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Method and Apparatus for Powered Descent Guidance

A method and apparatus for landing a spacecraft having thrusters with non-convex constraints is described. The method first computes a solution to a minimum error landing problem for a convexified constraints, then applies that solution to a minimum fuel landing problem for convexified constraints. The result is a solution that is a minimum error and minimum fuel solution that is also a feasible solution to the analogous system with non-convex thruster constraints.

Acikmese, Behcet↗

Computational Modeling of Mars Retropropulsion Concepts in the Langley Unitary Plan Wind Tunnel

Future human Mars missions will require powered descent starting at supersonic conditions, something which has never been done before at Mars. Computational powered descent flowfield simulations have been completed at full-scale Mars conditions, but the available ground test data are not appropriate for calibrating computational uncertainties for aerodynamic interference on proposed Mars descent vehicles. A test will be conducted in the NASA Langley Unitary Plan Wind Tunnel to begin addressing powered descent aerodynamics risks for large-scale human Mars entry concepts and to identify gaps in computational predictive capabilities. This paper covers pre-test computational flowfield predictions of two different models derived from full-scale reference vehicles: a blunt low lift-to-drag vehicle and a more slender geometry. Calculations of the blunt model include variations in nozzle configuration: nozzle location, size, area ratio, and pointing direction. There exist some significant differences between solvers, but some general trends are observed from simulations of the blunt model. First, aerodynamic axial force from the heatshield decreases with increasing thrust due to expanding plume blockage. Second, nozzles that point along the model axis result in lower aerodynamic axial force compared to nozzles that have a radial thrust component. Finally, placing the nozzles further away from the model nose preserves more heatshield axial force with increasing thrust compared to nozzles that are closer to the nose. For the slender model, the axial force from the heatshield is similar to the non-blowing axial force regardless of thrust magnitude, due to the nozzle arrangement on the heatshield. Once the test is completed, direct comparisons between the computations and test data will be made to determine computational uncertainties in a wind tunnel environment, to identify gaps in predictive capabilities, and to inform planning for future ground and flight test programs for Mars powered descent vehicles.

Supersonic Retropropulsion↗

Computational Modeling of Mars Retropropulsion Concepts in the Langley Unitary Plan Wind Tunnel

Future human Mars missions will require powered descent starting at supersonic conditions, something which has never been done before at Mars. Computational powered descent flowfield simulations have been completed at full-scale Mars conditions, but the available ground test data are not appropriate for calibrating computational uncertainties for aerodynamic interference on proposed Mars descent vehicles. A test will be conducted in the NASA Langley Unitary Plan Wind Tunnel to begin addressing powered descent aerodynamics risks for large-scale human Mars entry concepts and to identify gaps in computational predictive capabilities. This paper covers pre-test computational flowfield predictions of two different models derived from full-scale reference vehicles: a blunt low lift-to-drag vehicle and a more slender geometry. Calculations of the blunt model include variations in nozzle configuration: nozzle location, size, area ratio, and pointing direction. There exist some significant differences between solvers, but some general trends are observed from simulations of the blunt model. First, aerodynamic axial force from the heatshield decreases with increasing thrust due to expanding plume blockage. Second, nozzles that point along the model axis result in lower aerodynamic axial force compared to nozzles that have a radial thrust component. Finally, placing the nozzles further away from the model nose preserves more heatshield axial force with increasing thrust com- pared to nozzles that are closer to the nose. For the slender model, the axial force from the heatshield is similar to the non-blowing axial force regardless of thrust magnitude, due to the nozzle arrangement on the heatshield. Once the test is completed, direct comparisons between the computations and test data will be made to determine computational uncertainties in a wind tunnel environment, to identify gaps in predictive capabilities, and to inform planning for future ground and flight test programs for Mars powered descent vehicles.

Mars↗

End-to-End Performance Optimization of a Crewed Lunar Landing Mission Staged from a Near Rectilinear Halo Orbit

