The Effect of Catapult Arm Length on Distance Ball Is Thrown
Charlotte Hirsch
Takoma Park Middle School 2011-12
Abstract
In this experiment, I am testing whether Leonardo da Vinci’s leaf-spring catapult can be improved, so
that it throws a ball farther, by changing the length of the catapult’s arm. My hypothesis was if I make the arm
30.5 centimeters, then the ball will be launched the farthest because the arm will have a bigger range of swing
with more force and energy built up than the 17, 21.5, and 26 centimeter-long arms will have, without
overwhelming the leaf spring like the 35 centimeter-long arm might. In my experiment, I built a leaf-spring
catapult with a kit. I replaced the kit's plastic arm with 17 cm, 21.5 cm, 26 cm, 30.5 and 35 cm long wooden
rods (3/8 inch thick) with a measuring spoon at the end to hold the ball. I tested the average distance the ball
was thrown with each arm. The results of my experiment showed that as the catapult arm length increased, the
distance the ball traveled decreased. The 17 cm arm, the shortest arm, threw the ball the greatest distance: 2.649
meters. The longest arm (35 cm) threw the ball the shortest distance, 1.548 meters. My hypothesis was refuted
because the 30.5 centimeter-long arm didn’t throw the ball the farthest distance. These results could be used to
improve many object-throwing mechanisms that have arms similar to the one in this catapult. To make these
mechanisms throw objects farther, we now know that you have to shorten the throwing arm.
Key terms:

Catapult arm

Leaf spring

Da Vinci

Potential energy to motion

Mechanics

Tension
Arm
Base of
catapult
The independent variable
for this experiment is the length of
Introduction and Review of
the catapult’s arm, from the base of
Literature
the release cup to the end of the
Base of
I am testing whether or not
dowel rod. The levels are 17
Leonardo da Vinci’s leaf-spring
release cup
Drum release arm
centimeters, 21.5 centimeters, 26
catapult can be improved with a
centimeters, 30.5 centimeters, and
different length of arm. Also, if it
Figure 1: Photo of catapult used in
35 centimeters. The control level
can be improved, what is the
experiment – Taken by Charlotte
is 26 centimeters. Some scientists
length of arm that makes the ball
Hirsch.
that I have researched thought that
launch farthest? I am interested in
if the arm length is too long, it will
this topic because I love testing out simple
put
too
much
stress
on the leaf spring. That is why
mechanisms made from materials I find around the
my control is only 26 cm, the length of arm that
house, like rubber bands. Trying to build, improve,
came in the kit (I will be remaking that too, since it
and design the arm of Da Vinci’s catapult will
came in plastic and the rest of the arms will be
definitely be a lot of fun. I am also interested in the
wood). So, I made the two levels that are longer
historical aspect of this project. Researching the
than the control 30.5 cm (4.5 cm longer than the
ideas of Da Vinci and other catapult scientists will
control) and 35 cm (9 cm longer than the control).
be very interesting. I have no previous experience
To make things symmetrical, I chose 4.5 cm shorter
with this topic.
and 9 cm shorter for the other two levels. My
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The Effect of Catapult Arm Length on Distance Ball Is Thrown
dependent variable is the distance from the catapult
to where the ball first lands, measured in meters. I
will place a roll of paper on the ground in the
approximate range that the ball will probably land.
I will spot the place where the ball first hits the
paper and write down a number for the trial and
level on the paper where it hits (for Level 1,
numbers one through 7, for Level 2, numbers 8
through fourteen, and so on). I will measure from
the starting line (where the catapult is) to the mark
using a tape measure with meters and centimeters.
