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Justin Owen

Justin Owen

Coach A

AP Physics

9 November 2018

A Quote from the French Cow-tapult Masters:

“Ah fart in your general direction! Your mother was a hamster, and

your father smelt of elderberries!”

Introduction

A: The goal of this project was to build a catapult to launch a projectile as accurately as possible. The projectile could range from grapes to golf balls, or any object we could launch. The smaller catapults (1’x1’) had to shoot a smaller target than the larger catapults (anything greater than a 1’x1’ area base). The catapults are graded off of how consistently they can accurately hit a target.

Research

A: The catapult design that was decided upon was. the traditional ballista design which relies upon ropes in order to sling two arms forward. These were traditionally used to launch arrows at invaders in medieval times. Other designs include the mangonel and the trebuchet. The mangonel is the traditional style of catapult in which a basket on a stick travels forward and hits a crossbeam launching the projectile. The trebuchet relies on a weighted lever to propel a rope forward until it hits a snag firing the projectile. The last type of catapult is the onager. The onager relies upon a single twisted rope that propels an arm forward into a crossbeam to launch it’s projectile.

B: The Trebuchet is the type of catapult that is capable of the most range. This is because the rotational kinetic energy of the long arm is greater than the other catapults’ rotational kinetic energy resulting in more force being transferred to the projectile.Trebuchets also have a sling mechanism on the end which further increases the amount of force gained by rotation. This greater amount of energy allows for the projectile to move farther than other projectiles if wind resistance is negligible, and the projectiles are all launched at the same angle, preferably at 45 degrees above the horizon, as it is the angle at which projectile motion is ideal for distance.

On the other hand ballistae or ballistas are more accurate but with a shorter range. The ballista is a more accurate machine because it has two arms pulling one object with equal force along a given track making its projectile lethally accurate historically, with decreased range of projectile.

C: Catapults are known to have been in use since the 4th century BC, however there is earlier documentation in the book of 2nd Chronicles circa 750 BC in which a king oversees the making of “machines to launch great stones”. Early catapults were made by many civilizations such as the Greeks and Romans with ballista type devices to the Chinese with their man powered traction trebuchet in which instead of a counterweight people pulled on ropes to move the short arm. Catapults are normally associated with castles and medieval times, but the catapult was used as a weapon of war for far longer than castles had been in use. The catapult did however aid in the act of war against castles. Catapults could be used in numerous ways, to breach, kill, or infect. Catapults were used to bust down walls, most effective at this was the trebuchet as it puts the most force behind its projectile. Catapults were also used to launch flaming projectiles meant to kill defenders of the castle. The use of catapults alongside early biological warfare led to corpses being launched into cities to infect them with the plague, a strategy developed by nomadic Mongols.

D:

Materials and Methods

A: The design that we used was based off of a traditional ballista which relies on twisted ropes to provide torsion which pulls two arms forward towards the target. These arms are subsequently pulled backwards along a track and released with the projectile in tow. The projectile then launches forward towards the target preferably fast and hard.

B:

Designs and Procedures

A:

B: The procedure of building the ballista was to screw together a 2’x6” box with two holes equidistant from the center at 1” in diameter on each of the 2’ boards. Attached to the box was a 6’ long track with raised edges. Through the each hole was five lengths worth of standard size paracord, or nylon, rope. The rope was wrapped around 2, ⅝ “ diameter wooden dowels on each side of the 2’ boards. In the middle of the each of the wraps of rope there was a 3’ long 1’ diameter wooden dowel. Each of the dowels had a hole in the end connected by nylon rope with a leather patch located in the middle. To provide the force to the arms the nylon rope around the ⅝ “ dowels was twisted towards the center of the box, or clockwise for the left side rope, and counter-clockwise for the right side rope. The dowels were twisted in order to twist the rope and provide torsion. Each dowell was twisted equally in order to provide accurate and consistent force. The machine was then placed on a stand in order to keep its launch angle at a consistent 45 degrees, the best angle for projectile distance.

