Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Lift: generated by pressure difference between upper and lower surfaces. Camber: curvature of mean line, increases lift at zero angle of attack. Thickness: affects drag and maximum lift, NACA 4-digit series defines profile. Angle of attack: increasing AoA increases lift until stall. Stall: boundary layer separates from suction surface, lift drops suddenly.
Lift coefficient: CL = 2 pi times alpha for thin symmetric airfoil. Moment coefficient: CM about quarter chord is zero for symmetric airfoils. Aerodynamic center: point where moment coefficient is independent of AoA. Camber effect: adds lift at zero AoA proportional to maximum camber.
Pressure drag: form drag from pressure distribution, reduced by streamlining. Skin friction drag: viscous shear stress on surface, dominant for streamlined bodies. Induced drag: due to finite wing span, CDi = CL squared over pi AR e. Wave drag: energy lost to shock waves in transonic and supersonic flow. Drag polar: CD vs CL squared, slope is 1 over pi AR e.
Mach number: M = V over a, ratio of flow speed to speed of sound. Critical Mach: freestream Mach where local sonic flow first appears. Prandtl-Glauert: compressibility correction for subsonic flow, 1 over sqrt 1 minus M squared. Shock waves: normal and oblique, pressure rises discontinuously. Expansion fans: isentropic acceleration around convex corners.
| Pitfall | Fix |
|---|---|
| Applying thin airfoil theory at high AoA | Valid only for small angles, below stall |
| Ignoring compressibility near Mach 0.3 | Apply Prandtl-Glauert correction above M=0.3 |
| 2D analysis for finite wing | Apply finite wing correction for induced drag |
| Inviscid analysis near separation | Use viscous solver for high AoA or bluff bodies |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level analytical chemistry knowledge. Use when working with chromatography, spectroscopy, electroanalytical methods, sample preparation, quantitative analysis, calibration, statistics, or instrumental analysis. Also use when the user mentions 'HPLC', 'GC', 'mass spectrometry', 'atomic absorption', 'ICP', 'titration', 'calibration curve', 'detection limit', 'NMR', 'chromatography', 'electrochemistry', 'sample preparation', or 'method validation'.
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