Amanda+and+Jacqueline's+Trebuchet

 ** Amanda and Jacqueline's Trebuchet Project ** **//While trebuchets may be a medieval weapon, they are very sophisticated when it comes to the physics principles associated with these "dangerous structures." Not only do they encompass a wide range of physics concepts, but there are also different ways to fabricate trebuchets, as well as different models. For the purposes of this project, we decided to construct a floating-arm trebuchet.//     __Applicable Physics Concepts:__ **  **1. Projectile Angle**

The angle at which the projectile is released has a tremendous effect on the overall distance of the throw. The If the projectile was released earlier than the optimum angle, it would go upwards, and the force behind the throw is lost in the momentum needed to project the ornament upwards, and not forward. On the other hand if the ornament or projectile is released later than the desired angle, the projectile would hit the ground and would not use all of the force supplied by the use of a counterweight. We found that in order for the projectile to travel its farthest distance (not taking into account any other possible variables such as air resistance or mass of the projectile, etc), it should be released at a 45 degree angle. This is because, when calculating the theoretical vertical and horizontal velocities, at a 45 degree angle, both velocities would be equal and as such creating more hang-time, balancing the two forces.


 * 2. Centripetal Force

Centripetal force is the inward central force that acts on an o **** object when in rotation. This is the force that acts upon the sling and the projectile (Christmas ball) when in motion. This force causes the sling to continue moving toward the center of the rotation, thus causing it to arc and launch the projectile forward. This force also allows the Christmas ball to remain in the sling until it is released.

3. Gravity and Newton's Laws of Motion

Newton's 2nd law states that F=ma. This applies to our trebuchet because the force exerted by the trebuchet arm is directly linked to the acceleration of the arm as well as the mass of the counterweight. Furthermore, because we built a floating-arm trebuchet, our counterweight is accelerated by the force of gravity. This means that the acceleration of our arm is greater because not only do we have the counterweight pulling it down, but we also have the acceleration due to gravity pulling the entire arm downward. These two forces together allow our arm to gain more momentum. **  The final physics principle we took into consideration is terminal velocity. Terminal velocity states that at a certain point, any projectile will reach a point in motion, or in our case free-falling, where it cannot go any faster, though technically the acceleration of gravity would continually speed up the object falling. The reason this is relevant in out project is because when deciding the amount of weight to use as a counterweight, we needed to remember that after adding a certain amount of weight, it does not mean that it will fall any quicker.
 * 4. Terminal velocity** 

** __Materials:__  <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;">- Screws - Nails ** - 6 washers - 2 bolts ** - Power drill with multiple drill bits - Table saw - Hand saw ** - Power sander - Scrap plywood - Scrap pieces of wood (2 X 2) ** - 55 cm fir ( 1 X 2) - 3 plastic wheels - 3/8'' threaded rod ** - 2 metal eye hooks **
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - 6 capnuts
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - 2 soup cans
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - Machining router
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - 140 cm fir (1 X 3)
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - String **
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%; font-weight: normal;"> - Fabric (3 X 2)


