Connie's+and+Sureni's+Project

=== **Design Project: Trebuchet ** ** By: Sureni Gomis and Connie Fu ** ===


   Welcome to the page of Sureni Gomis and Connie Fu where you will find information pertaining to the entire construction process of our trebuchet.


To build an effective trebuchet, as defined by the equation //P = d/ml //  (where //<span style="font-family: Arial,Helvetica,sans-serif;">P // <span style="font-family: Arial,Helvetica,sans-serif;"> is the efficiency score, <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 121%;">//<span style="font-family: Arial,Helvetica,sans-serif;">d // <span style="font-family: Arial,Helvetica,sans-serif;"> is the distance traveled by the projectile, <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 121%;">//<span style="font-family: Arial,Helvetica,sans-serif;">m // <span style="font-family: Arial,Helvetica,sans-serif;"> is the mass of the entire trebuchet, and <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 121%;">//<span style="font-family: Arial,Helvetica,sans-serif;">l // <span style="font-family: Arial,Helvetica,sans-serif;"> is the length of the arm).

<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">**<span style="font-family: Arial,Helvetica,sans-serif;">Introduction **<span style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-family: Arial,Helvetica,sans-serif;"> The trebuchet is an ancient warfare machine that has been in consistent use during the Middle Ages. Despite its primitive nature and uses, it was a very effective machine in terms of hurling various projectiles. There are a variety of applicable physics principles that pertain to the structure of a trebuchet: projectile motion, Newton's laws of motion, kinematics, gravtitational force, and centripetal/centrifugal force. <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * 1) **Projectile motion:** A projectile is an object that follows the trajectory of a parabolic path, of which gravity is the only force to act upon its flight (and air resistance). When the projectile is launched at an angle, there are horizontal and vertical components. The optimum angle that results in a maximized displacement is 45<span style="font-family: Arial,Helvetica,sans-serif;">°; however, air resistance affects this result.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">**Newton's laws of motion:** The laws can be applied to predict the projectile motion. In the first law, Newton states that an object in motion stays in motion and an object at rest stays at rest, unless acted upon an outside force. In terms of the trebuchet, the projectile is launched and expected to go in a straight line, but outside forces, such as air resistance and gravity, act upon it. Therefore, the projectile travels in a parabolic shape. In Newton's second law, it's stated that F = ma. Acceleration of the projectile is dependent on the mass and the net force acting upon it. The third law states that for every action, there is an equal and opposite reaction. When the counterweight lowers one end of the arm, the other end of the arm with the lighter load (projectile) reacts by swinging forward.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">**Kinematics:** By using kinematics, the projectile motion can be calculated by using measurements of velocity and distance.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">**Gravitational force:** Gravity is always pulling downward. A trebuchet is set up so the counterweight is used as potential energy to throw projectiles. By holding the counterweight high, it is creating a resistance to the gravity pulling down. Once the resistance is released (letting go of the counterweight), the stored potential energy becomes kinetic energy.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif;">**Centripetal/Centrifugal force:** An object traveling in a circular path, the sling, depends on the mass of the object, the speed of rotation, and the distance from the center. By swinging the sling around, the projectile is forced to the end of the string, prohibiting it from falling from its circular flight.

====<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Materials <span style="font-family: Arial,Helvetica,sans-serif; font-weight: normal;"> (including all designs created from initial to final) ** <span style="font-family: Arial,Helvetica,sans-serif;"> ====

<span style="font-family: Arial,Helvetica,sans-serif;">
 * <span style="font-family: Arial,Helvetica,sans-serif;">an assortment of K'NEX pieces (including wheels)
 * <span style="font-family: Arial,Helvetica,sans-serif;">1 Styrofoam cup
 * <span style="font-family: Arial,Helvetica,sans-serif;">string (about 2 m in length)
 * <span style="font-family: Arial,Helvetica,sans-serif;">fabric (cloth of any kind that can be used for a sling pouch)
 * <span style="font-family: Arial,Helvetica,sans-serif;">a small box that can fit several large batteries (for weight)
 * <span style="font-family: Arial,Helvetica,sans-serif;">tape
 * <span style="font-family: Arial,Helvetica,sans-serif;">scissors
 * <span style="font-family: Arial,Helvetica,sans-serif;">tape measure
 * <span style="font-family: Arial,Helvetica,sans-serif;">calculator
 * <span style="font-family: Arial,Helvetica,sans-serif;">pencil
 * <span style="font-family: Arial,Helvetica,sans-serif;">Christmas ornament (5 g) -- as supplied by the teacher
 * <span style="font-family: Arial,Helvetica,sans-serif;">weigh scale

