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Contrary to popular belief, and notwithstanding two hundred years of scientific study (Gruntman , 2004), the problem of accurately predicting rocket ascent remains largely unsolved. The difficulties trace to a variety of altitude-, speed-, and launch-site-dependent random forces that act during rocket ascent, including: i) aerodynamic forces (Sutton & Biblarz, 2001), ii) forces due to wind and atmospheric turbulence (Flemming et al., 1988; Justus & Johnson, 1999; Justus et al., 1990; Leahy, 2006), iii) forces produced by rocket construction imperfections (Schmucker, 1984), and iv) impacts with air-borne animals and debris (McNaughtan, 1964). Significantly, our physical understanding and ability to model the dynamical effects of each of these random features is fairly well-developed. By contrast, understanding of the physical origins, as well as the dynamical effects of altitude-dependent, in-nozzle random side loads, has only recently begun to emerge (Keanini et al., 2011; Ostlund, 2002; Srivastava et al., 2010). Referring to figures 1 through 3, we find that side loads represent the end result of a chain of in-nozzle fluid dynamic processes. During low altitude flight, under over-expanded flight conditions, a pressure gradient can exist between the high pressure ambient air surrounding the rocket and nozzle, and the low pressures extant within the nozzle. This pressure gradient can force ambient air upstream along the nozzle wall; eventually, inertia of the ambient inflow is overcome by the pressure and inertial forces associated with the outflow, producing a near-wall recirculation region. To the supersonic flow outside the near-wall boundary layer, the recirculation zone functions as a virtual compression corner, producing an oblique shock (Keanini & Brown, 2007; Ostlund, 2002; Summerfield et al., 1954). See figures 1 through 3. Due to the altitude dependence of Pa = Pa(H(t)), where Pa is the ambient pressure and H(t) is the rocket’s time-dependent altitude, the nominal location of the oblique shock, xshock = xshock(H(t)), also varies with altitude. Random side loads arise due to two coupled flow features: i) The oblique shock produces a sharp, adverse pressure rise within the near-wall outflow boundary layer, forcing the boundary layer to separate from the nozzle wall; see figure 1. ii) The shape of the boundary Shock-Induced Turbulent Boundary Layer Separation in Over-Expanded Rocket Nozzles: Physics, Models, Random Side Loads, and the Diffusive Character of Stochastic Rocket Ascent 7

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Shock-Induced Turbulent Boundary Layer Separation in Over-Expanded Rocket Nozzles: Physics, Models, Random Side Loads, and the Diffusive Character of Stochastic Rocket Ascent