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Concepts and Challenges for Environmentally Friendly En Route Operations

A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectory is derived using Singular Perturbation Method. The regions of airspace favorable to persistent contrails formation are modeled as high-risk areas that aircraft should avoid and are adjustable. The tradeoffs between persistent contrails formation and additional travel time are investigated for wind-optimal trajectories and various contrails-avoidance trajectories at 10 different cruising altitudes for flights departing from Chicago and San Diego to New York. The additional travel times required for avoiding 100% persistent contrails formation at various flight altitudes ranged from approximately 0% to 4.3% for flights from Chicago to New York. For flights between San Diego and New York, additional traveling times vary between 1.3% and 5% depending on the cruise altitude and the percentage of contrail avoidance. Talk will present the results of aircraft fuel consumptions that are proportional to the travel time for cruising aircraft.

Sridhar, Banavar↗

Space Launch System and Missions to Near Rectilinear Halo Orbits

The first major evolution of NASA’s Space Launch System (SLS) will begin its flights starting in the mid-2020’s. This new configuration, called Block 1B, replaces the Interim Cryogenic Propulsion Stage with a larger Exploration Upper Stage (EUS). The additional capability provided by the new upper stage will allow SLS to send heavier payloads into deep space. One destination of interest to the SLS program is called a Near Rectilinear Halo Orbit (NRHO). This is a type of lunar orbit with multiple advantages for deep space exploration. These benefits include Earth/lunar access, low station-keeping requirements, and high communication potential with Earth. Therefore, it is a leading candidate for the proposed Lunar Orbital Platform-Gateway (LOP-G). This paper will provide a detailed assessment of the SLS Block 1B requirements and capabilities for sending payloads to an NRHO. Analysts at Marshall Space Flight Center are producing a multi-year mission availability scan for the SLS Block 1B configuration to a predefined NRHO orbit. The analysis produces an optimized trajectory for each day of the scan window. A maximized payload and minimized propellant requirement are determined for each day. All maneuvers from launch to the end of the Trans-Lunar-Injection (TLI) are being modeled as finite burns. Injections into an NRHO are being modeled as impulsive maneuvers. The payload element is arbitrary, but includes sufficient mass to represent a large habitat or propulsion module. The resulting parameters of payload capability, delta-v requirements, and launch windows length vary over the course of the scan. Many launch days in the scan are eliminated in post-processing as they violate mission constraints such as payload mass and propellant usage to insert into an NRHO. Based off previous one-year scan results for the SLS Block 1B Design Analysis Cycle 2 (DAC-2), it is expected that there will be one to three days per week where the payload is able to insert into an NRHO within SLS constraints objectives. This scan provides results for longer than one-year, allowing analysts to better understand the launch availability and energy requirements of SLS Block 1B over time. The in-space mission design and scans utilize Copernicus, an n-body trajectory optimization tool originally developed out of the University of Texas at Austin with further development at Johnson Space Center in Houston, TX. To seed the in-space trajectory, Copernicus uses a plugin to call a database of SLS ascent trajectories optimized in the Program to Simulate Optimized Trajectories II (POST2). The ascent trajectories are developed using a framework that parametrizes payload mass and LEO inclination, and targets a 100 nmi (nautical mile) altitude circular parking orbit. Though this analysis is specific to the SLS program, it will provide a summary of mission design benefits and constraints associated with generic NRHO access, and may be applied to other programs or concepts that will utilize this orbit.

Statham, T. L.↗

Performance Analysis and Design Synthesis (PADS) computer program. Volume 3: User manual

The two-fold purpose of the Performance Analysis and Design Synthesis (PADS) computer program is discussed. The program can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general purpose branched trajectory optimization program. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent. The second module uses the method of quasi-linearization, which requires a starting solution from the first trajectory module.

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Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

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Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 1

The Performance Analysis and Design Synthesis (PADS) computer program has a two-fold purpose. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module. For Volume 1 see N73-13199.

