✈️ Airfoil Vortex Panel & Induced Drag

Compute NACA 4-digit airfoil lift coefficient (CL), induced drag (CDi), parasitic drag (CD0), lift-to-drag ratio (L/D), and pitching moment using lumped vortex panel theory.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

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⚡ Solves 30

💾 Downloads 410 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

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✈️ Cambered NACA Airfoil & Bound Vortex Circulation Field

Real-time visual simulation of angle of attack pitch, suction surface acceleration & trailing edge Kutta condition

📝 Configuration & Presets

🛩️ NACA 2412 (General Aviation) 🚁 NACA 0012 (Symmetric) 🛬 NACA 4415 (High-Lift STOL) 🦅 Sailplane (AR = 22)

📐 Wing Geometry & Flight Attitude

Chord Length c [mm]:

Wing Aspect Ratio AR:

Angle of Attack α [degrees]:

Oswald Efficiency Factor e:

🧪 NACA 4-Digit Airfoil Profile

Max Camber m [% chord]: 1st digit (e.g. 2 for 2%)

Camber Position p [tenths]: 2nd digit (e.g. 4 for 40%)

Max Thickness t [% chord]: Last 2 digits (e.g. 12 for 12%)

Lifting-Line Formulations:
• 3D Lift Slope: C_Lα = a₀ / [ 1 + a₀ / (π AR) ]
• Lift Coeff: C_L = C_Lα (α − α₀_L)
• Induced Drag: C_Di = C_L² / (π e AR)
• Total Drag: C_D = C_D0 + C_Di | L/D = C_L / C_D

📊 Airfoil Aerodynamic Results

📊 Output Summary
💾 Fortran Source

Aerodynamic Efficiency (L/D)

L / D = 15.9

Lift Coeff: C_L = 1.221 | Total Drag: C_D = 0.0767

α = 8.0°

Induced Drag (C_Di) 0.0681 88.7 % of total drag

Parasitic Profile Drag (C_D0) 0.0086 Skin friction + form

Zero-Lift Angle of Attack (α_0L) -4.60° Camber effect

Quarter-Chord Moment (C_M,c/4) -0.0377 Pitching moment

📈 Lift Coefficient C_L vs Angle of Attack α (deg)

📉 Drag Polar: Lift C_L vs Total Drag C_D

=================================================================
 THERMOFLUIDCALC — AIRFOIL VORTEX PANEL AERODYNAMICS REPORT
=================================================================
Case Title                 : NACA 4415 High-Lift STOL Utility Aircraft Wing
Wing Planform              : Chord = 1800 mm, Aspect Ratio AR = 8.5, Oswald e = 0.82
NACA Profile Definition    : NACA 4415 (m = 4.0%, p = 0.4, t = 15%)
Operating Angle of Attack  : 8.00 degrees (Zero-lift alpha0 = -4.60 deg)
-----------------------------------------------------------------
LIFT COEFFICIENT (CL)      : 1.2209
TOTAL DRAG COEFF (CD)      : 0.07672
Parasitic Skin Drag (CD0)  : 0.00865
Induced Vortex Drag (CDi)  : 0.06807 (88.7% of CD)
LIFT-TO-DRAG RATIO (L/D)   : 15.91
Pitching Moment (CM_c/4)   : -0.0377
3D Lift Slope (dCL/dalpha) : 0.0969 per degree
=================================================================

📘 Calculation Methodology & Airfoil Theory Standards

Lumped Vortex & Lifting-Line Theory

Thin airfoil theory replaces the mean camber line with a distributed bound vortex sheet satisfying the Kutta condition at the sharp trailing edge:

                    CL = 2π (1 + 0.77 t/c) [ α − α0L ] / [ 1 + 2/AR ]
                

Induced Drag & Aspect Ratio

Tip vortices generated by finite span create downwash $w$, tilting the lift vector backward and producing vortex-induced drag $C_{Di} = C_L^2 / (\pi e AR)$.

Key Engineering Assumptions

Incompressible subcritical flow ($Mach < 0.3$).
Pre-stall linear attached flow regime ($\alpha < 14^\circ$).
Standard NACA 4-digit analytical thickness and camber distributions.

ThermoFluidCalc Engineering Report