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Contemporary Impact Analysis Methodology for Planetary Sample Return Missions

Development of an Earth entry vehicle and the methodology created to evaluate the vehicle's impact landing response when returning to Earth is reported. NASA's future Mars Sample Return Mission requires a robust vehicle to return Martian samples back to Earth for analysis. The Earth entry vehicle is a proposed solution to this Mars mission requirement. During Earth reentry, the vehicle slows within the atmosphere and then impacts the ground at its terminal velocity. To protect the Martian samples, a spherical energy absorber called an impact sphere is under development. The impact sphere is composed of hybrid composite and crushable foam elements that endure large plastic deformations during impact and cause a highly nonlinear vehicle response. The developed analysis methodology captures a range of complex structural interactions and much of the failure physics that occurs during impact. Numerical models were created and benchmarked against experimental tests conducted at NASA Langley Research Center. The postimpact structural damage assessment showed close correlation between simulation predictions and experimental results. Acceleration, velocity, displacement, damage modes, and failure mechanisms were all effectively captured. These investigations demonstrate that the Earth entry vehicle has great potential in facilitating future sample return missions.

Perino, Scott V.↗

CFD Modeling of Launch Vehicle Aerodynamic Heating

The Loci-CHEM 3.2 Computational Fluid Dynamics (CFD) code is being used to predict Ares-I launch vehicle aerodynamic heating. CFD has been used to predict both ascent and stage reentry environments and has been validated against wind tunnel tests and the Ares I-X developmental flight test. Most of the CFD predictions agreed with measurements. On regions where mismatches occurred, the CFD predictions tended to be higher than measured data. These higher predictions usually occurred in complex regions, where the CFD models (mainly turbulence) contain less accurate approximations. In some instances, the errors causing the over-predictions would cause locations downstream to be affected even though the physics were still being modeled properly by CHEM. This is easily seen when comparing to the 103-AH data. In the areas where predictions were low, higher grid resolution often brought the results closer to the data. Other disagreements are attributed to Ares I-X hardware not being present in the grid, as a result of computational resources limitations. The satisfactory predictions from CHEM provide confidence that future designs and predictions from the CFD code will provide an accurate approximation of the correct values for use in design and other applications

Tashakkor, Scott B.↗

On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program

We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models.

Perlin, Marc↗

Outer skin protection of columbium Thermal Protection System (TPS) panels

A coated columbium alloy material system 0.04 centimeter thick was developed which provides for increased reliability to the load bearing character of the system in the event of physical damage to and loss of the exterior protective coating. The increased reliability to the load bearing columbium alloy (FS-85) was achieved by interposing an oxidation resistant columbium alloy (B-1) between the FS-85 alloy and a fused slurry silicide coating. The B-1 alloy was applied as a cladding to the FS-85 and the composite was fused slurry silicide coated. Results of material evaluation testing included cyclic oxidation testing of specimens with intentional coating defects, tensile testing of several material combinations exposed to reentry profile conditions, and emittance testing after cycling of up to 100 simulated reentries. The clad material, which was shown to provide greater reliability than unclad materials, holds significant promise for use in the thermal protection system of hypersonic reentry vehicles.

Culp, J. D.↗

Alternative Processing of High Temperature Hafnium and Zirconium Based Materials

The behavior of refractory hafnium and zirconium based materials are being investigated at NASA Ames as part of ongoing research aimed at developing superior heat resistant materials for aerospace applications. Hafnium and zirconium diboride based materials have shown high temperature capabilities in simulated reentry environments indicating that these materials may successfully operate as reusable oxidation resistant components for leading edge applications. Due to the refractory nature of these materials, processing of fine-grained uniform microstructures poses a number of challenges. To better understand the process-property-microstructure relationship, processing of these materials has been carried out with conventional hot pressing in addition to the novel approach of Spark Plasma Sintering (SPS). The two processing methods are compared and contrasted in an evaluation of the sintering behavior of high temperature diboride based materials and preliminary physical and mechanical properties are presented.

