Drag Acceleration Research Articles

Effect of Polar Cap Patches on the High‐Latitude Upper Thermospheric Winds

AbstractThis study focuses on the poorly known effect of polar cap patches (PCPs) on the ion‐neutral coupling in the F‐region. The PCPs were identified by total electron content measurements from the Global Navigation Satellite System (GNSS) and the ionospheric parameters from the Defense Meteorological Satellite Program spacecraft. The EISCAT incoherent scatter radars on Svalbard and at Tromsø, Norway observed that PCPs entered the nightside auroral oval from the polar cap and became plasma blobs. The ionospheric convection further transported the plasma blobs to the duskside. Simultaneously, long‐lasting strong upper thermospheric winds were detected in the duskside auroral oval by a Fabry‐Perot Interferometer (FPI) at Tromsø and in the polar cap by the Gravity Recovery and Climate Experiment satellite. Using EISCAT ion velocities and plasma parameters as well as FPI winds, the ion drag acting on neutrals and the time constant for the ion drag could be estimated. Due to the arrival of PCPs/blobs and the accompanied increase in the F‐region electron densities, the ion drag is enhanced between about 220 and 500 km altitudes. At the F peak altitudes near 300 km, the median ion drag acceleration affecting neutrals more than doubled and the associated median e‐folding time decreased from 4.4 to 2 hr. The strong neutral wind was found to be driven primarily by the ion drag force due to large‐scale ionospheric convection. Our results provide a new insight into ionosphere‐thermosphere coupling in the presence of PCPs/blobs.

Rapid and Near-Analytical Planning Method for Entry Trajectory under Time and Full-State Constraints

A rapid trajectory-planning method based on an analytical predictor–corrector design of drag acceleration profile and a bank-reversal logic based on double-stage adaptive adjustment is proposed to solve the entry issue under time and full-state constraints. First, an analytical predictor–corrector algorithm is used to design the profile parameters to satisfy the terminal of altitude, velocity, range, time, and flight-path angle constraints. Subsequently, an adaptive lateral planning algorithm based on heading adjustment and maintenance is proposed to achieve the flight stage adaptive division and determination of the bank-reversal point, thereby satisfying the terminal position and heading angle constraints. Concurrently, a rapid quantification method is proposed for the adjustable capacity boundary of the terminal heading angle. On this basis, a range-and-time correction strategy is designed to achieve high precision and the rapid generation of a three-degree-of-freedom entry trajectory under large-scale lateral maneuvering. The simulation results demonstrated that compared with the existing methods, the proposed method can adaptively divide flight stages, ensuring better multitask applicability and higher computational efficiency.

Composite continuous fast nonsingular terminal sliding mode trajectory tracking control for Mars entry vehicle

SummaryThis paper presents a composite continuous fast nonsingular terminal sliding mode (CCFNTSM) trajectory tracking control method for Mars entry vehicle. Firstly, the trajectory tracking is transferred into the tracking of the pre‐designed drag acceleration. Secondly, the finite‐time disturbance observer (FTDO) is introduced to estimate the matched and mismatched disturbances. And then, the dynamical fast nonsingular terminal sliding mode manifold is designed based on the estimation information. Finally, the CCFNTSM controller is constructed and its continuity is guaranteed by employing the power function of sliding variable to replace the constant switching gain. Numerical simulation results validate the effectiveness of the proposed control method.

Drag augmentation for collision avoidance in LEO

Space debris proliferation in Low Earth Orbit (LEO) has heightened the urgency for effective Collision Avoidance Manoeuvres (CAMs). This work presents a pioneering framework aimed at devising a novel collision avoidance manoeuvre design for drag-augmentation small platforms. The framework facilitates the alteration of drag acceleration by adjusting the satellite’s ballistic coefficient through cross-sectional area changes. This approach generates controlled deviations in the nominal trajectory, offering a feasible solution for collision avoidance without necessitating thrusters or fuel consumption.The paper introduces an analytical method for propagating drag augmentation manoeuvres and applies it for collision avoidance studies purposes. The formulation followed to implement this manoeuvre within a numerical propagator is presented, as well as the optimisation process developed for the application of drag augmentation manoeuvres in collision avoidance scenarios. Real-world applications showcase the suitability of these approaches, confirming the use of drag augmentation manoeuvres to avoid collisions in LEO. Additionally, the requirements and boundaries of the strategy, including altitude restrictions and satellite-specific properties, are discussed.

