The document describes the design, construction, and testing of a trebuchet built by a student for a class project. The trebuchet was required to launch a water-filled ping pong ball 12 meters, which it successfully accomplished after several design iterations. The student used analysis and calculations to optimize the design in areas such as forces on components, stress levels, and launch angles. Through rigorous testing and redesign, the student was able to complete the project of building a functional trebuchet meeting the specified performance goals.

1. Trebutchet Project
Gerard Simon Prosper
Abstract
This report explains the construction of a trebuchet.
This was the second project for MMAE 232 class.
The trebutchet’s requirement was to launch a Ping-
Pong ball which was filled with water to a certain dis-
tance which was 12 meters. The trebuchet successfully
launched the Ping-Pong ball 12 meters after multiple
trials.
1. Introduction
Having the ability to come up with a something
new can be done successfully by an engineer. Design-
ing a trebuchet was not an easy task and a lot of work
had to be put into the initial design. Changes were made
after construction as these mistakes were not picked in
the initial design process.
We were provided with two types of Medium Den-
sity Fibreboard ( MDF ) wood which were 24”x 18”x
1/4” and 24”x 18”x 1/8”. For each type, ten pieces were
supplied to us to utilize together with a 1/4” acrylic rod
to build the trebuchet. It was launched by way of a re-
mote servo trigger. The acrylic rod acted as a pivot sus-
tained the rotation without breaking.
Many parts of mechanical design were used in the
creation of the trebuchet. The arm consisted of a long
arm and short arm and it were both joined together using
wood glue and wood screw. The other parts of the de-
sign was kept simple, the arm was held back by a servo
which was attached to the frame where it also held a
pin. This kept the arm from launching and the projec-
tile from flying. The lever arm was weighed down by
four counter weights at the opposing end. This process
also utilized programming a self-activating trigger and
the use of an acrylic rod for the throwing arm to rotate.
The acyclic rod was held firm by a bridge that was de-
signed. It was a success where the trebucthet launched
the ping pong ball 12 meters.
The final design of the Trebucthet after construc-
tion is shown (see Fig.(1)).
Figure 1. Final Production of Trebutchet
Figure 2. 3D Graph used to identify Arm Length
and Time Frame for the Launch Window

2. Table 1. Values for Trigger Calculation
Variable Value
Length of short arm (l) 330 mm
Length of long arm (L) 560 mm
Total mass of counter weight (m) 2 kg
Gravitational force (g) 9.81 m/s2
Launch Angle in degrees (θ) 87.97
2. Concept Generation and Evaluation
There are various methods to build a successful tre-
butchet. One of the key points here is to ensure that the
structure is strong and rigid to prevent failure. We did
this by interlocking our edges. A Matlab code was pro-
vided by our lecturer that find the best possible launch
window by varying two parameters which the distance
from pivot point to projectile and length from pivot to
hinge. Also varied were the length of rope attaching
ping pong ball to the arm, pivot height and the effi-
ciency in the Matlab coding This was done to save time
in building a failed trebuchet. The code then takes these
varied parameters and using the equations that describe
the kinematics of a trebuchet launching a ball, creates
a three-dimensional mesh-grid plot of launch distance
vs. arm length and time (see Fig.(s)) which is used
to locate the optimal lengths of the pivot arm. It will
also provide a graphed estimation of how far our tre-
buchet will launch as well as how much force will be
applied to the acrylic rod, which the arm rotates around.
A nested ’for’ loop and a ’surf’ command were done
in the code to achieve the required three-dimensional
mesh-grid plot graph (see Fig.(2)).
3. Analysis
Before any construction began, analysis has to be
done to ensure that the item will be able to function
without any flaws. This is applicable for the trebuchet
also. Prior to any prototype design done in Autodesk
Inventor, we took a deeper look at the various forces
that was acting at different parts of the trebuchet. The
force from the servo to release the trigger was initially
calculated. This force allows the arm to begin its swing
and will cause deflection in the acrylic rod. From the
force calculated above, the deflection in the acrylic rod
can be calculated to ensure that the acrylic rod will not
break upon release from the trigger.
Figure 3. Free Body Diagram of Forces Acting
on the System
Table 2. Values for Servo Torque Calculation
Variable Value
Torque Servo Can Produce 350 N mm
Distance from Pin to Origin ( x ) 40 mm
Coefficient of Friction(µ) 0.8
Ftrigger 11.56 N
3.1. Force Acting on the Trigger
When calculating the force acting on the trigger
from the trebuchet, we first draw a free body diagram
of all the forces acting on the system (see Fig.(3)) to
determine the force acting on the trigger. By summing
the moments about point O, we were able to to come up
with the following equation :
Ftrigger =
l(mg)
Lsin(θ)
(1)
Ftrigger is the force acting on the trigger, l is the
Figure 4. Free Body Diagram of Forces Acting
on the Trigger