Gasch, Matthew↗

Benchmarking Cylindrical Blast Wave Theory Against the OSIRIS-REx Sample Return Capsule Reentry

Weak shock theory based on cylindrical blast waves has been used to interpret meteor infrasound, but it has not been systematically benchmarked against a non-ablating hypersonic source with independently known parameters. The objective of this study is not to propose a new theoretical framework, but to evaluate the operational validity of the existing suite of blast radius formulations against a high-fidelity ground truth dataset. The OSIRIS-REx Sample Return Capsule reentry on 24 September 2023 provides such a benchmark because the capsule geometry, trajectory, and infrasound emission points are constrained from mission data and ray tracing, reducing source-side uncertainty associated with ablation. Using observations from 39 infrasound stations, this benchmarking study evaluates six published blast radius (${R}_{0}$ ) formulations and three weak-shock transition coefficients ( C ) within a stratified atmospheric propagation model to predict signal period and peak overpressure. The benchmarking identifies the Sakurai formulation as the best-performing formulation for non-ablating bodies, with the Jones/Plooster formulation performing comparably when a physically appropriate C is adopted. Sakurai and Jones/Plooster yield linear-period median absolute percentage residuals of 9% and 11%, respectively. The period predictions show only weak sensitivity to C at these propagation distances. The Mach-diameter approximation commonly used in meteor studies overestimates ${R}_{0}$ by more than a factor of 3 in the absence of ablation. Finally, these results establish a performance baseline for applying cylindrical blast wave theory to effectively non-ablating hypersonic bodies and demonstrate that the signal period is a robust observable for constraining ${R}_{0}$.

atmospheric entry↗

LAURA Users Manual: 5.7

This users manual provides in-depth information concerning installation and execution of Laura, version 5. Laura is a structured, multi-block, compu- tational aerothermodynamic simulation code. Version 5 represents a major refactoring of the original Fortran 77 Laura code toward a modular structure afforded by Fortran 2003. The refactoring improved usability and maintain- ability by eliminating the requirement for problem-dependent re-compilations, providing more intuitive distribution of functionality, and simplifying inter- faces required for multi-physics coupling. As a result, Laura now shares gas-physics modules, MPI modules, and other low-level modules with the Fun3D unstructured-grid code. In addition to internal refactoring, several new features and capabilities have been added, e.g., a GNU-standard instal- lation process, parallel load balancing, automatic trajectory point sequencing, free-energy minimization, and coupled ablation and flowfield radiation.

CFD hypersonics reentry↗

Shock waves and shock tubes; Proceedings of the Fifteenth International Symposium, Berkeley, CA, July 28-August 2, 1985

A detailed survey is presented of shock tube experiments, theoretical developments, and applications being carried out worldwide. The discussions explore shock tube physics and the related chemical, physical and biological science and technology. Extensive attention is devoted to shock wave phenomena in dusty gases and other multiphase and heterogeneous systems, including chemically reactive mixtures. Consideration is given to techniques for measuring, visualizing and theoretically modeling flowfield, shock wave and rarefaction wave characteristics. Numerical modeling is explored in terms of the application of computational fluid dynamics techniques to describing flowfields in shock tubes. Shock interactions and propagation, in both solids, fluids, gases and mixed media are investigated, along with the behavior of shocks in condensed matter. Finally, chemical reactions that are initiated as the result of passage of a shock wave are discussed, together with methods of controlling the evolution of laminar separated flows at concave corners on advanced reentry vehicles.

Bershader, D.↗

Thermal certification tests of Orbiter Thermal Protection System tiles coated with KSC coating slurries

Thermal tests of Orbiter thermal protection system (TPS) tiles, which were coated with borosilicate glass slurries fabricated at Kennedy Space Center (KSC), were performed in the Radiant Heat Test Facility and the Atmospheric Reentry Materials & Structures Evaluation Facility at Johnson Space Center to verify tile coating integrity after exposure to multiple entry simulation cycles in both radiant and convective heating environments. Eight high temperature reusable surface insulation (HRSI) tiles and six low temperature reusable surface insulation (LRSI) tiles were subjected to 25 cycles of radiant heat at peaked surface temperatures of 2300 F and 1200 F, respectively. For the LRSI tiles, an additional cycle at peaked surface temperature of 2100 F was performed. There was no coating crack on any of the HRSI specimens. However, there were eight small coating cracks (less than 2 inches long) on two of the six LRSI tiles on the 26th cycle. There was practically no change on the surface reflectivity, physical dimensions, or weight of any of the test specimens. There was no observable thermal-chemical degradation of the coating either. For the convective heat test, eight HRSI tiles were tested for five cycles at a surface temperature of 2300 F. There was no thermal-induced coating crack on any of the test specimens, almost no change on the surface reflectivity, and no observable thermal-chemical degradation with an exception of minor slumping of the coating under painted TPS identification numbers. The tests demonstrated that KSC's TPS slurries and coating processes meet the Orbiter's thermal specification requirements.

