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Methodologies to determine forces on bones and muscles of body segments during exercise, employing compact sensors suitable for use in crowded space vehicles

Work under this grant was carried out by the author and by a graduate research assistant. An instrumented bicycle ergometer was implemented focusing on the stated objective: to estimate the forces exerted by each muscle of the feet, calf, and thigh of an individual while bicycling. The sensors used were light and compact. These were probes to measure muscle EMG activity, miniature accelerometers, miniature load sensors, and small encoders to measure angular positions of the pedal. A methodology was developed and implemented to completely describe the kinematics of the limbs using data from the sensors. This work has been published as a Master's Thesis by the Graduate student supported by the grant. The instrumented ergometer along with the sensors and instrumentation were tested during a KC-135 Zero-Gravity flight in July, 1994. A complete description of the system and the tests performed have been published as a report submitted to NASA Johnson Space Center. The data collected during the KC-135 flight is currently being processed so that a kinematic description of the bicycling experiment will be soon determined. A methodology to estimate the muscle forces has been formulated based on previous work. The methodology involves the use of optimization concepts so that the individual muscle forces that represent variables in dynamic equations of motion may be estimated. Optimization of a criteria (goal) function such as minimization of energy will be used along with constraint equations defined by rigid body equations of motion. Use of optimization principles is necessary, because the equations of motion alone constitute an indeterminate system of equations with respect to the large amount of muscle forces which constitute the variables in these equations. The number of variables is reduced somewhat by using forces measured by the load cells installed on the pedal. These load cells measure pressure and shear forces on the foot. The author and his collaborators at NASA and at the University of Alabama, Tuscaloosa, are continuing the work of reducing the experimental data from the KC-135 flight, and the implementation of the optimization methods to estimate muscle forces. As soon as results from these efforts are available, they will be published in reputable journals. Results of this work will impact studies addressing bone density loss and development of countermeasures to minimize bone loss in zero gravity conditions. By analyzing muscle forces on Earth and in Space during exercise, scientists could eventually formulate new exercises and machines to help maintain bone density. On Earth, this work will impact studies concerning arthritis, and will provide the means to study possible exercise countermeasures to minimize arthritis problems.

Figueroa, Fernando

Implementation of a three degree of freedom, motor/brake hybrid force output device for virtual environment control tasks

The advent of high resolution, physical model based computer graphics has left a gap in the design of input/output technology appropriate for interacting with such complex virtual world models. Since virtual worlds consist of physical models, it is appropriate to output the inherent force information necessary for the simulation to the user. The detailed design, construction, and control of a three degree freedom force output joystick will be presented. A novel kinematic design allows all three axes to be uncoupled, so that the system inertia matrix is diagonal. The two planar axes are actuated through an offset gimbal, and the third through a sleeved cable. To compensate for friction and inertia effects, this transmission is controlled by a force feedforward and a closed force feedback proportional loop. Workspace volume is a cone of 512 cubic inches, and the device bandwidth is maximized at 60 Hz for the two planar and 30 Hz for the third axis. Each axis is controlled by a motor/proportional magnetic particle brake combination fixed to the base. The innovative use of motors and brakes allows objects with high resistive torque requirements to be simulated without the stability and related safety issues involved with high torque, energy storing motors alone. Position, velocity, and applied endpoint force are sensed directly. Different control strategies are discussed and implemented, with an emphasis on how virtual environment force information, generated by the MIT Media Lab Computer Graphics and Animation Group BOLIO system, is transmitted to the device controller. The design constraints for a kinesthetic force feedback device can be summarized as: How can the symbiosis between the sense of presence in the virtual environment be maximized without compromising the interaction task under the constraints of the mechanical device limitations? Research in this field will yield insights to the optimal human sensory feedback mix for a wide spectrum of control and interaction problems. A flexible research tool that is designed as an easily reproducible product prototype has been constructed to explore the variety of possible force interaction.

