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Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator

Easily calculate and compute supersonic mach cone & oblique shock wave angle (θ-β-m) calculator with accurate equations, live formulas, and expert guidance.

Must be below maximum detached shock angle.

Calculated Result
35 degrees

Oblique Shock Wave Angle (β)

Oblique Shock Wave Angle (β)

35 degrees

Oblique Shock Angle Beta Deg

35

Mach Wave Angle Mu Deg

24.6

Downstream Mach Number M2

1.92

Normal Mach Number Mn1

1.38

35 — degrees

Calculation Breakdown

  1. Applied FormulaSolves the supersonic oblique shock relation ($ heta$-$eta$-$M$) and Mach cone angle for supersonic aircraft intake ramps, missile noses, and wedge bodies.\mu = \arcsin\left(\frac{1}{M}\right), \quad \tan\theta = 2 \cot\beta \left[ \frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2} \right]

Mach Cone & Oblique Shock Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.08.8182635Oblique Shock Wave Angle (β)

What Is the Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator?

This tool computes supersonic mach cone & oblique shock wave angle (θ-β-m) calculator with high precision arithmetic.

How Does the Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator Work?

Solves the supersonic oblique shock relation (hetaheta-eta-MM) and Mach cone angle for supersonic aircraft intake ramps, missile noses, and wedge bodies.

Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator Formula & Variables

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

μ=arcsin⁡(1M),tan⁡θ=2cot⁡β[M12sin⁡2β−1M12(γ+cos⁡2β)+2]\mu = \arcsin\left(\frac{1}{M}\right), \quad \tan\theta = 2 \cot\beta \left[ \frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2} \right]

Solves the supersonic oblique shock relation (hetaheta-eta-MM) and Mach cone angle for supersonic aircraft intake ramps, missile noses, and wedge bodies.

How to Use the Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator

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

Step-by-Step Example Calculation

Supersonic Mach Cone & Oblique Shock Wave Angle (θ-β-M) Calculator Example

Input Values:

freestreamMachNumberM1:2.4
wedgeDeflectionAngleThetaDeg:12
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required degrees.

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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