Milhoan, James D.↗

Interplanetary and Interstellar Dust Particles: Reentry Heating and Capture in Aerogel

Studies of interplanetary and interstellar dust can provide significant information on the evolution of the solar system or stars, respectively. However, for reliable analysis it is crucial to know how the particles have been modified during reentry (in the case of interplanetary dust particles, or [DP's) and impact into the capture medium. In the case of stratospheric capture, particles will be heated by atmospheric drag. Subsequent capture of the particles will result in heating, ablation, accretion of the capture medium and possible fragmentation. Modeling of these processes is a useful way of assessing their effects on the interpretation of the compositional data for these particles. Previous work on reentry heating has shown that heat diffusion alone cannot adequately account for temperature gradients observed in IDP's. In fact, for any reasonable thermal parameters, calculations show the particles to be nearly isothermal. Here we extend those studies to include phase transitions. These preliminary results are promising and show a significant temperature gradient for a 100 micron (diameter) particle. The actual capture of the particles in silica aerogel is being modeled using a comprehensive shock hydrodynamic code (called CTH). Various options of this code were investigated to attempt to make the most appropriate choice of methods of impact, equations of state, and processes of energy transfer from capture material to particle. The initial calculations with the code used only 'reasonable' estimates for the physical parameters of silica aerogel. Through the literature searches and personal contacts with the knowledgeable scientists, the best possible mechanical and thermal data have been made available for these computations.

Szydlik, Paul P.↗

Investigation of hypersonic rarefied flow on a spherical nose of the AOTV

The Navier-Stokes (NS) equations were integrated numerically for investigating the flow characteristics on the forepart of the spherical nose of a space vehicle such as the AOTV or AFE by a modified Accelerated Successive Replacement (ASR) scheme under hypersonic rarefied conditions. Technical feasibility of the mathematical approach was demonstrated by computing the flowfield on a spherical nose under conditions that the AFE encounters at times t = 15 and 20 seconds after its reentry into the atmosphere. Local similar solutions for the merged layer flow along the stagnation line of the sphere were developed. These are correct to the same degree of accuracy as the NS equations. These solutions provided stagnation line boundary conditions for the domain of integration on the spherical noise. Also, a parametric study of the stagnation line solution was made with a view to understand the flow characteristics in tunnels with different ambient fluids. Analytical expressions for surface slip temperature, jump conditions, and concentration level in the presence of the real gas effects at the top of the Knudsen layer were derived and used to calculate the stagnation line flowfield with nonequilibrium dissociation and ionization. A number of graphics were drawn to illustrate the basic physics of the flowfields. The present analysis can be extended to include real gas effects and to bodies of arbitrary shapes. It can further provide boundary conditions for integrating the NS equations in the near wake region.

Jain, Amolak C.↗

Ignition and combustion of bulk metals under elevated, normal and reduced gravity conditions

This research effort is aimed at providing further insight into this multi-variable dependent phenomena by looking at the effects of gravity on the ignition and combustion behavior of metals. Since spacecraft are subjected to higher-than-1g gravity loads during launch and reentry and to zero-gravity environments while in orbit, the study of ignition and combustion of bulk metals at different gravitational potentials is of great practical concern. From the scientific standpoint, studies conducted under microgravity conditions provide simplified boundary conditions since buoyancy is removed, and make possible the identification of fundamental ignition mechanisms. The effect of microgravity on the combustion of bulk metals has been investigated by Steinberg, et al. on a drop tower simulator. However, no detailed quantitative work has been done on ignition phenomena of bulk metals at lower or higher-than-normal gravitational fields or on the combustion characteristics of metals at elevated gravity. The primary objective of this investigation is the development of an experimental system capable of providing fundamental physical and chemical information on the ignition of bulk metals under different gravity levels. The metals used in the study, iron (Fe), titanium (Ti), zirconium (Zr), magnesium (Mg), zinc (Zn), and copper (Cu) were selected because of their importance as elements of structural metals and their simple chemical composition (pure metals instead of multi-component alloys to avoid complication in morphology and spectroscopic studies). These samples were also chosen to study the two different combustion modes experienced by metals: heterogeneous or surface oxidation, and homogeneous or gas-phase reaction. The experimental approach provides surface temperature profiles, spectroscopic measurements, surface morphology, x-ray spectrometry of metals specimens and their combustion products, and high-speed cinematography of the heating, ignition and combustion stages of the metal specimen. This paper summarizes the results obtained to date from experiments conducted under normal and high-gravity conditions.