Russo, Massimo

Nonstationary Gravity Wave Forcing of the Stratospheric Zonal Mean Wind

The role of gravity wave forcing in the zonal mean circulation of the stratosphere is discussed. Starting from some very simple assumptions about the momentum flux spectrum of nonstationary (non-zero phase speed) waves at forcing levels in the troposphere, a linear model is used to calculate wave propagation through climatological zonal mean winds at solstice seasons. As the wave amplitudes exceed their stable limits, a saturation criterion is imposed to account for nonlinear wave breakdown effects, and the resulting vertical gradient in the wave momentum flux is then used to estimate the mean flow forcing per unit mass. Evidence from global, assimilated data sets are used to constrain these forcing estimates. The results suggest the gravity-wave-driven force is accelerative (has the same sign as the mean wind) throughout most of the stratosphere above 20 km. The sense of the gravity wave forcing in the stratosphere is thus opposite to that in the mesosphere, where gravity wave drag is widely believed to play a principal role in decelerating the mesospheric jets. The forcing estimates are further compared to existing gravity wave parameterizations for the same climatological zonal mean conditions. Substantial disagreement is evident in the stratosphere, and we discuss the reasons for the disagreement. The results suggest limits on typical gravity wave amplitudes near source levels in the troposphere at solstice seasons. The gravity wave forcing in the stratosphere appears to have a substantial effect on lower stratospheric temperatures during southern hemisphere summer and thus may be relevant to climate.

Alexander, M. J.

Force Balance and Substorm Effects in the Magnetotail

A model of the quiet time middle magnetotail is developed using a consistent orbit tracing technique. The momentum equation is used to calculate geocentric solar magnetospheric components of the particle and electromagnetic forces throughout the current sheet. Ions generate the dominant x and z force components. Electron and ion forces almost cancel in the y direction because the two species drift earthward at comparable speeds. The force viewpoint is applied to a study of some substorm processes. Generation of the rapid flows seen during substorm injection and bursty bulk flow events implies substantial force imbalances. The formation of a substorm diversion loop is one cause of changes in the magnetic field and therefore in the electromagnetic force. It is found that larger forces are produced when the cross-tail current is diverted to the ionosphere than would be produced if the entire tail current system simply decreased. Plasma is accelerated while the forces are unbalanced resulting in field lines within a diversion loop becoming more dipolar. Field lines become more stretched and the plasma sheet becomes thinner outside a diversion loop. Mechanisms that require thin current sheets to produce current disruption then can create additional diversion loops in the newly thinned regions. This process may be important during multiple expansion substorms and in differentiating pseudoexpansions from full substorms. It is found that the tail field model used here can be generated by a variety of particle distribution functions. However, for a given energy distribution the mixture of particle mirror or reflection points is constrained by the consistency requirement. The study of uniqueness also leads to the development of a technique to select guiding center electrons that will produce charge neutrality all along a flux tube containing nonguiding center ions without the imposition of a parallel electric field.

Kaufmann, Richard L.

Benefits of Force Limiting Vibration Testing

Force limited random vibration testing is used at NASA John Glenn Research Center (formerly NASA Lewis Research Center) for qualifying aerospace hardware for flight. The benefit of force limiting testing is that it limits overtesting of flight hardware, by controlling input force and acceleration from the shaker (dual control) to the test article. The purpose of force limiting is to replicate the test article resonant response for the actual flight mounting condition. The force limiting testing technology has been implemented at the Jet Propulsion Laboratory for the past 10 years on various spacecraft testing programs. The Cassini mission to Saturn, most notably, utilized force limiting vibration testing as part of the spacecraft system level vibration testing. NASA John Glenn Research Center is responsible for microgravity combustion and fluid science research on the Shuttle and the International Space Station. Qualification testing of delicate and vibration sensitive science instrumentation is particularly challenging to successfully qualify for flight. In order to facilitate the testing process, force limiting has been implemented to minimize overtesting of flight hardware. This paper will address recent flight camera testing (qualification random vibration and strength testing) for the Combustion Module-2 mission and the impact of Semi-empirical Method force limits.

