Radius For Cylinder-Wedge Body Shape Calculator

Formula Used:

\[ r = \frac{R_{curvature}}{1.386 \times \exp\left(\frac{1.8}{(M_r - 1)^{0.75}}\right)} \]

Radius:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radius For Cylinder-Wedge Body Shape Formula?

The formula calculates the radius for a cylinder-wedge body shape using the radius of curvature and Mach number. This is particularly important in aerodynamics and fluid dynamics for analyzing flow patterns around specific body shapes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{R_{curvature}}{1.386 \times \exp\left(\frac{1.8}{(M_r - 1)^{0.75}}\right)} \]

Where:

\( r \) — Radius (m)
\( R_{curvature} \) — Radius of Curvature (m)
\( M_r \) — Mach Number
\( \exp \) — Exponential function

Explanation: The formula accounts for the relationship between curvature radius, Mach number, and the resulting radius for cylinder-wedge body shapes in supersonic flow conditions.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for aerodynamic design, particularly in supersonic and hypersonic flow regimes where shock waves and expansion fans significantly affect flow patterns around body shapes.

4. Using the Calculator

Tips: Enter radius of curvature in meters and Mach number as a dimensionless quantity. Both values must be positive numbers with Mach number greater than 1 for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: Why is this formula specific to cylinder-wedge body shapes?
A: The formula is derived from empirical data and theoretical analysis specific to the aerodynamic characteristics of cylinder-wedge configurations in supersonic flow.

Q2: What range of Mach numbers is this formula valid for?
A: The formula is primarily valid for supersonic Mach numbers (typically >1.2) where the assumptions about shock wave formation hold true.

Q3: How accurate is this calculation method?
A: The formula provides good approximation for preliminary design calculations, though computational fluid dynamics may be needed for precise analysis.

Q4: Are there limitations to this equation?
A: The formula may be less accurate at very high Mach numbers or for body shapes that significantly deviate from the ideal cylinder-wedge configuration.

Q5: Can this be used for subsonic flow conditions?
A: No, this formula is specifically derived for supersonic flow conditions where Mach number effects dominate the flow behavior.