Rahman-Hopkins+Trebuchet

=F.D.N. (Ferdinand Domela Nieuwenhuis) Trebuchet =

Associated with the [|Rahman-Hopkins Project] (Redirected from [|Totally Awesome])

On November 13th, 2009, Tab Rahman and Erin Hopkins embarked on building one of the [|Greatest Trebuchets of All Time] (of all time!). Now, after the [|first launching] of the the Rahman-Hopkins project, we bring you, the reader, the in-depth look at the [|project] as it has been developed, and completed. 2 Applicable Physics Principles > 2.1 Projectile Motion > 2.2 Newton's Laws > 2.3 Forces > 2.4 Kinematics  3 Materials 4 Procedure > 4.1 Base Structure > 4.2 Arm > 4.3 Sling > 4.4 Final Adjustments > 4.5 Labeled Diagrams  5 Testing 6 Trials and Trebulations 7 Analysis Of Changes 8 The Sling > 8.1 Sling 1 > 8.2 Sling 2 > 8.3 Sling 3 > 8.4 Sling 4  9 Final Comments ||
 * **Contents**  1 Background Information

Background Information
The trebuchet (derived from the french word //trebucher// meaning "to throw over") was originally developed by the Chinese in 300 BC, and used man-power to launch its projectiles. This system was based on the earlier version of catapults, using ropes and tension to make it work. The more modern version of the trebuchet, which would use counterweights rather than manpower to launch its projectiles, came to be around the 12th century, the earliest recordings show it being used in the Holy Roman Empire's crusades. It is not clear where exactly the counter-weight version of the trebuchet was first engineered, though some claim that it was developed in France.

Trebuchets were considered to be fearsome siege weapons, and essential in a campaign (as anyone who has ever played Age of Empires would know). Surpassing catapults in range and power, a trebuchet could throw a 300 lb. weight over 900 ft. (compared to a catapult, which could not throw something as heavy, and could only throw a 60 lb. weight about 500 ft) with more precision and force than any other projectile weapon before. Relatively simple to transport piece by piece, engineers would instruct soldiers how to set it up at the locations of battle, thus giving them a convenient weapon to take down large fortresses (such as [|Dover Castle] in England) and the people barricaded inside them. Often, trebuchets would launch boulders and large flaming objects at the fortress. As they ran out of these, they would launch other things like dead animals, manure, and body parts into the castle in order to spread disease in a closed environment.

The development of gunpowder effectively made the trebuchet obsolete battle, with cannons being more efficient and effective against enemy ranks. How ever, modifications to the trebuchet are still being made to this day to make it more effcient (in the interest of science). One of the developments, created in 1998, is the Floating Arm Trebuchet (FAT), which drops the counterweight straight down, rather than having is swing in free air, in order to utilize more energy from the weight into the throwing arm and projectile.The Rahman-Hopkins project construction a FAT trebuchet for this design project.

Projectile Motion
The building of a trebuchet has very obvious connections to the physics principle of projectile motion - the trebuchet's sole purpose is to throw projectiles. While those projectiles can range from dead animals to holiday baubles, the basic principles behind throwing or firing the projectiles remains the same. When air resistance is ignored, all objects fall at the same rate. This means that an object with a constant horizontal motion will still fall and hit the ground at the same time as an object that was just dropped from the same location, because the acceleration of gravity is always the same. Objects projected from a level field follow a parabolic shape. Instead of having only a horizontal velocity, since the projectile is launched at an angle, there are vertical and horizontal components. The angle at which a projectile releases is very important to its range and hang time. A large angle, such as 60 degrees, will greatly increase a projectile's hang time, but decrease the range. A smaller angle, such as 30 degrees does the opposite of the larger angle; increases range and decreases hang time. The optimal angle to release a projectile for the best balance of range and hang time (it actually goes the farthest) is 45 degrees.