====<span style="font-family: Arial,Helvetica,sans-serif;">**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Procedure **<span style="font-family: Arial,Helvetica,sans-serif;"> (to build trebuchet) ====

<span style="font-family: Arial,Helvetica,sans-serif;"> When deciding to build our trebuchet, we did not have any formal plans written, although we had a basic idea. Our initial thoughts were to include a support, a counterweight, a bending counterweight arm, projectile pouch and sling, and wheels. We searched online for ideas of how we might build the trebuchet using K’NEX. Our first prototype was []. Initially, we built this model just so we could have an idea of how K’NEX might work in terms of a trebuchet. The steps to build this are:
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Build two supports in a rectangle plus a triangle shape using K’NEX.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">Connect the two supports on the bottom and as well as at the top vertex of the triangle.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Build arm and pivot. The counterweight side should have its own pivot in order for the counterweight to drop straight down in a perpendicular direction as opposed to swinging down.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">Make the counterweight with large K’NEX wheels. Connect the wheels to the arm.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif;">Cut the Styrofoam cup so that the Christmas ornament can fit inside it, and attach it to the other end of the arm.
 * 6) <span style="font-family: Arial,Helvetica,sans-serif;">Add wheels to the base.

<span style="font-family: Arial,Helvetica,sans-serif;">After building our first model, we decided to build another one that we planned to make more effective. We also based this model on a YouTube video: []. We thought this model would be more effective in terms of distance. <span style="font-family: Arial,Helvetica,sans-serif;">
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Build two supports using cubes of K’NEX, and add diagonals to the cubes (to form triangles) to increase strength. The support should be in a triangle shape. In our third prototype, we added pillars to the triangle to extend the height as well as the arm length.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">Connect the two supports together at the base and as well as the top vertex of the triangle.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Build arm and pivot. The counterweight side should have its own pivot in order for the counterweight to drop straight down as opposed to swinging down. The sling side should include a hook for the sling to hook onto; a small K'NEX piece can be used as a hook, attached to the arm.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">Build the counterweight by adding large batteries to a small box. Tape the box together and add a string to it. Tie the counterweight to the arm.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif;">Make a triangle sling out of fabric and add string to it. Add the sling to the arm. Tie one end of the sling to the arm and have a loop on the other end of the sling.

====<span style="font-family: Arial,Helvetica,sans-serif;">**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Labeled Diagram <span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif; font-weight: normal;"> <span style="font-family: Arial,Helvetica,sans-serif; font-weight: normal;">(f **<span style="font-family: Arial,Helvetica,sans-serif;">inal design - prototype 1) ====

<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif; font-size: 121%;"> <span style="font-family: Arial,Helvetica,sans-serif;">

====<span style="font-family: Arial,Helvetica,sans-serif;">**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Procedure **<span style="font-family: Arial,Helvetica,sans-serif;">(to test trebuchet) ====

1. Place projectile in cup. 2. Push the cup down and let go. 3. Observe and record distance traveled by the projectile. 4. Repeat steps 1 – 3 eight times.
 * Prototype 1:**

1. Move the sling around the pivot point so that the sling is underneath and on the same side as the weight; everything needs to be centered. 2. Place projectile in sling pouch. 3. Hook the open end of sling onto the arm's hook. 4. Pull pouch back and let go. 5. Observe and record the distance traveled by the projectile. 6. Repeat steps 1 – 5 eight times. <span style="font-family: Arial,Helvetica,sans-serif;">
 * Prototypes 2 & 3:**

====<span style="font-family: Arial,Helvetica,sans-serif;">**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Trial Results **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> (final design - prototype 1)====

<span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">
 * <span style="font-family: Arial,Helvetica,sans-serif;">**Trial** || <span style="font-family: Arial,Helvetica,sans-serif;">**Mass (g)** || <span style="font-family: Arial,Helvetica,sans-serif;">**Arm length (cm)** || <span style="font-family: Arial,Helvetica,sans-serif;">**Distance (cm)** || <span style="font-family: Arial,Helvetica,sans-serif;">**P=d/ml** ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">1 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.8 || <span style="font-family: Arial,Helvetica,sans-serif;">11.1 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">2 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.5 || <span style="font-family: Arial,Helvetica,sans-serif;">9.2 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">3 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.5 || <span style="font-family: Arial,Helvetica,sans-serif;">9.2 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">4 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">2.0 || <span style="font-family: Arial,Helvetica,sans-serif;">12.3 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.6 || <span style="font-family: Arial,Helvetica,sans-serif;">9.8 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">6 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.8 || <span style="font-family: Arial,Helvetica,sans-serif;">11.1 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">7 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.7 || <span style="font-family: Arial,Helvetica,sans-serif;">10.5 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;">8 || <span style="font-family: Arial,Helvetica,sans-serif;">0.5 || <span style="font-family: Arial,Helvetica,sans-serif;">0.325 || <span style="font-family: Arial,Helvetica,sans-serif;">1.8 || <span style="font-family: Arial,Helvetica,sans-serif;">11.1 ||
 * <span style="font-family: Arial,Helvetica,sans-serif;"> || <span style="font-family: Arial,Helvetica,sans-serif;">**Average: 10.5** ||

