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NASA NTRS1999

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Green, Lawrence↗

NASA NTRS1999

Navier-Stokes Analysis of the Flowfield Characteristics of an Ice Contaminated Aircraft Wing

An analytical study was performed as part of the NASA Lewis support of a National Transportation Safety Board (NTSB) aircraft accident investigation. The study was focused on the performance degradation associated with ice contamination on the wing of a commercial turbo-prop-powered aircraft. Based upon the results of an earlier numerical study conducted by the authors, a prominent ridged-ice formation on the subject aircraft wing was selected for detailed flow analysis using 2-dimensional (2-D), as well as, 3-dimensional (3-D) Navier-Stokes computations. This configuration was selected because it caused the largest lift decrease and drag increase among all the ice shapes investigated in the earlier study. A grid sensitivity test was performed to find out the influence of grid spacing on the lift, drag, and associated angle-of-attack for the maximum lift (C(sub lmax)). This study showed that grid resolution is important and a sensitivity analysis is an essential element of the process in order to assure that the final solution is independent of the grid. The 2-D results suggested that a severe stability and control difficulty could have occurred at a slightly higher angle-of-attack (AOA) than the one recorded by the Flight Data Recorder (FDR). This stability and control problem was thought to have resulted from a decreased differential lift on the wings with respect to the normal loading for the configuration. The analysis also indicated that this stability and control problem could have occurred whether or not natural ice shedding took place. Numerical results using an assumed 3-D ice shape showed an increase of the angle at which this phenomena occurred of about 4 degrees. As it occurred with the 2-D case, the trailing edge separation was observed but started only when the AOA was very close to the angle at which the maximum lift occurred.

Chung, J.↗

NASA NTRS2011

Measurement of CPAS Main Parachute Rate of Descent

The Crew Exploration Vehicle Parachute Assembly System (CPAS) is being designed to land the Orion Crew Module (CM) at a safe rate of descent at splashdown. Flight test performance must be measured to a high degree of accuracy to ensure this requirement is met with the most efficient design possible. Although the design includes three CPAS Main parachutes, the requirement is that the system must not exceed 33 ft/s under two Main parachutes, should one of the Main parachutes fail. Therefore, several tests were conducted with clusters of two Mains. All of the steady-state rate of descent data are normalized to standard sea level conditions and checked against the limit. As the Orion design gains weight, the system is approaching this limit to within measurement precision. Parachute "breathing," cluster interactions, and atmospheric anomalies can cause the rate of descent to vary widely and lead to challenges in characterizing parachute terminal performance. An early test had contradictory rate of descent results from optical trajectory and Differential Global Positioning Systems (DGPS). A thorough analysis of the data sources and error propagation was conducted to determine the uncertainty in the trajectory. It was discovered that the Time Space Position Information (TSPI) from the optical tracking provided accurate position data. However, the velocity from TPSI must be computed via numerical differentiation, which is prone to large error. DGPS obtains position through pseudo-range calculations from multiple satellites and velocity through Doppler shift of the carrier frequency. Because the velocity from DGPS is a direct measurement, it is more accurate than TSPI velocity. To remedy the situation, a commercial off-the-shelf product that combines GPS and an Inertial Measurement Unit (IMU) was purchased to significantly improve rate of descent measurements. This had the added benefit of solving GPS dropouts during aircraft extraction. Statistical probability distributions for CPAS Main parachute rate of descent and drag coefficient were computed and plotted. Using test data, a terminal rate of descent at splashdown can be estimated as a function of canopy loading.

Ray, Eric S.↗

NASA NTRS1950

Linearized compressible-flow theory for sonic flight speeds

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Heaslet, Max A↗

NASA NTRS1960

Supersonic Aerodynamic Characteristics of a Low-Drag Aircraft Configuration having an Arrow Wing of Aspect Ratio 1.86 and a Body of Fineness Ratio 20