McNelis, Mark E.

The Effect of Two-Dimensional Forcing on Self-Similar Turbulent Plane Wakes

Three direct numerical simulations of time-evolving turbulent plane wakes with velocity deficit Reynolds numbers of about 2,000 have been simulated using a spectral numerical method with up to 600 x 260 x 160 modes. The initial conditions for the simulations are generated from direct numerical simulations of a turbulent boundary layer (momentum thickness Reynolds number of 670), and varying amounts of additional two- dimensional, forcing. In order to preserve the self-similar flow evolution, the forcing is implemented by multiplying all the two-dimensional modes in the initial condition by a constant factor. In the "natural" case no additional forcing is used; in the "forced" and "heavily forced" cases this factor is 5 and 20, respectively. The wake spreading rate Is increased by factors of 1.7 and 7.1 for the two forced cases. The Reynolds stresses are also increased by a similar or even larger factor. These results indicate that the plane wake is much more sensitive to initial forcing than the plane mixing layer. As in the plane mixing layer, two-dimensional forcing promotes more organized large-scale vortical flow structures and these structures axe sometimes separated by "braid regions" containing streamwise "rib" vortices, unlike in the unforced wake.

Rogers, M. M.

Validation of Force Limited Vibration Testing at NASA Langley Research Center

Vibration tests were performed to develop and validate the forced limited vibration testing capability at the NASA Langley Research Center. The force limited vibration test technique has been utilized at the Jet Propulsion Laboratory and other NASA centers to provide more realistic vibration test environments for aerospace flight hardware. In standard random vibration tests, the payload is mounted to a rigid fixture and the interface acceleration is controlled to a specified level based on a conservative estimate of the expected flight environment. In force limited vibration tests, both the acceleration and force are controlled at the mounting interface to compensate for differences between the flexible flight mounting and rigid test fixture. This minimizes the over test at the payload natural frequencies and results in more realistic forces being transmitted at the mounting interface. Force and acceleration response data was provided by NASA Goddard Space Flight Center for a test article that was flown in 1998 on a Black Brant sounding rocket. The measured flight interface acceleration data was used as the reference acceleration spectrum. Using this acceleration spectrum, three analytical methods were used to estimate the force limits. Standard random and force limited vibration tests were performed and the results are compared with the flight data.

Rice, Chad

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

Patnaik, Surya N.

Vibrational force alters mRNA expression in osteoblasts

Serum-deprived mouse osteoblastic (MC3T3E1) cells were subjected to a vibrational force modeled by NASA to simulate a space shuttle launch (7.83 G rms). The mRNA levels for eight genes were investigated to determine the effect of vibrational force on mRNA expression. The mRNA levels of two growth-related protooncogenes, c-fos and c-myc, were up-regulated significantly within 30 min after vibration, whereas those of osteocalcin as well as transforming growth factor-beta1 were decreased significantly within 3 h after vibration. No changes were detected in the levels of beta-actin, histone H4, or cytoplasmic phospholipase A2 after vibration. No basal levels of cyclooxygenase-2 expression were detected. In addition, the extracellular concentrations of prostaglandin E2 (PGE2), a potent autocrine/paracrine growth factor in bone, were not significantly altered after vibration most likely due to the serum deprivation state of the osteoblasts. In comparison with the gravitational launch profile, vibrational-induced changes in gene expression were greater both in magnitude and number of genes activated. Taken together, these data suggest that the changes in mRNA expression are due to a direct mechanical effect of the vibrational force on the osteoblast cells and not to changes in the local PGE2 concentrations. The finding that launch forces induce gene expression is of utmost importance since many of the biological experiments do not dampen vibrational loads on experimental samples. This lack of dampening of vibrational forces may partially explain why 1-G onboard controls sometimes do not reflect 1-G ground controls. These data may also suggest that scientists use extra ground controls that are exposed to launch forces, have these forces dampened on launched samples, or use facilities such as Biorack that provide an onboard 1-G centrufuge in order to control for space shuttle launch forces.

