Physics Extended Essay (Ballistics)

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INTRODUCTION

1._Background Information

For thousands of years human beings have been fighting in battles, always trying to find new ways of killing each other and winning. Combat was getting more and more sophisticated and human force was not sufficient enough to conquer a castle or destroy a ship. That was the time when ancient engineers introduced siege warfare, when “simple yet complicated hurling machines that rely on the fundamentals of math and physics using levers, force torsion, tension, and traction” were brought to the battlefield. One of the most unique and destructive siege weapons was the ancient Greek ballista, used by Alexander the Great and later improved by the Romans. Ballista is a “torsion-powered machine,” and unlike other ancient weaponry, it casts bolts and hurls stones straight and low, keeping the parabola as horizontal as possible. For that reason, projectiles travel farther and the gradient of the trajectory remains small – not sleep. It is a very accurate missile weapon, but because of its fairly lightweight bolts, the ballista does, however, lack the high momentum of heavy rocks (80 – 140 kg) launched by trebuchets and mangonels. The operating crews were able to load spherical (stones) and shaft (bolts) projectiles according to the situation and the needs. The former were fired in order to destroy masonry and light structures (castle gates, siege towers), while the latter were often used against armored troops. Original models of the ballistae could hit targets 300 or even 400 meters away.

In order to determine which shaft projectiles ancient engineers considered the most effective, I have developed the following research question: “An investigation into the relationship between the wingspans of a projectile stabilizing fin and the force exerted, displacement moved (?) and the velocity of the projectile.” Considering the physical properties described below, I hypothesize that small fins will fly faster and exert more force, while greater wingspan will increase the gliding distance, thus increasing the displacement. Two different fin shapes will be investigated: triangular and quadrangular. Having 4 fins on each bolt would provide much more stability, but we will follow the way that has been used by ancient Greeks, Macedonians and Romans – this ballista was designed for two-finned bolts.

I have chosen this topic because ancient warfare offers a wide spectrum of theories and principles based on physics and mathematics, simultaneously giving me an opportunity to recreate one of the ancient siege machines myself. While ballistae and projectile motion are an interesting topic, it also brings different principles of physics together for a thorough research experiment. Using a representative model of a real ancient ballista I have assembled for this project, I will investigate the measurement (?) of these physical quantities, trying to optimize them in order to find the most effective shaft projectiles for this ancient siege engine.

2._Scope of work:

There are five main physical principles involved behind the science of the ballista:

I. Torque
Ballista’s true power lies in the skeins. A skein is a ‘twisted bundle of rope’, where the actual force is ensured by torsion, while the rope is fully twisted because of the applied torque (rotated about axes). Skeins entangle bowstring arms that help to fire the projectile. Torsion springs, when twisted, store mechanical energy. The more the skeins are twisted, the more energy will be exerted on the projectile. In other words, “the amount of force (actually torque) it exerts is proportional to the amount it is twisted.”[2] Such technique makes it “…possible to shoot lighter weight projectiles with higher velocities over a longer distance.”[3] The objective of the experiment is to keep the amount of torque at maximum all the time by winding up the skein blocks in order to make the experiment as fair as possible and obtain the highest...
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