Victoria+and+Britt's+Trebuchet

Physics 30 - Period 3 - Trebuchet Assignment  The Making of Scarlet By: Victoria Schramm and Britt Agrey

__Introduction__ A trebuchet is a medeival weapon that was used in war. It was used to fire projectiles over castle walls. Boulders were usually thrown but soon the trebuchet was used in a more devious way, throwing carcases of dead animals into castle squares spreading disease and weakening their opponents (ref.2). The trebuchet became a fearful weapon to any enemy but it was not until 2009 that the best and most deadly trebuchet was produced, and her name was Scarlet.

Our trebuchet works by having a heavy counterweight on the short arm of a type-1 lever which turns on an axel thus pulling the long arm upwards (ref. 3). The long arm has a string attached to it. The other end of that string it attached to one end of a pouch which carries a projectile. A second string connects the other end of the pouch to a nail in the end of the long arm. The pouch is pulled upwards by the two strings, which act to lengthen the arm providing more momentum with which to drive the projectile, but the strings are not as heavy as the wood. The projectile would be released when the nail on the long arm gets to an angle of 90 degrees, and that would optimally be when the lever is at an angle of 45 degrees.

__Applicable Physics__ We were able to make such a legendary trebuchet, cenuries in the making, by analyzing and applying some basic physics principles. The force of gravity is what pulls the counterweight down. Since F= ma (Force= mass**x**acceleration), we used a weight that had a significant mass. We did some research to find out what the optimal ratio of counterweight to projectile weight was and found that it was 133 to 1 and then built our trebuchet so that it could support a 562 gram counterweight to fire the 4.9 gram christmas ball that was our projectile(ref. 1). Having the arm with the counterweight be short and the other arm be longer allows the most amount of momentum to be transfered to the long arm. Using a length of string to attach the pouch to the long arm, has the effect of making the long arm even longer. This causes even more momentum to be transfered to the string. The string pulls on the pouch causing it to fly off the base of the trebuchet and to follow an arc up into the air. The projectile is released when the second string slips off the nail. Centripetal force is what holds the sling taut as it swings out and the forces which try to straighten out the sling are what cause the loop to fall off the nail on the long arm, releasing the projectile to follow its range (ref. 3). We placed wax paper over the cardboard of the base so that it reduced the coefficient of friction between the pouch and the base allowing the pouch to move across it faster when the same amount of force was pulling it. We also added wheels to our trebuchet. This allowed more energy to be transfered into the firing of the projectile because as the arm starts to move a small amount of momentum causes the trebuchet to move on its wheels, which in turn, allows the counterweight to drop vertically downwards instead of in an arc (as would have happened with no wheels), which transfers even more momentum to the long arm. Newton's Laws also apply to the trebuchet. These laws dictate how the trebuchet acts while in motion and at rest, for the arm, counterweight, projectile, etc.

__These are the materials we used to make Scarlet__:
 * Wood: two pieces of 11"x1.125"x3/4" (length**x**width**x**depth)(the pieces that stand up tall), two 14.25"x0.75"x0.75" (go down the base), three 5"x1.5"x0.75 (go across the base), two right angle triangles (90 degrees) 5.5"x5.75"x0.5" (see diagram and pictures), and one piece of 18"x1"x0.625" for the arm.
 * Staples
 * Screws
 * Nails
 * Wood glue
 * Fabric
 * String
 * Metal chain
 * Counterweight
 * Wheels (4)
 * The plastc wheel protectors (8)
 * Little metal ring
 * Metal rod (axel)
 * Cardboard (enough to fit across base)
 * Wax paper
 * Loop Hook (2)
 * Decorative materials
 * Scotch and duct tape
 * marker
 * Our projectile: a christmas ball provided by our teacher

__The tools we used to put the trebuchet together__:
 * power mitre saw
 * hack saw
 * drill press
 * hand drill
 * screwdriver
 * hammer
 * vice-grip pliers
 * air-powered stapler
 * scissors
 * bench vice