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OTIS Modeling of IBEX Flight

When a launch vehicle carries a payload into space, it must follow a very particular trajectory to achieve its desired orbit. Modern rockets have very tight delta-v budgets and many forces work to rob the rocket of energy, placing limits on the performance of the launch vehicle. Trajectory optimization evolved out of this need to economize on every bit of energy of a launch vehicle. Today NASA uses Optimal Trajectory by Implicit Simulation (OTIS) to optimize trajectories based on given parameters. The Interstellar Boundary EXplorer (IBEX) mission profile is unique and required special alterations to the standard OTIS data output.

deZarraga, Gaston↗

Transformation techniques for minimax optimal control problems and their application to optimal flight trajectories in a windshear - Optimal abort landing trajectories

The optimal-control problem of abort-landing trajectories in the presence of low-altitude wind shear is investigated analytically. The vertical-plane Newtonian motion of a point-mass aircraft in a steady wind field is modeled, and a sequential gradient-restoration algorithm is applied. Numerical results showing the effects of wind-shear intensity, initial altitude, and power-setting rate are presented in extensive graphs and discussed in detail. Optimal trajectories for strong or severe wind shears are found to begin with a descent, followed by level flight and then an ascent after leaving the shear region.

Miele, A.↗

Using Wind Observations from Nearby Aircraft to Update the Optimal Descent Trajectory in Real-Time

The ability to meet a controlled time of arrival during a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. However, if the wind forecast used to compute the initial trajectory plan is not accurate enough, the guidance system will need to correct time deviations from the plan during the execution of the descent. Previous work proposed an on-board guidance strategy based on model predictive control, which repeatedly updates the trajectory plan in real-time from the current aircraft state and for the remainder of the descent. However, the wind conditions downstream, at altitudes not explored yet, were difficult to predict due to the lack of data. This paper shows the potential benefits of using wind observations, broadcast by nearby aircraft, to reconstruct the wind profile downstream. The wind profile in the trajectory optimization problem is modeled as a spline, which control points are updated to fit the observations before re-planning the trajectory. Results from simulations using realistic wind data show that the performance of model predictive control significantly improves when including up-to-date wind observations, in terms of time and energy errors at the metering fix and fuel consumption.

Dalmau, Ramon↗

Feedback laws for fuel minimization for transport aircraft

The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

Price, D. B.↗

Comparison of Low-Thrust Control Laws for Application in Planetocentric Space

Recent interest at NASA for the application of solar electric propulsion for the transfer of significant payloads in cislunar space has led to the development of high-fidelity simulations of such missions. With such transfers involving transfer times on the order of months, simulation time can be significant. In the past, the examination of such missions typically began with the use of lower-fidelity trajectory optimization tools such as SEPSPOT to develop and tune guidance laws which delivered optimal or near- optimal trajectories, where optimal is generally defined as minimizing propellant expenditure or time of flight. The transfer of these solutions to a high-fidelity simulation is typically an iterative process whereby the initial solution may nearly, but not precisely, meet mission objectives. Further tuning of the guidance algorithm is typically necessary when accounting for high-fidelity perturbations such as those due to more detailed gravity models, secondary-body effects, solar radiation pressure, etc. While trajectory optimization is a useful method for determining optimal performance metrics, algorithms which deliver nearly optimal performance with minimal tuning are an attractive alternative.

SOLAR ELECTRIC PROPULSION↗

Effect of Aeropropulsive Interactions and Design Sensitivities on Optimal Hypersonic Ascent Trajectories

In this paper, trajectory optimization is used as a tool to better understand the performance characteristics of hypersonic Single-Stage-To-Orbit(SSTO) vehicle exhibiting significant aeropropulsive interactions. The energy state approximation is used to determine a straightforward method of determining the scramjet-powered phase of the mission. The energy state method is then used to generate fuel-optimal trajectory results over this portion of the mission for a vehicle configuration of this class. The fuel-optimal unconstrained trajectory is marked by low-altitude acceleration, while a dynamic pressure-constrained trajectory is seen to ride the dynamic pressure constraint for the entire scramjet mission phase. The significance of aeropropulsive interactions in affecting vehicle performance is also investigated.

