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The Da Vinci Model

   

Leonardo Da Vinci invented several catapults, but in our experiment we tested the most commonly known one. The catapult is powered by a large wooden leaf spring, which serves as an accumulator. Though no record of this catapult being built during Leonardo's lifetime exist, lifesize replicas have been constructed by contemporary enthusiasts.

The Da Vinci model is loaded by turning a winding mechanism that turns a drum. That drum is connected to the catapult armature and pulls on the springs connected to the bow of the leaf spring, where tension builds up. When the winding mechanism is disengaged from the drum, the tension on the bowstrings is released, causing them to pull back to their original placement, and pulling the gear and armature with them.

The Da Vinci Model was one of Leonardo Da Vinci's various inventions in his notebook that were never made during his lifetime. Da Vinci designed his catapult to be able to launch projectiles over great distances with great speed. But it did not have a usual trajectory such as that of the trebuchet and mangonel. The Da Vinci Model was not made to launch projectiles low and fast, or high and powerful. Because it was loaded by winding the crank, one person can launch the Da Vinci Model alone.

Conclusion

There is no catapult that is the best at everything. Each catapult has its own advantages and disadvantages. Hundreds of years ago, generals chose which catapult to use based on their current situation.
To tear down a stone wall of a castle, the mangonel would be the most suitable choice. To haul sick cows and burning wood inside of a castle, the trebuchet would be the best choice.
Because there were so many situations in which catapults were deployed, engineers built many different varieties of catapults to use. Catapults played a vital role in sieges and battles because they could bring down structures and cause havoc in the opposing army. For this reason, almost every culture developed some kind of a catapult over the years.
Eventually, cannons replaced catapults, but their long-lasting legacy will never fade away...

Projectile Analysis

It is impossible for us to pick the best projectile in terms of the amount of damage it caused, because you have to factor in the speed of the projectile, the mass, the density (hardness), surface area, force it hits the target, and etc. We simply had no equipment to measure this.

However, it is quite simple just to measure the distance and the height each projectile flew.

The lightest object, the plastic hollow ball, flew the farthest. Newton's third law of motion was thus proven, since the lightest object flew the farthest and the heaviest object (the large marble) flew the least when the same force was applied to them. For height, it was similar between the plastic hollow ball, small marble, and die. 

But it must be noted that these ranges of each projectile isn't everything, because a ping pong ball that flies 5,000 light-years through space isn't going to do that much damage unless the velocity is way over 1,000 mph.

Catapult Analysis

The mangonel established itself as the catapult with the most range, as it surpassed both the Da Vinci model and the trebuchet when it came to distance. The Da Vinci model did not do too much worse, it still performed considerably better than the trebuchet. The trebuchet did come in last, for it sacrificed distance for height. When it comes to height, the trebuchet did show the highest reaching trajectory, with the Da Vinci model and the mangonel not performing nearly as well. As for launching force, the mangonel did surprisingly worse than its counterparts, who had similar launching forces, with the Da Vinci model a little bit ahead of the trebuchet. The consistencies of the mangonel and Da Vinci model were pretty similar, but the trebuchet's consistency in distance, height, and launching force was considerably worse. The mangonel did outperform the Da Vinci model by a bit, making it the most consistent catapult. Rather than looking at the individual performance of each catapult for each test, we looked at the overall performance of each catapult, and decided that the trebuchet's performance in the average distance, height, and launching force earned the top spot.

Testing Out the Models-2 (Directions and Procedures)

   Our experiment consists of two parts: a) the testing of the catapults and b) the testing of the projectiles. After testing each catapult's performance, we tested different projectiles on the Trebuchet model. 
 To test the catapults, we used a small standard, cheap, made-in-china marble. 

 The Experiment

  Materials: Scale models of the mangonel, trebuchet, and Da Vinci catapults, small hollow plastic ball, small marble, large marble bouncy ball, cubic die, scale, spring scale, ruler, tape measure, and calculator.

