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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,261 records · Page 70

OPTIMIZING MEASUREMENTS OF THE NEAR-SURFACE WATER CYCLE ON MARS: INSIGHTS FOR HABITABILITY.

The Martian regolith may act as a sink and source of water vapor for the lower atmosphere through processes such as frost formation, physisorption, solid-state hydration, and brine formation [e.g., 1- 12]. These processes are all dependent on temperature and humidity, as well as regolith properties such as porosity, tortuosity, and composition. In particular, the salty nature of the Martian regolith may increase its role in atmosphere-regolith interactions as hygroscopic salts interact with the ambient water vapor. Although to date experimental works near Mars-relevant conditions have constrained some of the potential effects of a salty regolith on water vapor exchange processes [e.g., 13-18], vital in situ measurements are lacking to link these to the near-surface water cycle on Mars. This is because previous and ongoing environmental payloads for landed Mars missions were not designed to investigate atmosphere-regolith exchange processes [12, 19-20]. Resolving the Martian near-surface water cycle is relevant to both climatic processes and astrobiology. There is the potential to presently form (meta)stable brines on Mars; their stability would be largely controlled by water vapor exchange processes [9, 21]. Here we argue for optimizing in situ measurements of water vapor exchange processes and regolith properties to advance our understanding of the local scale Martian water cycle and inform habitability studies.

E G Rivera-Valentin↗

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 hours. Here, we present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DNN-based policies for stochastic AC OPF

We report a prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal–dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Improvement of Atmospheric Objective Analysis Over Sloping Terrain and Its Impact on Shallow-Cumulus Clouds in Large-Eddy Simulations

Surface topography strongly impacts the regional atmospheric circulation dynamically and thermodynamically. Over the Great Plains in the United States, the gently tilted slope is an important factor that impacts clouds, convection and regional circulations. This study enhances an atmospheric constrained variational analysis by using a terrain-following sigma vertical coordinate and applies to the data collected at the Southern Great Plain (SGP) site of the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program. Sensitivity studies are performed to examine the impact of the terrain effects on the derived large-scale atmospheric forcing fields and the simulated shallow-cumulus clouds in large-eddy simulation (LES) driven by the forcing. We found that the terrain impacts on the large-scale forcing fields are mainly at lower levels and are strongly controlled by up/downslope winds. The response of the derived forcing to the slope of the terrain is monotonic, but the response of the simulated shallow-cumulus clouds is more complex and depends on several factors. Overall, the terrain impact is small over SGP due to the small slope angle. However, the flat-surface assumption may cause larger biases in the large-scale forcing fields at locations with steeper terrain. The new sigma-coordinate algorithm, with its consideration of surface slope, should be more suitable to derive large-scale objective analysis over regions with steep terrain for application to force single-column models, cloud resolving models and LES models.

54 ENVIRONMENTAL SCIENCES↗

Subsurface Redox Interactions Regulate Ebullitive Methane Flux in Heterogeneous Mississippi River Deltaic Wetland

Abstract As interfaces connecting terrestrial and ocean ecosystems, coastal wetlands develop temporally and spatially complex redox conditions, which drive uncertainties in greenhouse gas emission as well as the total carbon budget of the coastal ecosystem. To evaluate the role of complex redox reactions in methane emission from coastal wetlands, a coupled reactive‐transport model was configured to represent subsurface biogeochemical cycles of carbon, nitrogen, and sulfur, along with production and transport of multiple gas species through diffusion and ebullition. This model study was conducted at multiple sites along a salinity gradient in the Barataria Basin at the Mississippi River Deltaic Plain. Over a freshwater to saline gradient, simulated total flux of methane was primarily controlled by its subsurface production and consumption, which were determined by redox reactions directly (e.g., methanogenesis, methanotrophy) and indirectly (e.g., competition with sulfate reduction) under aerobic and/or anaerobic conditions. At fine spatiotemporal scales, surface methane fluxes were also strongly dependent on transport processes, with episodic ebullitive fluxes leading to higher spatial and temporal variability compared to the gradient‐driven diffusion flux. Ebullitive methane fluxes were determined by methane fraction in total ebullitive gas and the frequency of ebullitive events, both of which varied with subsurface methane concentrations and other gas species. Although ebullition thresholds are constrained by local physical factors, this study indicates that redox interactions not only determine gas composition in ebullitive fluxes but can also regulate ebullition frequency through gas production.

