Question: How can you adjust the angle and speed of a projectile thrown by a trebuchet?

Student Exploration: Trebuchet

Vocabulary: air resistance, counterweight, counterweight trebuchet, efficiency, gravitational potential energy, kinetic energy, launch angle, payload, projectile, siege engine, torque

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

During the Middle Ages, armies often attacked castles using large siege engines such as the counterweight trebuchet at left. What challenges might you face if you attacked a castle?

While attacking a castle whatever is in the trebuchet might not be as big and wont do as much damage.                                                                  What are some ways to defend a castle against attack? Build upon the stone and keep building until you cant build anymore.                                     

Gizmo Warm-up

A counterweight trebuchet acts like a giant see-saw. Hanging from the “short arm” of the beam is a heavy counterweight. From the “long arm,” a sling holds the payload, usually a rock. In the Trebuchet Gizmo™, you can design your own trebuchet to attack a city or castle.

On the purple bar, check that tool tips () are on. Move your cursor over each red dot to see the name of the part. Use letters to label each part in the diagram to the right.

A) Counterweight, B) payload, C) fulcrum, D) short arm, E) long arm, F) sling, G) prong

Click Launch test. Describe the motion of a trebuchet.              The trebuchet was preferred over a catapult due to its greater range capability and greater accuracy. A trebuchet works by using the energy of a falling (and hinged) counterweight to launch a projectile (the payload), using mechanical advantage to achieve a high launch speed

Activity A: Trebuchet design

Get the Gizmo ready: Click Reset. On the Design tab, check that theCounterweight is 4500 kg, Payload is 160 kg,Fulcrum is 9.0 m, Short arm is 3.0 m, Long arm is 9.0 m, Sling is 5.0 m, and Prong angleis 40°.

Introduction: Once the payload is in the air, it is called a projectile. In this activity, you will see how each dimension of the trebuchet affects the angle and speed of the projectile.

Question: How can you adjust the angle and speed of a projectile thrown by a trebuchet?

Test: Click Launch test. Look at the results displayed at lower right.

What is the initial angle of the launch?                                    

The launch angle is measured from the horizon, as shown:

Which trebuchet dimensions do you think will have the biggest effect on the launch angle?

Experiment: While keeping all of the other settings the same, experiment with different sling lengths. You can change the sling length by dragging the bottom of the sling, or by entering the desired length in the Sling length text box. For each sling length, click Launch test and record the launch angle and initial speed of the projectile. Click Reset between each test.

Sling length	5.0 m	6.0 m	7.0 m	8.0 m	9.0 m
Launch angle	5.0	6.0	7.0	8.0	9.0
Initial speed	31.05	33.04	35.04	37.04	39.04

Analyze: How does increasing the sling length affect the launch angle and initial speed of the projectile? counterweight's initial potential energy is converted to kinetic energy of the payload                                                                                         

Experiment: You can change the angle of the prong by dragging its tip inside the circle or by entering the desired angle in the Prong angle text box. Check that the Counterweight is 4500 kg, Payload is 160 kg, Fulcrum is 9.0 m, Short arm is 3.0 m, Long arm is 9.0 m, andSling length is 9.0 m. For each prong angle, record the launch angle and initial speed.

Prong angle	0°	20°	40°	60°	80°
Launch angle	4.96	8.96	12.96	16.96	22.96
Initial speed	1.0	2.0	4.0	6.0	8.0

(Activity A continued on next page)
Activity A (continued from previous page)

Analyze: How does increasing the prong angle affect the launch angle and initial speed of the projectile?

Compare: Moving the counterweight farther from the fulcrum will increase the torque, or rotational force, on the beam of the trebuchet. However, it will also mean that the counterweight has to move farther to move the long arm the same distance.

Set up the trebuchet using the measurements given with each table below. For each trebuchet, explore different Short arm lengths and record the initial speed of the projectile.

Trebuchet 1

Counterweight = 4,000 kg, Payload = 200 kg, Fulcrum = 9.0 m, Long arm = 9.0 m, 
Sling = 9.0 m, and Prong angle = 40°.

Short arm length	1.0 m	2.0 m	3.0 m	4.0 m	5.0 m	6.0 m
Initial speed

Trebuchet 2

Counterweight = 6,000 kg, Payload = 40 kg, Fulcrum = 9.0 m, Long arm = 9.0 m, 
Sling = 9.0 m, and Prong angle = 40°.