The main scientific principle of this
experiment is the mechanics of a catapult arm. The
arm of a catapult (the long lever that swings and
launches the projectile) is a very important part of
the catapult. Catapults vary in the way they power
the arm to launch a ball. In the leaf-spring catapult,
tension is used to swing the arm. The arm is
attached to the drum (the cylinder that the arm
pivots on). A string that is wrapped around the
drum is attached on either end to two curved pieces
that form a slightly open arc. The string is tight,
and pulls on the springy arc pieces. When a drum
release arm (a piece that holds the drum in place) is
released, potential energy (the energy stored in a
body of matter as a result of its position) and
tension cause the drum to rapidly spin on its axle.
The arm attached to the drum rotates and releases
the projectile.
“Hucbald ap Urp” (pseudonym, real name
not available) constructed an experiment called “A
Leonardo da Vinci Leaf-spring Catapult” on April
14, 2007. He used a 100-foot tape measure to find
the distance the catapult threw a ball (from ground
level to ground level). The results ranged from 28
to 33 feet. He found that small rocks tended to stay
in the release cup for longer. This study relates to
my experiment because it tests a leaf-spring
catapult, just like I am. Although he did not change
the length of the arm, it is still helpful to know
about how far the ball will go if I keep the length of
the arm the same.
Alexis Cooley and Kim Jensen constructed
an experiment about “The Study of the Catapult”
(the date of the experiment is not available). They
were finding out the relationship between the length
of arm and the velocity of the ball’s flight. The
catapult they used was made of a large triangle. For
the experiments with the fewest human/weather
errors, the data showed that the shorter the throwing
Journal Article
arm, the greater distance of flight. This contradicts
the r*F= Torque formula (torque is the measure of a
turning force on an object/force around a given
point, and r is the distance from the pivot point to
the point where force is applied), which says that
the longer the arm, the farther it should have
launched. Their guess of why their data went
against this is that the longer arm caused the ball to
launch high, but not far horizontally. Or the arm
could have been so long that it overwhelmed the
small strength of the spring; the longer the arm, the
more stress on the weakening spring. This study
tested almost exactly what I am testing; but they
tested the effect of the length of arm on velocity,
while I am testing the effect of the length of arm on
just distance. Also, the scientists mentioned that it
is possible that if the arm is too long, it will
overwhelm the spring. This is very helpful for
when I pick my measurements of arms, so I won’t
make the arms too long.
Students sponsored by NIST (their names
are not available) did a study on statistics, “The
Fractional Factorial Example,” and used a catapult
to construct their experiment (the date of the study
is unknown). The catapult used was powered by a
rubber band. They tested and changed the
important factors that affect the distance the golf
ball is thrown, such as: band height, start angle,
number of rubber bands, arm length, and stop angle.
They also found out what was needed (what
factors/how many or much) for the ball to reach
three distances. The results showed that as the arm
length increased, the distance (from catapult where
ball lands) increased. This relates to my experiment
because one of the things these students changed
and tested was arm length. Arm length is my
Independent Variable too, and the results of this
experiment are helpful for writing my hypothesis.
The background research and previous
studies have helped me choose the levels of arm
length. Research has shown that if the arm is too
long, it will be too heavy for the leaf-spring. That
led me to choose levels that aren’t extremely long.
If I make the arm 30.5 centimeters, then the
ball will be launched the farthest, because the arm
will have a bigger range of swing with more force
and energy built up than the 17, 21.5, and 26
centimeter-long arms will have, without
overwhelming the leaf spring like the 35
centimeter-long arm might. In the NIST
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The Effect of Catapult Arm Length on Distance Ball Is Thrown
experiment, the results showed that a longer arm
makes the ball go further. Also, in “The Study of
the Catapult,” even though their data showed that
the shorter arm launches the ball farther, they
admitted that a physics formula proves that the
longer the arm, the farther the ball travels. Alexis
Cooley and Kim Jensen also said that their longer
arms may have been so long that they put stress on
the spring. Because of the reasons explained in
Cooley and Jenson’s paper, I am not predicting that
the longest level of arm will throw the ball the
farthest.
number. I repeated this process six more times (for
a total of 7 trials). I took the arc shaped stopper off
the end of the arm sticking out of the drum. I slid
this arm out and un-taped the plastic measuring
spoon.
