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Scientific model of a firework


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Posted

Hi,

 

I’m Thomas, and I’m currently studying in a french engineering school. I apologize for my imperfect English.

 

As part of a scientific project, I need to develop a scientific model of a classic aerial firework, and more particularly the explosion. I’ve done some researches, but I haven’t found yet conclusive data. Here are some of my questions, and I hope you can provide some answers!

 

1° Let’s consider a classic bomb, a sphere of black powder, with the stars all around (one row) and two spheres of separation: one between the powder and the stars, the other between the stars and the air. In what material are these two spheres?

 

2° The black powder produces the explosion. I know the powder deflagrates, but it is confined in a sphere. I assume there is an increase of pressure and heat, while the reaction is happening. My question: is there a deflagration to detonation transition, i.e. does the powder detonate because it is confined ?

 

3° Do you know the average pressure in the sphere just before it breaks? Do you choose the material of the sphere according to the desired radius of the blast?

 

4° If it detonates, there is a very powerful shock wave. Is it responsible for the homogeneous bursting? I mean, it could explode like a balloon, all the air getting away from the same “source”.

 

5° How can you predict the radius of the explosion? With which formula? At the moment the sphere explodes, there is a pressure gradient. I assume the acceleration of the stars could be given with this pressure gradient and the force of the air displacement (fluid mechanics). Is this correct?

 

I thank you for all your precious answers!

 

Thomas

Posted

1. The outer sphere will be plastic or multiple layers of paper, the inner sphere will be a single layer of paper, or there will be no inner separator at all.

 

2. No, there is no detonation.

 

3. Don't know the pressure. Yes, you can modify the strength of the shell to alter the break. By pasting more layers of paper (in the case of paper shells) or tape (in the case of plastic shells) you can produce a harder break.

 

4. It doesn't detonate, but I think the principle is still the same, in the center of the shell is a large amount of high pressure gas that wants to expand. The gas pushes the stars away from the center.

 

If the shell isn't of uniform strength you will get a lopsided break where the stars project out in one direction more than the others.

 

5. Trial and error :)

Posted

1. The stars and black powder may or may not be separated. Black powder fills all empty space between the stars, after which black powder may simply be poured into the center of the hemispheres, or a layer of tissue paper is places over the stars which divides them. When tissue paper is added it is used to allow the hemispheres to more easily be snapped together without the contents falling out, as well as holding the stars in place slightly more securely. There are some other benefits that allow simpler assembly of shells using tissue paper to isolate the burst, but they are of no consequence to the result.

 

The outer layer of the shell is always made of paper strips wet with any number of adhesives. This is added after the shell as been snapped together. Inside of that layer are two hemispheres that may be made of either paper or plastic. The material choice is a matter of price and preference, the visible differences between the two are negligible. The shell walls real strength comes from the pasted outer layer.

 

2. Black powder does not detonate regardless of the confinement. The composition only allows for combustion reactions. Black powder does contain one component technically capable of detonation, but the initiation requirements are far beyond what the combustion of black powder can provide in any circumstance.

 

3. The pressure reaches several hundred PSI. The exact pressure is not able to be determined without physical shell by shell testing because of the variables. The pressures vary depending on the thickness of the pasted layer of the shell, and also may increase with the addition of fiberglass reinforced tape. Quality and composition of the burst also would impact the pressures dramatically.

 

4. No detonation occurs. The homogeneous bursting is due to an ignition point in the center of the shell, even wall strength from quality pasting, and solid construction.

 

5. We don't predict the radius - at least I don't. It's given a good guess and a field test. Predicting the result comes with experience. Should an equation exist, it would need to contain the pressure, temperature, and types of gas produced within the shell, the weight and size of the stars, the ability of the gas to accelerate the stars depending on their shape, and the effect of the air slowing them (which would need to take into account the burn rate lowering their size, surface area, and mass - which changes for each star type). If you feel like figuring all that out and turning it into an equation, go for it.

Posted
1° Let's consider a classic bomb, a sphere of black powder, with the stars all around (one row) and two spheres of separation: one between the powder and the stars, the other between the stars and the air. In what material are these two spheres?

 

The inner separator is typically thin paper, and the outer shell casing is made from several layers of pasted paper, or simply an injection molded plastic such as polyethylene or polypropylene.

 

2° The black powder produces the explosion. I know the powder deflagrates, but it is confined in a sphere. I assume there is an increase of pressure and heat, while the reaction is happening. My question: is there a deflagration to detonation transition, i.e. does the powder detonate because it is confined ?

 

Detonation does not occur within the shell. A very large quantity and substantial run-up distance is required for black powder to DDT.

 

Black powder also does not really respond to changes in pressure like many propellants do. To quantify this, the burn rate of a propellant can be expressed as a power law:

 

R = C * P(n)

 

Where R = reaction rate, P = pressure, C = a constant, and n = an experimentally determined value that applies to each propellant.

 

The value of n for black powder is very close to 0, which means that its burn rate is fairly constant over a wide pressure range.

 

3° Do you know the average pressure in the sphere just before it breaks? Do you choose the material of the sphere according to the desired radius of the blast?

 

This can be calculated, but it will depend on many factors, such as the material used, the inside diameter of the shell, the wall thickness, and the burn rate of the black powder, which does vary significantly from user to user. A mathematical model would be fairly complex, but it could be done.

 

However, pyrotechnics is much more an art than a science, and most people base their designs on trial and error/word of mouth rather than hard science and mathematical modeling.

 

4° If it detonates, there is a very powerful shock wave. Is it responsible for the homogeneous bursting? I mean, it could explode like a balloon, all the air getting away from the same "source".

 

A detonation would be unfavorable, as high velocity shockwaves are not effective at accelerating objects with high inertia. The pressure spike is extremely high, but the duration is very low. If the burst charge detonated, it would powder the stars and throw the dust a couple feet. Black powder reacts relatively slowly, which produces a lower internal shell pressure, but a much higher duration.

 

Uniform bursting is simply a result of the spherical shape of the shell and it's contents, and even shell wall thickness.

 

5° How can you predict the radius of the explosion? With which formula? At the moment the sphere explodes, there is a pressure gradient. I assume the acceleration of the stars could be given with this pressure gradient and the force of the air displacement (fluid mechanics). Is this correct?

 

With me being a high school student, and you being in engineering, I'd expect that you're more qualified to answer this than myself. In the model that I'm thinking of, you would need to calculate the rate of gas production and determine the burst pressure of the shell, then calculate the pressure drop once the shell bursts and integrate over time to find the final velocity of the stars. Figuring out the horizontal displacement would be more difficult than a traditional external ballistics model, as the stars are burning, and the mass is constantly changing. It might be best to just treat the stars as standard spheres with constant mass and sectional density, but it really depends on how complex you want this to be.

 

You're speaking of pressure gradients and force on the stars, so clearly you're on the right track.

Posted
Anybody like video? I think this is a terrific example of the hows and whys when it comes to shells getting fire.

 

http://pyrobin.com/files/fireworks-slomo-german.wmv

 

D

 

 

WOW!!!! Great video that really helps explain alot of things of how it works, even if you don't know the tounge in which they speak.

Posted
WOW!!!! Great video that really helps explain alot of things of how it works, even if you don't know the tounge in which they speak.

 

 

Excellent Vid!!! I just wish I knew what they were saying.

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