ThermoFluidCalc Engineering Report

Supersonic Conical Shock Wave Analysis (Taylor-Maccoll) — 2026-08-23 20:54:56
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📐 Supersonic Conical Shock (Taylor-Maccoll)

Solve 3D axisymmetric supersonic conical flow, computing attached conical shock wave angle (θs), cone surface Mach (Mc), surface pressure coefficient (Cp), and wave drag (CDw).

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
📊 Solver Telemetry ● ACTIVE
👁️ Consultations 43
⚡ Calculs faits 36
💾 Téléchargements 260 📦 Code Fortran 4.4 KB
📅 Mise en service Jun 2026
⏱️ Latence < 1 ms
⚡ Outils & Rapports :
💾 Télécharger Fortran 90

📐 Supersonic Axisymmetric Cone & Attached Conical Shock Wave

Real-time visual simulation of 3D conical flow streamlines deflecting across Taylor-Maccoll shock cone

📝 Configuration & Presets

🚀 Missile Cone (Mach 2.5, 15°) 🎯 Interceptor (Mach 4.0, 20°) ⚡ Hypersonic Sharp (Mach 6, 10°) ✈️ Pitot Probe (Mach 1.8, 12°)
🚀 Upstream Flow & Gas
Air / Diatomic gas: 1.40
📐 Cone Geometry
Typical sharp nose: 5° to 30°
Taylor-Maccoll Conical Formulations:
• Conical Shock Angle: θs < βwedge (3D relief effect)
• Surface Pressure Coeff: Cp = (Pc − P₁) / (½ γ P₁ M₁²)
• Conical Wave Drag: CD,wave = Cp (referenced to base area)
• Shock Jump: P₂/P₁ = [ 2γ (M₁ sin θs)² − (γ−1) ] / (γ+1)

📊 Conical Aerodynamic Results

📊 Output Summary
💾 Fortran Source

Conical Shock Wave Angle (θs)
θs = 12.50°
Cone Surface Mach: Mc = 5.10 | Pressure Coeff: Cp = 0.045
CDw = 0.045
Surface Pressure Coefficient (Cp) 0.045 Static Cp on cone body
Cone Wave Drag Coefficient (CDw) 0.045 Based on frontal area
Shock Static Pressure Ratio (P₂/P₁) 1.80 Normal shock component
Shock Density Ratio (ρ₂/ρ₁) 1.51 Across conical shock

📈 Conical Shock Angle θ_s (deg) vs Upstream Mach M₁

📉 Wave Drag Coeff C_Dw vs Cone Half-Angle θ_c (deg)

=================================================================
 THERMOFLUIDCALC — SUPERSONIC CONICAL SHOCK (TAYLOR-MACCOLL) REPORT
=================================================================
Case Title                 : Hypersonic Sharp Conical Flight Body (Mach 6.0, 10°)
Upstream Mach (M1)         : 6.00 (gamma = 1.40)
Cone Half-Angle (theta_c)  : 10.00 degrees
-----------------------------------------------------------------
CONICAL SHOCK ANGLE (ts)   : 12.50 degrees (Attached 3D shock)
Cone Surface Mach (Mc)     : 5.10
Surface Pressure Coeff Cp  : 0.0446
Cone Wave Drag Coeff CDw   : 0.0446 (Base area reference)
Shock Static Pressure P2/P1: 1.80
Shock Density Ratio r2/r1  : 1.51
=================================================================

📘 Calculation Methodology & Taylor-Maccoll Standards

3D Axisymmetric Conical Relief

Unlike a 2D planar wedge where flow behind the shock is uniform, flow past a cone undergoes continuous isentropic 3D expansion between the shock and cone surface:

θs,cone < βwedge & Pcone < Pwedge

Taylor-Maccoll Differential Solution

Ray velocity $V_r(\theta)$ and tangential velocity $V_\theta(\theta)$ obey the non-linear ODE subject to tangency $V_\theta(\theta_c) = 0$ at the cone wall.

Key Engineering Assumptions

  • Attached conical shock wave ($M_1 > 1.1$, $\theta_c < \theta_{c,max}$).
  • Calorically perfect inviscid gas ($\gamma = 1.40$).
  • Zero angle of attack ($\alpha = 0^\circ$ axisymmetric alignment).