Trebuchet Calculator Program
Intro
“The word ‘trebuchet’ has been used for convenience to designate the rotating-beam siege machines, in the full knowledge that other terms were also used in the Middle Ages, and that the question of nomenclature remains unresolved.” (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 271)
Now, since we covered that part, let’s get started. There are basically two types of trebuchets, the traction trebuchet, which was operated by men pulling ropes and the counterweight trebuchet, which provided the necessary force by using a counterweight.
If you want to do hand calculations to design a trebuchet with the best range, you will need to understand the physics involved. Figure 2, below, shows a diagram of a trebuchet with the main parts labeled. Autodesk Inventor software is available as a free download for students from: Autodesk, Inc. Inventor Professional for Education. A trebuchet is a device that converts potential energy to kinetic energy From basic physics we know that the range of a projectile with initial velocity v and angle αis Thus, the maximum theoretical range of a trebuchet is given by Mgh cw mv projectile 2 2 1 → g v R 2 2 sinαcosα = h m M R p 2 cw max =.
Traction Trebuchet
Let’s begin with the traction trebuchet, which is an older and simpler design. It is assumed that it is a Chinese invention and made its way to Europe via the Arab world around the 9th century. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 119; Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 271-272) It was the dominant form of artillery in Western warfare during the period of 1000 to 1300 AD. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 119)
The traction trebuchet was a rather simple construction, the frame was static and connected to the dynamic beam with an axle. On one end of the beam was a nest, sling or other element for holding the payload attached and on the other end several ropes for men pulling down the beam in order to provide enough force to propel the payload. The beam was divided into two arms by the axle. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 274)
Some numbers
According to Donald Hill the most detailed account for traction trebuchets are from Chinese sources and he mentions the following numbers that are also similar to Arabic sources, but take them with a large grain of salt: (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 274)
The relation in length for the long and short parts of the beam was 6:1 or 5:1 for light machines and 2:1 or 3:1 for heavy traction trebuchets. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 274; France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 119)
Now, the number of ropes in the illustration is not correct, they were usually around 40 to 125 ropes and pulled by 40 to 250. Yet, the highest given number in the records was up to 1200 men, which sounds ludicrously high. Thus, although it was a rather simple machine, the handling required quite some training and coordination. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 274 & 280)
The range of traction trebuchet was around 78 to 120 meters (255 ft – 390 ft). Whereas the payload was quite varied from 1 kg up to 59 kg (2 lbs to 130 lbs). (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 274 & 280)
Now, one drawback of the Traction Trebuchet was that the men operating the machines had a varying pull on the ropes, thus the firing range was likely changed from shot to shot even without accounting for exhaustion. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 121) Something that was not the case with the Counter-weight Trebuchet, so let’s take a closer look at it.
Counterweight Trebuchet
Hill states about the Counterweight Trebuchet:
“This machine appears to have been invented somewhere in the Mediterranean area in the late twelfth century, and to have spread outward very rapidly from its point of origin into norther Europe and western Islam. But the question of the exact provenance of the invention, whether in Europe or in Islam, is not resolved.” (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 275-276)
Trebuchet Calculator Program Free
The Counterweight Trebuchet was more complex, instead of men pulling down the beam, another axle with a counterweight was fixed on the end of the beam. Furthermore, a mechanism for pulling down and fixating the long arm was added, which was usually a winch. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 121) The counterweight was filled with stone, sand, lead or other heavy material. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 276-277) Another major factor was the use of a long sling, which was not unique to the Counterweight trebuchet, but more on this later.
The beam ratio of the Counterweight Trebuchet was also around 5:1 or 6:1. From what we know it seems that counter-weight trebuchets were used with heavier missiles. From a 14th century siege (Tlemecen) marble missiles were recovered, the largest had a weight of 230 kilograms (510 lbs). There are other accounts for other sieges giving a value of about 250 kg (560 lbs). But the usual weight was probably more around 45 to 90 kg (100 to 200 lbs).
Now, let’s look at the range, there are no proper accounts according to Hill, but he assumes that 275 m (900 ft) should be correct. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 277-278) Whereas another scholar notes that modern replicas suggest a range in the order of only 100-120 m, which would be about the same as the traction trebuchet. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 123)
Why did it took so long?