A free-flight rocket-propelled-model investigation was conducted at Mach numbers of 1.2 to 1.9 to determine the longitudinal and lateral aero-dynamic characteristics of a low-drag aircraft configuration. The model consisted of an aspect-ratio -1.86 arrow wing with 67.5 deg. leading-edge sweep and NACA 65A004 airfoil section and a triangular vertical tail with 60 deg. sweep and NACA 65A003 section in combination with a body of fineness ratio 20. Aerodynamic data in pitch, yaw, and roll were obtained from transient motions induced by small pulse rockets firing at intervals in the pitch and yaw directions. From the results of this brief aerodynamic investigation, it is observed that very slender body shapes can provide increased volumetric capacity with little or no increase in zero-lift drag and that body fineness ratios of the order of 20 should be considered in the design of long-range supersonic aircraft. The zero-lift drag and the drag-due-to-lift parameter of the test configuration varied linearly with Mach number. The maximum lift-drag ratio was 7.0 at a Mach number of 1.25 and decreased slightly to a value of 6.6 at a Mach number of 1.81. The optimum lift coefficient, normal-force-curve slope, lateral-force-curve slope, static stability in pitch and yaw, time to damp to one-half amplitude in pitch and yaw, the sum of the rotary damping derivatives in pitch and also in yaw, and the static rolling derivatives all decreased with an increase in Mach number. Values of certain rolling derivatives were obtained by application of the least-squares method to the differential equation of rolling motion. A comparison of the experimental and calculated total rolling-moment-coefficient variation during transient oscillations of the model indicated good agreement when the damping-in-roll contribution was included with the static rolling-moment terms.

Gillespie, Warren, Jr.↗

NASA NTRS2016

Permeability of Two Parachute Fabrics - Measurements, Modeling, and Application

Two parachute fabrics, described by Parachute Industry Specifications PIA-C-7020D Type I and PIA-C-44378D Type I, were tested to obtain their permeabilities in air (i.e., flow-through volume of air per area per time) over the range of differential pressures from 0.146 psf (7 Pa) to 25 psf (1197 Pa). Both fabrics met their specification permeabilities at the standard differential pressure of 0.5 inch of water (2.60 psf, 124 Pa). The permeability results were transformed into an effective porosity for use in calculations related to parachutes. Models were created that related the effective porosity to the unit Reynolds number for each of the fabrics. As an application example, these models were used to calculate the total porosities for two geometrically-equivalent subscale Disk-Gap-Band (DGB) parachutes fabricated from each of the two fabrics, and tested at the same operating conditions in a wind tunnel. Using the calculated total porosities and the results of the wind tunnel tests, the drag coefficient of a geometrically-equivalent full-scale DGB operating on Mars was estimated.

Cruz, Juan R.↗

NASA NTRS2017

Permeability of Two Parachute Fabrics: Measurements, Modeling, and Application

Cruz, Juan R.↗

NASA NTRS2000

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

NASA NTRS1991

Dust particles from comets and asteroids collected at the Earth's orbit: Parent-daughter relationships

The relative contributions of comets and asteroids to the reservoir of dust in the interplanetary medium is not well known. There are direct observations of dust released from comets and there is evidence to associate the IRAS dust bands with possible collisions of Asteroids in the main belt. It is believed that one may combine lab analysis of the physics and chemistry of captured particles with orbital data in order to identify comet and asteroid parent bodies. It is possible to use the collected orbits of the dust to connect with its source in two ways. One is to consider the long time orbit evolution of the dust under Poynting-Robertson drag. The other is to look at the prompt orbit change of dust from comets onto trajectories that intersect the earth's orbit. In order to characterize the orbits of dust particles evolved over a long period of time, a study of its orbital evolution was undertaken. Various parameters associated with these dust orbits as they cross the Earth's orbit were considered in order to see if one may discriminate between particles evolved from comets and asteroids. The method was to calculate by a numerical procedure the orbits of dust particles after they left their parent bodies. It appears that as the particles pass the Earth's orbit, asteroidal grains and cometary grains can be differentiated on the basis of their measured orbital eccentricities even after much planetary perturbation. Broad parent daughter associations can be made on this basis from measurement of their trajectories intercepted in earth orbit.

Jackson, A. A.↗

NASA NTRS1996

Aerodynamic shape optimization using control theory

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Reuther, James↗

NASA NTRS2003

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗

NASA NTRS1985

Mass property control of a spin stabilized spacecraft with restrictive mission and weight constraints

In the primary experiment of the spin stabilized San Marco D/L spacecraft, the drag effects on a light spherical shell coupled to a relatively massive center body will be measured. To achieve the precise mass property control, the centroids of both the shell and the center body must coincide with each other and with the center of pressure of the shell. Precise spin balancing is needed for launch and orbital stability, and the deployable antennas need accurate alignment. Corrective measures, developed after the preliminary mass measurements showed flaws in the mass property control, are described in detail. Inertia booms and a yo-yo despin system were developed as add-on units, spin balance measurements about all three geometric axes were used to define weight minimized correction within the outer shell envelope, and boom tip mass differentials were optimized for the most favorable inertia ratio margin achievable within the mission weight constraints. The weight versus orbital lifetime trade-offs were also considered.

