What Is the Mach Cone & Shock Wave Angle Calculator?
The Mach cone is the conical boundary enclosing all sound waves emitted by a supersonic body.
How Does the Mach Cone & Shock Wave Angle Calculator Work?
Individual spherical acoustic wavelets emitted at consecutive points along the path are enveloped by a conical tangent surface.
Mach Cone & Shock Wave Angle Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
\sin(\mu) = \frac{1}{M} \implies \mu = \arcsin\left(\frac{1}{M}\right), \quad 2\mu = 2 \arcsin\left(\frac{1}{M}\right)
Sine of Mach cone half-angle mu is reciprocal of Mach number M. Full envelope angle is 2 times mu.
How to Use the Mach Cone & Shock Wave Angle Calculator
- Enter the supersonic flight Mach number (greater than 1.0).
- Optionally adjust ambient speed of sound for altitude.
Step-by-Step Example Calculation
Mach 2.0 Supersonic Flight
Input Values:
machNumber:2.0
speedOfSoundMPerS:340
Worked Steps: At Mach 2, the shock wave opens at half-angle μ = 30° (60° total cone) with a flight velocity of 680 m/s (1,521 mph).
Understanding Your Result
Mach Angle (μ): Angular half-width of the shock envelope from the velocity vector.
Total Cone Angle (2μ): Total angular spread of the conical disturbance.
Flight Speed: Velocity in m/s, mph, and km/h.
Factors That Affect the Result
- Mach number (primary) and ambient atmospheric temperature altering local speed of sound.
When Should You Use This Calculator?
- Aerospace propulsion analysis, sonic boom ground footprint prediction, and ballistics trajectory modeling.
Assumptions & Limitations
- Applies to weak Mach waves (acoustic limit). For blunt bodies or finite wedge angles, oblique shock angles (β) are larger than the Mach angle.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact inviscid gas dynamics acoustic Mach wave formulation.