Composition
Here is a short video to show and explain the composition of a firework
The composition of Fireworks
As the video will show you there are 5 main parts to fireworks:
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Breaks
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Time Delay Fuse
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Stars
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Black Powder (Gunpowder)
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Launch Tube
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Main Fuse
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Lift Charge
The breaks contain the other vital substances and help it produce enough resistance to explode across the sky. Running inside the breaks is a time delay fuse which as the firework ascends through the air continues to burn. At each of the break ends, coloured stars will ignite in all directions. For the lauch tube, most fireworks are launched from rows of steel tubes secured in troughs of sand however if the firework doesn't fit in correctly, the firework could misfire. The main fuse as shown in the diagram on slide 7 runs down the fast-acting slide fuse to the lift charge which is where the explosion to send the firework as high as 1000 ft. happens.

Equations in fireworks
Equations in Oxidisers, Nitrates
2KNO3 k2O + N2 + 2.5 O2
This is a chemical equation to show how and what oxidersers do; supply oxygen to allow combustion.
And it is allready balanced.
Here is a perfect image that shows the reaction that takes place in sparklers.

Here is image of a catherine wheel ,suspended in the air, in action.
How does design of different fireworks affect its function?
There are many different types of fireworks that all have different effects.
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Catherine Wheel - Are pinned down and have their black powder spiralling round to create a spinning, effect and they cannot fly off.
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Sparkler - Are made with Magnesium, which when heated creates a bright light. Thurthermore it doesn't have to move so it doesn't need any black powder.
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Rocket - They are designed to fly up into the air and explode when they reach they peak. This is achived by putting a large ammount of black powder on the inside of the firework (75% potassium nitrate, 15% charcoal and 10% sulphur).