There is a need for a rapid method of defining and modifying trajectories for time-dependent analysis of aircraft maneuvers and spacecraft launch and recovery. Normal aircraft missions are readily modeled in an analytical domain, as typified by the Breguet range equation and similar mathematical approaches. These aren’t usable for complicated trajectories such as a pull-up, climb, parabolic pushover, and recovery to level flight as might be used by a carrier aircraft releasing a Pegasus-like launch vehicle. No equation can directly model this – it takes a simulation.
For launch vehicles, a simple vertical launch trajectory can be modeled by a time-dependent code using AOA or pitch rate optimization to attain a target flight path angle at engine cutoff. However, many launch vehicles trajectories will require complicated guidance logic that depends upon events determined “on the fly.” For example, the Pegasus-like launch vehicle might be dropped from its carrier aircraft at a certain speed and altitude, coast for 5 seconds while the carrier banks away, start its motors and accelerate in level flight until a certain speed is reached, pull up at 2 g’s until a desired climb angle is reached, climb at that angle until free of the atmosphere, then arc over to a desired burnout angle. Again, this takes a simulation.
These sorts of trajectories can be modeled in a high-end code like POST or OTIS, but it takes an expert a considerable amount of time to define the trajectory and guidance logic. Alternatively, a complicated aircraft or spacecraft trajectory can be “flown” by the analyst in a real time simulation, but that isn’t likely to be optimal nor is it exactly repeatable. Also, the results depend upon the piloting skills of the analyst.
So, there is a need for a scheme that lets you quickly build and run a complicated time-domain trajectory. The guidance logic should be defined in an intuitive, vehicle-related manner, and should be tied to an easy-to-build flight vehicle data file that can be readily changed for trade studies.
A method called “Trajectory Script” was developed to fill this need. It has been implemented in the ROAST trajectory module of the RDSwin aircraft design and analysis software, but could be applied to any time-dependent trajectory analysis. This methodology will be discussed in the remainder of this paper.
The RDSwin-Professional12 aircraft design software, developed by this author and marketed through Conceptual Research Corporation, is an integrated design environment which includes a design layout module for concept development, analysis modules for aerodynamics, weights, propulsion, stability, cost, performance, range, sizing, and optimization. The technical methods employed in RDS are largely based on those described in this author’s textbook Aircraft Design: A Conceptual Approach.
ROAST is the flight simulation and launch trajectory analysis module of RDSwin-Pro. ROAST determines what an airplane or aerospace vehicle will do in response to various control inputs from an initial starting speed and altitude. For launch vehicles, it determines speeds and altitudes that can be reached with a given amount of fuel/propellant. The program outputs a large table (figure 1) detailing the simulation second-by-second, including speed, altitude, angle of attack, flight path angle, dynamic pressure, distance, weight, fuel burn, and more. ROAST also graphs the results including altitude vs. distance, velocity vs. time, and many more.
While deliberately not as sophisticated as the industry-standard POST and OTIS trajectory codes, ROAST has faired well in calibration comparisons to POST and is far simpler to set up and run. This makes it an ideal tool for initial evaluations and parametric trade studies, but it should not be relied upon for “final” answers.
II.Trajectory Script Overview
ROAST includes four automatic guidance schemes suitable for launch trajectories, namely Minimize AOA, Set AOA, Find Pitch Rate, and Set Pitch Rate. ROAST also allows the user to “fly” the vehicle in real time, using a joystick or arrow keys to control angle of attack. During real-time operation the user can also bring up a menu of autopilot guidance commands such as angle of attack hold or climb angle seek.
The Trajectory Script method allows specifying a sequence of those autopilot guidance commands. These are implemented in response to “triggers” based on what the vehicle is doing during its flight. Using a Trajectory Script, the guidance commands for the air-dropped Pegasus-like vehicle described above can be defined in just a few minutes, then run in ROAST in a few seconds more.
A Trajectory Script is just a text file. It can be created and modified with any text editor, including one as simple as MS NotePad. In the ROAST implementation of RDSwin, a new or existing Trajectory Script is opened in an editable pop-up box when beginning an analysis.
III.Trajectory Script Format
A Trajectory Script is a text file consisting of a series of “Event Triggers” paired with flight control commands. Triggers are greater-than or less-than tests applied to calculated flight parameters such as altitude, velocity, or load factor, or to vehicle status parameters such as fuel weight or drag. When a particular trigger is satisfied, its stated command becomes active. Examples include setting throttle or angle of attack, or tracking a commanded parameter such as climb angle or velocity...