Differential Drag Research Articles

Aerodynamic Evaluation of Static and Dynamic Stability Characteristics of Double-Delta Wings

Vortex interactions and breakdown play a critical role in determining the static and dynamic stability of aircraft, particularly at high angles of attack. This study investigates the relationship between vortex interactions and aircraft stability characteristics, focusing on how chord ratio, angle of attack, and sideslip angle influence stability metrics. Utilizing force and moment measurements along with pressure-sensitive paint (PSP) for surface pressure distributions, the results show the effects of varying double-delta wing chord ratios at a target Mach number of 0.15. The stability metrics derived from force and moment measurements demonstrate directional stability improvements with increasing sideslip angle due to larger vortex-induced differential drag induced by advanced windward wing vortex breakdown. This asymmetric vortex breakdown was confirmed through PSP-measured surface pressure distributions. The study metrics revealed trend reversals in lateral stability due to the varying state of vortex systems on different models, and higher reduced frequencies, pitch rates, and chord ratios correlated with greater dynamic instability and sensitivity. This is attributed to the more rapid and extensive vortex breakdown associated with these higher parameters. These findings provide deeper insights into the flow physics governing high-alpha maneuvers, offering a foundation for future research, enhancing the design and performance of next-generation aircraft.

Analysis of Surface Drag Reduction Characteristics of Non-Smooth Jet Coupled Structures

To enhance the service life of shipping equipment and minimize surface wear, this study employs biomimetic principles, integrating fitted structures with jet dynamics to model three configurations: non-smooth structures, single jet structures, and non-smooth jet-coupled structures. We utilized the SST k-ω turbulence model for numerical simulations to investigate the drag reduction characteristics of these structural models. By varying the jet angle and speed, we analyzed the changes in viscous resistance, pressure differential resistance, and drag reduction rates at the wall surface. Furthermore, the mechanisms of compressive stress, velocity fields, vortex structures, and shear stress on drag-reducing surfaces were elucidated, revealing how these factors contribute to drag reduction in non-smooth jet-coupled structures. The results indicate that the non-smooth jet-coupled structure exhibits superior drag reduction performance at a main flow field velocity of 20 m/s. As the jet velocity increases, the viscous drag on the surface of the non-smooth jet-coupled structure decreases, while the pressure differential drag increases. Conversely, variations in the jet angle have a minimal effect on viscous drag but lead to a reduction in pressure differential drag. Specifically, when the jet velocity is set at 1 m/s, and the jet angle is 60°, the drag reduction achieved by the non-smooth jet-coupled structure peaks at 7.48%. Additionally, the non-smooth jet-coupled structure features a larger area characterized by low shear stress, along with an increased boundary layer thickness at the bottom; this configuration effectively reduces surface velocity and consequent viscous drag.

Innovative Systems Engineering Solutions for Power-Positive Operations: Navigating the Multi-Constraint Challenges of the SWARM-EX CubeSat Mission

Although the small stature of CubeSats and their standardized deployer options help to lower unit development cost and facilitate launch opportunities, the physical size limits of CubeSats prove to be a double-edged sword vis-à-vis sustaining a stable power state while hosting instruments with high power demands and often strict pointing requirements. For the Space Weather Atmospheric Reconfigurable Multiscale-EXperiment (SWARM-EX), this issue is magnified by the mission’s ambitious goals; to comply with mission requirements, a SWARM-EX spacecraft is required to concurrently (1) point the science instruments no more than 30° off ram when they are operational, (2) point the GPS patch antenna no more than 30° off zenith at least once per orbit, (3) point the boresight of the X-Band patch antenna no more than 18° from the ground station during downlink, (4) maximize the differential cross-sectional area during differential drag maneuvers, and (5) maximize solar array power generation at all times. Consequently, leading-edge CubeSat missions like SWARM-EX require innovative systems engineering solutions to remain power-positive during on-orbit operations. Through the design of a comprehensive module-based concept of operations, orbital power generation simulations, intricate constrained attitude profiles, and a configurable battery state of charge simulation tool, the SWARM-EX mission designers have conceived a plan to retire the risk of not maintaining a power-positive state while successfully meeting all mission requirements; it is the aim of the authors to illuminate these strategies as a case study.

