Each firecracker in the string is linked by a short length of quickmatch or visco fuse. The flame front travels down that fuse at a roughly constant linear burn rate v, set by the fuse's own chemistry (a black-powder core wrapped in cotton/paper), so the ignition delay to the next cracker is simply:
t_ignite(k→k+1) = L / v_eff
v_eff = v_burn · (1 − 0.6 · humidity) [moisture slows the burn]
p_transfer = contact · (1 − 0.7 · humidity), clamped [splice reliability]
At each splice, the flame must physically bridge from one cracker's spent charge to the next fuse's exposed powder core. Real quickmatch chains fail this way constantly — a loose wrap, a damp twist, or a poor crimp lets the fire smoulder out before it reaches the next fuse, which is why this simulation rolls a genuine pass/fail at every splice instead of guaranteeing the chain continues. When a splice succeeds, the igniting cracker's charge heats trapped air and combustion gas far faster than it can vent through the crimped paper tube, so pressure inside spikes in tens of milliseconds until the casing ruptures — the "pop" — releasing a burst of hot gas and flame that both flashes visibly and (given good contact) kindles the next fuse almost immediately.
- Fuse burn rate — the fuse's intrinsic propagation speed; higher means shorter ignition delays between crackers.
- Splice contact quality — how tightly each fuse end is wrapped to the next charge; lower quality both slows heat transfer and raises the chance a given splice fails outright.
- Humidity — water in the fuse core both slows the burn front and starves the flame of the heat needed to jump a splice, so a humid chain propagates slower and fizzles more often — a real, well-documented failure mode of pyrotechnic fuse.
- Fuse segment length — longer runs between crackers mean a longer burn time per hop, and more time for a marginal flame to smoulder out before it arrives.