Deriving Lift and Drag: An Angular Momentum Application

Earlier papers derived angular momentum as the complete description of motion, with linear momentum as its projection onto a line (From Energy to Angular Momentum, DOI 10.5281/zenodo.24125261), and showed that air passing a surface unevenly changes the surface's measured weight (Center of Mass Shifts, DOI 10.5281/zenodo.24049629). The sticking is mutual: air held down to a surface is the surface held up to the air, the no-slip condition. Along a surface moving through air, the air is caught, slips, and is caught again. The slips build the slipping layer, and its thickness cancels. What remains is an outward motion toward the air that grows as the square of the air's speed past each patch: ṗ = ½ρu²A cos φ. Air catches air catches surface, which sets the factor at one half. The outward motion's vertical net over both faces is lift. Per unit span, L = ½ρ ∫ (u_t² − u_b²) dx along the chord. A tilted plate's faces differ because the bottom face advances into the air beneath it while the top face leaves room above it. The air's molecules, always moving, fill that room from the front, so the top face passes its air faster. Read along the stream, the same catches give drag: the outward motion's streamwise net and the carry along the surface. On Fage and Johansen's flat plate at 3°, 6°, and 9°, the calculated lift coefficient is 0.328, 0.650, and 0.959 against 0.330, 0.686, and 0.879 measured. A simple bubble at the leading edge brings it to within 1.2%. Past the plate's peak, at 15° and 20°, the bubble narrows the overshoot from 85% and 115% to 18% and 40%. Dividing the lift by ½ρU²X gives the lift coefficient, so existing toolchains can take it from the outward motion instead of from a wind tunnel.