Constraint tightening-based control for small-satellite formations using differential aerodynamic forces

Aerodynamic forces hold significant promise for controlling small-satellite formations in low Earth orbit. However, significant challenges still exist regarding complex input constraints and their application to multi-satellite formations. This paper proposes a constraint tightening-based control scheme for small-satellite formations, utilizing differential drag and lift as actuating forces. Two attitude adjustment strategies, namely the reorientation strategy and the single-radial rotation strategy, are compared in terms of their control effectiveness and applicability. Relative aerodynamic coefficients are employed as control inputs in view of their solid reachable region, followed by the development of a decoupling algorithm for determining pointing angles. Through a method that tightens the reachable region using liner models, the input constraints are linearized and can be explicitly expressed. Subsequently, an observer-based Model Predictive Control (MPC) algorithm is formulated to meet these linearized input constraints and provide feedforward compensation for system disturbances. This discrete algorithm enables practical onboard implementations owing to its low computational complexity. Additionally, a concept of overall computation for all satellites’ attitudes is proposed to adapt the control scheme for multi-satellite formations. Hardware-in-the-loop simulations are conducted to evaluate the control scheme's performance in along-track and circular formations, accounting for uncertainties in aerodynamic forces and attitude dynamics.

Estimation of the possibility of matching the relative motion of nanosatellites under active aerodynamic control

The article discusses the prospects of utilization of aerodynamic control to maintain the formation of nanosatellites of the CubeSat class. The purpose of this work is to estimate the limits of the application of active aerodynamic control to stabilize the relative motion of two CubeSat 3U satellites in a sun-synchronous orbit with a height of 570 km. A review of theoretical information about aerodynamic forces acting on artificial Earth satellites is carried out, within the framework of which models of the Earth's upper atmosphere are considered. Aspects of creating a differential drag force for nanosatellites as an active control actuating mechanism are considered. To study the orbital motion of satellites under the action of aerodynamic control using the General Mission Analysis Tool program, a group flight of two spacecraft was simulated taking into account the factors causing orbital disturbances. Based on the results of experiments, the dynamics of the inter-satellite distance was studied, and a conclusion was made about the possibility of using an aerodynamic differential force to achieve a stable relative motion.

Ground Track Control Using Differential Drag for Small Earth Observation Satellite Constellations

This paper presents a framework for the acquisition and the maintenance of ground track configurations of small Earth observation satellite constellations. Specifically, the relative ground track spacings at the equator are controlled using differential drag to achieve the desired Earth coverage pattern without a propulsion system. The proposed framework is based on a divide-and-conquer approach to solving the optimal differential drag constellation management problem and comprises five processes for solving the related subproblems. The proposed framework can be used to manage end-to-end applications, from establishing the initial acquisition plan for the target ground track configuration, to the closed-loop command generation for the ground track acquisition and maintenance. Using the proposed framework, optimal acquisition plans with the minimum time and minimum altitude losses can be identified in a systematic way. The usefulness of the proposed method is demonstrated based on simulations incorporating the uncertainties in drag prediction.

A planning tool for optimal three-dimensional formation flight maneuvers of satellites in VLEO using aerodynamic lift and drag via yaw angle deviations

Differential drag is a promising option to control the relative motion of distributed satellites in the Very Low Earth Orbit regime which are not equipped with dedicated thrusting devices. A major downside of the methodology, however, is that its control authority is (mainly) limited to the in-plane relative motion control. By additionally applying differential lift, however, all three translational degrees-of-freedom become controllable. In this article, we present a tool to flexibly plan optimal three-dimensional formation flight maneuvers via differential lift and drag. In the planning process, the most significant perturbing effects in this orbital regime, namely the J2 effect and atmospheric forces, are taken into account. Moreover, varying atmospheric densities as well as the co-rotation of the atmosphere are considered. Besides its flexible and high-fidelity nature, the major assets of the proposed methodology are that the in-and out-of-plane relative motion are controlled simultaneously via deviations in the yaw angles of the respective satellites and that the planned trajectory is optimal in a sense that the overall decay during the maneuver is minimized. Thereby, the remaining lifetime of the satellites is maximized and the practicability and sustainability of the methodology significantly increased. To the best of the authors knowledge, a tool with the given capabilities has not yet been presented in literature. The resulting trajectories for three fundamentally different relevant formation flight maneuvers are presented and discussed in detail in order to indicate the vast range of applicability of the tool.