Newton's Laws
Of the Three Laws, the one that applies to this project is Newton's Second Law: The force of an object is equal to its mass times its acceleration //(F=ma)//. When building the trebuchets, the objects force would be determined by how much it's mass was, and how fast the trebuchet was able to accelerate it. The ideal projectile would be something heavy (such as a boulder, or dead people parts). However, when given something light (such as a so-called "unbreakable" holiday bauble), the acceleration has to be greater in order for the force of the object thrown a great distance, but it also cannot reach terminal velocity too quickly. It's a tricky balancing act.

Forces
The most important force applied to a trebuchet is gravity. Gravity is the force that is working with the counterweight (the heavier the weight, the more Newtons are being applied), causing the projectile to launch in the air. Air resistance was also a factor when launching the projectile, as we were not launching it in a vacuum.

Kinematics
Dealing with the acceleration, velocity, and the distance traveled of the object used kinematics.

Materials
In order to recreate this project in your own homes, here is an expansive list of materials you will need.


 * 60 cm wood planks x 4
 * 13 cm wood planks x 10
 * 19 cm wood planks x 2
 * 14 cm wood planks (runners) x 2
 * 8.5 cm wood planks (runners) x 2
 * 18.5 cm wood planks (bottom supports) x 2
 * 55 cm wood plank (arm)
 * 5 cm wood pieces x 2
 * 35 cm wood pieces (projectile track) x 2
 * Wood blocks (any size) x 2[[image:SDC10072.JPG width="252" height="189" align="right" caption="One of the earlier models of the Rahman-Hopkins project, however, it is still fairly close to the final product."]]
 * 1" wheels x 2 (for spacers)
 * 3" Wheels x 3
 * 1/4" Bolts x 2
 * 1/4" Nuts x 2
 * 1/2" Nuts x 4
 * 2" nail (for release)
 * Weights (250 grams) x 2
 * Screws (size 6, varied lengths) x 26
 * Brad Nails, 1" x 16
 * Wood Glue
 * Plywood Base (fairly large and sturdy, you can cut off unused parts later)
 * 1/2" Flat Washers
 * 1/2" Thread Rod
 * Fabric 9 cm x 6.5 cm
 * Thread (A thicker variety)
 * Small metal tube 4 cm long
 * Medium metal tube 4 cm long
 * Larger plastic tube 4 cm long

For a complete list of materials used for the F.D.N. Trebuchet, please send a letter to the Rahman-Hopkins Project Head office, located in Europe, probably in Spain. (Even though this appears to be a completed list)

Base Structure

 * 1) Cut all of the wood pieces to the length mentioned in the materials section.
 * 2) Draw out the desired location for the eight leg pieces and four tower pieces on the base wood. Pay special attention to making sure that the distance in between the two lines is large enough to fit the sling and projectile through. The tower pieces should be out further than the other base pieces to make sure that the wheels can actually run through the original side to the other side when the trebuchet is being fired.
 * 3) Screw the pieces on to the base.
 * 4) Notch out the 19 cm pieces (and two of the 13 cm pieces for the other side) so that they can wrap around the tower pieces and screw them down to the shorter base pieces.
 * 5) Brad nail the two longer runner board pieces to the side where the wheels will initially hit, and the shorter ones to the side which will take the recoil. (These will be brad nailed into the 19 cm notched pieces).
 * 6) Brad nail the 5 cm pieces at the tops of the towers to keep them together so that they can run smoothly down the shafts.
 * 7) Cut out two blocks (size is not a particular issue) and place the guide wheel in between them. Screw them to the sides of the notched pieces on the side that the arm will be firing from, and drill a hole where you can run a bolt through both the pieces and the wheel. Attach all of these things to the structure.
 * 8) Drill two small holes at the top of each tower that your can run a small nail through as the release mechanism for the trebuchet.
 * 9) Depending on the length of your arm (like ours) you may need to screw some extra beams underneath the base to make sure that the trebuchet's arm doesn't hit the ground when firing.
 * 10) Glue the two 35 cm wood pieces to the insides of the supports to ensure the projectile does catch anything on its way out of the track. Cut out a semi circle in the middle of each of the pieces for the weights to fall into.
 * 11) Attach a piece of wood on each end underneath the structure for stability as well as to make sure the arm doesn't hit the ground while firing. Unless the arm is shorter than on the Rahman-Hopkins Project, these pieces are necessary.