Procedure(for both parts of the experiment):

1. Determine the volumes of the different projectiles by measuring their diameter and using the following equation:      For the die, use LxWxH=V. Record your data in in cm3  in Data Table A (Projectile Volume).
2. Determine the masses of the different projectiles by placing them on the scale and recording their mass to the nearest tenth in grams in Data Table B (Projectile Mass).
3. 1. 1. 1. 3. Line up all three catapults at one line. Fire them all using the small marble. Using the tape measure, measure the distance the projectile travels before hitting the ground. Do this three times. Calculate the average of the three times. Record all this data in Data Table C (Catapult Data).
4. 1. 3. Keeping the catapults in the same position, fire them all with the small marble, using the tape measure to measure the height of the highest point of the projectile's trajectory. Do this three times. Then calculate the average projectile height for each catapult. Record all data in Data Table C (Catapult Data).
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      5. Fire each catapult, but while restraining the arm or beam using the spring scale. Do this three times, then calculate the average for each catapult. This is the launching Force. Record all data in newtons in Data Table C (Catapult Data).
6. 1. 1. 5. 6. Calculate the range for each set of trials for each catapult from each of the trials, and that is the Consistency/Accuracy of each catapult variable. Record this data in Data Table C (Catapult Data)

         
         
7. 1. 1. 5. 6.        After determining the best catapult, use that catapult to measure the distance of the different projectiles. Do this three times and calculate the average. Record all data in Data Table D (Projectile Data).
8. 1. 1. 5. 6. Now do the same , but this time measure the projectile height. Do three times and calculate the average.  Record all data in Data table D (Projectile Data).
9. 1. 1. 5. 6. Now use the same method as in Step 6 to calculate the accuracy/consistency of the catapult variables. 
10. Record this data in Data Table D (Projectile Data).

  

Testing Out the Models-1

   After we researched about different types of catapult models, we wanted to test them. So we bought three kits of catapults: the trebuchet model, the mangonel model, and the Da Vinci model. 
   We had a question: Which catapult will have the best performance considering the distance and height that projectiles are thrown, the consistency of the catapults, and the launching force of each catapult? Which Projectile will have the best performance considering the same variables?
After coming up with the question,we hypothesized that the trebuchet would have the greatest projectile height and accuracy/consistency, the mangonel would have the greatest distance, and the Da Vinci model would have the greatest potential energy.
I will talk about the detailed procedures of our experiment in our next post, Testing Out the Models-2.

The Da Vinci Model

The Da Vinci Model was one of many inventions sketched by Leonardo Da Vinci in his various notebooks. A life-size model of the Model was not constructed until today, by contempory enthusiasts with the necessary materials. Da Vinci designed his catapult to be able to launch projectiles over great distances with great speed. But it did not have a usual trajectory such as that of the trebuchet and mangonel. The Da Vinci Model was not made to launch projectiles low and fast, or high and powerful. Because it was loaded by winding the crank, one person can launch the Da Vinci Model alone.

The Da Vinci model is loaded by turning a winding mechanism that turns a drum. That drum is connected to the catapult armature and pulls on the springs connected to the bow of the leaf spring, where tension builds up. When the winding mechanism is disengaged from the drum, the tension on the bowstrings is released, causing them to pull back to their original placement, and pulling the gear and armature with them.

The Trebuchet

The word trebuchet comes from the french word trébuchet. The older versions of trebuchets, called "traction trebuchets" had pulling men rather than a counterweight. The counterweight trebuchet (shown above), was meant to fire projectiles over castle walls, thus launching projectiles high into the air.

The trebuchet is loaded by pulling the beam back and keeping the beam restrained, while a projectile is loaded into the pouch, located at the end of the sling attached to the beam. The beam is then released, pulled by the counterweight, and causing the sling to swing around above the moving beam. One of the strings of the sling that is attached to the finger at the end of the beam is detached, letting the projectile's inertia push the projectile forward.

The heavier the counterweight is, the further the projectile will fly. The weight (gravity) makes an object fly in this case.

   

The trebuchet was mainly used to haul rocks and other projectiles into enemy castles and fortresses. The advantage of the trebuchet is that you can launch just about anything, since you load projectiles on a pouch. A few common items might be rocks, burning wood, and dead or sick cows.

Also, it can launch things with accuracy and consistency, as long as the counterweight remains the same. The heavier the counterweight is, the farther and higher the projectile will fly.

Unlike the mangonel, trebuchets launch objects far and high. They were used to haul objects like dead cows and fire balls inside of a castle or a fortress.