Lovell, T. Alan↗

Helicopter trajectory planning using optimal control theory

A methodology for optimal trajectory planning, useful in the nap-of-the-earth guidance of helicopters, is presented. This approach uses an adjoint-control transformation along with a one-dimensional search scheme for generating the optimal trajectories. In addition to being useful for helicopter nap-of-the-earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and the threat envelopes are incorporated in the equations of motion. Second-order necessary conditions are examined.

Menon, P. K. A.↗

Autorotation flight control system

The present invention provides computer implemented methodology that permits the safe landing and recovery of rotorcraft following engine failure. With this invention successful autorotations may be performed from well within the unsafe operating area of the height-velocity profile of a helicopter by employing the fast and robust real-time trajectory optimization algorithm that commands control motion through an intuitive pilot display, or directly in the case of autonomous rotorcraft. The algorithm generates optimal trajectories and control commands via the direct-collocation optimization method, solved using a nonlinear programming problem solver. The control inputs computed are collective pitch and aircraft pitch, which are easily tracked and manipulated by the pilot or converted to control actuator commands for automated operation during autorotation in the case of an autonomous rotorcraft. The formulation of the optimal control problem has been carefully tailored so the solutions resemble those of an expert pilot, accounting for the performance limitations of the rotorcraft and safety concerns.

Bachelder, Edward N.↗

Trajectory design for the Comet Rendezvous Asteroid Flyby 1995-1996 opportunities

Recent reprogramming of NASA's Comet Rendezvous Asteroid Flyby (CRAF) mission has motivated an examination of the comet rendezvous opportunities available with launch dates in 1995 and 1996. Various interplanetary transfer modes have been investigated including direct, Delta V-earth-gravity- assist and Venus/earth gravity assist trajectories. Optimal trajectories have been generated and their performance assessed for a spacecraft using a chemical propulsion system and the upgraded Titan/Centaur launch vehicle. Of the viable options available, a new CRAF baseline mission has been selected. One important result of the present study is that while there are comet rendezvous trajectories with launch dates throughout the next decade, 1997 marks the beginning of a hiatus of opportunities with short flight times to the comet targets which promise the greatest potential science return.

Myers, Mark R.↗

Optimal aircraft performance during microburst encounter

The effects of microburst characteristics on the optimal penetration performance of jet transport and general aviation aircraft are presented. The purpose is to determine the best possible performance that can be achieved in a broad range of microbursts. A secondary goal is to illustrate good strategies for dealing with a range of microbursts during takeoff and landing. Over 1100 optimal trajectories were computed for two aircraft types flying through idealized microbursts using a Successive Quadratic Programs trajectory optimization algorithm. Contours of safety metrics are plotted as functions of the length scales, magnitudes, and locations of horizontal wind shears and vertical downdrafts. These performance contours show three length-scale regimes for optimal microburst penetration. At short length scales, hazards usually associated with gustiness predominate (e.g., high normal load factor, rotational upset). At intermediate length scales, a degraded ability to maintain flight path and/or vertical velocity poses the most serious threat. At very long microburst length scales, excessive touchdown velocities may result. The ability to transit a microburst successfully also varies strongly with microburst location. The results show that both aircraft types could penetrate some very severe microbursts if optimal control histories were followed. Nevertheless, these control strategies assume perfect prior knowledge of the wind, and practical limits to successful encounter with real-time control capabilities would be lower. The optimally controlled jet transport can successfully penetrate higher intensity microbursts than can the general aviation aircraft.

Psiaki, Mark L.↗

Adaptive Critic Neural Network-Based Terminal Area Energy Management and Approach and Landing Guidance

Reusable Launch Vehicles (RLVs) have different mission requirements than the Space Shuttle, which is used for benchmark guidance design. Therefore, alternative Terminal Area Energy Management (TAEM) and Approach and Landing (A/L) Guidance schemes can be examined in the interest of cost reduction. A neural network based solution for a finite horizon trajectory optimization problem is presented in this paper. In this approach the optimal trajectory of the vehicle is produced by adaptive critic based neural networks, which were trained off-line to maintain a gradual glideslope.

Grantham, Katie↗