Mach Angle Calculator Formula

Understand the math behind the mach angle calculator. Each variable explained with a worked example.

Use the Mach Angle Calculator

Formulas Used

Mach Angle (radians)

mach_angle_rad = asin(1 / mach_number)

Mach Angle (degrees)

mach_angle_deg = asin(1 / mach_number) * 180 / pi

Cone Half-Angle

cone_half_angle = asin(1 / mach_number) * 180 / pi

Variables

VariableDescriptionDefault
mach_numberMach 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.

mach_number = 2
  1. 01mu = arcsin(1 / 2.0) = arcsin(0.5)
  2. 02mu = 30° (or 0.5236 radians)
  3. 03The shock cone has a half-angle of 30 degrees.

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