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The effect of pitch rate on abort landing caused by wind shear encounters is discussed. Optimal trajectories, airspeed, and wind shear warning systems are briefly discussed. The bulk of the presentation is in viewgraph form.
The Saturn V launch vehicle represented a jump in capability for heavy lift launch vehicles, enabling the Lunar Orbit Rendezvous approach to planetary exploration employed by the Apollo program 50 years ago. Following Apollo, and the development of the Space Transportation System, the NASA space exploration program shifted focus from lunar exploration to long-term, sustained, re-usable access to Low Earth Orbit. With the recent focus of NASA on the Artemis program and continued exploration of cislunar space as a precursor to Martian exploration, the shift has swung back to heavy lift capability. To meet this need, NASA has developed the Space Launch System. While the vehicle is a new design, it is heavily influenced by the engineering solutions and approach used on the Saturn V while taking advantage of the state of the art of launch vehicle design. The approach to abort, for example, shares many familiarities with the triggers and concept of operations used on Saturn V. Analysis approaches to dispersed trajectory performance are also very similar, but advances in computing technology have enabled a much more expanded set of inputs that can be modelled and assessed in a rapid manner. Additionally, guided flight algorithms share similar first principles but have expanded to include day of launch wind information. Trajectory optimization has also advanced significantly due to the availability of computing resources, but similar maneuvers and profiles are flown across both vehicles. Also, while the approach of onboard inertial navigation has been maintained between the two programs, the shift from platform to strapdown systems enables reduced complexity in the system design while maintaining required performance. As described, the Space Launch System is the evolution of NASA launch vehicle designs, owing a large heritage to the Saturn vehicle program and incorporating advances in propulsion systems, avionics, computing, and sensor technology over the past 50 years.
Aircraft penetration landing in the presence of strong-to-severe wind shear is investigated analytically. The optimal-control problem for vertical-plane trajectories is considered, using angle of attack as one control parameter with either (1) a power setting (PS) which remains constant at its preshear value, (2) a PS which increases to its maximum value, or (3) a PS which is controlled (as the second parameter). The problem formulation is explained in detail, and numerical results obtained with the primal sequential gradient-restoration algorithm of Miele and Wang (1986) are presented in extensive tables and graphs. It is found that the touchdown requirements can only be satisfied by optimal trajectories using scheme (1) (but only at low altitudes) or scheme (3); the characteristics of the latter trajectories are explored.
Aircraft operations need to meet the combined requirements of safety, efficiency, capacity and reduced environmental impact. Aircraft routes can be made efficient by flying wind optimal routes. However, the desire to reduce the impact of aviation emissions and contrails may result in trajectories, which deviate from wind optimal trajectories leading to extra fuel use. The lifetime associated with different emissions and contrails varies from a few hours to several hundred years. The impact of certain gases depends on the amount and location of the emission, and the decision-making horizon, in years, when the impact is estimated. The Absolute Global Temperature Potential (AGTP) is used as a metric to measure the combined effects of emissions and contrails. This paper extends earlier work by the authors to include the effect of oxides of nitrogen in the development of aircraft trajectories to reduce the combined effects of carbon dioxide, oxides of nitrogen (NOX) and contrails. The methodology is applied to air traffic in the continental US. The paper shows the trade-offs between reducing emissions and the cost of extra fuel using a fuel sensitivity index, defined as the reduction in AGTP per kg of fuel. The paper shows the performance of the optimization strategy for decision intervals of 10, 25 and 100 years. Based on the simplified models, the inclusion of NOX emissions has a slight influence on the minimal climate impact trajectories when the decision horizons are around 25 years.
Aircraft operations need to meet the combined requirements of safety, efficiency, capacity and reduced environmental impact. Aircraft routes can be made efficient by flying wind optimal routes. However, the desire to reduce the impact of aviation emissions and contrails may result in trajectories, which deviate from wind optimal trajectories leading to extra fuel use. The lifetime associated with different emissions and contrails varies from a few hours to several hundred years. The impact of certain gases depends on the amount and location of the emission, and the decision-making horizon, in years, when the impact is estimated. The Absolute Global Temperature Potential (AGTP) is used as a metric to measure the combined effects of emissions and contrails. This paper extends earlier work by the authors to include the effect of oxides of nitrogen in the development of aircraft trajectories to reduce the combined effects of carbon dioxide, oxides of nitrogen (NOX) and contrails. The methodology is applied to air traffic in the continental US. The paper shows the trade-offs between reducing emissions and the cost of extra fuel using a fuel sensitivity index, defined as the reduction in AGTP per kg of fuel. The paper shows the performance of the optimization strategy for decision intervals of 10, 25 and 100 years. Based on the simplified models, the inclusion of NOX emissions has a slight influence on the minimal climate impact trajectories when the decision horizons are around 25 years.