Construction

A: My partner and i spent a day cutting and putting together our wooden ballista. The twisting of the ropes to provide torsion was done in class prior to our launch in order to ensure safe transportation of the project. Adjustments were made to the design such as adding 6” supports onto the square frame in order to stop the boards from breaking under the force of the Δropes.

Data and Results

A: Disclaimer: The data our catapult produced may be somewhat inaccurate as the ballista tore itself apart under the force of the ropes. The estimations for our data are as follows;

Distance(m): 10m

Time(s): 2.43s

Muzzle Velocity(m/s): Vi=16.02m/ [email protected] 45 degrees above the horizon

Percent Error(%): Percent error can not be calculated as the data is estimations from test firing, however I predict that it would be relatively low as the catapult seemed consistent. I would predict it lies between 2.5 and 5%. Possible sources of error would be slight movements in the ballista upon launching, or due to the fact that wind resistance is not factored into the calculations, but does occur in real life.

B: Calculations

Muzzle Velocity: Δx=Vit+½at2

(10m)=Vi(2.43sec)+1/2(-9.8m/s)(2.43sec)2

Vi=16.02m/ [email protected] 45 degrees above the horizon

Percent Error: Percent error cannot be calculated with these estimations.

C: The ballista that we built for this project launched 10 meters and stayed in the air for 2.43 seconds. The projectile ( a standard golf ball) launched from the end of the track of the ballista with a speed of 16.02 m/s at 45 degrees above the horizon assuming negligible air resistance. The golf ball immediately started de-accelerating upwards due to the Earth’s imparted force of gravity at -9.8m/s. We know that the ballista launched at a 45 degree angle due to our precise measurements made using trigonometry on the boards that we cut for the base.

Conclusions

A:

i:The ballista built for this project did not perform as well as expected. I think that the reason the ballista underperformed was due to a loss of energy between the ropes that provided torsion and the arms pulling the projectile along the track. Another place energy would have been lost was to the boards along the square frame of the ropes. Much of the force was imparted there causing the boards to bend and result in less taught rope. This could be remedied by using 2-4” thick board as opposed to the 1” thick board that was used.

ii:One of the laws of the universe is that energy can never be created nor destroyed. This means that the energy from our taught ropes had to be expelled somewhere which was upon the projectile, arms, frame, and friction from the track. In order to minimize loss of energy to the surroundings of the machine, sources of friction should be limited as much as possible. Much energy is lost due to heat from the friction of two objects rubbing one another in this case the ropes, track, and ball.

iii:Projectile motion is the 2 dimensional movement of an object through a known plane formed by the x and y axises. Velocity for a projectile can be determined in both the x and y planes, where x normally represents horizontal and y represents vertical. Velocity can also be determined s a combination of the two with trigonometry and representative angles. A projectile is defined as an object that experiences no outside forces from the x direction after it begins moving.

iv:Torque is defined as a rotational force put upon an object. Torque plays a major role in all catapults as it is what provides the force to move the arm, or is the force of the arm, which in turn launches the projectile. In a typical catapult the arm is rotated around a point which imparts force upon the object in its basket. In a ballista two twisted ropes provide torque to two arms through the torion of the rope being twisted. This torsion creates torque force which pulls the arms which pull the string which imparts linear force upon the projectile launching it forward.

v:The ballista’s design could be improved by using sturdier materials that allow the rope to undergo more torsion before snapping the frame. If this change was made then the ropes could have been twisted more than they already had been, allowing for them to store more potential energy, which would in turn be transferred to potential energy to the arms the sling, and finally the projectile increasing the effective range of the ballista.

B: The ballista that was built to satisfy the constraints of this project did not fire the farthest, but it did fire extremely consistently. The two arms of the ballista provided equal force on each side of the dragline pulling the projectile, this allowed for the ballista to fire with the accuracy of its long last historical ancestor. Unlike its ancestor however, this ballista was not built with materials strong enough to resist the force of the twisted ropes and thus when twisted too tightly and pulled back for launch the frame splintered in what appeared to be a glorious explosion, but really was just extremely startling and mildly infuriating.

References

http://www.medievalwarfare.info

https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque

http://www.bu.edu/moss/mechanics-of-materials-torsion/