A presentation displaying the effect of angle measure and counterweight mass on horizontal trebuchet projectile distance.

1. The Effect of Angle
Measure and
Counterweight Mass
on Horizontal
Trebuchet Projectile
Distance
By: Avinash Kanakam

2. Introduction

3. Purpose
● The purpose of this project is to find the optimal
counterweight to projectile weight ratio and release angle
that can produce the farthest distance travelled by a
projectile.
● The independent variables are the counterweights and
angle measures used.
● The dependent variable is the horizontal distance the
projectile travels.

4. Hypothesis
● If the multiple factors that affect the trebuchet launch
distance are its angle measurement from the horizontal
and counterweight mass:projectile mass ratio, then a 45
degree angle measurement and ratio of 100:1 should
produce the greatest launch distance.

5. Background
● The trebuchet relies solely on the conversion of gravitational potential energy of
the counterweight dropping into kinetic energy for the projectile to fly in the air, as
given by:
○ MGH = ½m(v^2 )
● Where m is mass, g is gravitational acceleration, v is release velocity, and h is the
distance the counterweight falls. This equation shows the potential energy to
kinetic energy conversion, and that you can supposedly add infinite counterweight
mass to get more velocity with a constant projectile weight. However, that is
actually impossible as the golf ball can only hold enough energy whereas the
excess is released.
● An equation that calculates the distance of a trebuchet is where a = release angle,
v = initial velocity, and g = gravitational acceleration:
○ 2v^2(sin a)(cos a) / g

6. Background Part. 2
● This equation is what is commonly shown determine the best release angle. The
way to get the best out a is to set it to 45 degrees, which reduces the equation to
simply
○ v^2/g
● A trebuchet counterweight is what accelerates the payload arm up which
releases the projectile. The accepted ratio of counterweight to projectile weight
is usually 100:1. This means that for a 50 gram golf ball, the supposed best
counterweight is around 5 kilograms. Having the counterweight fall for a longer
time builds momentum, which should therefore transfer more energy into the
projectile, allowing it to fly farther.

7. Materials
Trebuchet Construction
● Birch, Oak, and Green Wood
● Metal Rod (50 cm.)
● Screws (10, Wood, 5 cm.)
● Nails (10, Wood, 7.5.)
● Wooden Plate (30 cm x 30 cm.)
● Small cup (holds golf ball)
● Straight edge
● Protractor
● Power Saw
● Electric Drill
● Rope (15 m.)
● 1”x1” PVC pipe
● Drill Bits (1.5 , 2.5, 3.5 cm. spade)
● Hammer
● Screwdriver
● Chisel
● Pencil
● Level
● Wood glue
Experimental Materials
● Golf Ball (50 grams)
● 3 bricks, and 1 half brick (2.5 kg for one
whole brick)
● Measuring Tape (10 m long)

8. Method - Building the Trebuchet
1. Make a rectangular base (3 ft long and 4 in. wide, 1 foot long and 4 in. wide)
2. Make 2 height pillars (30 in. each) and side supports for each height pillar (20 in. each)
3. Attach an arm, consisting of a payload arm to a counterweight arm (37.5 in and 10 in.),
strengthening it by 3 layers from fulcrum to counterweight hole.
4. Drill 1 in. holes through arm and 1 ⅜ in.through the height pillars to place metal rod and
connect arm to Trebuchet, by inserting the rod through frame and arm. Use a level to make
sure the arm is straight
5. Use the PVC pipe and place one of each at the end of rod. Use wood glue to ensure it sticks.
6. Cut ½ holes at the end of the counterweight arm.
7. Attach a cup at the top of the payload arm to hold a projectile and at the end of the
counterweight arm use rope to tie in plate to hold counterweights
8. Measure the place of the arm at each release angle (30, 45, 60) using a protractor and add a
wooden rod to act as a stopper at each marked spot.