Low-Earth-Orbit Constellation Phasing Using Miniaturized Low-Thrust Propulsion Systems

Many low-Earth-orbit constellations consist of multiple small satellites that are launched together in batches, and which make use of differential atmospheric drag for subsequent deployment and phasing. Depending on the initial altitude, this process can potentially take many months, or even years, to complete, and satellite altitudes can only ever be decreased, potentially affecting mission lifetimes. Miniaturized low-thrust propulsion systems are one option to achieve faster phasing and can additionally increase the constellation lifetime through drag compensation. Here, an analytical and numerical study comparing differential drag and low-thrust propulsion for constellation phasing is performed. Satellite electrical constraints associated with power generation and battery cycling life represent important factors that can decrease the performance of an onboard propulsion system. Despite these constraints, low-thrust propulsion can reduce total phasing times by an order of magnitude, or more, for altitudes in the range 300–700 km, while also increasing satellite flexibility and introducing a number of operational advantages. Remaining propellant can be used for drag compensation and collision avoidance maneuvers, while also reducing deorbiting times by many years.

Economic justification for the use of a vertical axis wind power plant in wind conditions of Russia

The purpose of the study is to provide an economic justification of the application efficiency of vertical axis wind-driven power plants using the principle of differential blade drag under low natural wind speeds from 1 to 15 m/s. The estimated cost is determined by the resource-index method. Calculations are made in two stages: at the first stage a statement is compiled where the consumption of resources for the design volume of work is determined according to the state unit estimate standards collections; at the second stage a local resource estimate is made, and the resource consumption in natural units is converted to cost estimates (in the prices of 2000 year). Local estimates are made using the GRAND-SMETA software package. All costs of construction materials for the wind turbine and supporting structure were assumed at the commercial cost, which was translated to the budget cost of October 2019 using deflators. The transition indices from the prices of 2000 to the prices of 2019 are applied to the cost of materials and machinery operation (without remuneration of engine-drivers) as well as to the amount of labour remuneration for installers and engine-drivers. The cost of the installation set calculated by the strength at 20 m/s natural speed is 1643.591 thousand rubles. This allowed to determine the cost of 1 kWh, which depends on the service life and the average annual wind speed. At a wind speed of 4 m/s the cost is 7.12 rub/kWh; at a wind speed of 8 m/s it is 2.19 rub/kWh. At wind speeds from 5 m/s to 11 m/s with equal exposure time intervals, the average cost of 1 kWh will be within 3.14 rub/kWh. Conducted studies have confirmed the effective use of the proposed vertical axis wind power plant under conditions of low natural wind speeds in Russia. The installation is proved to be competitive in comparison with the traditional methods of energy generation.

Input-output linearized spacecraft formation control via differential drag using relative orbital elements

The derivation, implementation, and performance assessment of a differential drag based algorithm, designed for spacecraft formation control using a relative orbital elements formulation, is presented. In contrast to similar approaches found in literature, the underlying motion dynamics model used to derive the control law includes J 2 perturbation as well as atmospheric drag perturbation based on a nonlinear density model. The basic idea of the control algorithm is to algebraically transform the nonlinear plant into a linear substitute. The resulting control law can be interpreted as combined feedforward and feedback PID control, applied to the linear substitute model. Motion dynamics and perturbations are accounted for in a feedforward branch while a PID feedback branch undertakes the cancellation of errors caused by model uncertainties and unmodeled physics. For linearized plant models, the computation of a feedforward branch is straight forward from the state transition matrix. In the nonlinear case proposed in this paper, the inclusion of a feedforward signal is achieved using the input-output linearization technique, yielding a nonlinear and globally valid control law. Sample numerical simulations are presented to support the validity of the controller and to demonstrate its performance compared to a simple PID controller. Simulation results show enhanced tracking performance of the mean along-track separation reference signal and reduced control effort. Moreover, input–output linearization enables the control of a large set of operating points using one set of control parameters.