Image source: http://www.real-world-physics-problems.com/catapult-physics.html 

The Mangonel

   

The word mangonel is derived from the greco-latin word manganon, meaning "engine of war". It does not have very good accuracy, but hurls projectiles with great speed and power, with the intention of destroying castle walls.

Typical mangonels are powered by a torsion-type string, which is twisted when the catapult arm is pulled back. A handle can be used to tighten or loosen the spring. When the catapult is fired, the spring pulls the catapult arm back to its original position, launching the projectile.

The twisted rope is usually called a torsion bundle. It consists of several lengths of rope with the arm inserted in between them. The rope is then twisted manually on both sides of the arm using levers. When released, the torsion bundle turns the arm at high speed, launching the projectile. The figure below illustrates how a torsion bundle is twisted.   

Parts of the information from:   http://www.real-world-physics-problems.com/catapult-physics.html

The mangonel was mainly used to fire large rocks and other potentially destructive projectiles at castle walls with the aim of destroying or breaching them. The advantage of the mangonel was that it was very practical on the battlefield as well as in the siege or assault of a castle. Mangonels hurled rocks, burning objects, and anything else available to the attacking or defending forces. Because the mangonel hurls objects a low trajectories, these types of projectiles could inflict considerable damage to a variety of targets.

   The two major disadvantages of a mangonel are the inconsistent accuracy, which I mentioned above, and the degrading materials. Since first disadvantage is already thoroughly explained above, I will explain the second disadvantage.
   The mangonel uses tension, which uses ropes. Ropes can lose their elasticity, and both wood and ropes can wear down in natural states. Because of this, battle commanders had to monitor their catapults in case they need replacements. The two disadvantages combined together lowered the accuracy of the mangonel. 






Image source: http://www.real-world-physics-problems.com/catapult-physics.html

General Information

   Three major types of catapults are the mangonel, trebuchet, and Da Vinci model. All three were primarily made of wood. Each used a different type of force to provide energy for the launching of a projectile. The mangonel used torsion, for a torsion spring was used to swing the arm. The trebuchet used gravity, with a weighted counterweight suspended at the opposite end of the beam to which the launching pouch is attached. The Da Vinci model used tension, with a bow that was connected to the armature by ropes, which were tightened using a winding mechanism and released to fire. The mangonel launches projectiles in a faster, further and lower altitude trajectory. The trebuchet launches projectiles in a higher and shorter distance trajectory, but could get more power from a heavier counterweight. The Da Vinci model launches projectiles with a trajectory  that has height and distance between those of the mangonel and trebuchet.

The main types of Catapults

Here are the main types catapults, sorted by the source of power:

1. The Mangonel Catapult (Uses Torsion and Tension)
2. The Trebuchet (Uses Weight)
3. The Da Vinci Model (Uses both Tension and Gear)
4. The Ballista (A Giant Crossbow)
5. The Onager (Uses Torsion)

To minimize confusion, I will explain few things:

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1. Almost all cultures have made some kind of a catapult, so there are dozens of different names for the same type of catapult. So it's the kind of force the catapult uses that's important, not the name.

A Brief History of Catapults

Introduction to Catapults

     Armies, ancient or modern, have always been consisted of three basic types of fighting units: the infantry, cavalry, and the artillery. Over time, the weapons of these fighting units have changed, but their role in battle remains the same.
    The infantry are soldiers who fight on foot who try to kill enemy soldiers before getting killed. The Cavalry are highly mobile fighting groups that support the infantry. The artillery men are specially-trained soldiers that use long-ranged weapons such as howitzers to attack the enemy from distance. These soldiers are not mobile. They go to a particular location, and fire the enemy. Artillery are especially effective against fixed targets such as bridges, fortresses, and castles.
    In the modern times, the artillery men use cannons,, howitzers, rockets, and missiles. In the ancient and the medieval  ages, they used machines called catapults to haul rocks, burning wood, dead cows, and etc. They could be simple or complex. They could be made from any material. They can use any kind of force to power them, including tension, torsion, and weight.
    Therefore, definition of catapults are broad. According to marriam-webster dictionary, a catapult is an ancient military device for hurling missiles. There are many different types of catapults, which will be covered in later posts.