Most people don't realize the vast world of physics that takes place during every fireworks show. The science of pyrotechnics involves many physics applications that must be considered to produce entertaining displays. Pyrotechnicicans must take into account the relationships between vectors, velocities, projectiles and their trajectories, the explosion forces behind burst patterns, etc. These are the topics covered by this page.

To the right you can see a table that lists all commonly used shell sizes and their corresponding initial mortar velocities. These velocities are the speeds that the shells are traveling as they are fired out of the mortar. The 2" through 6" shells are used at almost all fireworks shows and are used almost exclusively at small shows. The 8", 10", and 12" shell sizes are usually used at only large fireworks shows as they are more expensive than the smaller sizes. The 24" and 36" shell sizes are even more expensive because they produce extremely large burst patterns. These monstrous aerial shells are only used at the largest shows and during special circumstances. As you can see in the table, larger shell sizes produce greater initial mortar velocities. This happens because the larger mortars used to fire larger shells have the capacity to house greater amounts of blackpowder/pyrex used to propel the shells out of the mortar. Greater amounts of blackpowder/pyrex, when burned, produce more excess gases than do smaller amounts. These larger amounts of excess gases cause the shell to be pushed or propelled out of the mortar faster, resulting in greater initial velocities. The greater initial velocities produced by larger shells result in the shell attaining a greater height before it explodes and emits its bright flash of light. Shells usually travel about 100 feet vertically for every inch they are in diameter; depending on the angle they are fired from.

The relationships between the initial velocities and the distances traveled by the shells can be understood and manipulated by using the following formulas and mathematical methods:

Y=VyT+0.5GT^2

Y=vertical height, Vy=initial vertical velocity, T=hang time, G=acceleration due to gravity

X=VxT

X=horizontal distance, Vx=initial horizontal velocity, T=hang time

The Pythagorean Theorem - a^2 + b^2 = c^2

a or b = vertical or horizontal velocity, c=resultant initial velocity

The Trigonometric Functions - sine, cosine, and tangent

In a right triangle sine=opposite side/hypotenuse, cosine=adjacent side/hypotenuse, tangent=opposite side/adjacent side

2"- 12" Shell Trajectories Fired at 75 Degrees

The first two formulas you see are primarily used to chart trajectories like in the graph on the left that shows the flight paths of 2" through 12" shells fired at 75 degrees. These graphs are very useful tools that allow pyrotechnicians to visualize how high and how far their shells will travel during a show. This information can be used to aid the process of choreographing the show to music, and determining if some shells will exceed the safe zone for that particular site. The Pythagorean Theorem is used to find a certain initial velocity value if the other two are known. This is helpful in determining information needed for the other formulas. The Trigonometric Functions are also used to find initial velocity values, but are used to find vertical heights, horizontal distances, and firing angles as well. Pyrotechnicians use these mathematical methods along with charts, graphs, and computer programs derived from them to plan their impressive displays.

Pyrotechnicians must also consider shell burst sizes when planning shows. They must know how big certain bursts are when compared to others so that the choreographing of the show is in sync and so they don't exceed their safe zone requirements. As with initial mortar velocities, the bigger the shell size the larger the effect. It follows the same principle in that larger shells contain greater amounts of chemicals that when ignited produce greater explosion forces than do smaller shells. This results in varied burst sizes. Shell burst sizes are usually about 45 feet in diameter for every inch in shell size, depending on how tightly the shell is packed. As you can see in the diagram on the right, the differences in burst sizes can be extremely huge. It is just one more thing that pyrotechnicians must take into account to produce entertaining and attractive fireworks shows.

Through this page and the ones preceding it, we hope you have learned a little more about the science behind the spectacle of an entertaining fireworks show. Pyrotechnicians must master many different types of science in order to create attractive displays. We now invite you to take what you have learned in these pages and apply it to our interactive fireworks page. You can experiment with fireworks in the same ways that pyrotechnicians do, and in essence, create your own show!

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