Investigation on the Aerodynamic Efficiency of Braking Spoiler for High Speed Train Applications

The demand for high speed rail networks is rapidly increasing in developing countries like India. One of the major constraints in the design and implementation of high speed train is the braking efficiency with minimum friction losses. Recently, the aerodynamic braking concept has received good attention and it has been incorporated for high speed bullet trains as a testing phase. The braking performance is extremely important to ensure the passenger safety specifically for the trains moving at more than 120[Formula: see text]km/h. In this paper, an Indian train configuration WAP7 (wide gauge AC electric passenger, Class 7) has been assumed with the locomotive and one passenger car. Aerodynamic braking system design is done by opening a spoiler over the train to amplify the aerodynamic drag at high speeds. The magnitude of braking force depends on the position and orientation of the braking spoiler. It creates differential drag forces at various deflection angles to decelerate the trains instantaneously in proportion to the running speeds. Drag created by the braking spoiler is observed numerically with the help of CFD simulation tools for further validation through wind tunnel experiments. Striking aerodynamic results are obtained with and without braking spoilers on the passenger cars and the spoiler at [Formula: see text] orientation makes greater drag coefficient as compared to the other angles.

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.

Decentralized differential drag based control of nanosatellites swarm spatial distribution using magnetorquers

Nanosatellites in the swarm initially move along arbitrary unbounded relative trajectories according to the launch initial conditions. Control algorithms developed in the paper are aimed to achieve the required spatial distribution of satellites in the along-track direction. The paper considers a swarm of 3U CubeSats in LEO, their form-factor is suitable for the aerodynamic control since the ratio of the satellite maximum to minimum cross-section areas is 3. Each satellite is provided with the information about the relative motion of neighboring satellites inside a specified communication area. The paper develops the corresponding decentralized control algorithms using the differential drag force. The required attitude control for each satellite is implemented by the active magnetic attitude control system. A set of decentralized control strategies is proposed taking into account the communicational constraints. The performance of these strategies is studied numerically. The swarm separation effect is demonstrated and investigated.

Charge-product control approach to electrostatic leader-follower formations in LEO plasma wakes

The feasibility of using electrostatic forces to stabilize a close-proximity leader-follower formation is investigated. The leader craft is equipped with a set of affixed spheres whose charge is modulated to hold the charged follower craft along a proscribed trajectory to its nominal leader-relative position. This charge structure and the follower craft are constrained to remain in the plasma wake generated behind all LEO craft because the more-dense ambient plasma outside the wake prevents object charging and electric field propagation. Once the formation is achieved, a controlled electric field is generated by the leader to counter relative accelerations from perturbations like differential drag and solar radiation pressure, holding the follow near its nominal position. Two controllers are derived for the system described, incorporating Coulomb accelerations and linearized gravity and drag accelerations. Simulations are run under unmodeled perturbations and sensor noise for different scenarios, demonstrating the challenges and benefits associated with electrostatic actuation.

