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Most of all, we chose this topic because we like to blow stuff up and cause our own non violent explosions. In order to better understand the physics of fireworks, we decided to investigate the history behind the understanding and conception of fireworks. Originally, fireworks were created in China. The art of combining pyrotechnics and casing them has existed since the sixth century. The Chinese made explosives as defense mechanisms against the Mongol invaders in the late 13th century, thereby employing pyrotechnics for other means than art. From China, fireworks proliferated to Europe where the first records indicate gunpowder rockets as early as 1258 AD. Despite China’s initial invention and progress, Europe exceeded the technology in the 14th century, around the same time the gun was invented. Gunpowder and shot for the military were made by firemakers, or skilled military tradesmen. They were also required to make victory fireworks for celebrations of victory and times of peace. Throughout the Renaissance, rival philosophies of pyrotechnics evolved. One originated in Italy, and the other in Germany. The Italians believed that pyrotechnics should entail the use of elaborate fireworks, while the German school emphasized scientific advancements and the use of technology. Both Italian and German schools added greatly to the furthering of pyrotechnics. By the 1600's, fireworks were mainstream entertainment and were used on an extraordinary scale in Europe. Two hundred years later, fireworks escalated in popularity in the United States. However, the injuries resulting from their misuse, especially to children prompted government officials to greatly restrict their use, and eventually make them illegal in nearly all 50 states. All fireworks work basically on the same principals. This involves a very rapid chemical change in the interior of the firework. It is basically similar to the chemical change of a match burning, however in fireworks this process occurs much faster. The principles involved in launching fireworks are comparable to parachutes, or the technology used to launch space shuttles into outer space. The explosion in the interior of the firework creates momentum and energy, all of which is displaced in a single direction. The conservation of momentum dictates that the momentum of the whole system does not change. Therefore, if the gas from the explosion exits the back of the rocket, then the rocket must move in the opposite direction. (Or up and out and away!) Another interesting thing is that if the firework is falling and then it explodes it will continue to freefall—this causes the pattern of sparks to go out in all directions. This does not, however, alter the overall shape of the exploded firework since it will still be moving in a downward movement, giving the explosion the shape of a parasol. Should the firework explode at the peak of its height- it will explode in all directions like a dandelion. Finally, should the firework explode on its way down, an occurance that happens rarely-- it will take the shape of an inverse parasol. The main materials used in firework manufacture may be divided into several categories: Oxidizing agents, fuels, color producing agents, substances which improve effects such as color and light, and substances which produce smoke, binding agents, phlegmatizers, stabilizers, substances which accelerate or retard combustion, aids in production, such as solvents, and lubricants. However, some of these functions tend to overlap, so for simplicitys sake, we have included here only the commonly used materials. The burning speed of a firework mixture is controlled by a variety of factors, the major three being particle size, temperature, and pressure. Firework compositions are usually mixed in a special type of a structure. It is standard procedure to use several buildings, one for sulphur mixtures, for chlorate compositions, another for ammonium perchlorate and finally, one for magnesium. All of these types of fireworks require some type of container. In the past, tubes of paper and occationally wood has been utilized- nonetheless, paper remains the most popular and the cost effective. Several exceptions are signal flares which are usually pressed into either steel plastic, or aluminum tubes. There are very many types of visual and audio effects for fireworks. As this is relatively unimportant to our research we will only briefly list them: Stars, colored fires, Bengals, lances, Portfires, Torches, Roman candles, comets, Mines, Noisemakers, Rockets, Drivers, saxons, tourbillions, shells, Gerbs, fountains, rains, squibs, Cones, Pinwheels, Crackers, and Smoke bombs are the better known types. Indoor Fireworks and Professional pyrotechnic displays will be ignored since they operate on somewhat different principals. They also require more professional handling. (obviously.) For our experiment we have decided to focus solely on rockets, because of their relative simplicity and since we only wanted to use basic trigonometry in our experiments as Ailia is only in Algebra 2 Trigonometry, and Marla is in Advanced Pre calculus. For the experiment itself, we have found several equations which we are considering applying. The first equation we came across is how to calculate the size of fireworks, which is size (feet)= 6pi (time in seconds) *angle in degrees. If accuracy is not a consideration however, it is possible to round 6 pi up to 20, since 6 pi is actually 18.85… The next equation we found was with the physics of aerial shell fireworks. There was a chart listing all the commonly used shell sizes and their corresponding initial mortar velocities. (we will enclose the chart as a reference on the back. ) The relationships between the initial velocities and the distances traveled by the shells may be found using this formula: Vertical height= Initial vertical velocity * Hang time + 0.5 * Acceleration due to gravity* Hang time ^ 2. However, in light of the constraints placed upon us, we have designed our own experiment. Since fireworks are out of season and illegal at this time, we have decided on using bottle rockets, the most harmless and easily accessible variety. With our knowledge of arcs and trigonometry, we can calculate the height of a firework based on the distance traveled and the angle at which it is fired. Once we have that information, we can figure out the initial velocity of a firework based on its angle of trajectory. Given the distance traveled of a firework (we’ll call that distance d) we can find the apex of the firework’s trajectory. The apex is always half the total distance traveled (we’ll call that x which is equal to d/2). Based on the degree of the angle of trajectory as well as the horizontal distance traveled to apex, we can determine the height that the firework reaches at its peak. We know from Trig that the tangent of an angle (we’ll be using the tragectory angles of 30, 45 and 60 degrees) is height over distance traveled. (Tangent of theta= x divided by y (height of firework at its peak) Thus, with that information at our disposal, we are able to plug the height back into the following equation: Vertical height = Initial vertical velocity * Hang time + 0.5 * Acceleration due to gravity (9.8m/s)* Hang time ^ 2 … and we will be able to calculate the initial vertical velocity of fireworks fired off at various trajectories. This will enable us to prove the validity of the preceeding equation and allow us to use Trig for a “real world” experiment. Given that a rocket fired from a trajectory of 60 degrees will reach the highest apex, we believe that this rocket will have the highest vertical velocity. This will be the case due to the fact that we think that hang time and acceleration due to gravity will be fairly consistent throughout all trajectories. Therefore, the highest vertical height will yield the highest initial vertical velocity. In proving the trig concept that the tangent of an angle is equal to height over distance traveled, (y/x) we can carry this idea over and find the size of an airborne firework that has exploded. Earlier in this proposal, we explained the equation that one can use in order to determine the size of an exploded firework—that equation is as follows: 18.85 (6pi)* time (in seconds) *angle of trajectory =size This equation is essentially the same as our earlier notion that the height of the bottle rocket is equal to the tangent of the angle at which it is fired –(unknown height over distance traveled divided by two.) What makes this slightly different from the height equation is that rather than finding the height of the rocket at its peak, this equation allows you to find the size of the firework once it has exploded (as that takes the place and is substituted as the “height”) There are many variables and trivial differences present between the products of different manufacturers, however few other than the experts will notice them. Pyrotechnics is obviously a risky hobby in which very few people can dabble, unlike most other leisure activities. In this pastime of fireworking, progress is actually the development and creation of new effects. By experimentation, a new chemical composition may create a star effect not achieved previously, and such. For an example, titanium was a relatively new addition. Throughout the history of fireworks, diminutive groups of aficionados have continuously brought pyrotechnics to new heights. Fireworks still remain the perfect spectacle for celebration, experimentation and art. Pyrotechnics will no doubt continue on as an expression of art. Bibliography: Word Count: 1648
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