03 NATURAL GAS↗

Joint ptycho-tomography with deep generative priors

Abstract Joint ptycho-tomography is a powerful computational imaging framework to recover the refractive properties of a 3D object while relaxing the requirements for probe overlap that is common in conventional phase retrieval. We use an augmented Lagrangian scheme for formulating the constrained optimization problem and employ an alternating direction method of multipliers (ADMM) for the joint solution. ADMM allows the problem to be split into smaller and computationally more efficient subproblems: ptychographic phase retrieval, tomographic reconstruction, and regularization of the solution. We extend our ADMM framework with plug-and-play (PnP) denoisers by replacing the regularization subproblem with a general denoising operator based on machine learning. While the PnP framework enables integrating such learned priors as denoising operators, tuning of the denoiser prior remains challenging. To overcome this challenge, we propose a denoiser parameter to control the effect of the denoiser and to accelerate the solution. In our simulations, we demonstrate that our proposed framework with parameter tuning and learned priors generates high-quality reconstructions under limited and noisy measurement data.

97 MATHEMATICS AND COMPUTING↗

A Contextually Supervised Optimization-Based HVAC Load Disaggregation Methodology

This paper presents a novel contextually supervised optimization-based approach for disaggregating heating, ventilation, and air-conditioning (HVAC) loads using smart meter or Supervisory Control and Data Acquisition data. To disaggregate the load into HVAC loads, large and infrequently used loads (LIUL), and base loads, we formulate an optimization problem to minimize a set of five loss terms, consisting of the reconstruction errors of the overall load profile, the ramp rate losses, and three distinct loss functions linked with the HVAC load, base load, and LIUL, respectively. To enhance accuracy, we incorporate two forms of contextual information into the problem formulation. First, we utilize mutual information to estimate HVAC energy consumption. Second, we employ a base load dictionary to constrain HVAC load estimation errors. The obtained HVAC load profiles are fine-tuned by abnormal ramp detection followed by binary hypothesis testing. Here, the proposed method is developed and tested using sub-metered residential and commercial building data. Simulation results show that the proposed method outperforms existing methods across various data resolutions and load aggregation levels, showing excellent transferability and generalizability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Beyond sequence similarity: toward function-based screening of nucleic acid synthesis

Synthetic nucleic acids are a key input to modern biotechnology, yet they represent dual-use materials that require robust screening to mitigate biosecurity risks. The prevailing screening paradigm, which identifies sequences of concern (SoCs) through sequence similarity to controlled pathogens and toxins, may not fully capture risks posed by AI tools that can decouple biomolecular function from reliance on known sequences. Rapidly advancing biodesign capabilities enable the generation of genes and proteins that might evade sequence-based detection. We highlight the critical need for function-based screening approaches that can detect sequences capable of hazardous biological functions, regardless of similarity to known SoCs. We examine the feasibility of function-based screening with an initial focus on proteins, arguing that, while protein sequence space is vast, biologically functional proteins are significantly constrained by biophysical and biochemical requirements that can be learned and modeled. We propose a concrete implementation framework organized along a continuum of complexity, starting with toxins as the most tractable targets before expanding to more complex pathogenic functions. We then discuss open challenges and describe a research and development strategy to address them.

59 BASIC BIOLOGICAL SCIENCES↗

SPARROW: Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

The Steam Propelled Autonomous Retrieval Robot (SPARROW) for Ocean Worlds was a Phase I mission concept study funded under the NASA NIAC program. This report represents the findings of that study and recommendations for future work. SPARROW, envisioned as a soccer ball-sized payload to a primary lander mission, is a propulsively hopping robot for the exploration of Europa's rugged, icy surface. A multi-thruster, passively gimballed robot within a protective, spherical shell, SPARROW is able to freely rotate, self-right, and tumble over chaotic terrains. Europa's abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW is to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixel—still far larger than a typical rover. A key benefit of SPARROW's hopping, impact-tolerant design, is that it eliminates the need for a priori information regarding terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is believed to be entirely terrain agnostic. In this report we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientific interest, and iii) to characterize the impact of SPARROW's range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW's sensitivity to uncertainty in: initial pose, thrust profile, and vehicle-terrain interaction. A science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa's evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Autonomous↗

Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports

A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.

multidisciplinary optimization↗

Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports

A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.

low-boom supersonic transports↗

Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports

A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.

low-boom supersonic transports↗

Biomimetic Metal-Free Hydride Donor Catalysts for CO 2 Reduction

The catalytic reduction of carbon dioxide to fuels and value-added chemicals is of significance for the development of carbon recycling technologies. One of the main challenges associated with catalytic CO 2 reduction is product selectivity: the formation of carbon monoxide, molecular hydrogen, formate, methanol, and other products occurs with similar thermodynamic driving forces, making it difficult to selectively reduce CO 2 to the target product. Significant scientific effort has been aimed at the development of catalysts that can suppress the undesired hydrogen evolution reaction and direct the reaction toward the selective formation of the desired products, which are easy to handle and store. Inspired by natural photosynthesis, where the CO 2 reduction is achieved using NADPH cofactors in the Calvin cycle, in this study we explore biomimetic metal-free hydride donors as catalysts for the selective reduction of CO 2 to formate. Here, we outline our recent findings on the thermodynamic and kinetic parameters that control the hydride transfer from metal-free hydrides to CO 2 . By experimentally measuring and theoretically calculating the thermodynamic hydricities of a range of metal-free hydride donors, we derive structural and electronic factors that affect their hydride-donating abilities. Two dominant factors that contribute to the stronger hydride donors are identified to be (i) the stabilization of the positive charge formed upon HT via aromatization or by the presence of electron-donating groups and (ii) the destabilization of hydride donors through the anomeric effect or in the presence of significant structural constrains in the hydride molecule. Hydride donors with appropriate thermodynamic hydricities were reacted with CO 2 , and the formation of the formate ion (the first reduction step in CO 2 reduction to methanol) was confirmed experimentally, providing an important proof of principle that organocatalytic CO 2 reduction is feasible. The kinetics of hydride transfer to CO 2 were found to be slow, and the sluggish kinetics were assigned in part to the large self-exchange reorganization energy associated with the organic hydrides in the DMSO solvent. Finally, we outline our approaches to the closure of the catalytic cycle via the electrochemical and photochemical regeneration of the hydride (R–H) from the conjugate hydride acceptors (R + ). We illustrate how proton-coupled electron transfer can be efficiently utilized not only to lower the electrochemical potential at which the hydride regeneration takes place but also to suppress the unwanted dimerization that neutral radical intermediates tend to undergo. Overall, this account provides a summary of important milestones achieved in organocatalytic CO 2 reduction and provides insights into the future research directions needed for the discovery of inexpensive catalysts for carbon recycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

EGS Stimulation Design with Uncertainty Quantification at the EGS Collab Site

Engineering a robust hydraulic connection between wells is one of the most difficult aspects of enhanced geothermal systems (EGS). Designing and constructing such hydraulic connections requires and understanding of the in situ state of stress and the heterogeneities and discontinuities that naturally exist and may control the stimulation. Even with comprehensive stress and formation characterization programs substantial uncertainty remains in these key parameters. This is especially the case in high-temperature EGS environments where drilling conditions are often difficult and a far fewer logging and testing options are available. This paper presents a new approach for explicitly quantifying the uncertainties in the state of stress using a Bayesian Markov Chain Monte Carlo method. This approach produces a probability distribution for the stress tensor, including a general 3D orientation, that reflects the uncertainties in all the observations or indicators used to constrain the stress state. This method is demonstrated on the characterization data for the EGS Collab Experiment 2 site. The output of the analysis is used to guide the design of the planned stimulations. In the case of research projects like EGS Collab, explicitly quantifying the uncertainties in the stress state allow for more rigorous hypothesis testing by allowing conclusions drawn from the experiments to be interpreted in the context of the uncertain knowledge about conditions in the test bed.