NASA Discipline Cell Biology

Rapid adaptation to Coriolis force perturbations of arm trajectory

1. Forward reaching movements made during body rotation generate tangential Coriolis forces that are proportional to the cross product of the angular velocity of rotation and the linear velocity of the arm. Coriolis forces are inertial forces that do not involve mechanical contact. Virtually no constant centrifugal forces will be present in the background when motion of the arm generates transient Coriolis forces if the radius of body rotation is small. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished as movement began. The reaching movements were made prerotation, during rotation at 10 rpm in a fully enclosed rotating room, and postrotation. During testing the subject was seated at the center of the room and pointed radially. Neither visual nor tactile feedback about movement accuracy was present. 3. In experiment 1, subjects reached at a fast or slow rate and their hands made contact with a horizontal surface at the end of the reach. Their initial perrotary movements were highly significantly deviated relative to prerotation in both trajectories and end-points in the direction of the transient Coriolis forces that had been generated during the reaches. Despite the absence of visual and tactile feedback about reaching accuracy, all subjects rapidly regained straight movement trajectories and accurate endpoints. Postrotation, transient errors of opposite sign were present for both trajectories and endpoints. 4. In a second experiment the conditions were identical except that subjects pointed just above the location of the extinguished target so that no surface contact was involved. All subjects showed significant initial perrotation deviations of trajectories and endpoints in the direction of the transient Coriolis forces. With repeated reaches the trajectories, as viewed from above, again became straight, but there was only partial restoration of endpoint accuracy, so that subjects reached in a straight line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center

Global Radiative Forcing of Coupled Tropospheric Ozone and Aerosols in a Unified General Circulation Model

Global simulations of sea salt and mineral dust aerosols are integrated into a previously developed unified general circulation model (GCM), the Goddard Institute for Space Studies (GISS) GCM II', that simulates coupled tropospheric ozone-NOx-hydrocarbon chemistry and sulfate, nitrate, ammonium, black carbon, primary organic carbon, and secondary organic carbon aerosols. The fully coupled gas-aerosol unified GCM allows one to evaluate the extent to which global burdens, radiative forcing, and eventually climate feedbacks of ozone and aerosols are influenced by gas-aerosol chemical interactions. Estimated present-day global burdens of sea salt and mineral dust are 6.93 and 18.1 Tg with lifetimes of 0.4 and 3.9 days, respectively. The GCM is applied to estimate current top of atmosphere (TOA) and surface radiative forcing by tropospheric ozone and all natural and anthropogenic aerosol components. The global annual mean value of the radiative forcing by tropospheric ozone is estimated to be +0.53 W m(sup -2) at TOA and +0.07 W m(sup -2) at the Earth's surface. Global, annual average TOA and surface radiative forcing by all aerosols are estimated as -0.72 and -4.04 W m(sup -2), respectively. While the predicted highest aerosol cooling and heating at TOA are -10 and +12 W m(sup -2) respectively, surface forcing can reach values as high as -30 W m(sup -2), mainly caused by the absorption by black carbon, mineral dust, and OC. We also estimate the effects of chemistry-aerosol coupling on forcing estimates based on currently available understanding of heterogeneous reactions on aerosols. Through altering the burdens of sulfate, nitrate, and ozone, heterogeneous reactions are predicted to change the global mean TOA forcing of aerosols by 17% and influence global mean TOA forcing of tropospheric ozone by 15%.

Liao, Hong

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Cantrell, John H., Jr.

Method of Calibrating a Force Balance

A calibration system and method utilizes acceleration of a mass to generate a force on the mass. An expected value of the force is calculated based on the magnitude and acceleration of the mass. A fixture is utilized to mount the mass to a force balance, and the force balance is calibrated to provide a reading consistent with the expected force determined for a given acceleration. The acceleration can be varied to provide different expected forces, and the force balance can be calibrated for different applied forces. The acceleration may result from linear acceleration of the mass or rotational movement of the mass.

