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Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator

Easily calculate and compute oblique shock wave angle (theta-beta-mach relation) calculator with accurate equations, live formulas, and expert guidance.

Supersonic incoming flow Mach number.

Ramp or wedge turning angle in degrees.

Working fluid gamma (1.4 for air).

Calculated Result
0 °

Shock Angle (β)

Shock Angle (β)

0 °

Shock Wave Angle Beta Deg

0

Downstream Mach M2

1.87

Static Pressure Ratio P2 Over P1

2.47

Normal Component Mach Mn1

1.5

0 — °

Calculation Breakdown

  1. Applied FormulaSolves the non-linear Theta-Beta-Mach relation for the weak planar oblique shock wave angle beta, downstream Mach number M2, and static pressure jump across supersonic ramps.\tan\theta = 2\cot\beta \frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2}, \quad M_{n2} = f(M_{n1})

Oblique Shock Theta-Beta-M Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.50.81.0Shock Angle (β)

What Is the Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator?

This tool computes oblique shock wave angle (theta-beta-mach relation) calculator with high precision arithmetic.

How Does the Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator Work?

Solves the non-linear Theta-Beta-Mach relation for the weak planar oblique shock wave angle beta, downstream Mach number M2, and static pressure jump across supersonic ramps.

Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator Formula & Variables

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

tan⁡θ=2cot⁡βM12sin⁡2β−1M12(γ+cos⁡2β)+2,Mn2=f(Mn1)\tan\theta = 2\cot\beta \frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2}, \quad M_{n2} = f(M_{n1})

Solves the non-linear Theta-Beta-Mach relation for the weak planar oblique shock wave angle beta, downstream Mach number M2, and static pressure jump across supersonic ramps.

How to Use the Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator

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

Step-by-Step Example Calculation

Oblique Shock Wave Angle (Theta-Beta-Mach Relation) Calculator Example

Input Values:

upstreamMachNumberM1:2.5
flowDeflectionAngleThetaDeg:15.0
specificHeatRatioGamma:1.40
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required °.

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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