This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.
Space launch vehicles use day-of-launch steering commands based upon the upper-level (UL) atmospheric environments in order to alleviate wind induced structural loading and optimize ascent trajectory. Historically, UL wind measurements to support launch operations at the National Aeronautics and Space Administration's (NASA) Kennedy Space Center (KSC), co-located on the United States Air Force's Eastern Range (ER) at the Cape Canaveral Air Force Station use high-resolution (HR) rawinsondes. One inherent limitation with rawinsondes is the approximately one-hour sampling time necessary to measure tropospheric winds. Additionally, rawinsonde drift during ascent due to the ambient wind environment can result in the balloon being hundreds of kilometers down range, which results in questioning whether the measured winds represent the wind environment the vehicle will experience during ascent. This paper will describe the use of balloon profile databases to statistically assess the drift distance away from the ER launch complexes during HR rawinsonde ascent as a function of season. Will also discuss an alternative method to measure UL wind environments in closer proximity to the vehicle trajectory when launching from the ER.
The objective was the development of practical flight procedures and guidance for near-optimal trajectories during inadvertent wind shear encounters following takeoff. The approach was to conduct preliminary development of candidate strategies using batch simulation of the point mass B737-100 performance model and to evaluate candidate guidance strategies in piloted, real time, six degrees of freedom simulation.
The impact of aircraft emissions and contrails on the environment adds an additional aspect to aircraft trajectory optimization. This study developed a three-dimensional trajectory optimization algorithm for trans-Atlantic flights in cruise to generate aircraft trajectories that minimize environmental impacts due to CO2 emissions and contrails in the presence of winds. The climate-optimal trajectory is developed using dynamic programming that adjusts a wind-optimal aircraft heading while determining the optimal locations, altitudes and times for en-route step climbs. Flying wind-optimal routes minimize aircraft travel time, fuel burn and associated emissions during cruise while adjusting aircraft heading and en-route step climbs at the optimal locations and times minimize climate impact of contrails. This capability integrates an air traffic management simulation with aircraft fuel burn and emissions models, contrail formation and dispersion models, simplified climate response models, and a common climate metric. A study was conducted to evaluate the potential cost and benefits of flying climate-optimal routes in North Atlantic Airspace and their impacts to the Organized Track System design based on the trans-Atlantic air traffic during a day, July 12, 2012. Results show eastbound flights achieved a larger environmental benefit with less additional fuel burn than westbound flights that operated in strong headwinds that caused more additional fuel burn and aircraft emissions to avoid traversing contrails favorable regions.
Space launch vehicles develop day-of-launch steering commands based upon the upper-level atmospheric environments in order to alleviate wind induced structural loading and optimize ascent trajectory. Historically, upper-level wind measurements to support launch operations at the National Aeronautics and Space Administration's (NASA's) Kennedy Space Center co-located on the United States Air Force's Eastern Range (ER) at the Cape Canaveral Air Force Station use high-resolution rawinsondes. One inherent limitation with rawinsondes consists of taking approximately one hour to generate a vertically complete wind profile. Additionally, rawinsonde drift during ascent by the ambient wind environment can result in the balloon being hundreds of kilometers down range, which results in questioning whether the measured winds represent the wind environment the vehicle will experience during ascent. This paper will describe the use of balloon profile databases to statistically assess the drift distance away from the ER launch complexes during rawinsonde ascent as a function of season and discuss an alternative method to measure upper level wind environments in closer proximity to the vehicle trajectory launching from the ER.
The North Atlantic oceanic airspace (NAT) is crossed daily by more than a thousand flights, which are greatly affected by strong jet stream air currents. Several studies devoted to generating wind-optimal (WO) aircraft trajectories in the NAT demonstrated great efficiency of such an approach for individual flights. However, because of the large separation norms imposed in the NAT, previously proposed WO trajectories induce a large number of potential conflicts. Much work has been done on strategic conflict detection and resolution (CDR) in the NAT. The work presented here extends previous methods and attempts to take advantage of the NAT traffic structure to simplify the problem and improve the results of CDR. Four approaches are studied in this work: 1) subdividing the existing CDR problem into sub-problems of smaller sizes, which are easier to handle; 2) more efficient data reorganization within the considered time period; 3) problem localization, i.e. concentrating the resolution effort in the most conflicted regions; 4) applying CDR to the pre-tactical decision horizon (a couple of hours in advance). Obtained results show that these methods efficiently resolve potential conflicts at the strategic and pre-tactical levels by keeping the resulting trajectories close to the initial WO ones.