A crewed lunar landing mission staged from a Near Rectilinear Halo Orbit (NRHO) presents a unique set of challenges not considered before for the Apollo-type direct missions. The NRHO does not have a fixed orbital plane and its period also changes with time, due to which the mission performance is very sensitive to the timing and location of the NRHO departure and arrival burns for a near-polar surface landing site. For such type of mission staged from the NRHO, an end-to-end optimization approach for the entire mission, from the NRHO departure to surface landing and from surface lift-off to the NRHO insertion, is well-suited for extracting the maximum performance out of this design. In this paper, an integrated approach for performing end-to-end optimization of a NRHO-staged crewed lunar landing mission is proposed that optimizes the in-space and powered flight segments simultaneously using Copernicus trajectory optimization tool. Copernicus is augmented with analytical approximations for the in-space, powered descent, and powered ascent segments in this work to improve the convergence of its multiple-shooting based direct optimization method. New analytical solutions are derived for the different phases of the powered flight segments by solving associated guidance problems. These analytical solutions act as initial guesses for starting the numerical optimization of the integrated mission in Copernicus. An example lunar landing mission is simulated to validate the proposed end-to-end optimization approach and the results are compared with the conventional patched trajectory approach.

Bharat Mahajan↗

Flight Investigation of Effects of Transition, Landing Approaches, Partial-Power Vertical Descents, and Droop-Stop Pounding on the Bending and Torsional Moments Encountered by a Helicopter Rotor Blade

Flight tests have been conducted with a single-rotor helicopter, one blade of which was equipped at 14 percent and 40 percent of the blade radius with strain gages calibrated to measure moments rather than stresses, to determine the effects of transition, landing approaches, and partial-power vertical descents on the rotor-blade bending and torsional moments. In addition, ground tests were conducted to determine the effects of static droop-stop pounding on the rotor-blade moments. The results indicate that partial-power vertical descents and landing approaches produce rotor-blade moments that are higher than the moments encountered in any other flight condition investigated to date with this equipment. Decelerating through the transition region in level flight was found to result in higher vibratory moments than accelerating through this region. Deliberately induced static droop-stop pounding produced flapwise bending moments at the 14-percent-radius station which were as high as the moments experienced in landing approaches and partial-power vertical descents.

Ludi, LeRoy H.↗

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.↗

Status of Mars Retropropulsion Testing in the Langley Unitary Plan Wind Tunnel

Future Mars human landings will be enabled by a powered descent phase starting at supersonic conditions, something which has never been done before on a Mars mission. Significant aerosciences challenges exist due to jet interactions between the retrorocket engine plumes, freestream flow, and vehicle that will affect the aerodynamic behavior during powered descent. Historically, wind tunnel tests have been used to study the interactions with inert gas exhaust simulants in place of rocket engines. On the computational side, flowfield simulations have been completed at full-scale conditions, but the available ground and flight data are not appropriate for calibrating computational uncertainties for aerodynamic interference on proposed Mars descent vehicles, due to insufficient data, dissimilar vehicle geometries, and disparate operating conditions. A wind tunnel test has been designed to begin addressing powered descent aerodynamics risks for large-scale human Mars entry concepts and to identify gaps in computational predictive capabilities. The test will be conducted in the NASA Langley Unitary Plan Wind Tunnel and is designed with improvements in model design and data products over past tests. The test campaign will be run using sub-scale model geometries derived from NASA powered descent reference vehicles: a blunt low lift-to-drag vehicle and a more slender geometry that generates higher unpowered lift. Both models have been fabricated and are ready for testing. The blunt model is equipped with the flexibility to examine the effects of nozzle pointing direction, number, location, size, and area ratio. The main measurements are heatshield aerodynamic interference forces and moments with a custom flow-through balance, discrete and distributed heatshield pressure, and high-speed flowfield visualization. This paper covers the test objectives, facility, models and instrumentation, and planned test matrix.

Supersonic Retropropulsion↗

Flight Investigation of Effects of Selected Operating Conditions on the Bending and Torsional Moments Encountered by a Helicopter Rotor Blade

Flight tests have been conducted with a single-rotor helicopter to determine the effects of partial-power descents with forward speed, high-speed level turns, pull-outs from autorotation, and high-forward-speed high-rotor-speed autorotation on the flapwise bending and torsional moments of the rotor blade. One blade of the helicopter was equipped at 14 percent and 40 percent of the blade radius with strain gages calibrated to measure moments rather than stresses. The results indicate that the maximum moments encountered in partial-power descents with forward speed tend to be generally reduced from the maximum moments encountered during partid-power descents at zero forward speed. High-speed level turns and pull-outs from auto-rotation caused retreating-blade stall which produced torsional moments (values up to 2,400 inch-pounds). at the 14-percent-radius station that were as large as those encountered during the previous investigations of retreating-blade stall (values up t o 2,500 inch-pounds). High-forward- speed high-rotor-speed autorotation produced flapwise bending moments (values up to 7,200 inch-pounds) at the 40-percent-radius station which were as large as the flapwise bending moments (values up to 7,800 inch-pounds) a t the 14-percent-radius station encountered during partial - power vertical descents. The results of the present investigation (tip-speed ratios up to 0.325 and an unaccelerated level-flight mean lift coefficient of about 0.6), in combination with the related results of at zero forward speed produce the largest rotor-blade vibratory moments. However, inasmuch as these large moments occur only during 1 percent of the cycles and 88 percent of the cycles are at moment values less than 70 percent of these maximum values in partial-power descents, other conditions, such as high-speed flight where the large moments are combined with large percentages of time spent,must not be neglected in any rotor-blade service-life assessment.

