Entry Guidance Using Analytical Atmospheric Skip Trajectories

A TMOSPHERIC skip-entry trajectories were designed for the Apollo lunar missions [1] and are being considered again for new vehicles with similar low-lift-to-drag L=D ratios [2]. A skip entry begins at entry interface (EI) with hyperbolic or nearhyperbolic speed and shallow flight-path angle, and the aerodynamic lift force is used to continually rotate the velocity vector upward until the vehicle exits the sensible atmosphere. After atmospheric exit, the vehicle follows a Keplerian coast arc until it reenters the atmosphere. Skip-entry trajectories offer the advantage of downrange control by targeting a desired exit state (velocityVexit and flight-path angle exit) at atmospheric skip-out. Bank angle is the single control variable during entry, and rotating the vehicle about its velocity vector modulates the vertical component of the aerodynamic lift force. The Apollo entry guidance system used closed-form trajectory solutions to predictVexit and exit, and these analytical equations were developed by applying simplifying approximations to the nonlinear equations ofmotion [3]. Total downrange distance was computed by piecing together range estimates for the initial atmospheric skip path, the Keplerian coast arc, and the final atmospheric flight after reentry. Bank angle was adjusted until the predicted downrange distance matched the range-to-go. Although the Apollo entry guidance method proved to be very successful, it had limited range-prediction accuracy (its maximum range capability was set at 2500 n mile, or a great-circle arc of about 41 deg) [3]. Current design goals for a new low-L=D vehicle include extending range capability for abort scenarios and other contingencies. Bairstow [4] and Brunner and Lu [5] both developed numerical predictor–corrector guidance methods that propagate the skip trajectory forward in time by numerically integrating the full nonlinear equations of motion. Bank angle is adjusted in an iterative fashion until the predicted range matches the range-to-go. The predictor–corrector guidance schemes in [4,5] successfully produce skip trajectories with maximum downrange distances of 5400 n mile (90-deg range angle) and 4300 n mile (72-deg range angle), respectively. This Note presents a guidance method based on analytical entry trajectories. The skip-entry phase is predicted by using closed-form expressions that are derived from a matched asymptotic expansion analysis [6–10]. Trajectory planning for the atmospheric skip is accomplished by iterating on the verticalL=D component until the desired downrange distance is produced. Numerical results are presented to demonstrate the effectiveness of the guidance method.