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Aerodynamics studies the motion of gases and their interaction with moving or stationary bodies. The resulting surface pressure and viscous stress determine lift and drag on an aircraft, a turbine blade or a moving vehicle.

A useful model depends on dimensionless comparisons. The Reynolds number compares inertial and viscous effects; the Mach number compares flow speed with the speed of sound. Low Mach number can justify an approximately incompressible flow, whereas transonic and supersonic motion may produce shock waves. A wing's lift follows from the complete pressure and momentum balance, rather than a requirement that air parcels passing above and below reunite simultaneously.

A German mathematician whose 1900 doctoral work, published in 1901, developed methods for approximate integration of ordinary differential equations. His name is paired with Carl Runge in the Runge-Kutta method. Evaluating several trial slopes within one step improves the approximation without requiring explicit higher derivatives of the solution.

He also worked on aerodynamics, motivated by the mathematical description of aircraft. The Kutta–Joukowski theorem relates lift to circulation around an aerofoil in its idealized flow model. His numerical integration and aerodynamic research both connect mathematical equations with quantities engineers need to calculate. ^[ref]

Homepage: mathshistory.st-andrews.ac.uk/Biographies/Kutta/