Detachment Distance Of Sphere Cone Body Shape Calculator

Formula Used:

\[ \text{Local Shock-detachment Distance} = \text{Radius} \times 0.143 \times \exp\left(\frac{3.24}{\text{Mach Number}^2}\right) \]

Local Shock-detachment Distance:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Local Shock-detachment Distance?

The Local Shock-detachment Distance is the distance of shock formation from the leading edge of a sphere cone body shape in supersonic flow. It represents the point where the shock wave detaches from the body surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Local Shock-detachment Distance} = \text{Radius} \times 0.143 \times \exp\left(\frac{3.24}{\text{Mach Number}^2}\right) \]

Where:

Radius — The radius of the sphere cone body shape (m)
Mach Number — The ratio of flow velocity to local speed of sound
exp — Exponential function

Explanation: This formula calculates the distance at which the shock wave detaches from the leading edge based on the body radius and flow Mach number.

3. Importance of Shock-detachment Distance Calculation

Details: Accurate calculation of shock-detachment distance is crucial for aerodynamic design, understanding flow separation patterns, and predicting pressure distribution around sphere cone body shapes in supersonic flows.

4. Using the Calculator

Tips: Enter the radius in meters and Mach number. Both values must be positive numbers (radius > 0, Mach number > 0).

5. Frequently Asked Questions (FAQ)

Q1: What factors affect shock-detachment distance?
A: The primary factors are the body radius and the flow Mach number. Higher Mach numbers generally result in smaller detachment distances.

Q2: How accurate is this formula?
A: This empirical formula provides reasonable estimates for sphere cone body shapes in typical supersonic flow conditions, but actual results may vary based on specific flow conditions and body geometry.

Q3: Can this formula be used for other body shapes?
A: This specific formula is designed for sphere cone body shapes. Other body shapes may require different formulas or computational methods.

Q4: What are typical values for shock-detachment distance?
A: The distance varies significantly with Mach number and body size, typically ranging from fractions of the radius to several times the radius.

Q5: How does temperature affect the calculation?
A: Temperature effects are indirectly accounted for through the Mach number, which depends on the local speed of sound that varies with temperature.