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Supersonic Conical Shock Wave Angle & Detachment Calculator

Conical supersonic flow exhibits 3D relieving effects compared to 2D planar wedge flows, resulting in weaker attached shocks and lower drag.

Approach supersonic flight Mach number

Semi-apex angle of conical body

Calculated Result
28 °

Conical Shock Angle (β)

Cone Half-Angle (θ)

20 °

Calculation Breakdown

  1. Taylor-Maccoll Fitβ ≈ 28°

Shock Angle vs Flight Mach

Interactive visualization based on your current inputs

β
0.08.3172533Mach 2.0Mach 3.0Mach 4.5Mach NumberShock Angle β (°)

What Is the Supersonic Conical Shock Wave Angle & Detachment Calculator?

Conical supersonic flow exhibits 3D relieving effects compared to 2D planar wedge flows, resulting in weaker attached shocks and lower drag.

G. I. Taylor and J. W. Maccoll formulated the governing non-linear ordinary differential equations for conical flow fields.

How Does the Supersonic Conical Shock Wave Angle & Detachment Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Supersonic Conical Shock Wave Angle & Detachment Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\beta \approx \theta + \frac{30}{M_\infty^{1.2}} \quad [\text{approximate attached fit}]

Conical shock wave angle relation.

How to Use the Supersonic Conical Shock Wave Angle & Detachment Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

Hypersonic Re-entry Forebody

Input Values:

freestreamMachM:4.0
coneHalfAngleDeg:15.0

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Shock wave angle β is smaller than that of a planar wedge with the same half-angle.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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