Distinguishing Density and Wind Perturbations in the Equatorial Thermosphere Anomaly

AbstractIn this paper, the equatorial thermosphere anomaly (ETA) is investigated using accelerometer measurements to determine whether the feature is density‐dominated, wind‐dominated, or some combination of the two. An ascending‐descending accelerometry (ADA) technique is introduced to address the density‐wind ambiguity that appears when interpreting the ETA in atmospheric drag acceleration analyses. This technique separates ascending and descending acceleration measurements to determine if a wind's directionality influences the interpretation of the observed ETA feature. The ADA technique is applied to accelerometer measurements taken from the Challenging Minisatellite Payload mission and has revealed that the ETA is primarily density‐dominated from 9:00 to 16:00 local time (LT) near 400 km altitude, with the acceleration perturbations behaving similarly between 2003 and 2004 across all seasons. This finding suggests that the perturbations in the acceleration due to in‐track wind perturbations are small compared to the perturbations due to mass density, while indicating that the formation mechanisms across these local times are similar and persistent. The results also revealed that in the terminator region at 18:00 LT the acceleration perturbations deviate appreciably between ascending and descending passes, indicating different or multiple processes occurring at this local time compared to the 9:00–16:00 LT ascribed to the ETA. These results help constrain ETA formation theories to specific local times and thermospheric property responses without the use of supplemental wind measurements, while also indicating regions where in‐track winds cannot always be neglected.

Influence of egg sacs on the swimming performance of freshwater cyclopoid copepods

Abstract Female cyclopoid copepods carry their embryos in egg sacs that impact swimming performance until nauplii hatch. We studied kinematic parameters and mechanical energy of small routine jumps and large escape jumps of non-egg-carrying (NEC) and egg-carrying (EC) females of Mesocyclops leuckarti and Macrocyclops albidus. The drag and body acceleration costs for EC females of M. leuckarti and M. albidus during routine jumps were 28 and 40%, respectively, higher than those for NEC females moving at the same speed. Maintaining position in the water column by small jumps was more costly for EC females, requiring 2.2–2.3 times more jumps and energy. Consequently, the persistence of EC females was limited in the open water. In M. leuckarti and M. albidus, the average speed and distances of jumps were 5–6 and 1.5–2.2 times higher, respectively, and the duration of jumps was 2.2–2.5 times shorter during escape than routine swimming. The maximum jumping speeds of NEC females, 40.6 and 50.5 cm s−1, respectively, were 12–14% higher than those of EC females, whereas their power and cost of transport were 16 and 23% lower, respectively. These results clearly indicated that egg sacs impair swimming and increase energetic costs of movement.

Multiple Leap Maneuver Trajectory Design and Tracking Method Based on Prescribed Performance Control during the Gliding Phase of Vehicles

A novel standard trajectory design and tracking guidance used in the multiple active leap maneuver mode for hypersonic glide vehicles (HGVs) is proposed in this paper. First, the dynamic equation and multiconstraint model are first established in the flight path coordinate system. Second, the reference drag acceleration-normalized energy (D-e) profile of the multiple active leap maneuver mode is quickly determined by the Newton iterative algorithm with a single design parameter. The range to go error is corrected by the drag acceleration profile update algorithm, and the drag acceleration error of the gliding terminal is corrected by the aerodynamic parameter estimation algorithm. Then, the reference drag acceleration tracking guidance law is designed based on the prescribed performance control method. Finally, the CAV-L vehicle model is used for numerical simulation. The results show that the proposed method can satisfy the design requirements of drag acceleration under multiple active leap maneuver modes, and the reference drag acceleration can be tracked precisely. The adaptability and robustness of the proposed method are verified by the Monte Carlo simulations under various combined deviation conditions.

