Evolution of airplane gust loads design requirements

Abstract

Nomenclature a = lift curve slope, per rad #„, bn — Fourier series coefficients for e.g. acceleration c = wing mean geometric chord, ft FK — flight profile alleviation factor FKm = flight profile factor due to airplane weight FKZ = flight profile factor due to altitude g = acceleration due to gravity, 32.2 ft/s g;j, hn = Fourier series coefficients for true gust velocity H = gust gradient distance, ft K, KK = gust load alleviation factors L = scale of turbulence, ft M = Mach number q = dynamic pressure, psf /?, = maximum landing weight/maximum takeoff weight R2 = maximum zero fuel weight/maximum takeoff weight S = wing area, ft s = distance along flight path, ft T = local atmospheric temperature, °R 7,,, /„ = real and imaginary parts of the e.g. acceleration transfer function T() = ambient atmospheric temperature, °R U = gust velocity, fps, true airspeed (7dc = derived equivalent gust velocity, fps, equivalent airspeed (7ds = design gust velocity, fps, equivalent airspeed £/dt = derived true gust velocity, fps, true airspeed £/rct = design reference gust velocity, fps, equivalent airspeed Utr = power spectral scale factor V = aircraft velocity, fps, true airspeed VB = rough air penetration speed, Kt, equivalent airspeed Vc = design cruise speed, Kt, equivalent airspeed VD = design dive speed, Kt, equivalent airspeed W = aircraft weight, Ib Zmo = maximum operating altitude, ft y = ratio of specific heats Aft = incremental load factor, g fjif, = airplane mass parameter p = air density, slugs/ft Introduction S UBSONIC aircraft respond to atmospheric turbulent air motions or eddies of, approximately, 30-2000 ft in extent. Smaller eddies will generally be averaged out over the surface of the aircraft, larger eddies typically will not cause sharp or excessive aircraft accelerations or structural loads on the airplane. Aircraft in supersonic flight respond to ever longer wavelengths as the flight speed is increased. From the aircraft design standpoint, atmospheric turbulence may be separated into two categories: 1) turbulence, which contributes to aircraft structural fatigue and passenger inconvenience and discomfort, is generally associated with the less intense, smaller scales (small eddy size or higher spatial frequencies as characterized by the turbulence power spectrum); and 2) turbulence that can cause aircraft upset, passenger injury, and possibly structural damage or failure is associated with the more intense larger scales of the turbulence spectrum. Whereas the first category may be in the inertial subrange of the turbulence power spectrum where local homogeneity and stationarity may be assumed, the second category is definitely associated with the larger energy-containing scales of turbulence that are definitely nonstationary and inhomogeneous. In fact, the second type of atmospheric turbulence may not be turbulence at all, but may be a part of, or derive directly from, the ordered convective or geostrophic motions of the atmosphere. Frictionally induced turbulence in the planetary boundary layer is dependent on wind speed near the ground and the surface roughness. Convective turbulence in the planetary boundary layer is dependent on the lapse rate (the rate of temperature change with altitude) and the depth of the mixing layer. Thus, the wind speed and surface roughness and the lapse rate and mixing layer thickness largely determine the intensity and scale of the boundary-layer turbulence. This low altitude boundary-layer turbulence will affect landing and takeoff operations for the larger commercial aircraft that normally cruise at high altitude, and it will be the primary cause of disturbance for small aircraft that operate at low altitudes. Usually, it can be characterized as random, locally stationary, and Gaussian, and the turbulence scale at the surface is of the order of 1000 ft and increases with altitude. It is only natural that pilots avoid flying into areas of obviously rough air such as thunderstorms or even cumulus clouds;