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

** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">2. Cut scrap pieces of wood into pieces 3. Drilled holes in plywood base where the support beams would be. There are 4 vertical support beams on each side of the plywood, all 5.5 cm from the side. The distance between the two sets of support beams, or the distance in the middle of the trebuchet where the arm is going to be put into is 10 cm. 4. Pre-drilled holes into scrap pieces of wood (support beams) 5. Screwed the support beams onto the plywood base 6. Cut and pre-drilled horizontal support beams. The horizontal support beams are 18 cm long, and are attached to the ends of the vertical support beams. These horizontal beams are going to also act as runners for the wheels on the arm to roll on. 7. Attached horizontal support beams to vertical support beams 8. Using the machining router, we cut grooves into the 1 X 3 fir (this may be seen in image ). We left 2.5 cm of space from the top of the 1 X 3 fir to ensure the piece was sturdy enough to handle to counterweights that will be added later. 9. Pre-drilled and attached 1 X 3 fir onto the plywood base, beside the center of the support beams 10. Cut threaded rod with table saw into 3 pieces of 18 cm, 8 cm, and 8 cm. 11. Drilled hole, 4 cm from the top of the 1 X 2 fir, where the 18 cm threaded rod was inserted in between the 2 standing1 X 3 fir pieces. Arm was secured in place with 2 washers and 2 bolts. (See image )
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;"> Trebuchet structure
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 99%; font-weight: normal;"> 1. Planned design based on as shown in image ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">12. Drilled hole, 18 cm from the top of the 1 X 2 fir, where the 8 cm threaded rod was inserted. 13. Attached wheels 18 cm from the top of the 1 X 2 fir (arm) by sliding them onto the 8 cm threaded rod. Secured with 2 washers and 2 capnuts. Note: in order to align the wheels with the support beams, we needed to insert a piece of scrap wood between the arm and each wheel (please see image ). <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">14. Guide for arm plus third wheel and threaded rod 15. Drilled holes through the soup cans, and slid them onto the 18 cm threaded rod. Secured them with 2 capnuts. 16. After a variety of test trials to determine the optimum counter weight, we inserted g of weight in screws into the 2 soup cans. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Sling **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 1. Cut two small holes into each end of the fabric <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">2. Tied one piece of string through the two holes at each end of the fabric to create a loop (2 loops total). The string used to tie the loops was 20 cm long. 3. Tied another piece of string to each loop, these pieces of string measured 15cm long. 4. Attached both pieces of loose string to an eye hook. 5. Screwed one eye hook in to the end of the trebuchet arm. 6. Slipped the second eye hook over a nail which was nailed into the end of the trebuchet arm. We sawed off the head of the nail to allow for the string to slip off easier, as well the nail was tilted slightly with pliers so the it angled up towards the top of the trebuchet approximately 10-20 degrees. <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> And this is the final product

<span style="font-family: Arial,Helvetica,sans-serif;">** __Testing the Trebuchet:__ **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">

**<span style="font-family: Arial,Helvetica,sans-serif;">Overall Procedure

In order to test our trebuchet, we first made sure that the trebuchet structure itself was functional. This meant assuring that the arm was the right length, and assuring that the wheels ran correctly on the supporting beams. Then we had to move on to testing the sling. In order to do this, we tested numerous different sling models and were constantly making modifications. For more detail about the different sling models tested, please refer to the section below. After we found a sling model that worked, we also had to test out different weights. Once again, please refer to the section below. Finally, we had to practice releasing the counterweight and sling at specific times in order to guarantee successful results. We practiced launching our trebuchet numerous times at our houses, and then also in the school hallways and cafeteria.

Sling **<span style="font-family: Arial,Helvetica,sans-serif;">

The sling was the most difficult part of the trebuchet to construct. We spent numerous hours with a variety of different sling designs to try to find the most efficient sling.

We first used a piece of fabric with the approximate dimensions of 4" by 4". We soon realized, however, that this sling was much too big, and resorted to a smaller sling pouch. After trying with a few different sized pouches, we chose to use the 3" by 2" pouch.

The next dilemma was finding the best way to attach the pouch to the metal eye hooks on the arm. At first we simply tied a piece of string into each hole (2 holes at either end of the pouch), and then tied two strings to one eye hook, and the remaining two strings onto the other eye hook. This, however, did not seem to give us very successful results. We then decided to tie a loop at either end of the string, and then use more string to attach each loop to one eye hook. This design seemed much more efficient and made it easier for the sling to slip off of the eye hook when in movement.

Finally, the last adjustments we had to make were with regards to the eye hooks and their placement on the trebuchet arm. At first, we had positioned each eye hook permanently on either side of the arm. We later realized that in order for the sling to release the ball, it needed to slip off on one side. Therefore, we placed one eye hook permanently in the side of the arm, and we positioned the second eye hook on a nail on the opposite side of the arm. This design still did not seem to work. We fiddled with the angle of the nail, and still no successful results. We finally decided to try putting both the permanent eye hook, as well as the nail on the end of the arm. We angled the nail upwards, in order to allow for easier release of the second eye hook, and this ultimately became our final design.

