Examples#

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This gallery walks through every public feature of engineeringkit.aerodynamics, one breakthrough per script: dynamic pressure and force coefficients, circulation lift, airfoil sections, finite wings, cruise performance, boundary layers, compressible flow and the standard atmosphere.

Units, assumptions and numerical validation gives the physical validity limits. Each script is self-contained and can be run directly with python examples/aerodynamics/<section>/<script>.py.

Sections#

forces – Bernoulli’s dynamic pressure, Cayley’s lift/drag split, Lilienthal’s coefficients and the Wrights’ correction of Smeaton’s coefficient.
circulation – the Kutta-Joukowski theorem on a spinning cylinder.
airfoils – NACA four-digit sections, thin-airfoil lift and pitching moment, and the Hess-Smith panel method.
wings – Prandtl’s lifting line, Glauert’s Fourier solution, induced drag and the Oswald drag polar.
performance – the jet and propeller Breguet range equations.
boundary_layer – Reynolds similarity, the Blasius layer and turbulent skin friction.
compressible – sound speed, the Mach cone, stagnation states, Prandtl-Glauert, normal and oblique shocks, the Prandtl-Meyer expansion, the de Laval nozzle, and Fanno and Rayleigh duct flow.
atmosphere – the International Standard Atmosphere.

Airfoils#

NACA four-digit section geometry, thin-airfoil lift and pitching moment, and the Hess-Smith panel method.

The NACA four-digit airfoil family (1933)

Thin-airfoil theory: lift slope 2π and the camber shift (1922-1926)

The Hess-Smith panel method (1967)

Thin-airfoil pitching moment and the aerodynamic centre (1922-1926)

Standard atmosphere#

Temperature, pressure and density with altitude.

The International Standard Atmosphere (1919-1952)

Boundary layers#

Reynolds-number similarity and laminar/turbulent flat-plate friction.

Reynolds’ dimensionless number and wind-tunnel similarity (1883)

Reynolds' dimensionless number and wind-tunnel similarity (1883)

Prandtl’s boundary layer and the Blasius solution (1904-1908)

Prandtl's boundary layer and the Blasius solution (1904-1908)

Turbulent skin friction and the one-fifth-power law (1927)

Circulation#

Lift as the product of density, speed and circulation.

The Kutta-Joukowski theorem on a spinning cylinder (1902-1906)

Compressible flow#

Sound speed, Mach waves, isentropic stagnation states, compressibility corrections, normal and oblique shocks, Prandtl-Meyer expansions, nozzles, and Fanno and Rayleigh duct flow.