Guidance schemes for near-optimum performance in wind shear are examined. The presence of a downdraft is assumed in addition to the horizontal shear. The takeoff problem is considered with reference to flight in a vertical plane. Trajectories for optimum performance in a wind shear are determined for different wind shear models and intensities. Methods of optimal control theory are used together with the dual sequential gradient-restoration algorithm for optimal control problems. Guidance schemes for near-optimum performance in a wind shear are developed, starting from optimal trajectories. These are gamma guidance, based on either the absolute of the relative path inclination, and theta guidance, based on the pitch attitude angle. These schemes are evaluated through numerical experiments in order to determine whether the resulting trajectories are sufficiently close to optimum and to compare these trajectories with those arising from alternative guidance schemes.
This study proposes a strategic trajectory planning framework to support development of Urban Air Mobility (UAM) traffic networks and optimization of UAM aircraft trajectories that are robust to uncertain wind fields. The development of UAM traffic networks considers static aviation constraints and dynamic weather constraints in urban airspace and the connections to ground transportation networks for preliminary selection of feasible time-optimal routes. The trajectory optimization of UAM aircraft utilizes an unscented optimal guidance approach to generate cost-optimal trajectories constrained on the selected sigma values of probability distribution of uncertain wind fields while ensuring that the end-point constraints are met for reducing wind-induced trajectory uncertainty. Unscented guidance commands are assessed based on trajectory perturbations at subsequent end-points in various wind fields by conducting Monte Carlo simulations.An example of wind-optimal UAM corridor and the associated trajectory-based operation volume is created utilizing the perturbations of the unscented trajectories for preliminary assessment of required aircraft separation minima without knowledge of aircraft navigation performance.
The flight trajectory of abort landing in the presence of windshear is examined with reference to flight in a vertical plane. It is assumed that the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative. Numerical results are obtained for several combinations of windshear intensities and initial altitudes. Guidance trajectories are considered, approximating the optimal trajectories and using local information on the state of the aircraft, the initial altitude, and the total wind velocity difference. Results are presented for optimal trajectories, guidance trajectories, simplified guidance trajectories, constant pitch trajectories, and maximum angle of attack trajectories.
A trajectory design process is presented for a proposed National Launch System (NLS) vehicle configuration. A software trajectory planner was developed to generate near optimal pitch plane trajectories for variable mission plans, variable launch site selections, and last minute wind conditions at the time of launch. In addition, the trajectory planner performs in-flight near optimal trajectory redesign in the event of an engine-out or unexpected wind dispersions. The trajectory planner iteratively simulates trial trajectories defined by variables corresponding to a parameterized trajectory shape. The trajectory planner optimizes these trajectory parameters according to the fuel used to realize the trajectories. For prelaunch scenarios, the trajectory planner generated near optimal trajectories of consistent fuel performance irrespective of the winds encountered at the launch site. In-flight trajectory redesigns were also shown to be effective in fulfilling the mission plan and preserving the structural integrity of the vehicle. The in-flight redesign results indicate that closed-loop guidance in the early stages of ascent is highly effective in accommodating engine failures or wind dispersions. All trajectory designs were verified using a 6DOF simulation with flight controllers.
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.
An optimal flight path algorithm using a simplified altitude state model and a priori climb cruise descent flight profile was developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. In addition, a method was developed for obtaining a performance model in simplified form which is based on standard flight manual data and which is applicable to the computation of optimal trajectories. The entire performance optimization algorithm is simple enough that on line trajectory optimization is feasible with a relatively small computer. The helicopter model used is the Silorsky S-61N. The results show that for this vehicle the optimal flight path and optimal cruise altitude can represent a 10% fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability because of helicopter weight, ambient winds, and the relative cost trade off between time and fuel. In general, reasonable variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost. For fuel optimal trajectories, the optimum cruise altitude varies from the maximum (12,000 ft) to the minimum (0 ft) depending on helicopter weight.
The control (via the angle of attack) of the vertical flight of an aircraft taking off at maximum power in a horizontal wind shear with downdraft is investigated analytically. Optimal trajectories to recover the initial path inclination or to recover quasi-steady flight (the relative values of the velocity, path inclination, and angle of attack) are derived using a Chebyshev approach and shown to be nearly identical in the shear but divergent after the shear. These results are then applied to construct a trajectory-guidance control comprising a variable-gamma guidance scheme for the shear trajectory, a constant-gamma guidance scheme for the immediate postshear trajectory, and a constant-rate-of-climb guidance scheme for the aftershear trajectory. Numerical results demonstrating the near-optimal performance of the control are presented in tables and graphs.