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Diffraction loss reduced by curving one reflector. In improved diplexer, adjustable reflector has toroidal curvature to reduce diffraction loss through open cavity ends. Primarily used in local oscillator diplexers, new design increases signal to noise ratios and therefore ranges of millimeter and submillimeter hetrodyne receivers.
The trajectory data are presented chronologically and are organized by holding the arrival date constant while varying the Earth departure date in increments of 10 days. Upon completion of the specified range of Earth departure dates, the arrival date is incremented and the range of departure dates is repeated. For long trip times, where the variation of the trajectory parameters is relatively small, the size of the increment of the arrival date is increased. The range of departure and arrival dates and their corresponding increments are given i n Table 4-1 for each launch opportunity. The criterion for the selection of these dates is that they encompass the region in which the Earth departure hyperbolic excess speed is less than or equal to 0.65 EMOS.
The trajectory data are presented chronologically and are organized by holding the arrival date constant while varying the Earth departure date in increments of 10 days. Upon completion of the specified range of Earth departure dates, the arrival date is incremented and the range of departure dates is repeated. For long trip times, where the variation of the trajectory parameters is relatively small, the size of the increment of the arrival date is increased. The range of departure and arrival dates and their corresponding increments are given in Table 5-1 for each launch opportunity. The criterion for the selection of these dates is that they encompass the region in which the Earth departure hyperbolic excess speed is less than or equal to 0.65 EMOS. There are two lines of print for each trajectory (departure-date/arrival date pair). In the first line the two left most columns contain the dates of departure and arrival. The next 18 columns of the first line can be divided into three groups: six columns of data related to departure, six columns pertinent to the heliocentric phase of the mission, and six columns related to arrival at the target planet. The second line of print contains, respectively, the Delta V requirements for departure and arrival, the total Delta V requirement, the heliocentric transfer trajectory type, and four parameters defining conditions at arrival. The value computed for the arrival Delta V is for entry into a circular orbit. The radius selected for this orbit, while necessarily somewhat arbitrary, is representative of the broad range of orbit radii which tend to minimize the arrival Delta V for the range of excess speeds between 0.1 and 0.8 EMOS. The value selected for Uranus and Neptune is 3 planet radii. Significant reductions in the computed Delta V can be realized by assuming entry into an elliptical orbit having a periapsis radius equal to the selected circular-orbit radius. The magnitude of the reduction can be determined from Figures 2-6 and 2-8 i n Section 2.
The tensile mechanical properties of ceramic matrix composites (CMC) in directions off the primary axes of the reinforcing fibers are important for architectural design of CMC components that are subjected to multi-axial stress states. In this study, 2D-woven melt-infiltrated (MI) SiC/SiC composite panels with balanced fiber content in the 0 degree and 90 degree directions were tensile loaded in-plane in the 0 degree direction and at 45 degree to this direction. In addition, a 2D triaxially-braided MI composite panel with balanced fiber content in the plus or minus 67 degree bias directions and reduced fiber content in the axial direction was tensile loaded perpendicular to the axial direction tows (i.e., 23 degrees from the bias fibers). Stress-strain behavior, acoustic emission, and optical microscopy were used to quantify stress-dependent matrix cracking and ultimate strength in the panels. It was observed that both off-axis loaded panels displayed higher composite onset stresses for through-thickness matrix cracking than the 2D-woven 0/90 panels loaded in the primary 0 degree direction. These improvements for off-axis cracking strength can in part be attributed to higher effective fiber fractions in the loading direction, which in turn reduces internal stresses on critical matrix flaws for a given composite stress. Also for the 0/90 panel loaded in the 45 degree direction, an improved distribution of matrix flaws existed due to the absence of fiber tows perpendicular to the loading direction. In addition, for the +67/0/-67 braided panel, the axial tows perpendicular to the loading direction were not only low in volume fraction, but were also were well separated from one another. Both off-axis oriented panels also showed relatively good ultimate tensile strength when compared to other off-axis oriented composites in the literature, both on an absolute strength basis as well as when normalized by the average fiber strength within the composites. Initial implications are discussed for constituent and architecture design to improve the directional cracking of SiC/SiC CMC components with MI matrices.