Now, at first look, it may be quite surprising why it took so long to develop the counterweight trebuchet, after all, it seems just a simple improvement, but Hill argues that is not the case. He notes:
“What is in fact surprising, when one comes to consider the dynamics of the counterweight trebuchet, is that it ever became a useful engine of war at all.” (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 280)
Why is it a complicated design? One of the main difference to the traction trebuchet is the fact that a lot of force is applied on the beam, when the trebuchet is readied and held in position. Whereas the traction trebuchet had the force only applied for a short amount of time. Thus, the counter-weight trebuchet had to be constructed with a stronger beam, which reduces its effectiveness quite considerably. Yet, one would assume that proper calculations or laborious trial and errors of various variations could produce an effective counterweight-trebuchet. Yet, Hill notes that without the addition of a long sling, there was no possible combination that would have made it feasible weapon. The long sling, basically provided an almost weightless extension of the beam, thus providing the additional force that compensated for the increased weight of the beam. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 280-282)
Although, the counterweight-trebuchet was quite a feat in engineering, its influence on warfare was limited and the balance between offense and defense was not altered significantly. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 123)
Traction vs. Counterweight Trebuchet
Let’s take a short look at the main differences of the Traction and Counterweight Trebuchets:
(France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 123-124; Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 275-279)
The main advantages of the traction trebuchet were that it was faster and cheaper to build and needed no specialists, unlike the counterweight trebuchet. It was also easier to transport and had a higher rate of fire. Yet, during operations it needed a large amount of manpower.
The main advantages of the counterweight trebuchet were its ability to fire larger stones and require less manpower during operations. The major drawbacks were it a complex machine and required specialists that were rare and few.
In terms of operating, it depends to a certain degree on the perspective, which one was, Hill notes the following:
“The first [traction] required greater skill in handling, the second in design.” (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 279)
But John France notes:
“The construction and operation of the counterweight-trebuchet was the province of specialist engineers, who were not always available, and it was ponderous to transport.” (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 123)
Hence, it really depends how one defines as handling and/or operating. I assume if one includes maintenance into handling that the counterweight trebuchet was harder to handle.
Overall, both types of trebuchets were used together during sieges. Looking at their advantages and disadvantages, traction trebuchets were probably used for throwing light missiles, whereas the counter-weight trebuchets used for heavy stones.
Effectiveness
Which brings us to the next point, the overall effectiveness of trebuchets.
In movies and computer games Trebuchets are often shown as weapons that can destroy city walls and towers easily. Yet, this depictions seems to be a big over exaggerated.
John France notes:
“Uninterrupted action by massed forces of large machines would surely have smashed masonry in time, but the conditions in which large numbers of such machines could be gathered and operated were relatively rare, and before the end of the twelfth century there is little evidence of artillery smashing the main masses of castles and walled cities.” (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 120)
Another aspect in attacking walls was, that the quality of the stones was very important, because if the stone shatters on the wall, the damage is quite limited. Thus, sometimes stones were transported a long way:
“At Acre, Richard used very hard stones brought from the West, which were so unusual that they were specially shown to Saladin.”” (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 124)
[Siege of Acre (1189-1191)]
One can expect that only a limited number of these special stones were available and used. Furthermore, Hill assumes that light trebuchets were used to throw missiles into the city, whereas the heavy trebuchets were used for attacking the walls. (Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare, p. 284) Thus, counterweight trebuchets with hard stones were probably used against fortifications, whereas traction trebuchets were used to attack softer targets like buildings.
It is assumed that the usage of heavy missile throwers was far greater in siege warfare in the Middle East than in Western Europe. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 124)
Note that trebuchets were not only used in the offense, quite on the contrary, there were also used effectively by defenders. Since they could be mounted on towers they would also outrange the attacker’s machine. Defenders used trebuchets against siege towers and the enemy artillery, thus providing what we would call counter-battery fire nowadays. (France, John: Western Warfare in the Age of the Crusades 1000-1300, p. 120)
Summary
To summarize, there were two main types of trebuchet that were used during the middle Ages. The traction trebuchet, which was a rather simple design were the force for firing was provided by men pulling down ropes. And the more complex counterweight Trebuchet were the force was provided by a counterweight, although it gives a rather simple impression, it was a quite complicated machine once you dive into the dynamics of it.