Parker, Peter A.

Plasmonic Force Propulsion Revolutionizes Nano/Picosatellite Capability

This project investigated a new type of small spacecraft propulsion for attitude control, specifically proximity and precision pointing control. Plasmonic force propulsion uses solar light focused on deep-subwavelength nanostructures to excite strong optical forces that accelerate and expel nanoparticle propellant. The goal of the project was to assess the feasibility of plasmonic force propulsion for nano/pico-satellite applications by evaluating key mission parameters for a nano/pico-satellite using plasmonic force propulsion in a NASA-relevant mission context. We achieved this goal and objective by evaluating plasmonic force propulsion within a NASA mission that required attitude control and precision pointing of a small satellite. We numerically simulated plasmonic force fields with asymmetric/gradient geometry and relevant solar light constraints, predicted nanoparticle velocity, mass flow rate, and resulting propulsion performance (thrust, specific impulse), and evaluated spacecraft position control resolution and pointing precision. Additionally we compared the precision pointing capabilities of plasmonic propulsion, as well as the mass, volume, and power requirements, with other state-of-the-art control techniques, such as reaction wheels and colloid/electrospray electric propulsion. The results are very exciting. Plasmonic force propulsion can significantly enhance the state-of-the-art in small spacecraft position and attitude control by 1-2 orders of magnitude. This is most succinctly shown in the figure below, which compares proximity and attitude control of plasmonic force propulsion (PFP) with other state-of-the-art thruster systems (μCAT, VAT, electrospray). Additionally this figure also shows the proximity and attitude control required for different existing (James Webb Space Telescope, Hubble) and future (LISA and Stellar Imager) NASA missions. While some of these NASA missions are not small spacecraft missions, the requirements serve to illustrate the fact that more precise proximity and attitude control will be required for future NASA science missions. Stellar imager is a proposed NASA missions that requires an extremely high pointing precision of 0.1 milliarcseconds (2.7x10(exp -7) deg.) for an ultraviolet telescope that has over 200× the resolution of the Hubble Space Telescope, is able to take images showing details on the surfaces of other stars, consists of 20-30 small "mirror sats" flying in formation to produce a giant mirror, and requires each mirror-sat to be placed with nanometer precision and control its attitude with milliarcsecond precision.

Rovey, Joshua L.

TURBOMAT-FR: Turbomachinery Aeroelastic Forced Response Analysis Automation Using MATLAB® Part 2

The primary aim of this effort is to develop a software tool named “Turbomachinery Aeroelastic Analysis Tool for Forced Response (TURBOMAT-FR)” using MATLAB® (The MathWorks, Inc.) scripts. The tool will aid in performing routine forced response analysis of turbomachinery fan blades with the aid of the modal summation method (MSUM). The MSUM approach requires a modal solution consisting of modal displacements, frequencies, and stresses. The MATLAB® scripts facilitate easy extraction of the required quantities from the computational fluid dynamics (CFD) and MSC Nastran (Hexagon AB) solution files. These quantities are subsequently utilized by the MSUM approach to perform a complete forced response analysis using the MATLAB® scripts. The MATLAB® scripts in TURBOMAT-FR are utilized in postprocessing of the MSC Nastran finite element analysis outputs in three types of solutions or steps, namely (1) stresses and displacements from static or steady response solution, (2) unsteady stresses and displacements from direct forced response solution, and (3) modal solution containing modal displacements and modal stresses. In step (4), separate MATLAB® scripts are also developed to read the processed outputs in step (3) and perform forced response analysis using MSUM. It should be noted that the direct forced response solution from step (2) will provide for a comparison with those obtained from the MSUM approach in steps (3) and (4). The TURBOMAT-FR MATLAB® scripts mentioned previously are presented in two reports designated Parts 1 and 2. Part 1 presents the scripts needed to accomplish steps (1) and (2). The current report, Part 2, presents the scripts needed to accomplish steps (3) and (4), noted previously. The TURBOMAT-FR MATLAB® scripts provided here in Part 2 facilitate the calculation of unsteady stresses using MSUM and provide an automated procedure associated with aeroelastic forced response analysis with different pressure files. The unsteady stresses calculated using MSUM can be compared with those presented in Part 1. A cantilevered blade-alone model subjected to a realistic pressure loading to a boundary was used for static and unsteady direct forced response analysis to demonstrate the effectiveness of the TURBOMATFR MATLAB® scripts.

