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Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator

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

Supersonic inlet Mach number.

Wedge turn angle.

Air γ = 1.40.

Calculated Result
36.9 degrees

Wave Angle (β)

Wave Angle (β)

36.9 degrees

Wave Angle Beta Degrees

36.9

Downstream Mach M2

1.87

Normal Mach M1n

1.5

Shock Regime

Attached weak oblique shock wave (standard aerodynamic wedge compression)

36.9 — degrees

Calculation Breakdown

  1. Applied FormulaSolves the classic compressible θ-β-M relation to find the attached oblique shock wave angle β and downstream supersonic Mach number M₂ over wedge compression corners.\tan\theta = 2\cot\beta \left[\frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2}\right]

Oblique Shock (θ-β-M) Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.09.2182837Wave Angle (β)

What Is the Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator?

This tool computes oblique shock wave wave angle (β), deflection (θ) & mach number calculator with high precision arithmetic.

How Does the Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator Work?

Solves the classic compressible θ-β-M relation to find the attached oblique shock wave angle β and downstream supersonic Mach number M₂ over wedge compression corners.

Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator Formula & Variables

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

tan⁡θ=2cot⁡β[M12sin⁡2β−1M12(γ+cos⁡2β)+2]\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 classic compressible θ-β-M relation to find the attached oblique shock wave angle β and downstream supersonic Mach number M₂ over wedge compression corners.

How to Use the Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator

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

Step-by-Step Example Calculation

Oblique Shock Wave Wave Angle (β), Deflection (θ) & Mach Number Calculator Example

Input Values:

upstreamMachM1:2.5
deflectionAngleThetaDeg:15
ratioOfSpecificHeatsGamma:1.4
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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