By the way if the concept of the traction trebuchet is too odd for you, you might check out the following real life video of one and for those who want to rebuild one in the sandbox game besiege, there is also at least one video.
Sources
Hill, Donald R.: Trebuchets, in: France, John: Medieval Warfare 1000-1300.
France, John: Western Warfare in the Age of the Crusades 1000-1300
Nicolle, David: Medieval Siege Weapons
Contamine, Philippe: War in the Middle Ages
Ohler, Nobert: Krieg & Frieden im Mittelalter
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FREE K-12 standards-aligned STEM
curriculum for educators everywhere!
Find more at TeachEngineering.org.
Partial Design Process These resources engage students in some of the steps in the engineering design process, but do not have them complete the full process. While some of these resources may focus heavily on the brainstorm and design steps, others may emphasize the testing and analysis phases.
Contributed by: AMPS GK-12 Program, Polytechnic Institute of New York University
Quick Look
Grade Level: 5 (4-6)
Time Required: 45 minutes
Expendable Cost/Group: US $10.00
This activity also requires non-expendable (reusable) LEGO MINDSTORMS EV3 robot kits and software for each group; see the Materials List for details.
Group Size: 4
Activity Dependency: None
Subject Areas: Algebra, Measurement, Physics, Science and Technology
Summary
Students work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.Engineering Connection
Engineers solve real-world problems. In fact, all engineers, including mechanical, electrical and chemical engineers, are faced with challenges that they solve via engineering designs, whether through the development of new technologies or improvements on existing functionality. In essence, engineers design and analyze solutions to generate new technology that is sophisticated and user friendly. Launching an object with precision is an ongoing challenge for people who use trebuchets; in this activity, students act as engineers to find solutions to this problem.
Learning Objectives
After this activity, students should be able to: Plockmatic 60 manual.
- Design a LEGO MINDSTORMS EV3 robot that can be used to launch objects.
- Program a robot using LEGO MINDSTORMS EV3 software.
- Determine the distance an object travels and relate it to its respective weight.
- Design and carry out a controlled engineering experiment.
Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards - Science
| NGSS Performance Expectation | ||
|---|---|---|
3-5-ETS1-1. Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost. (Grades 3 - 5) Do you agree with this alignment? Thanks for your feedback! | ||
| This activity focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost. Alignment agreement: Thanks for your feedback! | Possible solutions to a problem are limited by available materials and resources (constraints). The success of a designed solution is determined by considering the desired features of a solution (criteria). Different proposals for solutions can be compared on the basis of how well each one meets the specified criteria for success or how well each takes the constraints into account. Alignment agreement: Thanks for your feedback! | People's needs and wants change over time, as do their demands for new and improved technologies. Alignment agreement: Thanks for your feedback! |
| View other curriculum aligned to this performance expectation | ||
| NGSS Performance Expectation | ||
|---|---|---|
3-5-ETS1-2. Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem. (Grades 3 - 5) Do you agree with this alignment? Thanks for your feedback! | ||
| This activity focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Generate and compare multiple solutions to a problem based on how well they meet the criteria and constraints of the design problem. Alignment agreement: Thanks for your feedback! | Research on a problem should be carried out before beginning to design a solution. Testing a solution involves investigating how well it performs under a range of likely conditions. Alignment agreement: Thanks for your feedback! At whatever stage, communicating with peers about proposed solutions is an important part of the design process, and shared ideas can lead to improved designs.Alignment agreement: Thanks for your feedback! | Engineers improve existing technologies or develop new ones to increase their benefits, to decrease known risks, and to meet societal demands. Alignment agreement: Thanks for your feedback! |
| View other curriculum aligned to this performance expectation | ||
| NGSS Performance Expectation | ||
|---|---|---|
3-5-ETS1-3. Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved. (Grades 3 - 5) Do you agree with this alignment? Thanks for your feedback! | ||
