. vi) There is no possibility of
changes in the results at each iteration for the same values if input parameters [5–7].
©The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
M. E. Auer et al. (eds.), Online Engineering and Society 4.0, Lecture Notes in Networks and
Systems 298, https://doi.org/10.1007/978-3-030-82529-4_9
2 Development of Simulation Tool for Trebuchet
Virtual lab system is developed to provide access to faculty and students to encourage
“Experimental Learning”. Experiments in Virtual lab can be accessed using laptop or
smart phone and doesn’t require any specific software at the user end. The prime
objective is to provide remote-access to Labs in various disciplines of Science and
Engineering. This Virtual Labs Would caters to Students at their UG and PG courses,
to enthuse students to conduct experiments by arousing their curiosity. This would help
them in learning basic and advanced concepts through experimentation, to share costly
equipment and resources, which are otherwise available to limited number of users due
to constraints on time and geographical distances, to provide a complete learning
management system around the Virtual Labs where the students can avail the various
tools for learning, including additional web-resources The advantages of using Virtual
lab are user canconduct experiments at anytime from anywhere. User can conduct
experiments along with peers for better learning. The outcomes of any experiment by
measuring the desired parameters. Obtained analysis is used to generate report and
summarize the readings with outcomes.
2.1 Trebuchet Simulation Tool Design
This section describes the development of the simulation tool for a trebuchet for virtual
lab, to analyze by adding the counter mass, by varying the Length of the short arm and
by changing the angle respectively. For the design of simulation in the web area we go
with Hypertext Markup Language (HTML), cascading style sheets (CSS) and Java-
Script (JS). HTML is the standard Markup language for documents designed to be
displayed in a web browser.HTML describes the structure of a webpage semantically
and originally included cues for the appearance of the document. It can be assisted by
technologies such as and scripting languages such as JavaScript. CSS is a style sheet
language used for describing the presentation of a document written in a markup
language like HTML. CSS is a cornerstone technology of the World Wide Web,
alongside HTML and JS. JavaScript enables interactive web pages and is an essential
part of web applications. The simulation is developed in such a way so as to serve the
purpose of actual learning as the user gives the desired inputs and the output is
observed.
Trebuchet, (a form of catapult) is a siege machine that primarily throws a projectile
using a swinging arm. The schematic diagram of the Trebuchet used for the devel-
opment of simulator is shown in Fig. 1.
88 K. B. Mulamuttal et al.
Trebuchets are large constructions made of wood and usually immobile and must
be assembled on-site. The counter weight trebuchet has a long arm (load arm) that
throws the projectile and a short arm (force arm) that has counter weight attached to it
by hinge connection. Projectile here is a body, which is thrown near the Earth’s surface
and moves along a parabolic path under the action of gravity. A trebuchet is energized
by lowering the long arm and raising the weighted short arm so that the projectile is
thrown when the counter weight is released, on command.
The purpose of this experiment is to demonstrate the motion of a trebuchet and the
resulting projectile motion, and to determine certain parameters of the projectile
motion: range, height, time of flight and initial velocity.
The parameters mentioned above, vary accordingly with the counter weight, length
of the short arm, and the angle of release of the projectile. During the development of
the simulator for motion for Trebuchet, for few parameters certain initial conditions
need to be assumed. For the selected parameters the range of values need to be
provided for the users. Otherwise, a random value of the parameters will result in some
output which may not be possible in real time, like entering Mass as –ve value.
The Initial Conditions and the Range of the Variables are as Follows:
1. The initial position of the arm is at 180° i.e., vertical position.
2. The length of the load arm (long arm) is fixed at 10 m.
3. The mass of the projectile is fixed at 5 kg.
4. The length of the short arm can be varied from 2.5 m to 8 m.
5. The counter weight mass can be varied from 25 to 100 kg.
6. The shot angle can be varied from 0° to 90°.
Authorized user once get the access to conduct the simulation of Trebuchet
experiment can set the values of Length of the Short arm (m), Counter Mass (kg) and
shot angle (degree). For the selected values of the variable parameters with assumed
initial conditions the simulator gives the values of velocity, maximum height reached,
range it covered and time of flight. The design equations of the Trebuchet used in the
simulator to estimate all these parameters are listed below.
Fig. 1 Trebuchet setup for simulation
Simulation on Motion of a Trebuchet 89
Mathematical Equation:
Initial velocity V0¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ðmclgð1þcoscoshÞmbl1gð1þcoscoshÞÞ
mbþmcl
l1
2
s
Time of flight T ¼ðV0sinsinhÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðV0sinsinhÞ2þ2gh
p
g
Range ¼V0Tcoscosh
Maximum height hmax ¼V0sin hðÞ
2
2gþh0
h0¼10 þ10cosh
mc= Counter weight mass (kg).
mb= Mass of the projectile body (kg).
g = Acceleration due to gravity (m/s2).
l¼Length of the short arm (m).
l1= Length of the long arm (m).
h0= Height from ground level at the time of release (m).
T = Time of flight(s).
Vo= Initial velocity (m/s).
h¼Shot angle (deg).
