Presets
Playback
Engines and nozzle
Each engine has a fixed throat. Chamber pressure and the expansion ratio set the exit pressure and exhaust speed.
Vehicle and gas
More propellant raises delta-v; more payload or fewer engines lowers the thrust-to-weight ratio.
Model checks
The science
From chamber to plume
Hot gas accelerates through a throat and a bell. For an ideal gas the exit Mach number Me follows from the area ratio Ae/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)](γ+1)/(2(γ−1)). The exit pressure is pe = pc(1 + (γ−1)Me²/2)−γ/(γ−1) and the exhaust speed ve = √(2γ/(γ−1) · R Tc/Mw · [1 − (pe/pc)(γ−1)/γ]). The mass flow is set by the throat, ṁ = pc A* / c*.
Thrust and altitude
Thrust is F = ṁ ve + (pe − pa) Ae. As the air thins, pa falls and thrust rises toward its vacuum value; the specific impulse is Isp = F/(ṁ g0). If pe > pa the nozzle is underexpanded and the plume bulges; if pe < pa it is overexpanded and the plume is squeezed, and Mach diamonds mark the shock cells near equilibrium. A large bell is best in vacuum, a short one at sea level.
Ascent
The vertical equation of motion is m dv/dt = F − m g(h) − ½ ρ(h) v|v| Cd A, with an exponential atmosphere. Without drag and with constant g the result is the Tsiolkovsky equation with gravity loss, v = ve ln(m0/m) − g t.
Honest simplifications
The ascent is purely vertical (real launches pitch over), the atmosphere is isothermal, the gas has constant composition and gamma, there is a single stage, the drag coefficient is constant, and the plume drawing is schematic rather than a flow solution. No real vehicle is modelled.
Checks in the page
Check 1 compares a stepped ascent with the closed-form velocity and altitude. Check 2 compares the exhaust speed from the energy equation with Mach number times the local speed of sound. Check 3 checks mass continuity at the nozzle exit against the throat mass flow.
What to try
- Load Stubby sea-level nozzle and then Vacuum nozzle (eps 60): the short bell wins at the pad, the long bell wins high up. Watch the plume and graph 2.
- Load Too heavy to lift: the thrust-to-weight ratio stays below 1 and the rocket sits on the pad.
- Raise chamber pressure and watch the exit pressure, thrust and exhaust speed readouts change.
- In graph 4 compare the vacuum exhaust speed with the sea-level specific impulse line to see how much a good nozzle is worth.