Aerodynamics — ForgeCalc

Fluid & Freestream Conditions

Shared by all modules below. Defaults are sea-level ISA air (15 °C). γ = 1.4, R = 287 J/kg·K.

Density ρ (kg/m³)

Dynamic viscosity μ (Pa·s)

Temperature T (K)

Kinematic ν = μ/ρ (m²/s)

① Flow Parameters & Regimes

Reynolds, Mach, dynamic pressure, Strouhal shedding, and Knudsen for the freestream above.

Velocity v (m/s)

Characteristic length L (m)

Strouhal number St (cyl ≈ 0.21)

Mean free path λ (m, for Kn)

Formulas & regime thresholds

Re = ρvL/μ · flat-plate BL: laminar Re < 2×10⁵, turbulent > 5×10⁵, fully turbulent > 10⁷.

a = √(γRT), Ma = v/a · incompressible OK to Ma ≈ 0.3; subsonic <0.8, transonic 0.8–1.2, supersonic 1.2–5, hypersonic >5.

q = ½ρv² (dynamic pressure) · f = St·v/L (vortex shedding) · Kn = λ/L (continuum <0.01, slip 0.01–0.1, transitional 0.1–10, free-molecular >10).

② Wing Lift & Drag — Drag Polar

Finite-wing lift slope with induced downwash, lift & drag forces, and the drag polar C_D = C_D0 + C_L²/(πe·AR).

Velocity v (m/s)

Wing area S (m²)

Span b (m)

Oswald efficiency e

Angle of attack α (deg)

Zero-lift angle α₀ (deg)

2-D lift slope a₀ (per rad)

Parasite drag C_D0

Formulas

AR = b²/S · 3-D lift slope a = a₀/(1 + a₀/(πe·AR)) · C_L = a·(α − α₀) [rad].

L = ½ρv²S·C_L · induced C_Di = C_L²/(πe·AR) · C_D = C_D0 + C_Di · D = ½ρv²S·C_D · L/D = C_L/C_D.

Thin symmetric airfoil: C_L = 2πα. Stall at the critical angle (~15–20°) — this linear model does not capture it. Elliptic e=1, tapered ≈0.9, rectangular ≈0.8.

③ Boundary Layer — Flat Plate

Laminar (Blasius) and turbulent (1/7-power) flat-plate correlations: thickness, skin friction, displacement thickness, and transition location.

Freestream U (m/s)

Distance from LE, x (m)

Transition Reynolds (Re_x,tr)

Formulas

Re_x = ρUx/μ · transition at x_tr = Re_x,tr·μ/(ρU).

Laminar (Blasius): δ = 5x/√Re_x, δ* = 1.721x/√Re_x, θ = 0.664x/√Re_x, c_f = 0.664/√Re_x.

Turbulent (1/7-power): δ = 0.37x/Re_x^0.2, c_f = 0.0592/Re_x^0.2, δ* ≈ δ/8.

Wall shear τ_w = c_f·½ρU². Turbulent BL has higher friction but resists separation (fuller profile — the golf-ball-dimple effect).

Built from the vault Aerodynamics deep dive. First-order analytical models. For compressible nozzle flow, isentropic relations, and normal shocks see the Compressible Flow & Nozzle page; for hover/propeller performance see Rotor & Propeller.