I repeated that process with the 17 cm rod:
taping on the spoon, securing the rod into the drum,
launching the ball by pushing the release arm, and
marking the spot. I did this for 7 trials total. I
took the stopper off, slid the arm out, and un-taped
the measuring spoon to prepare for the next length
of arm. For the 21.5 cm, 30.5 cm and 35 cm arms, I
followed the same entire procedure. I measured the
Materials and Methods
distance from the end of the base of the catapult
I built a catapult by following the
closest to where
instructions in the
the ball lands to
Academy Da Vinci
the mark on the
Catapult kit (see
paper. I took the
appendix for
lowest and highest
instructions). I pulled
results off to make
off the arch-shaped
only five trials
stopper on the end of the
count.
arm included in the kit,
Throughout
and pulled the arm out
my entire
of the drum. I took a
experiment, my
1/8-teaspoon plastic
catapult stayed 10
measuring spoon and
cm off the ground.
attached it with a 3 inch
I kept the
piece of duct tape to the
projectile the same
end of the 26 cm dowel
so that it wouldn't
rod so that the spoon
affect the flight of
was in front of the
the ball. The
dowel rod. I used the
material of the arm
plastic arm from the kit
to saw an arm from the
(wood), release cup
dowel the exact same size
(plastic), and base of the
Figure 2: The effect of catapult arm length on the
as the plastic one. I pushed average distance the ball was thrown.
catapult (plastic) were
the rod through the hole 5
kept as controlled
centimeters into the drum,
variables. I kept the
and placed the small “u” shaped stopper over the
length of the piece of duct-tape attaching the spoon
end of it so it wouldn’t slide out. I placed the
to the arm controlled. For all 5 levels, the catapult
catapult on top of 5 books on the floor. I rolled
(aside from the arm) remained exactly the same.
paper onto the floor directly in front of the catapult
The design (but not length) of the arm also stayed
(in a straight line).
the same.
I pushed the arm as far back as it could go. I
Results
placed a plastic ball with a mass of less than 2
The catapult with a 17 cm arm threw the ball
grams and a 1.5 cm diameter inside the release cup
an average distance of 2.649 meters, having thrown
(the plastic measuring spoon). I pulled the release
the ball the greatest distance. The catapult with a
arm so that the drum spun on its axle, and the arm
21.5 cm arm had an average distance of 2.473
launched the ball. The ball hit the paper and I
meters. The control level arm (26 cm) threw the
marked the spot where it hit with its level and trial
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The Effect of Catapult Arm Length on Distance Ball Is Thrown
ball an average distance of 2.342 meters. The 30.5
had the same results; the shortest arm threw the ball
cm arm threw the ball an average of 1.896 meters,
the farthest. Their best guess for why this happened
followed by
had to do with
the 35 cm
the main
Distance ball is thrown (meters)
arm, which
scientific
Arm
Trial
Trial
Trial
Trial
Trial Trial
Trial
had an
principle of
length
Mean
1
2
3
4
5
6
7
average of
this
(cm)
1.548 meters.
experiment.
17
2.890
2.656
2.714
2.614
2.670
2.592
2.563
2.649
H
L
Overall, as
The
the catapult
21.5 2.539H 2.458 2.461 2.462 2.512 2.473 2.452L 2.473 mechanics of
arm length
the catapult
26
2.409H 2.361 2.402 2.365 2.294 2.290 2.273L 2.342 arm caused
increased, the
distance the
30.5 2.003H 1.586L 1.967 1.947 1.992 1.638 1.938 1.896 the ball to
ball traveled
travel higher
35
1.614
1.703
1.361
1.225
1.561
1.614
1.591
1.548
H
L
decreased.