| This activity focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Plan and conduct an investigation collaboratively to produce data to serve as the basis for evidence, using fair tests in which variables are controlled and the number of trials considered. Alignment agreement: Thanks for your feedback! | Tests are often designed to identify failure points or difficulties, which suggest the elements of the design that need to be improved. Alignment agreement: Thanks for your feedback! Different solutions need to be tested in order to determine which of them best solves the problem, given the criteria and the constraints.Alignment agreement: Thanks for your feedback! | |
| View other curriculum aligned to this performance expectation | ||
| NGSS Performance Expectation | ||
|---|---|---|
MS-PS2-2. Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Do you agree with this alignment? Thanks for your feedback! | ||
| This activity focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim. Alignment agreement: Thanks for your feedback! Science knowledge is based upon logical and conceptual connections between evidence and explanations.Alignment agreement: Thanks for your feedback! | The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. Alignment agreement: Thanks for your feedback! All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared.Alignment agreement: Thanks for your feedback! | Explanations of stability and change in natural or designed systems can be constructed by examining the changes over time and forces at different scales. Alignment agreement: Thanks for your feedback! |
| View other curriculum aligned to this performance expectation | ||
| NGSS Performance Expectation | ||
|---|---|---|
MS-ESS3-4. Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems. (Grades 6 - 8) Do you agree with this alignment? Thanks for your feedback! | ||
| This activity focuses on the following Three Dimensional Learning aspects of NGSS: | ||
| Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts |
| Construct an oral and written argument supported by empirical evidence and scientific reasoning to support or refute an explanation or a model for a phenomenon or a solution to a problem. Alignment agreement: Thanks for your feedback! | Typically as human populations and per-capita consumption of natural resources increase, so do the negative impacts on Earth unless the activities and technologies involved are engineered otherwise. Alignment agreement: Thanks for your feedback! | Cause and effect relationships may be used to predict phenomena in natural or designed systems. Alignment agreement: Thanks for your feedback! All human activity draws on natural resources and has both short and long-term consequences, positive as well as negative, for the health of people and the natural environment.Alignment agreement: Thanks for your feedback! Scientific knowledge can describe the consequences of actions but does not necessarily prescribe the decisions that society takes.Alignment agreement: Thanks for your feedback! |
| View other curriculum aligned to this performance expectation | ||
Common Core State Standards - Math
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs. (Grade 3) More Details
Do you agree with this alignment? Thanks for your feedback!
- Represent and interpret data. (Grade 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- Fluently divide multi-digit numbers using the standard algorithm. (Grade 6) More Details
Do you agree with this alignment? Thanks for your feedback!
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) More Details
Do you agree with this alignment? Thanks for your feedback!
International Technology and Engineering Educators Association - Technology
- Models are used to communicate and test design ideas and processes. (Grades 3 - 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- The process of experimentation, which is common in science, can also be used to solve technological problems. (Grades 3 - 5) More Details
Do you agree with this alignment? Thanks for your feedback!
State Standards
New York - Math
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs. (Grade 3) More Details
Do you agree with this alignment? Thanks for your feedback!
- Represent and interpret data. (Grade 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- Fluently divide multi-digit numbers using the standard algorithm. (Grade 6) More Details
Do you agree with this alignment? Thanks for your feedback!
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) More Details
Do you agree with this alignment? Thanks for your feedback!
New York - Science
- Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost. (Grades 3 - 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem. (Grades 3 - 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved. (Grades 3 - 5) More Details
Do you agree with this alignment? Thanks for your feedback!
- Plan and conduct an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) More Details
Do you agree with this alignment? Thanks for your feedback!
- Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems. (Grades 6 - 8) More Details
Do you agree with this alignment? Thanks for your feedback!
