The Relationship Between Mass of Projectiles and Their Launch Distances From a Catapult


Brian Jones

Cole Peyton

David Shriver


Table of Contents:



Research Question/Hypothesis


Background Information






Lab Diagram




Data Analysis/Conclusion






Return to Research


Research Question/Hypothesis:      :Top:


The goal of our experiment is to determine how different weights affect the launch distance in catapults. Keeping the launch angle the same, at 45 degrees, and the length of the sling the same, we will determine what the most effective weight will be, and how varying from that weight affects the distance of the launch. Our hypothesis is that very light weights will not go very far due to wind resistance and a lack of momentum, and very heavy weights will also fly short because of the heightened amount of force needed to move them at all. There will be some weight in the middle that will be a happy medium, depending on the size of the catapult and the force it can generate to propel the ping pong ball.


Background Information      :Top:


The desire for catapults stems from mankind’s consistent drive to make warfare a more mechanical practice. The concept of a catapult is quite simple, projecting a heavy or abnormal object a very far distance, yet human limitations required a mechanized solution. The first recorded historical reference to siege weapons goes back to “A.D. 339 when a biographer states that Dionysos I, Tyrant of Syracuse, brought together engineers from all over the Mediterranean for the purpose of developing an engine of war powered by a large bow - requiring more power than one man could muster” (Peter Hansen). Later, the “Romans adopted the torsion artillery invented by Greek engineers” and would successively use them in battle during the peak years of their empire (Alan Wilkins). The prosperity the catapult would have in battle became evident as, “The first weapons using gunpowder were introduced to the theatres of war in Europe during the 14th century but it took another 200 years before they replaced the old engines of war completely”(Hansen). Yet the concept of catapults today still has a variety of uses.


The modern day uses of catapults has evolved considerably from its origins of using a simple bow to launch an arrow into being implemented onto air craft carriers as a means of providing enough velocity to fighter jets to gain the necessary lift for takeoff. Although there are several different technologies that fall into the "catapult" category including the catapult, the ballista and the trebuchet, all three attempts to use stored potential energy rapidly converted into kinetic to propel heavy objects long distances. Both catapults and ballistas work by storing tension either in twisted ropes or in a flexed piece of wood. This is where a trebuchet differs, as it tends to consists simply of a pivoting beam and a counterweight that rotates the beam through an arc (see attached diagrams). Depending on the size and strength of materials used, a catapult’s capacity to thrust objects can range up to a thousand feet (HSW).


Procedure:      :Top:


1.             Gather materials

2.             Drill a hole in eight ping-pong balls

3.             Fill each ball with BBs in increments of 25, starting from 25 and going up to 200 BBs

4.             Stuff the balls with cotton to fill up remaining space

5.             Place duct tape over the holes in the balls

6.             Go to the post office and use the scale to weigh the ping-pong balls

7.             Set up catapult on the football field at the high school and stake it down so it doesn't move

8.             Send two people out in the field to watch where the ping-pong ball lands

9.             One person, at the catapult, load it with the 25-BB ping-pong ball

10.           Fire the Catapult

11.           The two people in the field watch for where the ball lands and places a steak where it landed

12.           Measure from the base of the catapult to the stake which is placed where the ball landed

13.           Record the distance the ball was launched

14.           Repeat steps 4-8, switching balls every five trials, until all ping-pong balls have been launched five times each


Materials:      :Top:


·               Catapult

·               10 tent stakes

·               Tape Measure

·               Ping pong balls

·               BBs

·               Paper

·               Pencil

·               Calculator

·               Scale

·               Cotton

·               Scale at the post office

·               Duct tape


Lab Diagram:      :Top:



Data:      :Top:


                                    Raw Data:    Excel  ::  Text


Data Analysis/Conclusion:      :Top:


This data supports our original hypothesis of finding a "happy medium" for the projectile weight. First starting out with the lighter ping-pong balls, we were getting short distances because of wind resistance on the balls. The 11.32-gram ball, for instance, only went an average distance of 15.80 meters. At this point, increasing the weight of the ping-pong balls generally made them launch farther. Overall, the 28.35-gram ping-pong ball went the farthest, with an average distance of 29.75 meters. After adding even more weight, the distances of the launches began to decline, eventually concluding with a 65.26-gram ping-pong ball traveling an average distance of 24.60 meters. This shows that our "happy medium" for our particular catapult is around 28 grams for a ping-pong ball sized projectile. To improve the experiment, a launch device instead of a sling, or a different type of catapult could be used. The experiment could also be done indoors where the variables such as the wind could be controlled. Possibly more trials could also produce more clear distinctions between masses, especially between the 50, 75, and 100 balls. Overall, the experiment yielded the expected results of a correlation between the mass of the projectiles and their launch distance from the catapult.


There are certain almost unavoidable uncertainties in dealing with outside trials. The main uncertainty presented by an outside project is the wind. Because the trials were all performed within the same couple of hours, and the wind fluctuates noticeably, it is almost definitely a cause of uncertainty in the data. During the trials the wind felt about 5 to 7 mph in the direction of the launches at some points, and then non-existent at other times. This may have accounted for some inconsistencies, but not enough to have skewed the data significantly. There also was the human error in determining exactly where the balls landed. Although there was snow on the ground, and the balls made marks in the snow, sometimes it was difficult to determine exactly where it landed because of footprints, etc. The final source of significant uncertainty in the data was present in the setup of the catapult for each trial. The launches could have been slightly inconsistent due to the inexact nature of the sling on the catapult. The sling and balls were set up in almost the same exact position every time, but slings are not always exact, and neither is the whole catapult mechanism necessarily. But, none of these uncertainties appeared to alter the data in any totally significant manner judging by the relative consistency of the data.


Sources:      :Top:


Roman Artillery Alan Wilkins Copyright Roman Military Research Society 2001

This is an excellent source for historical data and diagrams that pertain to the Roman Armies. This site was useful in acquiring a basic understanding of catapult uses.


Medeival Seige Technology and Countertechnology: The Catapult Andrew Vick

This source explained how the catapult evolved from its most simplistic form: the bow and arrow. This is also a good source for historical reference.


War Engines of the Middle Ages Peter Vemming Hansen Nyköbing Falster, Denmark. All rights reserved - Copyright 1998 Middelaldercentret

This web-site began to help us understand the actual physics of the catapult. It also contains quite a bit of historical information.


How does a catapult work? © 1998 - 2003 HowStuffWorks, Inc.

By far the best source for understanding the properties of physics that give the catapult its unique ability, such as torsion. This online library would be useful for just about any other research defense project.


Building a Catapult 

This is a very good site in building a catapult. We might build a catapult of buy a kit to make one, but this site gives good instructions on how to build one from scratch if we do. We could change the dimensions or sizes of pieces if we wanted to.


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