Yeah, I saw that photo, and thanks. But it didn't really explain to me how pieces of disconnected carbon ignite each other without some physical link. Unless somehow the inner particles create a cloud of fire that ignites the larger balls? That's the part I'm not getting.
I agree the article doesn’t really explain it. The short answer is the burst from the shell generates enough heat to ignite the payload (the stars) before they’re blown out into the sky. No fuse is needed because the payload is flammable enough to ignite but not so flammable that nothing interesting is seen from the ground. That sounds like a cop-out but it’s why designing fireworks is a science and art. :)
The purpose of gunpowder is to burn rapidly. Burning generates a lot of hot gas that tries to expand. The bomb's physical shell, along with the inertia of the stars, resists the expansion for a brief moment, creating pressure that's used to propel the stars away at high speeds, but also ensures that the burning gunpowder charge has time to ignite the stars before they fly away.
Gunpowder is meant to burn at controlled rates, but traditional gunpowder, black powder, used in fireworks and older firearms typically burns very quickly. Smokeless gunpowder for modern firearms have controlled burn rates. Depending on barrel length, etc. you may want the gunpowder to burn faster or slower to affect the ballistics. I imagine they use certain ratios of differing ingredients to control the rate of burn in fireworks as well.
Burn rate for black powder depends on particle size. Fine powder burns faster than coarse powder. So one characteristic of high-quality powder is uniform particle size.
But yes, changing the formulation also affects burn rate. For example, replacing potassium nitrate with potassium perchlorate yields a much faster burn.[0] Also replacing the carbon with aluminum dust gives you flash powder.[1]
