What does the area ratio control?

The area ratio, exit area over throat area, sets how much the supersonic gas expands between the throat and nozzle exit, which sets the exit Mach number and exit pressure. A larger ratio gives more expansion and higher exit velocity.

🔥 Rocket Engine — de Laval Nozzle

Q: What is specific impulse (Isp) and why does it matter?

Isp equals thrust divided by mass flow rate times standard gravity, measured in seconds. A higher Isp means the engine gets more thrust from the same amount of fuel, which determines how much payload a rocket can carry.

Q: Why does flow reach exactly Mach 1 at the nozzle throat?

The throat is the narrowest cross-section of the converging-diverging duct. For choked isentropic flow this is the only point where flow can transition from subsonic to supersonic, as long as the pressure ratio is high enough.

Q: What's the difference between underexpanded, overexpanded, and optimally expanded?

A nozzle is optimally expanded when exit pressure equals ambient pressure, maximizing thrust. If exit pressure is higher, the nozzle is underexpanded; if lower, it is overexpanded and loses thrust.

Q: Why do different propellants give such different Isp values?

Isp depends mainly on combustion temperature and exhaust molecular weight. Liquid oxygen and liquid hydrogen produce very light water-vapour exhaust and the highest Isp, around 450 seconds, while denser propellants trade efficiency for higher density and easier handling.

Explore how a de Laval nozzle converts hot, high-pressure combustion gases into supersonic exhaust, generating thrust. Adjust chamber pressure, nozzle area ratio, and propellant combination to see how each affects exit velocity, thrust, and specific impulse.

Propellant

Propellant combination

Chamber & Nozzle

Chamber pressure (MPa) 5.0 MPa Throat area (cm²) 50 cm² Area ratio ε = A_e/A_t 25 Ambient pressure (kPa) 101 kPa

Performance

Thrust—

Isp (vacuum)—

Isp (ambient)—

Exit velocity—

Exit pressure—

Mass flow—

Expansion—

Key equations:
c* = √(γRT_c/γ)/(Γ) — char. vel.
v_e = √(2γ/(γ-1)·RT_c·[1−(p_e/p_c)^((γ-1)/γ)])
F = ṁ·v_e + (p_e − p_a)·A_e
Isp = F / (ṁ·g₀)

How the de Laval Nozzle Works

The de Laval nozzle (converging-diverging nozzle) is the key component that converts thermal energy from combustion into directed kinetic energy. In the converging section, subsonic hot gas accelerates. At the throat — the narrowest point — flow reaches exactly Mach 1 (sonic conditions). In the diverging section, the flow becomes supersonic and continues to accelerate. The area ratio ε = A_e/A_t determines the exit Mach number and exit pressure. Optimal expansion (p_e = p_a) maximizes thrust for a given altitude. Underexpanded (p_e > p_a) and overexpanded (p_e < p_a) nozzles lose efficiency. High chamber pressure enables smaller throat area for the same thrust, reducing engine mass.

About this simulation

A rocket engine converts the thermal and chemical energy of combustion into thrust by accelerating hot gas through a de Laval nozzle — a converging-diverging duct that pushes subsonic flow up to exactly Mach 1 at the narrow throat, then continues accelerating it to supersonic speeds as the duct widens again. This simulation models that process end to end: choose a propellant combination, set chamber pressure, throat area, and nozzle area ratio ε = A_e/A_t, and watch the resulting thrust, exit velocity, and specific impulse (Isp) update in real time, along with whether the nozzle is under-, over-, or optimally expanded for the ambient pressure you've set.

🔬 What it shows

The animated cross-section shows combustion gas particles accelerating from the chamber, through the narrow throat (labelled "Throat M=1"), and out through the diverging supersonic section, with colour shifting to represent cooling exhaust. Dashed markers trace the throat location and current area ratio.

🎮 How to use

Pick a Propellant combination (LOX/LH₂, LOX/RP-1, N₂O₄/UDMH, or Solid), then drag Chamber pressure, Throat area, Area ratio ε = A_e/A_t, and Ambient pressure. The Performance box updates Thrust, vacuum and ambient Isp, exit velocity, exit pressure, mass flow, and whether the nozzle is under-, over-, or optimally-expanded.

💡 Did you know?

Modern LOX/LH₂ engines reach an Isp around 450 seconds — near the practical ceiling for chemical propulsion — because hydrogen's very low molecular weight lets exhaust gas reach far higher velocities than denser propellants like kerosene or solids at the same combustion temperature.

Frequently asked questions

What is specific impulse (Isp) and why does it matter?

Isp = F / (ṁ·g₀) measures how much thrust an engine produces per unit weight of propellant consumed per second, expressed in seconds. A higher Isp means the engine gets more thrust from the same amount of fuel, which directly determines how much payload a rocket can carry for a given amount of propellant.

Why does flow reach exactly Mach 1 at the nozzle throat?

The throat is the narrowest cross-section of the converging-diverging duct. For choked, isentropic flow this is the only point where the flow can transition from subsonic to supersonic — mass conservation and compressible flow theory force the local Mach number to equal 1 there, as long as the pressure ratio is high enough.

What does the area ratio ε = A_e/A_t control?

The area ratio sets how much the supersonic gas expands between the throat and the nozzle exit, which sets the exit Mach number and exit pressure p_e. A larger ε produces more expansion and higher exit velocity, but only pays off if the ambient pressure is low enough (e.g. at high altitude or vacuum) to avoid overexpansion.

What's the difference between underexpanded, overexpanded, and optimally expanded?

A nozzle is optimally expanded when the exit pressure p_e exactly matches the ambient pressure p_a, which maximizes thrust for that ambient condition. If p_e is higher than p_a the flow is underexpanded; if p_e is lower than p_a it's overexpanded, and the surrounding air pushes back on the exhaust, reducing thrust and risking flow separation.

Why do different propellants give such different Isp values?

Isp depends mainly on combustion temperature and the exhaust gas's molecular weight — lighter exhaust products moving at a given temperature reach higher velocities. LOX/LH₂ produces very light water-vapour exhaust and the highest Isp (~450s) of the presets here, while denser propellants like solid propellant or N₂O₄/UDMH trade some efficiency for higher density and easier handling.