Ludi, LeRoy H.↗

Status of Mars Retropropulsion Testing in the Langley Unitary Plan Wind Tunnel

Future Mars human landings will be enabled by a powered descent phase starting at supersonic conditions, something which has never been done before on a Mars mission. Significant aerosciences challenges exist due to jet interactions between the retrorocket engine plumes, freestream flow, and vehicle that will affect the aerodynamic behavior during powered descent. Historically, wind tunnel tests have been used to study the interactions with inert gas exhaust simulants in place of rocket engines. On the computational side, flowfield simulations have been completed at full-scale conditions, but the available ground and flight data are not appropriate for calibrating computational uncertainties for aerodynamic interference on proposed Mars descent vehicles, due to insufficient data, dissimilar vehicle geometries, and disparate operating conditions. A wind tunnel test has been designed to begin addressing powered descent aerodynamics risks for large-scale human Mars entry concepts and to identify gaps in computational predictive capabilities. The test will be conducted in the NASA Langley Unitary Plan Wind Tunnel and is designed with improvements in model design and data products over past tests. The test campaign will be run using sub-scale model geometries derived from NASA powered descent reference vehicles: a blunt low lift-to-drag vehicle and a more slender geometry that generates higher unpowered lift. Both models have been fabricated and are ready for testing. The blunt model is equipped with the flexibility to examine the effects of nozzle pointing direction, number, location, size, and area ratio. The main measurements are heatshield aerodynamic interference forces and moments with a custom flow-through balance, discrete and distributed heatshield pressure, and high-speed flowfield visualization. This paper covers the test objectives, facility, models and instrumentation, and planned test matrix.

Mars↗

Comparative Performance of Entry Simulations using Guided Human-Scale Landers at Mars

There has been ongoing interest in human exploration of Mars since the 1970s. Most studies to date have investigated moderate lift-to-drag ratio vehicles to investigate this problem. This paper considers the development and cross-simulation comparison of a slender-bodied, moderate lift-to-drag human-scale lander vehicle for Mars. The vehicle employs the Fully Numerical Predictor-corrector Entry Guidance to target a powered descent state, subsequently leveraging Fractional Polynomial Powered Descent Guidance laws to reach the desired touchdown target. Differences in simulation environment as well as nominal trajectory results are shared.

Evan Roelke↗

Comparative Performance of Entry Simulations using Guided Human-Scale Landers at Mars

There has been ongoing interest in human exploration of Mars since the 1970s. Most studies to date have investigated moderate lift-to-drag ratio vehicles to investigate this problem. This paper considers the development and cross-simulation comparison of a slender-bodied, moderate lift-to-drag human-scale lander vehicle for Mars. The vehicle employs the Fully Numerical Predictor-corrector Entry Guidance to target a powered descent state, subsequently leveraging Fractional Polynomial Powered Descent Guidance laws to reach the desired touchdown target. Differences in simulation environment as well as nominal trajectory results are shared.

Evan Roelke↗

Scaling and Similitude in Single Nozzle Supersonic Retropropulsion Aerodynamics Interference

Retropropulsion, or the firing of rocket engines or motors into the direction of flight, is a method of spacecraft deceleration and soft landing that dates back to the early 1960s. Current conceptual designs for landing humans on the surface of Mars require supersonic retropropulsion, or initiation of retropropulsion at supersonic freestream conditions, as part of an extended powered descent phase of flight. The objective of this work is to identify the design parameters and flow condition bounds for self-similar behavior of powered descent aerodynamic interference in relevant flight environments. In applications of sub-scale test data, an “unknown” uncertainty lies in scaling to and from full-scale environments and systems. The issue of scaling for the opposing flows characteristic of powered descent is the focus of the following analysis, using data from wind tunnel testing of figurations with a single, central nozzle as a point of departure.

Korzun, Ashley M.↗