3. length of the short arm, m is the total mass of the
counter weight, g is the gravitational force, L is the
length of the long arm and (θ) is the launch angle in
degrees. Equation (1), the information from the free
body diagram of the trigger(see Fig.(4)) and the data
(Table (1)) are used to calculate the force acting on the
trigger. We found the force acting on the trigger to be
11.56 Newtons.
To find the whether the torque produced by the
servo is enough to use for the trigger, we sum the
moments in the free body diagram of the trigger (see
Fig.(4)) about where the servo is attached. Using the
equation :
Mo = (xFtrigger)+τservo −x(τservoFtrigger) (2)
Where Mo is the moment about the origin of rota-
tion, x is the distance from the pin to the origin, Ftrigger
is the force acting on the trigger, and τservo is the torque
required by the servo for the trigger. Knowing ΣMo = 0,
we were able to solve for τservo and it brought us to (3) :
τservo = x(−µFtrigger +Ftrigger) (3)
Based on the values for trigger calculation (see Ta-
ble (2)) and as well as the knowledge from (3) we ob-
tained the torque required for the servo for the trigger of
92.48 N mm, which is less than 350 N mm, the torque
the can produce. Therefore, the trigger design was used.
3.2. Shear Stress within Acrylic Rod
We then moved on to calculate the force acting on
the acrylic rod due to counter weights. This will create
a bending moment in the rod (see Fig (5)), which could
cause the rod to fail.
To be certain the trebuchet will be able to launch
as calculated we calculated the shear stress using the
equation below :
τmax =
TR
Ip
(4)
where τmax is the maximum shear stress produced,
T is the bending moment or torque produced inside the
rod, R is the radius of the rod which is 3.175 mm and Ip
is the moment of inertia.
To find T, we use the following equation :
T = Ryz−F(z−
lA
2
) (5)
where Ry is the peak force obtained from Matlab
graph (see Fig (6)), lA is the length acrylic rod, z is the
total length of the arm from end to end and F is the
Table 3. Values for Torque inside rod Calcula-
tion
Variable Value
Peak Reaction Force (Ry) 22 N
Length of acrylic rod (la) 20 mm
Total length of arm (z) 0.8
Force of hanging mass (F) 19.62 N
Figure 5. Free Body Diagram of Forces Creat-
ing Bending Moment on Acrylic Rod
force or total weight of the counter weights(see Fig (7)).
Based on the data provided (see Table (3)), the torque
obtained is 2,314.40 N mm.
To obtain the moment of inertia, the following
equation was used :
Ip =
πd4
32
(6)
where d is the diameter of the acrylic rod which
is 6.35 mm. We obtained the moment of inertia to be
159.623 kg mm4.
With the torque and moment of inertia calculated
with the radius of the acrylic rod given, using (4), the
shear stress calculated is 46.048N/mm2 and is smaller
than the ultimate tensile force of acrylic rod which is 70
N/mm2.
3.3. Pin Deflection
Now that the shear stress is calculated, we are now
able to calculate the maximum pin deflection using the
below equation
δ =
FRylA
AE
(7)
where FRy is the peak force acting on the acrylic rod
from Matlab graph, lA is the length of the acrylic rod,
A is the area of the acrylic rod, E is elastic modulus

4. Figure 6. Graph Showing Reaction Force on
Pivot
Table 4. Values for Pin Deflection Calculation
Variable Value
Peak Reaction Force (FRy) 22 N
Length of acrylic rod (la) 20 mm
Cross Sectional Area of acrylic rod (A) 4.9879 mm2
Elastic Modulus of acrylic rod (E) 3,200 N/mm2
of the acrylic rod. Based on the data (see Table (4)),
we obtained a deflection of 0.02757 mm which is very
small and it is negligible.
4. Experimental Results
We successfully managed to launch 12 meters
which was satisfactory according to our standards. We
officially had five chances to launch and used the fur-
thest distance we obtained. Before this, we conducted
a trial run without the servo and the acrylic rod broke.
Upon inspection, we noted that prior to launch, the arm
was not aligned straight with the bridge that was hold-
ing the acrylic rod. Furthermore, the bridge itself was
not a rigid structure hence, it caused the acrylic rod
to be unstable. Besides this, the counter weight box
added an extra one kg to the existing two kg of counter
weight. Due to the sudden increase in force of the
counter weight, the bridge structure being unstable and
the arm not being aligned, all this caused the acrylic rod
to break into two pieces. We came with a new bridge
design with extra support for the acrylic rod and prior
to launch again, ensured that the arm was aligned in the
right way. We removed the counter weight box and just
tied all four of the acrylic rod and connected it to the
arm using a string. This proved effective as we manged
to launch 12 meters.
Figure 7. Free Body Diagram of Force acting
on Swing Arm
5. Discussion
We managed to attain 12 meters due to a few rea-
sons and one of it was the holder of the ping pong ball.
This holder kept the ping pong ball in place and released
it when required during the launching of the trebuchet.
In the beginning after all the pieces were cut, we started
to assemble them and realized that some parts had some
difficulty to fit into each other. This was due negligence
on our part as we should have cut the openings or holes
slightly bigger for the parts to be assembled. Neverthe-
less, to ensure that all the parts fitted together, we used
a hammer to knock the parts to fit. The base support
was divided into four where each side had two supports
to prevent the entire structure from failing. Further-
more, with the new design of the bridge, the arm with
the acrylic rod was rigid and prevented not too much
movement from side to side at the center of the bridge.
Overall this was a fun and exciting learning experience
that we could use in the future.
6. Conclusions
We had a goal which was to build a functional tre-
buchet that was able to launch a water filled ping pong
ball a certain distance. Through hard work and perse-
verance, this goal was achieved and we launched the
water filled ping pong ball 12 meters. The design pro-
cess was assisted by MatLab in giving us the proper
dimensions of our pieces for maximum results. The
project allowed us to further advance our Autodesk In-
ventor skills. The trebuchet remained functional all day,
and still is a sound machine. The skills and techniques
of design, analysis and clear thinking are a required skill
for engineering students. This project assisted in this
greatly.