Short arm length	1.0 m	2.0 m	3.0 m	4.0 m	5.0 m	6.0 m
Initial speed

Analyze: Compare Trebuchet 1 (T1) and Trebuchet 2 (T2).

How do the trebuchets differ?

For Trebuchet 1, which short arm length produced the greatest initial speed?  

For Trebuchet 2, which short arm length produced the greatest initial speed?  

In general, what short arm length maximizes the initial speed when the payload is very heavy compared to the counterweight?

How does the optimum short arm length change when the payload is very light compared to the counterweight? 

Activity B: Attack!

Get the Gizmo ready: Select the Launch tab. Check that the Siege of Acre is selected.

Introduction: The Siege of Acre occurred during the Third Crusade. Acre, a port city north of Jerusalem, was attacked by the combined armies of King Philip II of France and King Richard I of England. The crusaders used trebuchets to breach the city walls, eventually leading to the city’s surrender in July, 1191.

Goal: Design trebuchets to breach the walls of Acre and Castle Stirling.

Observe: To breach the walls of Acre, your projectile has to hit the walls with enough force.

What is the distance from the trebuchet to the city walls?

The projectile’s kinetic energy (KE) depends on its mass and speed, given by 

KE = m • v2. How much kinetic energy is required to break through?

On the Design tab, set the Counterweight to 4500 kg, Payload to 160 kg, Fulcrum to 9.0 m,Short arm to 3.0 m, Long arm to 9.0 m, Sling to 5.0 m, and Prong to 40°.

On the Launch tab, click Play (). How far did the projectile go, and what was its impact KE?   

Design: Click Reset (). Use what you have learned, as well as trial and error, to create a trebuchet that can fling a projectile and break the city walls. Use the Design tab to build your trebuchet, and then test your design with the Launch tab.

When you have created a successful trebuchet, click the screen shot camera () to take a picture of the broken city walls and the launch results. Paste the image into a blank document to turn in with this worksheet. Record the dimensions of your trebuchet below.

Counterweight:                   Fulcrum height:                     Long arm length:                 

Payload:                  Short arm length:                  Sling length:    Prong angle:                            

Challenge: Suppose King Philip could only build a 3,500-kg counterweight. Can you create a trebuchet with a 3,500 counterweight that can still break the walls of Acre? If so, take a screenshot and record the dimensions below.

Counterweight:                   Fulcrum height:                     Long arm length:                 

Payload:                  Short arm length:                  Sling length:    Prong angle:                            

(Activity B continued on next page)
Activity B (continued from previous page)

Observe: Click Reset. On the Launch tab, select Stirling Castle. In 1304, King Edward I of England ordered the construction of the world’s largest trebuchet, dubbed the Warwolf, to attack Stirling Castle in Scotland. Although the Scots tried to surrender before the trebuchet was finished, Edward refused to accept their surrender until after the power of the mighty Warwolf had been demonstrated, and part of the castle was demolished anyway.

What is the distance from the trebuchet to the castle walls?                 

How much kinetic energy is required to break through?                   

Design: Create a trebuchet that can fling a projectile and break the walls of Stirling Castle. When you have created a successful trebuchet, take a screenshot of the destroyed castle and add it to your document. Record the dimensions of your trebuchet below.

Counterweight:                   Fulcrum height:                     Long arm length:                 

Payload:                  Short arm length:                  Sling length:    Prong angle:                            

Challenge: The Warwolf hurled rocks as heavy as 160 kg at the castle walls. See if you can create a trebuchet that can hit Stirling Castle with a 160-kg projectile. If you succeed, paste a screenshot into your document and record the dimensions below.

Counterweight:                   Fulcrum height:                     Long arm length:                 

Payload:                  Short arm length:                  Sling length:    Prong angle:                            

Explore: Today, hobbyists build trebuchets for fun and competition. At the annual “Punkin Chunkin” contest, modern trebuchets have hurled pumpkins over 800 meters!

On the Launch tab, select Distance contest. Turn on Show grid. Try to build a trebuchet to hurl the payload as far as possible. Take a screenshot of your longest launch and record the trebuchet dimensions. If possible, compare your results to those of your classmates.

Counterweight:                   Fulcrum height:                     Long arm length:                 

Payload:                  Short arm length:                  Sling length:    Prong angle:                            

Summarize: What are the characteristics of trebuchets that can hurl objects the farthest?