Improved success rates of rendezvous maneuvers using aerodynamic forces

Several small, unconnected satellites flying in formation are a frequently discussed option to replace large satellites due to advantages such as increased flexibility, reduced costs and enhanced reliability. Using differential aerodynamic forces as a means to maintain the formation despite present perturbations, to perform formation reconfiguration or to initiate a rendezvous maneuver is a promising propellant-less alternative to chemical and/or electric propulsion systems. Subjected to uncertainties, dynamic variations and non-linearities its implementation in a real mission is, however, challenging. A common practice to either design suitable reference trajectories for robust control strategies or to gain deeper insights into the methodology is to use linearized relative motion models and a constant density assumption. Following this practice, multiple previous studies developed and enhanced analytic control algorithms to zero out the relative position and velocity of two spacecraft utilizing differential aerodynamic forces. Even though aerodynamic lift expands the controllability to all three translational degrees of freedom, it has been frequently neglected due to the low lift coefficients experienced in orbit so far. And even if considered, analysis has shown that the feasibility range of using the differential lift for the eccentricity control of the in-plane motion is extremely limited compared to using differential drag. However, two different possible options, namely applying enhanced algorithms to decrease the eccentricity before even initializing the eccentricity control phase as well as using advanced satellite surface materials targeting specular or quasi-specular reflection and thereby increasing the differential acceleration forces, have been suggested to increase the feasibility domain of the methodology. In this article, the effectiveness of the proposed adjustments is analyzed in a Monte-Carlo approach by applying them to the analytic control algorithms introduced in the literature. Since these are based on the linearized Schweighart-Sedwick equations, so is the presented analysis. Moreover, additional modifications to the algorithms are made to reduce the maneuver time of one of the respective control phases. The results show that the analyzed options noticeably improve the success rates of the maneuvers. Especially the feasibility range of the lift-based control algorithms is enlarged considerably. In addition, the implemented modifications are shown to consistently reduce the maneuver time of the respective control phase. Consequently, the presented analysis improves the current state of the art of the analytically designed rendezvous trajectories and provides valuable new insights into the methodology of using differential aerodynamic forces as a means of relative motion control.

Performance Analysis of Low-Gain Feedback for Saturated Differential Drag in a High-precision Orbit Propagator

Performance Analysis of Low-Gain Feedback for Saturated Differential Drag in a High-precision Orbit Propagator

Ionospheric Drag for Satellite Formation Control

Constellations of miniaturized satellites that provide novel and cost-effective capabilities are a growing trend for space systems. Economically viable miniature satellite constellations commonly necessitate the exclusion of propulsion systems. A difference in neutral aerodynamic forces between spacecraft, resulting from interactions with the thermosphere, is the prevailing propulsion-free method for maintaining low-Earth-orbit constellations. This work investigates charged aerodynamic forces, which are caused by an electrically charged platform’s interaction with the ionosphere (ionospheric drag), as an actuation mechanism for satellite formation control. Numerical propagations of the relative motion between identically shaped neutral and charged spheres, with artificial surface voltages ranging between and V, indicate that the ensuing magnitude of differential drag, due to ionospheric drag, can nullify an initial 1 m relative semimajor axis within 4 min in the most optimal conditions simulated. Thus, with no technology optimization, this work concludes that ionospheric drag caused by spacecraft charging is sufficient for actuating changes in the orbital semimajor axis; however, it is inferior when compared to techniques for generating differences in neutral drag. Future work will investigate the optimization of ionospheric aerodynamic technologies and techniques to increase the effectiveness of charged aerodynamic formation control.

Output Regulation Control for Satellite Formation Flying Using Differential Drag

This paper proposes a new approach of using differentials in aerodynamic drag in combination with thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation theory for formation-flying missions with combined control action is developed based on the Schweighart–Sedwick relative dynamics equations. The theory is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the perturbations. The parametric Lyapunov algebraic equation is proposed to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation-flying missions. Numerical simulations using a high-fidelity relative dynamics model and a high-precision orbit propagator are implemented to validate and analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm based on actual satellite models.

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed.

Assessment of constellation designs for earth observation: Application to the TROPICS mission

The orbit and constellation design process for Earth observation missions is complex and it involves trades between mission lifetime, instrument performance, coverage, cost, and robustness among others. This paper describes an orbit and constellation design study conducted during Pre-Phase A and Phase A for the NASA-funded Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of SmallSats (TROPICS) mission. Thousands of potential constellations were enumerated, simulated using an open-source astrodynamics library, and compared with one another across multiple dimensions, focusing on cost and coverage considerations. The robustness of different constellations to various hypothetical operational failures (e.g., loss of one satellite or one launch) was systematically assessed. A deployment strategy based on differential drag was proposed and analyzed for selected constellations. Finally, the orbital lifetime of various architectures was also studied with respect to NASA's 25-year de-orbiting recommendation. The contributions of this work include: (1) an exhaustive analysis of figures of merit commonly used in Earth observation orbit design; (2) A methodology to assess robustness of constellations based on a brute-force disjoint scenario simulation approach; (3) Results and recommendations from the mission analysis process for the TROPICS mission.