Thermospheric Density Estimation Method Using a First-Order Gauss–Markov Process

Low-Earth-orbit (LEO) spacecraft are significantly influenced by atmospheric drag. Accurately estimating thermospheric density is pivotal for the precise calculation of drag acceleration. However, thermospheric density along a specific orbit, computed using existing thermospheric models, has certain inaccuracies. In this work, a first-order Gauss–Markov process is used to model the deviation of atmospheric drag acceleration. With the Markov parameter of the initial state iteratively computed through sequential estimation and the smoothing method, the thermospheric density is derived from high-precision GPS measurements. In simulation scenarios, the root-mean-square error and relative error of the estimated thermospheric density reduce by about 45 and 50% relative to the prior density, respectively. Using the estimated density for orbit propagation, satellite trajectories’ one-day position and velocity error are, respectively, within 100 m and 0.1 m/s, and an average improvement in orbit precision is over 80%. The proposed method has been applied to the real Tsinghua Science Satellite (Q-SAT) GPS measurements for effectiveness verification. It shows strong adaptability under extreme space weather and during the occurrence of geomagnetic storms. Due to the estimated Markov parameter of the initial state obeying the Langevin dynamics properties, the proposed method also offers short-term thermospheric density forecasting potential.

Adaptive dynamic programming based composite control for profile tracking with multiple constraints

A composite control method based on adaptive dynamic programming (ADP) is developed to solve the profile tracking problem of the hypersonic gliding vehicle (HGV) with multiple constraints (flight and input constraints). First, based on the framework of the standard profile guidance method, a standard drag acceleration–velocity profile is planned as the tracking target, which satisfies the flight constraints. Second, a composite controller based on ADP and dynamic surface control (DSC) is proposed to track the planned profile and satisfy both the terminal conditions and the input constraint. An ADP method is developed to realize the optimal control through a critic neural network (NN) approximation for the solution of Hamilton–Jacobi–Bellman (HJB) equation. By using DSC method, the steady control is realized. Finally, the states of the closed-loop system and the weight estimation error are proved to be uniformly ultimately bounded, and the effectiveness of the proposed composite control method is verified via simulations.

Chebyshev-series solutions for nonlinear systems with hypersonic gliding trajectory example

In order to design a drag-based predictor-corrector entry guidance in the future, new analytical formulae, expressed as finite-term Chebyshev series, are developed for fast predicting a three-dimensional (3D) Hypersonic Gliding Trajectory (HGT) by proposing a Newton-like method to solve a highly nonlinear entry dynamics model. Specifically, first, a new reduced-order dynamics model is developed by properly simplifying the original dynamics model such that the drag acceleration (AD) and the ratio of the horizontal component of the lift to the drag (LDz), which are important for governing the 3D trajectory, emerge as key parameters of the dynamical equations. Then, AD and LDz are planned as polynomials of speed. However, the simplified model is still not easy to solve due to its high nonlinearity. To deal with the difficulty, a Newton-like method is proposed to transform the simplified model into Linear Differential Recurrence Equations (LDREs). By evaluating the LDREs repeatedly, a sequence of approximations of the 3D HGT can be generated, the limit of which is the trajectory specified by that simplified model. In fact, due to the fast convergence speed of the Newton-like method, the LDREs need be solved only twice to achieve high accuracy. By using Chebyshev series to approximate some complex terms appearing in the LDREs, the LDREs become analytically solvable. As a result, the approximate analytical solutions to the 3D HGT are obtained. Simulation results show that the analytical solutions need to consume less than 1 ms of time on a laptop computer and have errors of less than 4 percentage. The computational efficiency is fundamental for onboard predictor-corrector guidance.

