21st Century Pacific Students

Construct A Great Launcher of Siege

Assembled by: See Yang

Hans RoelleNicole SolariRim Madani(Thursday 4-6)

December 04, 2003

Overview/OutlineI. Project Description

II. History

III. Modern Improvements

IV. Design Tips and Guidelines

V. Safety Considerations

VI. Design & Construction

VII. Analysis & Proposed Design

VIII. Completion & Performance

IX. Suggestions

X. Acknowledgement

Project DescriptionTo design and construct a TREBUCHET that is able to launch a hacky sack as far and accurate as possible.

Trebuchet: “an ancient siege engine used for throwing objects”

TASKS

1. Research

2. Design development

3. Build actual model.

4. Performance Test

5. Final/Competition

6. Presentation

7. Final Report

History

Used for destroying barricading walls

4th century BC - first invented in China

6th century AD - made its way to Europe

(used to hurl stones, cows, rotting flesh, etc.)

In England, it was referred to as Ingenium

16th century - became obsolete

Modern Improvements

Usage of Newton’s Second Law of Motion to

modify designs (principles of physics)

The addition of wheels to increase momentum

Development of new materials for counter

weight (massive solid vs. rocks)

Different/stronger sling material

Usage of light weight building materials

Design Tips and Guidelines

Find ratio of counter weight vs. arm that best

optimizes hurl distance

Hinge the weight so it is free falling

Have the weight fall as vertically as possible for

maximum acceleration

Have counter weight arm at a minimum weight

Have stable based frame

When drilling the hole for the dowel, make sure it’s

as straight at possible

Use as much simplicity as possible

Safety Considerations Always wear safety goggles at every step of the construction

process and launching of the trebuchet

Keep a safe distance from the trebuchet when launching,

somewhere around six feet

Keep all appendages away from the sling or release

mechanism of the trebuchet to prevent injury to yourself or

others

Prevent yourself and others from putting harmful objects into

the sling as they may be hurled and injure someone

Do not use sharpened metals in construction as they may

injure someone during operation

ALWAYS TAKE SAFETY PRECAUTIONS BEFORE OPERATING!!!

Design and Construction

Requirements and Scoring Criteria

Limitations/Constraints

Hurl a Hacky Sack of weight 28.8g or 1 oz

Cannot exceed 4ft long x 3ft wide x 2.5 ft tall

Must use a counter weight that does not exceed 12 lbs

Must release arm from a distance no less than 10 ft

Weight penalty incurred per pound

Analysis and Proposed Design

Analyses Overview

I. Design criteria discussion

II. Analytical discussion

A. Theoretical energy analysis

B. Dynamic Computer Simulation

III. Proposed Design

A. Proposed Materials to be used

B. Estimated Cost

Design Criteria Discussion

In this portion of our project, we discussed how the truss should be put together, the base strength, the height, the arm length, the distance at which the counter weight is hanging from the arm, the length of the sling, and what material to use for the pouch.

Part DiscussionTruss Needs to be able to withstand horizontal

forces

Base Needs to be rigid

Height Must be within restriction and is able tooptimize hurling distance

Arm Should be as light weight as possible

Sling Length The distance will vary upon the releasemechanism

Pouch Material Should use light weight material withfrictionless surface

Analytical Methods

g

VR 2sin20Projectile range with no air

resistance:

Energy balance:2

20Vmghm m

c

Combining range and energy equation:

hm

mR

m

c2max

* R = projectile range

* g = gravity

* h = height

* mc = mass of counter weight

* mm = mass of missile (hacky sack)

* V0 = initial velocity

* In order to maximize the range, the total height needs to be maximized

Analytical Methods (cont.)

Dynamic Computer Simulation Discussion

In order to maximize the range, we experimented with all the variables in the figure to the left.

First, we started with all the given information. From there on, we experimented with different lengths of L1, L2, L3, L4, and L5. After finding the most efficient values for the variables, we experimented with the most efficient angles to be used.

Analytical Methods (cont.)

