Mach Angle Calculator Formula
Understand the math behind the mach angle calculator. Each variable explained with a worked example.
Formulas Used
Mach Angle (radians)
mach_angle_rad = asin(1 / mach_number)Mach Angle (degrees)
mach_angle_deg = asin(1 / mach_number) * 180 / piCone Half-Angle
cone_half_angle = asin(1 / mach_number) * 180 / piVariables
| Variable | Description | Default |
|---|---|---|
mach_number | Mach Number (M) | 2 |
How It Works
Mach Angle and Shock Cones
When an object travels faster than the speed of sound, it creates a conical shock wave. The half-angle of this cone is called the Mach angle.
Formula
mu = arcsin(1 / M)
where M is the Mach number (ratio of object speed to speed of sound). At Mach 1, the angle is 90 degrees (a flat wave front). As Mach number increases, the cone becomes narrower. At Mach 2, the angle is 30 degrees.
Worked Example
A fighter jet flying at Mach 2.0.
- 01mu = arcsin(1 / 2.0) = arcsin(0.5)
- 02mu = 30° (or 0.5236 radians)
- 03The shock cone has a half-angle of 30 degrees.
Frequently Asked Questions
Why must the Mach number be greater than 1?
The Mach angle only exists for supersonic flow (M > 1). At subsonic speeds, disturbances propagate in all directions and no cone forms. The formula arcsin(1/M) requires M > 1 to produce a real result.
What is the Mach angle at Mach 3?
At Mach 3, mu = arcsin(1/3) = 19.47 degrees. The higher the Mach number, the narrower and more swept back the shock cone becomes.
Is the Mach angle the same as a sonic boom?
The Mach angle defines the geometry of the shock cone. The sonic boom is the pressure disturbance heard on the ground when this cone sweeps past an observer. They are related but describe different aspects of the phenomenon.
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