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The physics behind every large ordinance fireworks show is very involved and can range from vectors, velocities, trajectories, projectiles, and the directed force explosions from the shell. All these concepts and relationships are explored throughout the following page. The large ordinances, or aerial shells, are the only ones being explored in this section. The same concepts apply to the smaller fireworks, such as bottle rockets and Blackcats©.

Aerial shells are the type of firework that is used at most Fourth of July celebrations. These shells range from the 2” salutes to the enormous 36” shells. There are different combinations of aerial shells used during a display, the most common are the two-break color and report shell, the American cylinder shell, and the Oriental style shell. After the shell has reached its designated altitude, a burst of chemicals ignite to produce the brilliant flash of colored light. The projectile is launched from steel or more recently PVC tubes (mortars).

The table to the right lists all commonly used shell sizes and their corresponding initial mortar velocities. The initial velocity of the shell is the speed at which the shell leaves the mortar. A typical show will use the 2" shells as salutes before the show starts. These shells usually don’t have any special effect except for the loud “bang” to suggest the start of the show. The most common shells used at a small fireworks display are below the 6" shell size. One could think of the price as being proportional to the size of the aerial shell, of course, the more intricate design and display from the firework itself, the more expensive. The expensive 8", 10", and 12" shell sizes are usually used at only large fireworks shows. The 24" and 36" shell sizes are the most expensive due to large burst patterns, materials, and production. The oversized aerial shells are rarely used due to the large hazards, cost, and scarcity of the shell.

The table also shows that the larger the shell sizes, the greater the initial mortar velocities. This is an interesting relationship, one would think that the larger mortars would be slower out of the tube due to size and weight; this is actually the opposite of what happens. As the shell diameter increases, the area increases by r2 and therefore more room is allocated for the propellant. As larger amounts of propellant are burned, excess gas is produced and creates the lifting force. This force is greater as the excess gas increases. These larger amounts of excess gases cause the shell to be pushed or propelled out of the mortar faster, resulting in a faster initial velocity. The higher the initial velocity the more altitude the shell can attain before it explodes and emits its bright flash of light and pattern. These aerial shells usually travel ~100 feet vertically for every inch in diameter for small angles of theta from the vertical angle.

The kinematics equations of motion can be used to demonstrate the relationship between the initial velocities and the distances traveled by the shell.
y = vyt + ½gt2
where y is the displacement in the y direction, vy is the initial velocity in the y direction, t is time, and g is the acceleration due to gravity
x = vxt
where x is the displacement in x direction, vx is the initial velocity in the x direction, and t is time

2" - 12" Aerial Shell Trajectory Fired at 75 degrees | Shell Burst

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