(and not
The arm
longer) as the
Figure 3: The effect of catapult arm length on distance the ball is
length had a
length of the arm
negative
increased.
thrown. XH= Highest XL= Lowest (neither included in mean)
correlation with
Througho
the distance the ball was thrown.
ut the experiment, I was very careful to keep all of
the control variables the same. But one source of
Discussion and Analysis
error that might have affected the results is that I
One of the possible reasons for the results of
might not have pulled the arm as far back as it could
this experiment has to do with the height of the path
go every time before I pulled the release arm. This
of the ball. A shorter arm put most of its power
might have affected the strength of the throw. Also,
into the distance the ball traveled, as opposed to the
in one trial that was not counted in the experiment,
height, therefore sending the ball at a lower height
a rubber band in the leaf spring popped off. This
and a longer distance. But as the length of the arm
suggested that the rubber bands might not have been
increased, more power was put into increasing the
the same tightness every trial, which might have
height of the ball instead of the distance. This
changed the amount of tension that held the arm
would cause the distance that the ball travels to
back.
decrease as the length of the arm increases.
This experiment could be used in the real
My hypothesis is refuted. I predicted that
world to improve many object-throwing
as the length of the arm increased, the distance the
mechanisms that have arms similar to the one in a
ball was thrown would increase as well. However,
catapult. The results of my experiment show that to
the results proved that as the length of the arm
launch the object farther, the mechanism should
increased, the average distance the ball was thrown
have a shorter arm. To launch the object higher, the
decreased. The 17 cm arm, the shortest arm, threw
mechanism should have a longer arm. Also, one
the ball the greatest distance: 2.649 meters. The
follow-up experiment that might further improve
longest arm (35 cm) threw the ball the shortest
mechanisms is to change the height of the catapult
distance, 1.548 cm.
itself while testing the distance. Other related
My testable question was answered. Da
experiments could test the height of the ball in the
Vinci's catapult can be made to throw the ball a
air and change the arm length, or test the distance
greater distance – but by shortening, not
the ball is thrown and change the length of the
lengthening, the length of the arm. The length of
rubber bands in the leaf spring.
arm that threw the ball the greatest distance was not
Acknowledgements
the length of arm that the kit came with (which
would be “Da Vinci’s arm length”).
I want to thank my mom, dad, and sister for
The results of my experiment corresponded
helping me with this project.
with some of my background research. "The Study
of the Catapult" by Alexis Cooley and Kim Jensen
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The Effect of Catapult Arm Length on Distance Ball Is Thrown
References
Academy Plastic Model Company, LTD. (2010).
Leonardo da Vinci catapult
[Brochure].
Appendix 1: Instructions for Building the
Catapult
Cooley, A., & Jensen, K. (n.d.). The study of the
catapult. Retrieved from
http://tuhsphysics.ttsd.k12.or.us/Research/IB03/Coo
lJens/Catapult.htm
Energy: Stop faking it! Finally understanding
science so you can teach it (pp. 1-6). (2002).
Retrieved from http://web.ebscohost.com
EPI Inc. (2011, March 11). Power and torque:.
Retrieved from http://www.epieng.com/piston_engine_technology/power_and_tor
que.htm
Gurstelle, W. (2004). The art of the catapult: Build
Greek balistae, Roman onagers, English trebuchet,
and more ancient artillery. Chicago, IL: Chicago
Review Press.
Military technology. (2011). In J. F. Guilmartin, Jr.
(Ed.), Encyclopedia britannica (mechanical
artillery). Retrieved from
http://www.britannica.com/EBchecked/topic/38239
7/military-technology
NIST. (2010, June 23). 5.4.7.2. fractional factorial
example [Experiment results]. Retrieved from
http://itl.nist.gov/div898/handbook/pri/section4/pri4
72.htm
Urp, H. A. (2007, April 14). A Leonardo da Vinci
leaf-spring catapult [Online article]. Retrieved
October/November, 2011, from
http://www.hucbald.ramst.ca/articles/leonardo_cata
pult.html
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