9. The Trebuchet (to the left) and it’s
counterweight hopper (below)

10. Experiment conduction
1. Load the projectile cup with a golf ball
2. Place a brick on the counterweight plate and hold the arm
down as much as possible
3. Release the Trebuchet and record how far it went in
centimeters (Repeat 2 times)
4. Do the same with all other counterweights at half brick
intervals

11. Protractor added to the
side measure release
angle (left)

12. Results

13. Table: Distance traveled in centimeters for every angle and counterweight mass condition

14. Graph 1: Collected data graphed, along with trendlines calculated with equations. R-squared values also displayed to
show accuracy of models.

15. Graph 2: Data modeled further with prediction of distances using actual data trendlines.

16. Graph 3: The Derivatives of the model equations per angle condition plotted with respect to mass in kg.

17. Data Analysis
● When the data was mapped out, a trendline was mapped for each angle’s
distance data and the equations of those trend lines were collected, which
were used to make a model predicting higher ratio distances.
● When the derivative of each of those lines was calculated and graphed, there
existed an x-intercept which would is the best counterweight to projectile ratio.
The x-intercept is the best ratio because it represents the vertex of the
parabola of the models, and therefore the maximum distance the projectile
would travel with the given conditions.
● In both they show that the best counterweight to projectile ratio is around 50
grams to 9-10 kilograms. This produces a ratio of around 200:1.

18. Conclusions

19. Conclusion
● The hypothesis was proven incorrect. The data modelling showed that the mass of a
counterweight higher than the ones tested produce a maximum distance, and the 60
degree angle measure proved to be the best angle measure for throwing.
● Though the mass ratio hypothesized was incorrect, the derivative of all the models did
intercept the x-axis at near the same place, meaning that a perfect ratio does exist. The
best ratio was determined to be 200:1 using modelling of the collected data, which was
proven to be accurate and precise due to high R2 values.
● The 60 degrees angle has a clear explanation as to why it would have gone the farthest,
but also presents something to be tested in the future. As the trebuchet had more time to
build angular momentum (since the stopper of 60 degrees was further up), it went farther
due to a higher initial release velocity. The 45 degree angle hypothesis does not account
for angular momentum, but only the initial release angle.

20. Applications
● On aircraft carriers, the relative of the trebuchet, the catapult, is used to throw
military aircraft at a speed that they cannot achieve on a small lift-off track.
● Trebuchets are used to learn about things associated with physics such as
force, load, and parabolic arcs.
● In hunting, trebuchets launch “clay pigeons” to allow hunters to practice their
shooting without hurting animals. In seasonal events such as the Pumpkin
Chunkin, trebuchets and other siege engines compete to see which can
launch a pumpkin the farthest.

21. Future Research
● The best way to expand this project in the future is to build a stronger trebuchet to
handle the higher counterweights.
● Also, it would be beneficial to look into why as each angle shot differently, and how
their distances compare in reality when they hit their perfect projectile to counterweight
ratio.
● More research can be done specifically on the relationship between projectile-
counterweight ratio and angle measure, as mapping the derivatives suggested one
might exist.
● With further research, the two independent variables can be linked to each other or
found as independent of each other.

22. Limitations
● Making the Trebuchet stronger with use of heavier wood or aluminum alloy
will definitely make it better.
● At times, especially at the higher counterweights, the trebuchet would shake
or wobble after a release, unfairly manipulating the projectile’s distance.
● The strong limitation of the results is simply the environment in which they
were tested. For one, throwing a projectile in soft grass is necessary as the
projectile can easily break or at least dent on impact of hard pavement.
● Unfortunately, testing a projectile in grass risks the unevenness of patches
around the field that would not be seen or accounted for.

23. Error analysis
● One thing that could’ve failed systematically is the stopper of Trebuchet, as it
would easily be able to bounce in the holding cup, directing some of its kinetic
energy back into the cup instead of flying out with it.
● Also, since the Trebuchet itself was outweighed by higher counterweights,
hitting a stopper can lift the Trebuchet itself off of the ground a little bit,
flinging it farther than it should have
● . A random error could by taking the measurement of how far the golf ball
went, since measuring it relied on memorizing where it first hit the ground,
and the observer who stood near the initial impact area could easily
misinterpret where it hit.