Perpetual Dynamic Soaring in Linear Wind Shear

CL, CD, CD0 = lift coefficient, drag coefficient, and drag coefficient with zero lift DSi = dynamic soaring number sample E, Emin = aircraft total energy and minimum sustainable total energy, J g = gravity acceleration, m∕s h, hmin = altitude and safety altitude, m K = drag-polar-induced drag gain k1, k2, k3 = necessary and sufficient conditions inequality parameters L, D = lift and drag forces, N L∕D, L∕D max = lift-to-drag ratio and maximum lift-to-drag ratio MCi = uniform distribution sample for Monte Carlo sampling m = mass, kg N = sample size S = wing area, m Va, Vmin = airspeed and stall airspeed, m∕s w, W,Wx;y;z = wind velocity vector, speed, and velocity components in x, y, and z, m∕s X, Xi = random variable and sample x, y, z = position coordinates, m _ x, _ y, _ z = velocity components in the ground frame, m∕s x, y, z = acceleration components in the ground frame, m∕s β = experimental verification confidence level γa = flight-path angle relative to the air, rad ∂wLWS∕∂h = wind gradient vector, s−1 ε = experimental verification margin of error μ, σ = random variable mean and standard deviation ρ = fluid (air) density, kg∕m φ = bank angle, rad ψ , ψW , ψdW = aircraft heading angle, wind direction, and wind gradient direction, rad