Materials List
Each group needs:
- LEGO MINDSTORMS EV3 robot, such as EV3 Core Set (5003400) for $389.95 at https://education.lego.com/en-us/products/lego-mindstorms-education-EV3-core-set-/5003400
- LEGO MINDSTORMS Education EV3 Software 1.2.1, free online, you have to register a LEGO account first; at https://www.lego.com/en-us/mindstorms/downloads/download-software
- computer, loaded with EV3 1.2.1 software
- 2-3 sheets of copy paper (recycled is fine)
Note: This activity can also be conducted with the older (and no longer sold) LEGO MINDSTORMS NXT set instead of EV3; see below for those supplies:
- LEGO MINDSTORMS NXT robot, such as the NXT Base Set
- computer loaded with the NXT 2.1 software
To share with the entire class:
- robot built from a LEGO MINDSTORMS EV3 kit
- access to a computer
- 1 eraser
- 1 tube of Chapstick®
- 1 tennis ball
- 1-2 gum drops
- 1 paper ball (made of a crumpled piece of printer paper)
- 1 ping pong ball
- tape measure
- scale
Worksheets and Attachments
Visit [www.teachengineering.org/activities/view/nyu_trebuchet_activity1] to print or download.More Curriculum Like This
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Pre-Req Knowledge
Basic concepts of a how a trebuchet functions.
Introduction/Motivation
Who loves watching objects fly through the air? (Give students times to discuss among themselves.) The term launch is often used to describe how far an object can travel. Trebuchets are devices that can launch object through the air. They were designed during medieval times to throw payloads (heavy objects) at enemies. Believe it or not, friendly competitions exist in some areas today in which trebuchets are used to launch pumpkins and even pianos. During this type of competition, a team wins when their trebuchet launches a pumpkin the farthest. Can you imagine how far a trebuchet would have to launch a pumpkin in order to win? (Give students time to guess a distance.)
In this activity, you design and test a trebuchet—actually a robot—to determine how far an object will travel based on its weight. Then, you adjust the angle and the length of the robot arm and determine how far different objects will travel, given modified variables. Basically, through experimentation, you learn how to design the best type of trebuchet to launch a variety of objects.
Why are we learning about trebuchets? I'm glad you asked! Trebuchets are an important educational tool because they demonstrate several principles encountered in basic physics—a branch of science that studies matter and its motion. Today, we will use computers and robots to model some of these physics concepts.
So, in this engineering activity, you apply math and science to predict how objects move through air as you design, build and program your own robotic creation to propel objects through the air. You also learn the importance of a variable, which is something that can be changed. By changing one variable at a time, you can determine what makes an object travel farther. Let's start launching!
Procedure
Background
During the first century, the Romans figured out different ways to make projectiles reach a certain location. During battle, they had to reiterate their designs in real time so that objects they hurled reached their opponents. The Romans applied a great deal of math and science, as well as trial and error, to solve this problem; the result of their efforts was the design of a crude, but effective, trebuchet—a type of catapult. Today, we use the trebuchet for both advanced solutions, as well as for entertaining purposes, such as catapulting pumpkins in friendly competition.
Before the Activity
- Gather materials and make copies of the How Far Does It Go? Worksheet, one per student.
- Load the EV3 software onto the computer.
- Divide the class into groups of four students each and assign each group member one of the following tasks: Launcher Driver (launches the object); Launcher Passenger (prepares the launcher); Measurer (measures how far the object travels); and Recorder (records the data observed from launches).
With the Students
Part 1: Preparing the Robot
- Have groups design their own robot launchers. Since many ways exist to design robots, tell students that this is an open-ended design project. (See some examples of student-designed projects in Figure 1.)
- Have students build their own robots before moving on to the programming stage. Since no set of instructions are provided for building, encourage students to be creative and work together to come up with viable designs.
- Following Figure 2, instruct students to program the robot to launch objects. If the program does not look like Figure 2, then instruct students to look in their pallet on the left side of the window for the program and make sure the motor, direction and power agree with Figure 2. The arrow in Figure 2 represents the direction, and the semi-circle filled with the orange color represents the power.
- Once programmed, have students plug the cable into motor A, located on the EV3 brick.
- Open the MINDSTORMS program and ask students to drag the motor block to the orange square; select the motor, power and direction. It is important that students understand they must have one motor do one rotation forward in order for the launcher to work.
Part 2: Preparing for the Launch
- Review correct measurement skills with students and teach them how to measure distance.
- Show students the variouis objects available to be launched, and ask them to predict which will travel the farthest.
