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Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator

Easily calculate and compute convergent-divergent (de laval) rocket nozzle area expansion ratio calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
12.51 ratio

Nozzle Area Expansion Ratio (eps = Ae / At)

Nozzle Area Expansion Ratio (eps = Ae / At)

12.51 ratio

Nozzle Area Expansion Ratio Eps

12.506351772606711

Nozzle Exit Diameter Mm

530.4648102218007

Nozzle Throat Area M2

0.017671458676442587

Nozzle Exit Area M2

0.221005478542674

12.51 — ratio

Calculation Breakdown

  1. Applied FormulaSolves the 1D gas dynamic area-Mach number relation for convergent-divergent supersonic de Laval nozzles, calculating exit Mach number (Me) and optimum expansion ratio (Ae/At).\frac{A_e}{A_t} = \frac{1}{M_e} \left[ \frac{2}{\gamma+1} \left( 1 + \frac{\gamma-1}{2} M_e^2 \right) \right]^{\frac{\gamma+1}{2(\gamma-1)}}

de Laval Nozzle Area Expansion Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.03.16.39.413Nozzle Area Expansion Ratio (eps = Ae / At)

What Is the Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator?

The Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator computes results using established domain formulas, verified conversion factors, and user-entered parameters.

How Does the Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator Work?

Solves the 1D gas dynamic area-Mach number relation for convergent-divergent supersonic de Laval nozzles, calculating exit Mach number (Me) and optimum expansion ratio (Ae/At).

Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

AeAt=1Me[2γ+1(1+γ−12Me2)]γ+12(γ−1)\frac{A_e}{A_t} = \frac{1}{M_e} \left[ \frac{2}{\gamma+1} \left( 1 + \frac{\gamma-1}{2} M_e^2 \right) \right]^{\frac{\gamma+1}{2(\gamma-1)}}

Solves the 1D gas dynamic area-Mach number relation for convergent-divergent supersonic de Laval nozzles, calculating exit Mach number (Me) and optimum expansion ratio (Ae/At).

How to Use the Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Convergent-Divergent (de Laval) Rocket Nozzle Area Expansion Ratio Calculator Example

Input Values:

nozzleExitMachNumber:3.5
specificHeatRatioGamma:1.22
throatDiameterMm:150
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required ratio.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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