Arm

 * 1) Cut the arm to the desired length (55 cm is optimum in our case).[[image:SDC10073.JPG width="252" height="189" align="right" caption="The original arm, which was later taken apart to make a longer arm that could drop the whole distance."]]
 * 2) Drill two holes in the arm (1/4" and 1/2") spaced out so that the wheels hit while the weight can gain its maximum drop. These will change depending on how your structure is built. Make the 1/2" hole very close to one end, and measure the length to the wheel hole from there.
 * 3) Attach the wheels and spacers to a bolt and nut them. Jimmy the threads so that the nut cannot come loose and have the wheels fall off.
 * 4) Run the thread rod through the wood and add four flat washers on either side for spacing. Tighten up a nut on either side and lock them using wrenches. Add the roller system (a small metal tube, covered by a slightly larger metal tube covered by a plastic tube) to each side. This will help cut down on the friction against the wood when the arm is being dropped. Add the square steel weights, and then a nut to each side. Lock the final nuts as well.
 * 5) Drill a small hole on either side (other end of the arm) for the fixed end of the sling to be attached and the pronged end. Screw one on each side. The angle and how much the prong will have to be turned for the sling to properly release will have to be fiddled with.

Sling

 * 1) Cut out a small piece of fabric (any type) for the pouch of the sling. Make sure it is large enough to cover about half or three-quarters of your projectile.
 * 2) To form the loop, take a piece of thread, and put it through two of the adjacent corners. Tie a knot on both of the corners with the ends of the string.
 * 3) Tie another piece of string at the center of each loop. Attach the second end of one to the fixed end for the sling, and the second end of the other to the small metal ring that will be hooked onto the prong and will release to throw the object during launch.

Final Adjustments

 * 1) Cut off any of the unnecessary wood from the base that may affect the weight of the trebuchet. This should help you accomplish higher points with the ratio.

Labeled Diagrams
For the ease of recreating this facet of the Rahman-Hopkins project, the diagrams below have been created. (You may have to increase the size to be able to read them)



Testing
The testing methods employed by the Rahman-Hopkins projects were quite simple. The base structure was made, and the very first thing that was considered was whether or not the arm would fall correctly, and the structure would be able to stand up to the weight of the falling arm. A few quick test trials showed us that the arm was working fine, and we moved on to constructing the sling. More information about the various sling models that were tested, and the testing methods of them, can be found in the sling section further down the page. After we created a sling model that we were pleased with, we moved on to actually testing its distance. We ran a couple of test trials in the atrium of the agriculture building on campus (after hitting the roof on both the fifth and fourth floors) and didn't finished due to time. We then continued our trials at school the next day in the woods shop. Our sling broke, and without the tools to fix it with us, we finished our trials the next morning on the third floor of Walter Murray. The final trial of course, was conducted in the boy's gym at Murray with the rest of our classmates.

Trials and Trebulations

 * **Trial** || **Mass (Kg)** || **Arm Length (m)** || **Distance (m)** || **P=d/ml** ||
 * 1 || 2.5 || 0.89 || 10.1 || 4.5 ||
 * 2 || 2.5 || 0.89 || 11.5 || 5.2 ||
 * 3 || 2.5 || 0.89 || 10.5 || 4.7 ||
 * 4 || 2.5 || 0.89 || 10.3 || 4.6 ||
 * 5 || 2.5 || 0.89 || 10.5 || 4.7 ||
 * 6 || 2.5 || 0.89 || 10.8 || 4.9 ||
 * 7 || 2.5 || 0.89 || 11.2 || 5.0 ||
 * 8 || 2.5 || 0.89 || 10.4 || 4.6 ||
 * 9 || 2.5 || 0.89 || 10.9 || 4.9 ||
 * **AVG** || **2.5** || **0.89** || **10.7** || **4.8** ||

Instead of using the original first 5 trials, as it had thought it would (earlier this morning), the Rahman-Hopkins project conducted more trials with the new weight (although it was totally irrelevant to the throwing distance), so that the entire project will be based on the final weight of the trebuchet, and not the initial weight which was 0.7 kg heavier than the cut down finished version.