Abbud-Madrid, Angel↗

Determining Exercise Strength Requirements for Astronaut Critical Mission Tasks: Reaching Under G-Load

The critical mission tasks assessments effort seeks to determine the physical performance requirements that astronauts must meet in order to safely and successfully accomplish lunar exploration missions. These assessments will determine astronaut preflight strength, fitness, and flexibility requirements, and the extent to which exercise and other countermeasures must prevent the physical deconditioning associated with prolonged weightlessness. The purpose is to determine the flexibility and strength that crewmembers must possess in order to reach Crew Exploration Vehicle controls during maneuvers that result in sustained acceleration levels ranging from 3.7G to 7.8G. An industry standard multibody dynamics application was used to create human models representing a 5th percentile female, a 50th percentile male, and a 95th percentile male. The additional mass of a space suit sleeve was added to the reaching arm to account for the influence of the suit mass on the reaching effort. The human model was merged with computer models of a pilot seat and control panel for the Crew Exploration Vehicle. Three dimensional paths were created that guided the human models hand from a starting position alongside its thigh to three control targets: a joystick, a keyboard, and an overhead switch panel. The reaching motion to each target was repeated under four vehicle acceleration conditions: nominal ascent (3.7G), two ascent aborts (5.5G and 7.8G) and lunar reentry (4.6G). Elbow and shoulder joint angular excursions were analyzed to assess range of motion requirements. Mean and peak elbow and shoulder joint torques were determined and converted to equivalent resistive exercise loads to assess strength requirements. Angular excursions for the 50th and 95th percentile male models remained within joint range of motion limits. For the 5th percentile female, both the elbow and the shoulder exceeded range of motion limits during the overhead reach. Elbow joint torques ranged from 10 N-m (nominal ascent) to 60 N-m (ascent abort). Shoulder joint torques ranged from 65 N-m (nominal ascent) to 280 N-m (ascent abort). Maximal equivalent exercise loads reached 30 lb in tricep extension, 9 lb in bicep curl, 110 lb in unilateral pullover and unilateral bench press for nominal conditions (lunar reentry), and 188 lb in unilateral pullover and unilateral bench press. The location of the pilot seat was found to be inadequately located to allow a 5th percentile female to reach the switches on the overhead panel. Elbow strength requirements were found to be well within population norms. Shoulder strength was found to be a limiting factor. Reaching under nominal ascent and lunar reentry conditions was found to require near maximal shoulder strength. Reaching under ascent abort conditions requires shoulder strength well beyond population norms. Pilot seats must adjust to accomodate a 5th percentile female. Exercise countermeasures must maintain maximal pullover and bench press strength to allow pilots to reach and operate controls during lunar reentry. Reaching will not be possible during ascent abort conditions. Flight controls should be built into armrests or flight control must be accomplished by autonomous systems during acceleration exceeding 4.6G.

Schaffner, Grant↗

Numerical Predictions of Dust-Induced Heat Flux Augmentation in Hypersonic Blunt-Body Flows Using a Discontinuous Galerkin Multiphase Flow Solver

Recent interest in human-scale missions to Mars has motivated the need for high-fidelity simulations of reentry flows. During a dust storm, there can be high levels of suspended dust in the Martian atmosphere, which cannot only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, thereby significantly augmenting the surface heat flux. Second-order finite-volume schemes are typically employed for hypersonic flow simulations, but such schemes suffer from a number of disadvantages. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other properties. To enable accurate computations of high-speed particle-laden flows, an Euler-Lagrange methodology was developed in which the Eulerian field of the carrier gas is calculated using a discontinuous Galerkin scheme while the disperse phase is treated with Lagrangian particle tracking. We discuss challenges associated with coupling these two formulations and how to handle them. Momentum and energy transfer between the carrier gas and the particle phase is considered, and the importance of accounting for interparticle collisions is assessed. In addition, we describe the physical model of the particle phase and examine effects of its uncertainties on the numerical solution. We demonstrate the performance of the Euler-Lagrange method in representative testcases, with focus on the accurate prediction of particle trajectories and heating augmentation. Quantitative comparisons with experiments are provided.

