Igniting the charge burns propellant into high-pressure gas almost
instantly; that gas then keeps expanding and pushing the projectile
as it travels down the bore, with pressure falling as the volume
behind it grows (the live pressure–position curve in the chart).
F = P(x)·A − F_friction
a = F / m_projectile
P(x) ≈ P_peak · exp(−x / L_decay) · burn(t)
- Charge mass — scales the peak chamber pressure and total energy released.
- Bore friction — resistive force from the rifling/bore surface opposing acceleration.
- Projectile mass — heavier shells accelerate more slowly for the same pressure, trading muzzle velocity for kinetic energy.
Real internal-ballistics codes solve this same pressure/travel
coupling (Le Duc / Vallier-type models) to size the chamber and
choose a propellant that reaches peak pressure early without
exceeding the barrel's safe pressure limit.