Mach Angle Calculator with Steps

Mach Angle Formula:

\[ \theta = \arcsin\left(\frac{1}{M}\right) \]

Mach Cone Angle (θ):

Definition: This calculator computes the angle of the Mach cone created by an object moving at supersonic speeds.

Purpose: It helps aerodynamics professionals and students understand shock wave behavior in supersonic flow.

The calculator uses the formula:

\[ \theta = \arcsin\left(\frac{1}{M}\right) \]

Where:

Explanation: The Mach angle decreases as the Mach number increases, showing how shock waves become more acute at higher speeds.

Details: Understanding Mach angles is crucial for aircraft design, sonic boom analysis, and understanding supersonic flow patterns.

Tips: Enter the Mach number (must be ≥ 1). The calculator will compute the corresponding Mach cone angle in degrees.

Q1: Why does the Mach number need to be ≥ 1?
A: Mach angles only exist for supersonic flow (M ≥ 1). At subsonic speeds, no Mach cone forms.

Q2: What happens at exactly Mach 1?
A: At M=1, the Mach angle is 90°, meaning the shock wave is perpendicular to the flow direction.

Q3: How does Mach angle change with speed?
A: As Mach number increases, the Mach angle decreases, making the cone more narrow.

Q4: What's a typical Mach angle for commercial jets?
A: The Concorde at Mach 2 had a Mach angle of about 30°.

Q5: Does this apply to all supersonic objects?
A: Yes, the formula applies to any object moving faster than the speed of sound in the medium.