Analysis of Changes
So far, the Rahman-Hopkins team has decided to make these modifications to their base structure:
 * 1) **Lengthening the arm:** The original arm length was 48 cm long. Once further structures had been built, the Rahman-Hopkins Project realized that it just wasn't long enough to catch on the wheel and keep its straight path. The new arm is longer than the original arm, but only long enough so that it can function properly and maximum drop can be obtained.[[image:SDC10074.JPG width="252" height="189" align="right" caption="The wheel runners that were added to make sure the wheels were moving straight."]]
 * 2) **Addition of Runners to Wheel Track:** Originally, the wheels ran freely on a 24 cm long, 1" board. We then changed this design to notch the 60 cm towers on the center of the F.D.N. Trebuchet, and added thin runners on the inside of the tracks in order to stabilize the wheels, and keep them running straight.
 * 3) **Addition of Plastic Rollers to Weight Thread Rod:** In the initial design, the thread rod on which he weights were placed were originally bare. The Rahman-Hopkins team anticipated that the threads on the rod would cause ridges in the board, potentially catch and throw off the weights, or (the biggest worry) cause unnecessary friction. Therefore, we covered the rods with plastic tubing, which would not only make the rod roll easier, it would also cause less frictional force against the wood.
 * 4) **Remeasuring the Central Towers****:** The towers at the center of the trebuchet (which are 60 cm tall) had to be spaced wider apart to account for the wheels to run on the track from one side to another. To account for the diameter of the object that we are throwing in our trials, we moved the two halves of the trebuchet further apart so that the object could freely get through to be fired correctly.
 * 5) **Sling Changes:** See the below section for changes that we made to our sling portion, for there are a significant amount.
 * 6) **Blocks on Third Wheel:** We cut down the lower side of the blocks on the third wheel because they were catching the thread of the sling and it was negatively affecting the way that the sling pulled through when fired because it caught the strings and would sometimes skew the path of the bauble, or throw it off entirely. This change also made the trebuchet much easier to load, because we didn't have to keep trying to make sure the strings were on the wheel anymore.
 * 7) **Bottom Supports:** Bottom supports were added to stop the arm from hitting the ground (we did not want to disturb the way the pin was hooked in because it was working, so we made the decision not to shorten the arm). The extra pieces also gave the trebuchet more support when the rest of the base structure.
 * 8) **Slimming the arm:** The arm was slimmed and tapered off on one side in the hopes of trying to get it to swing through faster, as well as decreasing the weight. We were pretty satisfied with this change made, although it was made early enough on in the final stages of testing that we cannot be completely certain of its overall effect.
 * 9) **Excess Wood:** The final thing that was changed before the final launching of the trebuchet was to cut down any excess wood that might keep the weight of the trebuchet up. This didn't affect the trebuchet's ability to throw - it threw the same distances before and after the cutting, but it did managed to cut our trebuchet down from 3.2 kg to 2.5 kg which helped us greatly with the denominator of the points equation. We cut back the upper supports that carried the wheels on both sides, and the base by a rather large amount, as well as slimmed up quite a few of the pieces.

The Sling
Because we found the sling to be so troubling, we at the Rahman-Hopkins project have decided to dedicate an entire section to the versions of slings we created, and our ongoing struggles to make our sling work properly and release the projectile. Although we believe we have a working model, changes could still be made. We hope to soon have pictures up of the slings models that we have built.