Burghardt, Jeffrey A.↗

Development of display design and command usage guidelines for Spacelab experiment computer applications

Individual Spacelab experiments are responsible for developing their CRT display formats and interactive command scenarios for payload crew monitoring and control of experiment operations via the Spacelab Data Display System (DDS). In order to enhance crew training and flight operations, it was important to establish some standardization of the crew/experiment interface among different experiments by providing standard methods and techniques for data presentation and experiment commanding via the DDS. In order to establish optimum usage guidelines for the Spacelab DDS, the capabilities and limitations of the hardware and Experiment Computer Operating System design had to be considered. Since the operating system software and hardware design had already been established, the Display and Command Usage Guidelines were constrained to the capabilities of the existing system design. Empirical evaluations were conducted on a DDS simulator to determine optimum operator/system interface utilization of the system capabilities. Display parameters such as information location, display density, data organization, status presentation and dynamic update effects were evaluated in terms of response times and error rates.

Dodson, D. W.↗

Advanced launch vehicle upper stages using liquid propulsion and metallized propellants

Metallized propellants are liquid propellants with a metal additive suspended in a gelled fuel or oxidizer. Typically, aluminum particles are the metal additives. These propellants provide increase in the density and/or the specific impulse of the propulsion system. Using metallized propellants for volume- and mass-constrained upper stages can deliver modest increases in performance for Low Earth Orbit to Geosynchronous Earth Orbit and other Earth orbital transfer missions. Metallized propellants, however, can enable very fast planetary missions with a single-stage upper stage system. Trade studies comparing metallized propellant stage performance with non-metallized upper stages and the Inertial Upper Stage are presented. These upper stages are both one- and two-stage vehicles that provide the added energy to send payloads to altitudes and onto trajectories that are unattainable with only the launch vehicle. The stage designs are controlled by the volume and the mass constraints of the Space Transportation System and Space Transportation System-Cargo launch vehicles. The influences of the density and specific impulse increases enabled by metallized propellants are examined for a variety of different stage and propellant combinations.

Palaszewski, B. A.↗

Evaluating and Constraining Models’ Stratocumulus and Cumulus Cloud Feedbacks in the Tropics using Satellite Observations to Reduce Uncertainties in Future Climate Projections

Low-cloud feedbacks are thought to be the greatest source of uncertainty in climate projections on the centennial scale. Past research has mainly focused on the global low-cloud feedback as a whole whereas only a few studies have examined separated contributions from the two main low cloud categories: stratocumulus (Sc) and shallow cumulus (Cu). Here we aim to evaluate and constrain Sc and Cu cloud feedbacks in models using satellite observations to ultimately reduce their contribution to the spread in equilibrium climate sensitivity. We utilize the Cumulus and Stratocumulus CloudSat-CALIPSO Dataset (CASCCAD) recently developed by Cesana et al. (2019), which discriminates Sc from Cu clouds. This algorithm – based on cloud morphological characteristics at the orbital level – outperforms previous cloud-type classifications stemming from passive-sensor measurements. We investigate the observed relationship between the Sc and Cu cloud cover in tropical subsidence oceanic regions and their link to the primary low-cloud controlling factors (sea surface temperature, estimated inversion strength). To gain further insight into the Sc-Cu cloud partitioning, we explore the Sc-Cu relationship during the four meteorological seasons (DJF, MAM, JJA, SON) as well as on monthly timescale. We find a substantial negative correlation between the Sc and Cu cloud cover on annual, seasonal and monthly timescales. We finally evaluate how well climate models of the Coupled Model Intercomparison Project phase 5 (CMIP5) and phase 6 (CMIP6) agree with the observations. These results establish a framework to advance model parameterizations of the underlying physical processes driving the stratocumulus and shallow cumulus clouds (turbulence and convection).

Cloud feedbacks↗

TRAGEN: Computer program to simulate an aircraft steered to follow a specified verticle profile. User's guide

The longitudinal dynamics of a medium range twin-jet or tri-jet transport aircraft are simulated. For the climbing trajectory, the thrust is constrained to maximum value, and for descent, the thrust is set at idle. For cruise, the aircraft is held in the trim condition. For climb or descent, the aircraft is steered to follow either (a) a fixed profile which is input to the program or (b) a profile computed at the beginning of that segment of the run. For climb, the aircraft is steered to maintain the given airspeed as a function of altitude. For descent, the aircraft is steered to maintain the given altitude as a function of range-to-go. In both cases, the control variable is angle-of-attack. The given output trajectory is presented and compared with the input trajectory. Step climb is treated just as climb. For cruise, the Breguet equations are used to compute the fuel burned to achieve a given range and to connect given initial and final values of altitude and Mach number.

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