Analysis of Orbital Atmospheric Density from QQ-Satellite Precision Orbits Based on GNSS Observations

Atmospheric drag provides an indirect approach for evaluating atmospheric mass density, which can be derived from the Precise Orbit Determination (POD) of Low Earth Orbit (LEO) satellites. A method was developed to estimate nongravitational acceleration, which includes the drag acceleration of the thermospheric density model and empirical force acceleration in the velocity direction from the centimeter-level reduced-dynamic POD. The main research achievements include the study of atmospheric responses to geomagnetic storms, especially after the launch of the spherical Qiu Qiu (QQ)-Satellite (QQ-Satellite) with the global navigation system satellite (GNSS) receiver onboard tracking the Global Positioning System (GPS) and Beidou System (BDS) data. Using this derivation method, the high-accuracy POD atmospheric density was determined from these data, resulting in better agreement among the QQ-Satellite-derived densities and the NRLMSISE-00 model densities. In addition, the POD-derived density exhibited a more sensitive response to magnetic storms. Improved accuracy of short-term orbit predictions using derived density was one of the aims of this study. Preliminary experiments using densities derived from the QQ-Satellite showed promising and encouraging results in reducing orbit propagation errors within 24 h, especially during periods of geomagnetic activity.

Analysis of precise orbit determination for maneuvering HY2C and HY2D satellites using DORIS/RINEX data

Accurate Low Earth Orbit satellite (LEO) orbits are essential for many applications, such as for assessing the change in current global mean sea level, or solving the ground coordinates and velocities of tracking system networks such as the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite). Maneuvers are required for any remote sensing satellite to maintain the reference orbit. The presence of orbit maneuvers poses a challenge for Precise Orbit Determination (POD). At present, most maneuver analysis is conducted using the reduced-dynamic POD approach thus making it impossible to separate specific forcing effects, such as atmospheric drag or maneuver acceleration, from the generic empirical acceleration parameters used in the approach to absorb remaining errors. Therefore, this paper adopts the dynamic model method to better evaluate maneuver accelerations estimated from HY2C and HY2D DORIS/RINEX data. And, we focus on the determination of highly accurate HY2C and HY2D orbits over spans which can include maneuver events. In the course of this study, a maneuver model strategy is developed, and we use the DORIS/RINEX data of HY2C and HY2D satellites to validate the method, and to show it is reliable. Our analysis results are: (1) The standard deviations of DORIS residuals for HY2C and HY2D satellites are respectively 0.45 mm/s and 0.43 mm/s, and these residual values have no significant fluctuations and systematic errors. (2) In the case when there are no DORIS tracking data over the maneuver period, extending the period by 30 s to include tracking will improve orbit accuracy sufficiently to even satisfy altimetry requirements. (3) Based on the developed maneuver model strategy, the radial orbit differences can achieve about 1.70 cm, that can satisfy high precision altimetry requirements of HY2C and HY2D satellites. (4) When the model strategy is used on days containing no orbit maneuvers, the average RMS (root mean square) of radial orbit differences for these days is 1.60 cm, which shows that our maneuver model strategy is also reliable.

Adaptive entry guidance for the Tianwen-1 mission

To meet the requirements of the Tianwen-1 mission, adaptive entry guidance for entry vehicles, with low lift-to-drag ratios, limited control authority, and large initial state bias, was presented. Typically, the entry guidance law is divided into four distinct phases: trim angle-of-attack phase, range control phase, heading alignment phase, and trim-wing deployment phase. In the range control phase, the predictor—corrector guidance algorithm is improved by planning an on-board trajectory based on the Mars Science Laboratory (MSL) entry guidance algorithm. The nominal trajectory was designed and described using a combination of the downrange value and other states, such as drag acceleration and altitude rate. For a large initial state bias, the nominal downrange value was modified onboard by weighing the landing accuracy, control authority, and parachute deployment altitude. The biggest advantage of this approach is that it allows the successful correction of altitude errors and the avoidance of control saturation. An overview of the optimal trajectory design process, including a discussion of the design of the initial flight path angle, relevant event trigger, and transition conditions between the four phases, was also presented. Finally, telemetry data analysis and post-flight assessment results were used to illustrate the adaptive guidance law, create good conditions for subsequent parachute reduction and power reduction processes, and gauge the success of the mission.