3 Results and Discussion on Trebuchet Simulator
Analysis of Trebuchet using the Trebuchet simulator will be discussed in this section.
Figure 2shows the Trebuchet simulator’s view with default length of the short arm as
2.5 m, counter weight is 25 kg and shot angle is 90°. Before pressing the start (play) button
of the simulation the output parameters Velocity, height, range and timeof flight are all zero.
Fig. 3 Initial set-up of the Trebuchet simulator
90 K. B. Mulamuttal et al.
.
In simulation window’s zoomed view of the side view of the trebuchet is displayed.
The arm length control, counter mass and release angle control sliders are given on the
right side in the variables panel and controls in control panel.
The slider knobs are used to vary the variable parameters one by one to a suitable
value to simulate and the play button in control panel is clicked to start the simulation.
This is shown in Fig. 4.
A change in the length of the Trebuchet’s arm can be observed, and the animation
shows the movement of the Trebuchet’s arm; also a reference diagram is shown at the
top to refer for the motion of the arm at the angle which is set. Then a projectile is
thrown and the trajectory of the projectile is observed.
The initial velocity, height, time of flight and the range of the projectile is computed
and displayed at the bottom of the simulation window as shown in the Fig. 5.It’s
interesting to observe that the simulator not only gives the values of the few parameters
related to Trebuchet, instead it give the visualization of the entire process during the
execution. This is the major difference between just using the equations to compute the
parameters and making the user feel the concept involved in the topic of interest.
Initially in Fig. 3the view of the Trebuchet is different and in the end at the time of
execution of the experiment it traces the entire trajectory of the mass, which makes this
simulator tool unique. This type of visualization will make students curious to try for
many possible combinations of variable parameters. Table 1gives the response of the
Trebuchet simulator for various input combinations. It can be observed that for first 4
readings of the Trebuchet, as the shot angle selected in 90°, the mass will fall at the
base of the structure itself hence the range is 0 m.
Fig. 4 Change of variable parameters
Simulation on Motion of a Trebuchet 91
There are a few limitations for this experiment; in the input parameters, the counter
mass weight is varied beginning from 25 kg and not from 0 kg till 100 kg. As we know
the basics of a Simple balance i.e., if one end of the pan has higher weight than the
other end of the pan then the pan which has higher weight comes down. According to
the equation of Initial velocity which is mentioned above, if the counter mass goes
below a certain value the equation takes negative values, to avoid that mass varied in
the above mentioned range. It is similar in case of the length of the short arm, to avoid
complex mathematical computations, the counter mass is restricted from 25 to 100 kg
and length of the short arm is fixed to vary in the range of 2.5 m to 10 m.
Fig. 5 Output of the Trebuchet simulator for the selected parameters
Table 1 Output parameters of Trebuchet simulator for various input combinations
Sl.
No
Length of the short
arm (m)
Counter
mass (kg)
Angle of
launch (h)
Velocity
(m/s)
Range
(m)
Maximum
height (m)
Time of
Flight (s)
1 2.5 25 90 6.17 0 11.9 2.16
2 2.5 100 90 18.86 0 27.78 4.24
3 8 25 90 11.95 0 17.14 3.05
4 8 100 90 14.74 0 20.86 3.52
5 2.5 100 0 26.67 53.34 20 2
6 2.5 25 45 8.06 14.27 18.7 2.5
7 2.5 100 45 24.64 74.61 32.25 4.28
8 6 100 40 21.7 62.41 27.45 3.74
9 2.5 100 43 24.81 76.34 31.63 4.21
10 2.5 25 0 8.73 17.46 20 2
92 K. B. Mulamuttal et al.
4 Conclusion
Paper titled “Simulation on Motion of a Trebuchet”has described the interaction
between the simulation of Trebuchet and the user to understand the concept of Tre-
buchet. User can now visualize the possible output from a Trebuchet for the given set
of input parameters. This simulator will help the user to predict the input parameter
settings to obtain the desired output parameters by carefully optimizing the input values
over repeated simulations. Remote user can vary the length of short arm, counter mass
and angle of launch and has very large combination of inputs for analysis. The analysis
of velocity, range, time of flight and maximum height can be done using the simulation.
The range varies from 0 to 78 m across the value of the counter mass. Analysis of these
values can be helpful in the analysis of transforming energy (potential energy to kinetic
energy) to designing the actual Trebuchet. There are many advantages of deploying a
virtual lab in educational environment which provides a better experience for engi-
neering students in an efficient, flexible and in a cost effective manner. User can do the
analysis and learn more repeatedly conducting experiments. Students have the liberty to
access the lab at anytime, from anyplace and perform at their own pace with their peer.
This saves time, provides more understanding and students can spend more time with
the tool to enhance their knowledge.
Acknowledgements. Authors of this paper express their gratitude for all those who helped in
developing the Remote Laboratory system. We also thank officials of Siddaganga Institute of
Technology (SIT), Tumakuru, the Management, Director, CEO and Principal and officials of
Center for System Design, NITK, Surathkal, Mangalore, Karnataka, India for their support in
making this project possible.
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Simulation on Motion of a Trebuchet 93
