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Mach Cone Angle Formula:
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The Mach cone angle is the angle formed by the shock wave created by an object moving at supersonic speeds. It represents the boundary between disturbed and undisturbed air and is inversely related to the Mach number of the object.
The calculator uses the Mach cone angle formula:
Where:
Explanation: As an object moves faster than sound, it creates a conical shock wave. The angle of this cone decreases as the Mach number increases.
Details: Calculating the Mach cone angle is essential in aerodynamics for understanding shock wave behavior, designing supersonic aircraft, and predicting sonic boom patterns. It helps engineers optimize vehicle shapes for reduced drag and better performance at supersonic speeds.
Tips: Enter the Mach number (must be ≥1). The calculator will compute the corresponding Mach cone angle in degrees. Higher Mach numbers result in narrower cone angles.
Q1: Why must the Mach number be ≥1?
A: Mach cone angles only exist for supersonic speeds (Mach ≥1). At subsonic speeds, no shock wave cone is formed.
Q2: What is a typical Mach cone angle for commercial supersonic aircraft?
A: For Concorde (Mach 2.0), the cone angle was approximately 60 degrees. Higher speeds produce narrower angles.
Q3: How does altitude affect Mach cone angle?
A: The Mach cone angle depends only on the Mach number, not altitude. However, the speed of sound varies with altitude, affecting the actual speed needed to achieve a given Mach number.
Q4: Can this formula be used for hypersonic speeds?
A: While the basic relationship holds, at very high Mach numbers (hypersonic regime), additional factors like real gas effects may become significant.
Q5: What is the relationship between cone angle and sonic boom intensity?
A: Narrower cone angles (higher Mach numbers) generally result in more focused, intense sonic booms on the ground, though other factors like altitude and vehicle shape also play important roles.