Analytical trajectory prediction for near-first-cosmic-velocity atmospheric gliding using a perturbation method

This paper investigates a special atmospheric glide problem where the gliding speed is close to the first cosmic velocity (FCV). Here, the centrifugal force and gravity almost balance each other, and thus in the local vertical direction the lift force required to maintain the glide is almost zero. However, all the existing analytical solutions for 3-D gliding trajectories were derived under the condition that the vertical component of lift is large enough, and thus become invalid for the special glide case. To overcome the shortage of the existing studies, we abandon the vertical component of lift, but instead plan the profile of drag acceleration (aD) to derive the analytical solutions for the 3-D special gliding trajectory. By simplifying the nonlinear equations of motion properly, a reduced-order system is obtained and governed by aD and L2/D, where L2/D represents the ratio of the local horizontal component of lift to drag. Subsequently, by proposing a perturbation method to expand the system in Taylor series with finite terms, two analytically solvable subsystems are developed. As a result, the analytical trajectory solutions are obtained successfully. Additionally, as verified by the simulation results, the new solutions are also applicable to the conventional glide problem where the speed is much less than the FCV, and found to be much more accurate than the existing solutions because the new solutions give full consideration to the coupling of the longitudinal and lateral equations.

Rapid Algorithm for Generating Entry Landing Footprints Satisfying the No-Fly Zone Constraint

An online estimation algorithm of landing footprints based on the drag acceleration-energy profile is proposed for an entry hypersonic vehicle. Firstly, based on the Evolved Acceleration Guidance Logic for Entry (EAGLE), drag acceleration-energy profiles are designed. To track the drag acceleration-energy profile obtained by the interpolation, a drag acceleration tracking law is designed. Secondly, based on the constraint model of the no-fly zone, flying around strategies are proposed for different conditions, and a reachable area algorithm is designed for no-fly zones. Additionally, by interpolating the minimum and maximum drag acceleration profiles, the terminal heading angle constraint is designed to realize the accurate calculation of the minimum and maximum downrange ranges by adjusting the sign of the bank angle. In this way, the distribution of landing footprints is more reasonable, and the boundary of a reachable area is more accurate. The simulation results under typical conditions indicate that the proposed method can calculate landing footprints for different situations rapidly and with the good adaptability.

Sounding the Atmospheric Density at the Altitude of LARES and Ajisai during Solar Cycle 24

During Solar Cycle 24, the passive spherical satellites LARES and Ajisai, placed in nearly circular orbits with mean geodetic altitudes between 1450 and 1500 km, were used as powerful tools to probe the neutral atmosphere density and the performances of six thermospheric models in orbital regimes for which the role of dominant atomic species is contended by hydrogen and helium, and accurate satellite measurements are scarce. The starting point of the analysis was the accurate determination of the secular semi-major axis decay rate and the corresponding neutral drag acceleration in a satellite- centered orbital system. Then, for each satellite, thermospheric model and solar activity level, the drag coefficients capable of reproducing the orbital decay observed were found. These coefficients were finally compared with the physical drag coefficients computed for both satellites in order to assess the biases affecting the thermospheric density models. None of them could be considered unconditionally the best; the specific outcome depending on solar activity and the regions of the atmosphere crossed by the satellites. During solar maximum conditions, an additional density bias linked to the satellite orbit inclination was detected.

Balancing differential drag with Coulomb repulsion in low earth orbit plasma wakes

A novel method for close-proximity formation flying under differential atmospheric drag using Coulomb forces is investigated for applications in Earth sensing, space-situational awareness (SSA), and aeronomy. Objects in LEO are supersonic with respect to the ambient environment, creating a thinned out wake region behind the craft as it travels through the ionosphere. Objects within this wake experience little drag acceleration and are able to attain voltages much greater than in the ambient ionospheric plasma, creating implications for the design and control of close-proximity leader–follower spacecraft pairs. The proposed system consists of a leader craft with a set of affixed, conducting spheres and a charged follower craft located in the wake of the leader. The differential drag acceleration between the leader and follower craft is countered by a controlled Coulomb repulsion to maintain precise separation. The charged structure on the rear of the leader craft is designed such that the charged follower craft sits in an electrostatic potential well which opposes off-axis perturbations. A conceptual method for controlling such a pair without the use of propellant using a set of charged spheres is investigated, with nonlinear models of the system’s relative motion derived and discussed. Linearized models are used to demonstrate the local controllability of the system to demonstrate the proposed system’s merit. This linear analysis is used to derive conditions on controllability and control performance under different charge geometries and environmental assumptions.

