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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
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
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 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
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
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>
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