Lang, W. E.↗

NASA NTRS2001

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗

NASA NTRS2011

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.

Scott, James R.↗

NASA NTRSDate not supplied

Machine Learning based Aircraft Performance Model Estimation for Trajectory Prediction

The accurate prediction of aircraft trajectory by ground-based decision support tools is a critical component of air traffic management in the US National Airspace System (NAS). Accurate predictions of where the aircraft will be in the future or when they will arrive at specific locations (e.g., fixes) is a key enabler for sequencing and efficient arrival management of flights. Traditional physics based aircraft trajectory prediction relies on a simplified point-mass total energy model whose parameters are referred to as Aircraft Performance Model (APM) parameters. Even though the performance coefficients and weight of an aircraft are a vital part of the aircraft performance model’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to decision-support tools. Current approaches freeze some coefficients to default base of aircraft data (BADA) values and optimize others. However, the APM parameters are highly coupled by the flight dynamics and prioritizing one parameter over others leads to bias and skewed predictions. To alleviate this problem, we provide a combined optimization framework to predict all the critical (thrust, drag and weight) APM parameters. This paper is focused on training Machine Learning (ML) models that map historical flights to optimized APM parameters that provide the best fit (in terms of prediction error). Our dataset obtained from NASA’s Sherlock data warehouse is comprised of thousands of historical flights and includes weather and track data collected from 2019. Using different subsets of relevant features (e.g., aircraft type), we trained several ML models to estimate the aircraft’s take off weight, drag polar coefficients (both parasitic and lift induced), and thrust settings (multiplier applied to the maximum engine thrust). The chosen flights are from three of the most common aircraft types (B738, B737, and A320) arriving at four airports (LAX, DEN, MSP, and DFW). Our ML approach is comprised of two different solutions: 1- using a subset of features that are known prior to the flight departure and do not change during flight (such as engine type, current temperature at departure & destination airports, aircraft type) and 2 - using a subset of temporal features of the flight trajectory (such as cruise altitude, Mach, airspeed, and rate of climb) in addition to the pre-departure features from the first solution. The labels or target variables are the APM parameters that were obtained by an optimized ordinary differential equations (ODE) fitting process (applied to individual flights). The ODE-fitting is very time intensive and is therefore performed offline. Thus, training an ML model to learn the relationship between the flight features and ODE-generated labels enables faster estimation of the APM parameters and is therefore amenable to real-time prediction. Various ML models including linear regression, random forest, XGBoost, and neural network were trained, and the results are compared. After model validation and hyperparameter-tuning, we observed that the Random Forest model outperformed the other three models by the overall mean square error (MSE) of 2% for the first solution and 1.5% for the second solution. Finally, the ML-derived parameters are compared against default BADA APM parameters using NASA’s Autonomy Development toolkit (ADK) simulation software. The simulation results for one of each aircraft type is shown and discussed.

Aida Sharif Rohani↗

NASA NTRS1980

Differential correction capability of the GTDS using TDRSS data

A differential correction (DC) capability was implemented in the Goddard Trajectory Determination System (GTDS) to process satellite tracking data acquired via the Tracking and Data Relay Satellite System (TRDRSS). Configuration of the TDRSS is reviewed, observation modeling is presented, and major features of the capability are discussed. The following types of TDRSS data can be processed by GTDS: two way relay range and Doppler measurements, hybrid relay range and Doppler measurements, one way relay Doppler measurements, and differenced one way relay Doppler measurements. These data may be combined with conventional ground based direct tracking data. By using Bayesian weighted least squares techniques, the software allows the simultaneous determination of the trajectories of up to four different satellites - one user satellite and three relay satellites. In addition to satellite trajectories, the following parameters can be optionally solved: for drag coefficient, reflectivity of a satellite for solar radiation pressure, transponder delay, station position, and biases.

Liu, S. Y.↗

NASA NTRS1990

Procedures for minimizing the effects of high solar activity on satellite tracking and ephemeris generation