Computer Simulation ResultsHurl Distance vs. Pivot Point

250

260

270

280

290

300

310

320

330

1.7 1.78 1.79 1.8 1.83 1.84 1.85 1.86 1.9 2

L5, Pivot Height (ft)

Hu

rl D

ista

nce

(ft

)

Hurl Distance (ft)

Hurl Distance vs. Counterweight sling length

0

50

100

150

200

250

300

350

0.7 0.8 0.9 0.95 0.99 1 1.01 1.05 1.1 1.2

Length (ft)

Dis

tan

ce

(ft

)

Hurl Distance

L5 (Pivot Height) Hurl Distance (ft)1.7 278

1.78 3161.79 3181.8 319

1.83 3221.84 3221.85 3211.86 3211.9 3122 285

Hurl Distance Counterweight Length217 0.7226 0.8258 0.9311 0.95321 0.99322 1322 1.01318 1.05306 1.1278 1.2

Hurl Distance vs. Ratio of L2 and L1

314

316

318

320

322

324

326

2.325 2.5 3 3.2 3.3 3.4

Ratio

Hu

rl D

ista

nce

(ft

) Ratio of L2/L1

Hurl Distance vs. Missile Sling Length

0

50

100

150

200

250

300

350

1.5 2 2.7 2.8 2.84 2.85 2.86 2.9 3

Length (ft)

Dis

tan

ce (

ft)

Hurl Distance

Hurl Distance Missile Sling Length104 1.5181 2304 2.7322 2.8324 2.84324 2.85324 2.86292 2.9269 3

Hurl Distance (ft) Ratio of L1 and L2323 2.325323 2.5325 3323 3.2321 3.3318 3.4

Angles vs. Time (up to point of release)

-2

3

8

13

18

23

00.

05 0.1

0.15 0.

20.

25 0.3

0.35 0.

40.

45 0.5

0.55 0.

60.

65 0.7

0.75 0.

80.

85 0.9

0.95 1

Time (seconds)

De

gre

es

(ra

dia

ns

)

Theta

Phi

Psi

Time (sec) Theta (degrees) Phi (degrees) Psi (degrees)0 2.484 0.658 0.913

0.025 2.472 0.663 0.9110.05 2.436 0.678 0.904

0.075 2.377 0.704 0.8930.1 2.296 0.744 0.883

0.125 2.195 0.798 0.8750.15 2.077 0.87 0.873

0.175 1.945 0.962 0.8810.2 1.801 1.077 0.9

0.225 1.647 1.218 0.9350.25 1.482 1.391 0.985

0.275 1.304 1.602 1.0510.3 1.105 1.866 1.132

0.325 0.872 2.21 1.2220.35 0.557 2.721 1.305

0.375 0.103 3.486 1.40.4 -0.184 3.926 1.767

0.425 -0.359 4.157 2.2970.45 0 -0.478 4.285

0.475 0 -0.568 4.3540.5 -0.651 4.397 4.294

0.525 -0.741 4.432 4.980.55 -0.837 4.457 5.657

0.575 0 -0.924 4.4560.6 -0.98 4.406 7.007

0.625 -0.985 4.283 7.70.65 -0.922 4.065 8.45

0.675 0 -0.763 3.6950.7 -0.455 3.057 10.51

0.725 -0.257 2.632 11.5150.75 -0.211 2.466 12.405

0.775 0 -0.211 2.3890.8 -0.196 2.34 14.163

0.825 -0.147 2.187 15.0720.85 0 0 2.072

0.875 0 0 2.0090.9 0 2.023 17.71

0.925 -0.11 2.118 18.5160.95 0 -0.197 2.281

0.975 -0.286 2.469 20.111 -0.341 2.621 20.934

Proposed DesignIn our proposed design, we made the base wide so the trebuchet would be stable. We also set our dimensions and lengths in accordance with the computer simulation. It seemed that in the simulation, by changing one measurement, the rest of the trebuchet lengths were changed.

Proposed Design (cont.)

Materials Used… Pine (1”x 2”) & (2”x 2”) Screws Wooden dowel (1) Nylon rope Shami Wood putty Eye bolts (appr. 4) PVC pipe (1- 3.5” dia.)

Estimated Cost… Due to the fact that

Nicole already has supplies at her house, we are fortunate enough to have our supplies donated.

If we do need supplies, we have estimated an amount of $25.

Construction and Performance

Construction methodsTo begin the project, we first sat down together and gathered all our thoughts. Before beginning to cut the pieces, we drew out a rough sketch of how we were going to put the trebuchet together.

Step 1: measure all the pieces Step 2: we put the base together Step 3: measure and cut all angles for the legs that are to fit

at an angle Step 4: screwing all the pieces together Step 5: getting the holes in for the dowel Step 6: cut the dimensions of the arm Step 7: fix the track Step 8: fix the sling, pouch, and release mechanism Step 9: fix the counterweight

Pictures

Pictures

Pictures

Pictures

Pictures

Pictures

Construction methods (cont.)