**Sling 1** ===** After the construction of the the first sling prototype (Sling 1) we attempted to fire the trebuchet. The first time we tried to fire, we used an odd shaped rubber eraser, which has a lot more mass than the actual projectile. The first firing didn't work out so well - the eraser ended up across the room unfortunately in the opposite way that it was supposed to be, and we lost the ring we had been using for the free floating end of the sling. After that, we reattached another ring and tried to fire again. Similar results occurred, and the Rahman-Hopkins Project decided to switch sling models. **===

**Sling 2**
The second version, Sling 2, worked just about as well as sling 1. This prototype had more fabric, and was just tied like a hammock at both ends. We also shortened the thread significantly for this trial - one of the only things we kept for the future prototypes. The projectile (now a foamy blue ball, slightly smaller but with similar mass to the projectile we will be using) tended to slip out the back, and not even make it around. This version of the sling was quickly debunked for Sling 3.

**Sling 3** The third version of our sling included a small, flat piece of fabric tied to two loops which were tied to longer strings. This had more, but little success, and unfortunately, tended to either carry the projectile all of the way through, or it would roll out of the back end and the sling would leave without it. It had a couple of shots where it hit the roof almost straight up as well. Still, once we watched video of it frame by frame (it goes way too fast to watch it live!) we decided that the style may have potential if we could make the sling a little bit larger to carry the projectile better. With Sling 3, we also fired a couple of shots with the Christmas bauble as well as the foamy blue ball.

Sling 4 (Final Model)
Sling 4 in comparison to Sling 3 is about 1 inch larger both in length and width. It was attached with thread which was about the same length as Sling 3. This has been our most successful model so far, because it has been the only model that has actually managed to fling the projectile. In addition to some changes we made the sling, we also rotated our hook about 20-30 degrees. In addition, the sling also was tilted a quarter turn to the side (with the longer string on the bottom and shorter on the top instead of them side by side) when ready to fire. All of these adjustments have made Sling 4 our current model, and it has managed to successfully fire for all the trials we put it through save a few at the start, and one poorly loaded one later on during our testing (we have currently fired it about 10 times). This sling has been fired using the Christmas bauble as the projectile.

Final Comments
The Rahman-Hopkins team was very happy with how the F.D.N trebuchet performed in the trials. In hindsight, we were able to critically look at our model, and think of some other modifications we would have made had we any extra time to fiddle around with it. First of all, we would shave off some more of the excess weight we had, as that was a problem during our trials. Though it could throw far, it was not as lightweight as we were hoping we could make it. Another thing we would have liked to modify is the release angle of the sling and the arm. The Rahman-Hopkins teams realized that had they put in some sort of mechanism that would make the arm release at the perfect 45 degree angle (or something close to that), our projectile would have gone much farther. We would have also liked to adjust the sling, testing our more lengths than we already had. The sling was the most touchy and difficult part of the process for us, and we didn't expect it to be as complicated to modify as it was. Barring all of this, we believe our process was very smooth comparatively, and we are happy with our results.

The Rahman-Hopkins team would like to thank Mr. Hopkins for providing us with his workshop, as well as his expertise, and for letting us pick his brain. We are sorry that we made you stay up past your bedtime, and very glad that you supervised us (because we are not very responsible with power tools). We would also like to thank Mr. Stensrud for letting us use the tech workshop to test out the F.D.N Trebuchet during school hours, and we are very grateful for that (we're pretty sure Ms. Louko still has battle scars from our launches on the third floor).

Edits

 * Dec. 3rd/09- Edits on page made by Tab and Erin under Erin's account.
 * Dec. 6th/09- Edits on page made by Erin under Erin's account.
 * Dec. 9th/09- Edits on page made by Tab under Tab's account.
 * Dec. 10th/09- Edits on page made by Erin under Erin's account.
 * Dec. 10th/09- Edits on page made by Tab under Tab's account.
 * Dec. 11th/09- Edits on page made by Erin under Erin's account.
 * Dec 12th/09- Edits on page made by Erin under Erin's account.
 * Dec.13th/09 Edits on page made by Tab under Tab's account.