T S R Reddy

Development of a new method in force limited vibration testing

The force limited vibration test approaches discussed in NASA-HDBK-7004C were developed to reduce overtesting associated with base shake vibration tests of aerospace hardware. This handbook outlines several different methods of specifying force limiting specifications. The basis for deriving force limiting specifications is related to the differences between mechanical impedances of typical aerospace hardware interfacing the mounting structures in flight configurations and the large impedances inherent in shaker vibration testing. Among these approaches, the semi-empirical method is presently the most widely used method to derive the force limiting specifications. This method is developed based on the assumption that the hardware interface responses are coherently excited. The inclusion of the incoherent excitation of the aerospace structures at mounting interfaces provides the basis for developing a more realistic force limiting specification that may be used to qualify flight hardware for launch environments using shaker testing. In this paper the semi-empirical method for defining force limiting specifications discussed in NASA handbook are reviewed using data recently obtained from a series of acoustic and vibration tests. A mathematical formation of a new force limiting approach based on considering the incoherent excitation of the hardware at their mounting interfaces is developed. Results from the analysis, which are correlated to the data obtained from a series of well instrumented acoustic and vibration tests, are discussed. The new approach provides much more realistic force limits that may further remove conservatism inherent in shaker vibration testing not accounted for by methods discussed in the NASA handbook.

Kolaini, Ali R.

Nano-Newton Electrostatic Force Actuators for Femto-Newton-Sensitive Measurements: System Performance Test in the LISA Pathfinder Mission

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10 −9 N while limiting fluctuations in the measurement band to levels approaching 10 −15 N=Hz 1/2 . We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical x axis joining the two TM, with the commanded actuation force entering directly into the mission’s main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency “in band” voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

M. Armanos

Seasonal delay of Sahelian rainfall driven by an east–west contrast in radiative forcing in idealized CESM experiments

Recent studies suggest the observed seasonal delay of rainfall over the Sahel is mainly driven by anthropogenic aerosol forcing, which features a robust east–west contrasting changes in recent decades, with negative and positive top-of-the-atmosphere shortwave radiative forcing in South and East Asia (SA&EA) and in North America and Europe (NA&EU), respectively. Their individual effects on the Sahel rainfall annual cycle remain unclear. Here, by designing idealized sensitivity experiments based on Community Earth System Model (CESM1.2), we show that both negative radiative forcing over SA&EA and positive radiative forcing over NA&EU contribute to the delayed phase and enhanced amplitude of Sahel rainfall annual cycle. To understand the underlying physical processes, both the convective quasi-equilibrium (CQE) and atmospheric energetic frameworks are utilized. Both frameworks can well explain the seasonal delay in the rainfall annual cycle over the Sahel under the regional radiative forcings, with the CQE framework showing stronger explanatory power. Based on the insights from both frameworks, we conducted a moisture budget analysis and found that the negative radiative forcing over SA&EA causes an anomalous low-level anticyclonic circulation, which transports more moisture to the Sahel. As the anomalous anticyclone is stronger in summer and fall compared to spring, rainfall is delayed in the Sahel. Further, under the influence of the positive radiative forcing over NA&EU, more warming in the northern hemisphere causes northward transport of moisture to the northern tropics associated with the cross-equatorial transport of energy. The moisture transport increases relativehumidity over the Sahel and enhances the effective atmospheric heat capacity that delays the seasonal rainfall.

54 ENVIRONMENTAL SCIENCES