In our actual building of the trebuchet, we changed a lot of the dimensions and design. The reason we changed our design and dimensions was so make it easier on our part. We ARE humans and cannot be exact, and our changes did make a difference.

Problems SolutionsAngles of Bracings Add wedges and end caps

Angling of truss Modify design so trusses would stand vertical

Use of nails to attach pieces Use screws instead of nails

Drilling the hole on the arm for the dowel

Added an extra piece to straighten the dowel

Release mechanism wouldn’t lock into place

Moving the release attachment

Size of swing arm Shorten the end of the swing arm where the counter weight is attached

Completion of the Trebuchet

Optimizing hurl distance* For our first trials, we kept the all the measurements as calculated

by the simulation.

Step 1: experimented with different sling length to find the optimum performance length (between 30-40 ft)Step 2: experimented with shortening and lengthening the distance between the counterweight and the ground (between 20-30 ft)Step 3: experimented with different release angles (distance varied between 0-40)Step 4: shorten the length of the arm connected to the counterweight (50 ft)Step 5: repeated steps 1, 2, and 3

Other factors that affected the range were the weight of the arm, the overall weight of the trebuchet, and air resistance.

What would we do differently?

Group Started earlier on the construction portion of the project Figured out the angles and lengths at reasonable

measurements

Trebuchet Maximizing height of trebuchet Use a lighter arm Add wheels Reduce the total weight Use different release pin Use different sling material Make the counterweight drop as straight at possible Drilling a straight hole through the arm

Conclusions and Recommendations

Most helpful design processes: Our design goals were met in terms of weight and size We learned a number of interesting aspects in math and

physics to help aid us in the design The construction process helped us understand that the

computer simulation was just a theoretical estimation of the results

Collaboration of ideas Examples of trebuchets on the web

Least helpful design processes: There weren’t different measurements The drawings we made were not detailed enough The weight of the arm

Recommendations (cont.)Recommendations for future trebuchet builders:

Using better materials, connections, and construction tools

Run as many test trials as you can Time management Try not to get off task Don’t be afraid to argue with your teammates to

get your point across Leave criticism with the project (don’t take it

personally) Have spare parts available Be flexible Have fun!!!

AcknowledgementBullock, Tom. 11 January 2000. Trebuchet. 8 October 2003

<http://www.tbullock.com/trebuchet.html> 

Carliste, Paul. 1 February 1998. The Trebuchet. 8 October 2003

<http://www.ameritech.net/users/paulcarliste/trebuchet.html> 

Geiselman, Kevin A. 27 May 2002. Ingenium. 8 October 2003

<http://tasigh.org/ingenium/medium.html> 

Gray Company Trebuchet Page. February 2000. 8 October 2003.\

<http://members.iinet.au/~rmine/gctrebs.html> 

Grimminck, Micheal. 16 April 2001. Basic Physics Formulae. 8 October 2003

<http://xs4all.nl/~mdgsoft/catapult/ballistics.html> 

Ludlam, Eric M. 1 June 2003. Siege-Engine.com. 8 October 2003

<http://www.siege-engine.com/>

 Radlinski, Filip. Welcome to the Physics of the Trebuchet. 8 October 2003

<http://www.geocities.com/Silicon Valley/Park/6461/trebuch.html>

 

Acknowledgement (cont.)

Ripcords Trebuchet Stuff. 23 August 2003. 8 October 2003.

<http://www.ripcord.ws/>

 Trebuchet. 10 February 2003. 8 October 2003.

<http://www.io.com/~beckerdo/other/trebuchet.html>

 Trebuchet. 8 September 2003. Wikipedia. 8 October 2003.

<http://www.wikipedia.org/w/wiki.phtml?title=trebuchet&printable=yes>

 Trebuchet.com. 8 October 2003.

<http://www.trebuchet.com>

 Trebuchet at NF/Observatory. 8 October 2003.

<http://www.nfo.edu/trebuche.htm>

 Vaarma, Jari. 20 July 2001. Siege Engine Page. 8 October 2003

<http://www.students.tut.fi/~vaarma/siege/siege.htm>

Acknowledgement (cont.)

Thank you Linda, Charlene, Hanh, and James for letting us borrow your power drill and donating screws.

Thank you to Professor Litton and Professor Golinbari for all your help.