We are currently experiencing a period of high solar radiation combined with wide short-term fluctuations in the radiation. The short-term fluctuations, especially when combined with highly energetic solar flares, can adversely affect the mission of U.S. Space Command's Space Surveillance Center (SSC) which catalogs and tracks the satellites in orbit around the Earth. Rapidly increasing levels of solar electromagnetic and/or particle radiation (solar wind) causes atmospheric warming, which, in turn, causes the upper-most portions of the atmosphere to expand outward, into the regime of low altitude satellites. The increased drag on satellites from this expansion can cause large, unmodeled, in-track displacements, thus undermining the SSC's ability to track and predict satellite position. On 13 March 1989, high solar radiation levels, combined with a high-energy solar flare, caused an exceptional amount of short-term atmospheric warming. The SSC temporarily lost track of over 1300 low altitude satellites--nearly half of the low altitude satellite population. Observational data on satellites that became lost during the days following the 13 March 'solar event' was analyzed and compared with the satellites' last element set prior to the event (referred to as a geomagnetic storm because of the large increase in magnetic flux in the upper atmosphere). The analysis led to a set of procedures for reducing the impact of future geomagnetic storms. These procedures adjust selected software limit parameters in the differential correction of element sets and in the observation association process and must be manually initiated at the onset of a geomagnetic storm. Sensor tasking procedures must be adjusted to ensure that a minimum of four observations per day are received for low altitude satellites. These procedures have been implemented and, thus far, appear to be successful in minimizing the effect of subsequent geomagnetic storms on satellite tracking and ephemeris computation.

Bredvik, Gordon D.↗

NASA NTRS1999

The Enigmatic Longevity of Granular Materials on Mars: The Case for Geologically Episodic Dune Formation

Martian sand dunes are concentrated in vast sand seas in the circumpolar belt of the planet's northern hemisphere, but they are also pervasive over the whole planet. Their occurrence is to be expected on a super-arid planetary surface subjected to boundary layer drag from a continually active atmosphere. Whilst their occurrence is to be expected, their survival is enigmatic. But the enigma only arises if the martian system is considered similar to Earth's --where sand is moved highly frequently, more or less on a seasonal basis. Experimentally it is readily demonstrated that active sand will soon wear down to small grains and eventually diminish to below the critical sand size required to sustain dune formation. According to conventional wisdom, sand moves at higher speeds on Mars than on Earth, and if it were to move as frequently as it does on Earth, then the dune-forming sand population should have long since disappeared, given the great longevity of the martian aeolian system (Sagan coined the term "kamikaze" grains to express this disappearance). No supply of sand could keep pace with this depletion, especially in light of the fact that Mars does not have very active weathering, nor significant crustal differentiation. On Earth, plate tectonics, magmatic activity, and general crustal differentiation over geological time have produced great concentrations of quartz crystals in the continental crustal masses. Not only are these quartz grains chemically and mechanically resilient, they are about the right size for being transported by either wind or water. Add to this, the geologically recent contribution of glacial grinding, and it is easy to see why there are dune field on Earth. So what are the martian dunes composed of, and how does the material survive the eons of attrition? In addition to experimental demonstrations of sand comminution in laboratory aeolian simulations, the problem can be approached from first principles. Sagan showed that by simple considerations of material strength versus mechanical work applied to the material, comminution to sub-sand size would be inevitable. Another semi-analytical approach might be taken by considering that the archetypal aeolian sand surface texture is an irregularly pitted ("frosted") surface composed of chipping hollows approximately 10 microns in diameter, 5 microns deep. Their volume = about 250 cubic microns, or about 1/25000 of the volume of a 100 micron diameter dune grain. Because a saltating grain always strikes another grain, then two surfaces are impacted. Thus each grain undergoes two impacts for every one saltation leap, when the impact statistics are considered for a closed dune system (it can be calculated that a grain can never undergo <1 impact, and never >2 per saltation leap). Hence, if we conservatively assume that there is damage to a grain each time it bounces, but with the minimum damage of only 2 microscopic craters per impact, then approximately 12,500 impacts are required to completely eliminate the grain. Of course, it would require only a fraction of this amount to reduce the grain to below sand size. A grain will make only several tens of saltation leaps on the stoss side of a dune before becoming buried on the lee slope. The dune then has to move its full length before the grain is exhumed again for abrasion. Even with this hiatus in transport, it is easy to see that terrestrial dunes need resupplying with sand in order to survive. In recent theoretical work it has been shown that martian aeolian transport may be initiated with high-speed grains, but this converts to a lower energy dynamic transport equilibrium in which a reptation population dominates grain transport (on Earth, at least half of the flux is by reptation and creep). On Mars, therefore, average grain speeds may be lower than those on Earth, or at least comparable. This would permit greater longevity for martian sands, but it would not go far enough to solve the survival problem. It may, however, explain why martian dunes are about the same size as terrestrial dunes. If martian saltation leaps were significantly longer than on Earth (as usually assumed), then a dune's lee slope would have to be correspondingly longer in order to trap the sand; this would scale up the whole dune structure. But with shorter trajectories in a reptation population, larger dunes would be unnecessary. Additional information is contained in the original.

Marshall, J.↗