**<span style="color: #407bdd; font-family: Arial,Helvetica,sans-serif;">Analysis **
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> When we initially commenced building our trebuchet, we debated whether to use K’NEX pieces or wood, but we eventually decided to use K’NEX pieces not only because it was the only resource we had access to, but also because of the lightness of the building materials. We built a prototype, which we eventually used as our final model (with some slight modifications), to test how efficient K’NEX pieces were, and it worked quite well – the pieces were quite strong together, but allowed for some flexibility, as well. We added wheels to help propel the motion of the trebuchet when it is in action.



<span style="font-family: Arial,Helvetica,sans-serif;">After building our prototype, we built a larger version that consisted of two right triangles to form the structure. However, we decided to build onto this structure to create more support for the arm of the trebuchet by adding two more right triangles to create two large triangles as the final structure.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> <span style="font-family: Arial,Helvetica,sans-serif;">

We experienced some difficulty trying to develop a sling for our trebuchet, but we discovered that using a triangular-shaped piece of cloth worked better than the various initial cup-shaped mechanisms we tried such as one made out of paper and out of plastic. The sling we constructed was about the same length as our arm, not including the part of the sling that releases when the trebuchet is in action. As for the counterweight, we discovered through research that using a weight that is about 75-100 times heavier than the projectile itself, which was about 5 grams. As we tried to improve our trebuchet’s efficiency once we successfully made a sling that worked properly, we experimented with using different types and measures of weights. We tried using a small box filled with large batteries, and eventually increased the weight by attaching a heavy candle holder to it. We then attempted to increase the weight even more by instead using exercise weights that weighed 1.4 kg each. We found that increasing the weight of the counterweight helped to increase our projectile distance in a sense, but it did not benefit us in the efficiency equation. We decided to extend the height of our structure by adding pillars to each of the triangles, in an attempt to maximize distance. However, the efficiency of our trebuchet was not improving as we were adding more weight, thus increasing the denominator of our equation, and the projectile distance was not increasing; in fact, it was mostly remaining the same throughout our changes (about 6-8 m). As well, we tried to add wheels to the large structure, but the K’NEX was not successful in supporting the structure on wheels. Each time we tried to stand the structure, the wheels would break off. <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;"> Since the efficiency of our trebuchet was poor, because our score from the equation was approximately “1”, we decided that we had to decrease the weight of the entire structure and arm. We reverted back to our initial prototype at the last minute and decided to further develop it with some modifications. We increased the height of the structure to maximize the projectile distance, and we decided not to use a sling since it did not work much effectively with the small structure. The efficiency of our trebuchet increased since we had a small denominator (small arm length and small weight of the entire structure) and a larger distance that the projectile travelled. After some testing, we were able to obtain an average score of around “10”. There were some inconsistencies as the projectile travelled around 1 m at some times and up to 2 m at other times, but we had to adjust the way we were launching the trebuchet to maximize the distance. However, we decided to use this trebuchet as our final design since we were able to increase the efficiency.

The following videos demonstrate the action of our trebuchet designs:


 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Sources: **

__http://radlinski.org/trebuchet/trebuch.html http://andypsionfan.users.btopenworld.com/trebsling/index.html http://www.globalspec.com/trebuchet/treb_game_release.swf http://www.algobeautytreb.com/ http://heim.ifi.uio.no/~oddharry/blide/vtreb.html http://www.calpoly.edu/~tsciorti/treb/ http://www.butlercc.edu/engineering/en115/en115_basic_treb_design.cfm [] http://www.instructables.com/id/the-knex-trebuchet/ http://www.medieval-castle-siege-weapons.com/trebuchet-physics.html http://www.siege-engine.com/SlingsAndPouches.shtml http://www.tasigh.org/ingenium/physics.html http://www.allbusiness.com/professional-scientific/scientific-research-development/422775-1.html__