Ionospheric drag for accelerated deorbit from upper low earth orbit

Orbit debris mitigation restrictions placed on the growing number of miniaturised spacecraft often constrain their operational altitudes to less than approximately 600km where drag accelerations are sufficient to deorbit the spacecraft within 25 year guidelines. Operation at higher, Low Earth Orbit (LEO) altitudes often necessitates active measures to deorbit miniaturised spacecraft such as propulsion systems. However, the inclusion of propulsion systems is not always desirable because of the added cost and complexity. This work investigates the feasibility of ionospheric drag, the component of drag caused by an electrically charged body’s exchange of momentum with the ionosphere, to accelerate the deorbit of miniaturised spacecraft in high LEO (600–1000 km altitude). This work studies how actively charging the surface of a miniaturised satellite in high LEO may enhance the overall magnitude of the drag acceleration, due to the ionospheric drag, acting to deorbit the spacecraft. This is achieved using surrogate models of the charged drag coefficient, as a function of plasma scaling parameters, generated by Particle-in-Cell simulations. The charged drag coefficient surrogate model is incorporated into an orbit propagator where deorbit times are predicted over various orbital and vehicular initial conditions. Results suggest that the magnitude of ionospheric drag can be an order of magnitude larger than the neutral drag at 850 km altitude compared to approximately half the magnitude of neutral drag at 500 km altitude. Therefore, ionospheric drag is relatively more efficient at deorbiting spacecraft at high LEO compared to neutral drag. Additionally, the magnitude of ionospheric drag is tailorable based on changes in the electrical surface potential of the satellite relative to a quasi-neutral free-stream plasma. The primary payload of many miniaturised spacecraft often require high-voltage electrical systems. These same electrical systems could conceivably be utilised to generate ionospheric drag via surface charging, at the end of the mission-life, at little additional cost or system complexity. Thus, the implications of this work include the possible uncovering of a simple mechanism for deorbiting miniaturised spacecraft from high LEO altitudes for compliance with orbit debris mitigation guidelines.

Differential drag-based multiple spacecraft maneuvering and on-line parameter estimation using integral concurrent learning

In this paper, a set of low Earth orbiting spacecraft consisting of multiple chasers and a single cooperative or unknown target, is considered for rendezvous and along-orbit formation maneuvers. Each maneuverable spacecraft can change its experienced atmospheric drag acceleration by extending/retracting dedicated surfaces. A Lyapunov-based adaptive controller is designed using an Integral Concurrent Learning (ICL)-based adaptive update law and the Schweighart-Sedwick equations of relative motion to regulate the in-plane relative states of each target-chaser pair. The controller is designed to compensate for uncertainties in atmospheric density, drag or ballistic coefficient and the velocity relative to the atmosphere of each spacecraft in the fleet. When the system is sufficiently excited, the controller also provides estimation of the uncertain parameters. Numerical simulations using nonlinear dynamics for each spacecraft and the NRLMSISE-00 atmospheric density model, are conducted to validate the performance of the controller.

Precise Reentry Maneuver Estimation Using Radar Trilateration

An iterated recursive filter is formulated for radar trilateration of reentry maneuvers. Using range and range rate measurements from three radars in a regional network, trilateration provides very accurate three-dimensional position and velocity measurements, which improves drag and lift acceleration estimates. A new first-order, nonlinear vector differential equation specifies the rate of change of acceleration (or jerk). Acceleration process noise is determined from dynamic pressure estimates and mean-square area-to-mass covariances, which are derived from probability density functions that statistically characterize a family of expected maneuvers. Trilateration accuracies are demonstrated for demanding reentry maneuvers. Monte Carlo simulations assess accuracy sensitivity to modeling assumptions and to off-nominal reentry trajectories.