- Ask students: What do you think will happen to the object's travel distance when the arm angle is changed?
- Ask students: What do you think will happen if you increase/decrease the angle or increase/decrease the length of the arm?
Part 3: The Launch
- Show students the objects to be launched again. Have them use a scale to determine and record the weight of each object.
- Direct students to take turns within their groups to launch objects. To do this, take an object and place it at the end of the arm for launching. (Note: Watch that students do not launch objects at each other.)
- Once launched, have groups measure the distance traveled (that is, the distance from the robot to the object); be sure students know the weight of each object before they launch it.
- Instruct students to record the object's distance traveled on their worksheets. Make sure they measure where the object first hits the ground, not where it rolls or slides to.)
- Once all groups have obtained data for their first trials, change the variables, repeating steps #2-4 for each variable change. First, change the angle of the arm and next, return the arm angle to its original setting but change the arm length).
- Direct students to complete the follow-up questions on their worksheets.
Vocabulary/Definitions
angle: The amount of rotation that separates two vectors.
constant: The quantity that remains constant in a given equation.
distance: The amount of space between objects.
length: The measure of how long something is from one end to another.
variable: The quantity that changes in a given equation.
Trebuchet Calculations And Principles
Assessment
Pre-Activity Assessment
Guessing Game: Have students weigh the different objects. Ask them to predict which object will go the farthest, giving reasons for their answers.
Activity Embedded Assessment
Design a Robot: Direct students to design robots that will be able to launch objects. Explain that this is called open-ended design since there is no one right way. Ask them to explain to you how their designed launchers function to launch objects.
Post-Activity Assessment
Worksheet: Have students use the How Far Does It Go? Worksheet to record their trebuchet experiment data and results. Review their data, graphs and answers to gauge their level of comprehension.
Tuning the Equation: Ask students what happens when both the arm length and arm angle are changed? Ask them how far the object goes when these two variables are manipulated together.
Re-Design: Ask students to think about how changing variables (that is, the arm length and arm angle) affected their robot performances. As engineers, how would they re-design their existing robots to launch an object the farthest? How would they modify the design if accuracy was more important than distance?
Investigating Questions
- Which object went the farthest? Why? (Answer: The paper object went the farthest because it was the lightest.)
- What happened when the length of the arm was changed? (Answers: When the length of the arm was increased, the velocity and power of the object increased. Also when the length of the arm is longer, the angle of release is smaller. When the arm is shorter, the distance the object traveled is shorter; when the arm is longer, the distance that the object traveled is longer.)
- What happened when the angle of the arm was changed? (Answers: When the angle is smaller, the distance is shorter; when the angle is bigger, the distance is larger.)
- As engineers, what concepts did you apply to solve this problem? (Answers: We applied math, science and our own creativity to effectively design trebuchets; engineers incorporate all of these concepts as they design, analyze and iterate product designs.)
Safety Issues
- Remind students to only launch towards unoccupied space, never towards other people.
Troubleshooting Tips
Remind students to test their launchers before they begin to launch the objects.
Remind students that all launches should be precise; they should not estimate their launches.
The rubber bands on their robot launchers should have some sort of tension; students may need to adjust the tension after they have launched an object.
Activity Scaling
For upper grades, have students experiment with other materials, and launch them with different angles and arm lengths. Specifically, challenge students to create robots with long arms and find out what length impairs the function of the arm. Additionally, experiment to find out what arm length is not strong enough to launch an object and what length provides the best launch.
References
Hewitt, Paul. Conceptual Physics. Upper Saddle River, NJ: Prentice Hall, 2002.
Zitzewitz, Paul. Physics Principles and Problems. Columbus, OH: McGraw-Hill, 2002.
Contributors
Jennifer S. Haghpanah, Janet YowellCopyright
© 2013 by Regents of the University of Colorado; original © 2013 Polytechnic Institute of New York UniversitySupporting Program
AMPS GK-12 Program, Polytechnic Institute of New York UniversityAcknowledgements
This activity was developed by the Applying Mechatronics to Promote Science (AMPS) Program funded by National Science Foundation GK-12 grant no. 0741714. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.
Last modified: April 29, 2019
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