__Procedure__
 * 1) Gathered the long list of materials we needed.
 * 2) Carefully measured the wood parts for the sides, cut them with a power mitre saw and proceeded to assemble them with wood glue and an air-powered stapler. This step included the side supports and both the horizontal and vertical components of the side.
 * 3) Connected both the completed side pieces by stapling three short pieces of wood down the center of the horizontal components.
 * 4) Connected the wheels to the frame of our trebuchet with screws, using plastic washers to protect the wheels.
 * 5) Constructed the swinging arm and the counterwieght. To build the arm we used a 18"x1"x0.625" piece of wood ,two loop hooks, and a hand drill. We fastened the wood into a vice and were able to drill two small holes into either end for the two loop hooks; One to hold the counterweight and one to tie the sling to. We also drilled a third hole for a nail on the same end as the loop hook to tie the sling to, it was drilled at approximately a 30-45 degree angle, from research we found that that was the best angle to have the sling and pouch on for the most efficient release time. This was so that when the nail was at a 90 degree angle (when the sling would release) the arm would be at a 45 degree angle.This nail is to hold the metal ring that the other side of the sling was attached to.
 * 6) Fashioned the counterweight, in using our 133 to 1 ratio we figured out that lead tire weights was the most efficient heavy object to use. We set the right amount (562 grams) of lead into two small plastic cases and taped them together with duct tape. We then fastened it to the loop hook with a twist tie, which we later found out was not strong enough; which is where we switched to using a small chain.
 * 7) Cut two pieces of string. One piece was tied to close-off one end of the pouch while the other was tied to the loop hook attached to the long end of the lever. One end of the other piece of string was tied to close-off the other end of the pouch, while the other end was attached to a small metal ring. Each piece of string measured 7.5" long (after being tied). The pouch is a rectangular piece of fabric, 6" by 5", tied into a "cup" shape with the string.

__Testing Procedure__ To test our trebuchet we set it up so it was ready to fire and then fired it. The very first time we fired our trebuchet it flipped over because it did not have wheels. The next time the christmas ball projectile was falling out of the sling to soon and going backwards. This was because our pouch was not cupping the ball and was to slippery, such that the ball could just fall out. We then tried different slings and pouches until we found one that worked the best. The trebuchet also worked better once we added the wax paper. Once we had altered the trebuchet until it had become the fearful and all powerful Scarlet that it is today we did eight trials with it, measuring the distance from the front of the trebuchet where it had fired to where the ball had first hit the ground after being thrown. We recorded these distances and then calculated the points that distance earned using the formula P= distance thrown (m)/ length (m) x weight of trebuchet (kg). See the results in the table below. (ref.4)

__Measurements and Calculations__
 * Trial || Mass (kg) || Arm Length (m) || Distance (m) || P= d/m**x**l ||
 * 1 || 1.6 || 0.85 || 4.80 || 3.53 ||
 * 2 || 1.6 || 0.85 || 5.60 || 4.11 ||
 * 3 || 1.6 || 0.85 || 5.33 || 3.83 ||
 * 4 || 1.6 || 0.85 || 6.16 || 4.52 ||
 * 5 || 1.6 || 0.85 || 5.71 || 4.19 ||
 * 6 || 1.6 || 0.85 || 5.10 || 3.75 ||
 * 7 || 1.6 || 0.85 || 5.08 || 3.74 ||
 * 8 || 1.6 || 0.85 || 5.46 || 4.01 ||
 * 9 || 1.6 || 0.85 || 5.15 || 3.79 ||
 * ||||  || Average || 3.94 ||

__Analysis of Changes to Optimize Efficiency__ Throughout the process of building our trebuchet we made a few changes, so​me simple and some more complex to optimize the efficiency of our trebuchet. One of the changes we made on our trebuchet was the addition of wheels, this helped in offsetting the sudden transfer in energy in our trebuchet and helped our ball go a longer distance. We also changed the pouch size and sling length many times, we found out that a short string and a smaller but open pouch works best. We also added wax paper to the base runway, which, as stated above, reduces the coefficient of friction. The material we used at first to connect the counterweight to the arm was to weak, so we changed the material from a twist tie to a metal chain. Also, we had to shape our runway carboard differently so the wheels would be able to move more efficiently. Lastly, we changed the length of the swinging arm by moving the pivot rod through the four different holes we drilled through the arm.

__Conclusion__ By using some suggestions from our references, the prinicples of physics, and trial and error experimentation we were able to construct the most fearsome pink trebuchet in all of history (or at least in grade twelve). We demonstrated Scarlet the trebuchet in physics class and were able to throw the christmas ball a distance of 5.15 m.

__Pictures __



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