**<span style="font-family: Arial,Helvetica,sans-serif;">Weight

Our counter-weight was another aspect of our trebuchet in which we made several adjustments. Ultimately, we found that it was not necessary to have an enormous weight, because our model (floating-arm trebuchet), utilizes the force of gravity and the acceleration due to gravity to pull the weights downward. At first, we tried using our trebuchet with very few weights. We discovered, however, that when we added more weight, the increase in distance was much more beneficial then the increase in weight. On the other hand, there was a limit to how much weight you could add without it counteracting the increase in distance. We therefore settled with a weight of _.

Arm length **<span style="font-family: Arial,Helvetica,sans-serif;">

When it came to testing the trebuchet, one of the most important adjustments we had to make was the arm length. Not only is this a factor in the equation P = d/ml, but it is also what determines if the trebuchet itself works. At first, our arm length was too long, therefore the arm would hit the ground during its rotation, and therefore it would not launch anything. Thus, we cut our arm length down to 55 cm to ensure enough space between the floor and the bottom of the arm. By cutting down the arm, we also improved our results with regards to the equation.

**<span style="font-family: Arial,Helvetica,sans-serif;">Excess wood

<span style="font-family: Arial,Helvetica,sans-serif; font-weight: normal;">The final adjustment we made to our trebuchet was cutting of the excess wood at the base. Because we made our trebuchet out of wood, it was reasonably heavy. Therefore, we wanted to eliminate as much weight as possible from our trebuchet. We cut of the excess plywood from the base, because this would not affect the functioning of the trebuchet, but it would decrease the overall weight. **<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">

**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">__Test Results:__ **<span style="font-family: Arial,Helvetica,sans-serif;"> || **Mass (kg)** || **Arm Length (m)** || **Distance (m)** || **P = d/ml** || || 2.6 || .87 || 8.2 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.6 || || 2.6 || .87 || 7.9 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.5 || || 2.6 || .87 || 8.5 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.8 || || 2.6 || .87 || 8.6 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.8 || || 2.6 || .87 || 7.2 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.2 || || 2.6 || .87 || 7.7 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.4 || || 2.6 || .87 || 8.0 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.5 || || 2.6 || .87 || 8.1 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 3.6 || || 2.7 || .87 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 5.6 m || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> 2.4 || || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> **Average** || <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> **3.55** || <span style="font-family: Arial,Helvetica,sans-serif;"> Note: The average is based on the first eight trials, since the ninth trial is not consistent with the rest of our testing. We think what happened on the ninth trial was that our hands were shaking because we were nervous and therefore the sling was not released at the proper timing, which would have affected our result.
 * **Trial #**
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<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">__**Analysis:**__

<span style="font-family: Arial,Helvetica,sans-serif; font-weight: normal;"> Overall, we believe that the floating arm trebuchet is an effective model, however it must be constructed accurately. There must also be plenty of time to test the trebuchet and make subsequent adjustments. While our trebuchet was not as effective as we would have liked it to be, we feel that it was still functional and successful.

If we were to build the trebuchet again, we would probably make it much lighter because the weight has a significant impact when using the equation P=d/ml. We would also make our trebuchet somewhat smaller, to allow for a shorter arm length, as well as a more compact model. Furthermore, it would be useful to investigate the possibility of constructing the trebuchet with a lighter material (example: PVC).

In hindsight, it would have also been beneficial to figure out mathematically the correct angle for the nail to be bent, or for the eye hook to be positioned, or even for the arm to be released so that we may have ensured a release angle of around 45 degrees. This would have allowed the projectile to travel further, and would have improved our overall results. **<span style="font-family: Arial,Helvetica,sans-serif;">

Edited by both Jacqueline and Amanda **