Ching, Eric J.↗

Cardiovascular and Body Fluid Adjustments During Bed Rest and Space Flight

Although a few scientific bed rest (BR) studies were conducted soon after World War II, advent of the space program provided impetus for utilizing prolonged (days-months) BR, which employed the horizontal or 6 degree head-down tilt (HDT) body positions, to simulate responses of healthy people to microgravity. Shorter (hours) HDT protocols were used to study initial mechanisms of the acclimation-deconditioning (reduction of physical fitness) syndromes. Of the major physiological factors modified during BR, reduced force on bones, ligaments, and muscles, and greatly reduced hydrostatic pressure within the cardiovascular system, the latter: which involves shifts of blood from the lower extremities into the upper body, increase in central venous pressure, and diuresis, appears to be the initial stimulus for acclimation. Increase in central venous pressure occurs in subjects during weightless parabolic flight, but not in astronauts early during orbital flight. But significant reduction in total body water (hypohydration) and plasma volume (hypovolemia) occurs in subjects during both BR and microgravity. Response of interstitial fluid volume is not as clear, It has been reported to increase during BR, and it may have increased in Skylab II and IV astronauts. Reduction of total body water, and greater proportional reduction of extracellular volume, indicates increased cellular volume which may contribute to inflight cephalic edema. Cerebral pressure abates after a few days of HDT, but not during flight. accompanied by normal (eugravity) blood constituent concentrations suggesting some degree of acclimation had occurred. But during reentry, with moderately increased +Gz (head-to-foot) acceleration and gravitational force, the microgravity "euhydration" becomes functional progressive dehydration contributing to the general reentry syndrome (GRS) which, upon landing the Shuttle, can and often results in gastrointestinal distress, disorientation, vertigo, fatigue, and fainting. Various pre-reentry hyperhydration procedures have been utilized to counteract the GRS. Thus, the somewhat decreased central venous pressure and lack of diuresis early in spaceflight suggests mechanisms other than the Gauer-Henry reflex are more important for maintaining fluid volume homeostasis in astronauts. Inflight hypohydration and hypovolemia are more important for maintaining fluid volume homeostasis in astronauts.

Greenleaf, John E.↗

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

To address the hitherto unknown mechanism of boundary-layer transition on blunt reentry capsules, the role of roughness-induced disturbance growth on a spherical-section forebody is assessed via optimal transient growth theory and direct numerical simulations (DNS). Optimal transient-growth studies have been performed for the blunt capsule experiments at Mach 5.9 in the Hypersonic Ludwieg tube at the Technische Universität Braunschweig (HLB), which included measurements behind a patch of controlled, distributed micron-sized surface roughness. Transient-growth results for the HLB capsule indicate similar trends as the corresponding numerical data for a Mach 6 experiment in the Actively Controlled Expansion (ACE) facility of the Texas A&M University (TAMU) at a lower Reynolds number. Both configurations indicate a similar dependence on surface temperature ratio and, more important, rather low values of maximum energy gain. DNS are performed for the conditions of the HLB experiment to understand the generation of stationary disturbances by the roughness patch and the accompanying evolution of unsteady perturbations. However, no evidence of either modal or nonmodal disturbance growth in the wake of the roughness patch is found in the DNS data; thus, the physical mechanism underlying the observed onset of transition still remains unknown.

Stefan Hein↗

Hypervolemia from Drinking Hyperhydration Solutions at Rest and Exercise

The mechanism of muscular fatigue from physical work and exercise (high metabolism) is not clear, but involves disturbances of muscle surface membrane excitation-contraction coupling from changes in sarcoplasmic reticulum Ca2+ release, cell H+ and Pi responses, and carbohydrate metabolism. Fatigue in people at rest (low metabolism) involves both psychological and physiological factors, probably in different proportions. One common factor appears to be the level and distribution of water and electrolytes within muscle cells and other vascular, interstitial, body fluid compartments. The vascular fluid volume, composed of plasma and red blood cells, is a primary regulatory factor for cardiovascular function; reduction of vascular volume (hypovolemia) and total body water (hypohydration) adversely affect exercise performance. Plasma volume and plasma ionic-osmotic constituent concentrations are also regulatory factors for body thermoregulation, which is often compromised from exercise induced hypovolemia and hypohydration. Rehydration of dehydrated people on earth is relatively easy with appropriate food (osmols), fluid, and a restful environment. But ad libitum drinking under stressful conditions; e.g., heat, exercise, or prior dehydration, results in involuntary dehydration defined as the delay in full fluid replacement (euhydration) during and following loss of body fluid. Astronauts, with their reduced total body water are euhydrated while in weightlessness, but become "dehydrated" during reentry and landing. Thus, people subjected to acute or chronic stress are probably somewhat "dehydrated" as well as fatigued. Many rehydration drinks are more concentrated (hypertonic-hyperosmotic) with respect to the normal plasma osmolality of 285 mOsm/kg H2O and more of the drink osmols are contributed by carbohydrates than by ionized substances. There have been few studies on the efficacy of various drink formulations for increasing body fluid compartment volumes, especially plasma volume, in rested hydrated subjects. Recent findings from our laboratory have indicated that drinks containing greater concentrations of ionized substances (Performance 1 and AstroAde) up to 157 mEq/L Na+ induced greater levels of hypervolemia in resting, moderately dehydrated men, and were also better than water for attenuating the characteristic hypovolemia during supine, submaximal, leg ergometer exercise.

Greenleaf, John E.↗