This paper presents a study of the direction angle sensitivity of radar backscatter from agricultural fields. The direction angle is defined as the angle between the incident plane and the perpendicular to the field row direction. Previous studies have concentrated on comparing the backscatter of agricultural fields imaged with 0, 45, and 90 degree direction angles. In contrast, this study concentrates on the backscatter changes occurring when the direction angle is modified by a few degrees or even by fractions of a degree. This is possible by using the output of the NASA/JPL AIRSAR processor, in which sixteen independent frames are formed, each one corresponding to the same radar scene imaged with a slightly different squint angle. The studied data set is an agricultural area in La Mancha, Spain acquired in June and July 1991 during the EFEDA experiment. This paper describes the observed backscatter variations of the agricultural fields with direction angle measured at P, L, and C bands. As expected, the backscatter is maximum for a 0 degree direction angle. For several fields, the backscatter at P and L bands drops by more than 10 dB for a 5 degree change in direction angle. Furthermore, the sensitivity to the direction angle decreases with increasing vegetation. The variations in backscatter are compared with model predictions. One model, which agrees with scatterometer data, underestimates the observed backscatter variations with direction angle by more than 10 dB. It does not take into account the possible coherent component of the radar signal. We believe the strong direction sensitivity of agricultural field backscatter obtained with SAR data is due to a Bragg resonant effect, resulting in a strong coherent return when the direction angle is zero. The observations are then projected to the case of spaceborne SAR data.
Shoaling wave fields generated in laboratory experiments were analyzed to determine the sensitivity of nonlinear interactions to the directional distributions of incident waves. Peaks in the directional spectra observed in shallow water were consistent with near resonating, quadratic interactions between two primary waves transferring energy to a third wave with the sum frequency and vector sum wavenumber of the primary waves. Directionally colinear waves forced a higher-frequency wave propagating in the same direction as the primary waves, while directionally spread (i.e., noncolinear) primary waves forced a higher-frequency wave that propagated in a direction between those of the interacting primary waves. Deepwater wave fields with similar frequency spectra but different directional spectra evolved to different shallow-water directional spectra, yet their shallow-water frequency spectra were remarkably similar. This result suggests that the shape of the directional spectrum of the incident wave field has only a small effect on the magnitudes of nonlinear energy transfer during shoaling. The principal effect of directionality in the incident wave field is on the directions, not the amplitudes, of the nonlinearly generated waves. The laboratory data demonstrate clearly the importance of triad interactions between noncolinear and colinear shoaling waves.
Energetic precipitating particles (EPPs) can cause significant direct constituent changes in the mesosphere and stratosphere (middle atmosphere) during certain periods. Both protons and electrons can influence the polar middle atmosphere through ionization and dissociation processes. EPPs can enhance HOx (H, OH, HO2) through the formation of positive ions followed by complex ion chemistry and NOx (N, NO, NO2) through the dissociation of molecular nitrogen. The HOx increases result in direct ozone destruction in the mesosphere and upper stratosphere via several catalytic loss cycles. Such middle atmospheric HOx-caused ozone loss is rather short-lived due to the relatively short lifetime (hours) of the HOx constituents. The NOx family has a considerably longer lifetime than the HOx family and can also lead to catalytic ozone destruction. EPP-caused enhancements of the NOx family can affect ozone directly, if produced in the stratosphere. Ozone decreases from the EPPs lead to a reduction in atmospheric heating and, subsequent atmospheric cooling. Conversely, EPPs can cause direct atmospheric heating through Joule heating. Measured HOx constituents OH and HO2 showed increases due to solar protons. Observed NOx constituents NO and NO2 were enhanced due to both solar protons and precipitating electrons. Other hydrogen- and nitrogen-ocntaining constituents were also measured to be directly influenced by EPPs, including N2O, HNO3, HO2NO2, N2OS, H2O2, ClONO2, HCl, and HOCl. Observed constituents ClO and CO were directly affected by EPPs as well. Many measurements indicated significant direct ozone decreases. A significant number of satellites housed instruments, which observed direct EPP-caused atmospheric effects, including Nimbus 4 (BUV), Nimbus 7 (SBUV), several NOAA platforms (SBUV/2), SME, UARS (HALOE, CLAES), SCISAT-1 (ACE-FTS), Odin (OSIRIS), Envisat-l (GOMOS, MIPAS, SCIAMACHY), and Aura (MLS). Measurements by rockets and ground-based radar also indicated EPP direct impacts. Atmospheric models have been used with some success in predicting the direct EPP impacts on the mesosphere and stratosphere. A review of the observed direct effects of EPP on the middle atmosphere will be given in this presentation.
Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work, we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction, a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms two other approaches in estimation efficiency: one that utilizes periodic spline quantile regression and another that generates data from the commonly used Abe-Ley distribution for cylindrical data. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios. Our method indicates significant changes in the variation of wind speed with respect to some directions.
Here, we investigate the effects of 3D printing build directions on the fracture properties of octet lattice metamaterials made of polylactic acid (PLA) and how these effects vary with the relative density of the lattices. Single-edge notch bend samples are 3D printed in two orthogonal build directions at various relative densities. Our results show that the work of fracture for octet lattices with build directions parallel to the crack plane is significantly higher than those with build directions perpendicular to the crack plane. We also observed that the ratio of specific work of fracture between the two build directions remains nearly constant across different relative densities. In contrast, the ratio of peak load between the two build directions decreases as relative density increases. Furthermore, the build direction dictates the fracture mechanism. While the perpendicular build direction predominantly results in a brittle (mode I) fracture, the parallel build direction leads to a complex, delamination-dominated (mode II type) fracture. This phenomenon is largely governed by the weak interfaces formed between the printed layers and their interaction with the lattice geometry. These results reveal that the build direction governs the fracture mechanism and work of fracture of these lattice metamaterials and is therefore an important design consideration.
This Handbook sets forth in two parts the following information for the guidance of users of the NASA Management Directives System. Part A is a master list of management directives in force as of March 31, 1993. Chapter 1 contains introductory informative material on how to use this Handbook. Chapter 2 is a complete master list of Agencywide management directives, describing each directive by type, number, effective date, expiration date, title, and organization code of the office responsible for the directive. Chapter 3 includes a consolidated numerical list of all delegations of authority and a breakdown of such delegation by the office or installation to which special authority is assigned. Chapter 4 sets forth a consolidated list of all NASA Handbooks (NHB's) and important footnotes covering the control and ordering of such documents. Chapter 5 is a consolidated list of NASA management directives applicable to the Jet Propulsion Laboratory. Chapter 6 is a consolidated list of NASA management directives published in the Code of Federal Regulations. Complementary manuals to the NASA Management Directives System are described in Chapter 7. Part B is the index to NASA management directives in force as of March 31, 1993. This part contains an in-depth alphabetical index to all NASA management directives other than Handbooks. NHB's 1610.6, 'NASA Personnel Security Handbook,' 1620.3, 'NASA Physical Security Handbook,' 1640.4, 'NASA Information Security Program,' 1900.1, 'Standards of Conduct for NASA Employees,' 5103.6, 'Source Evaluation Board Handbook,' and 7400.1, 'Budget Administration Manual,' are indexed in-depth. All other NHB's are indexed by titles only.
It is well established that perceptual direction discrimination shows an oblique effect; thresholds are higher for motion along diagonal directions than for motion along cardinal directions. Here, we compare simultaneous direction judgments and pursuit responses for the same motion stimuli and find that both pursuit and perceptual thresholds show similar anisotropies. The pursuit oblique effect is robust under a wide range of experimental manipulations, being largely resistant to changes in trajectory (radial versus tangential motion), speed (10 versus 25 deg/s), directional uncertainty (blocked versus randomly interleaved), and cognitive state (tracking alone versus concurrent tracking and perceptual tasks). Our data show that the pursuit oblique effect is caused by an effective expansion of direction space surrounding the cardinal directions and the requisite compression of space for other directions. This expansion suggests that the directions around the cardinal directions are in some way overrepresented in the visual cortical pathways that drive both smooth pursuit and perception.
Because the results of preliminary flight tests had indicated. the P-63A-1 airplane possessed insufficient directional stability, the NACA and the manufacturer (Bell Aircraft Corporation) suggested three vertical-tail modifications to remedy the deficiencies in the directional characteristics. These modifications included an enlarged vertical tail formed by adding a tip extension to the original vertical tail, a large sharp-edge ventral fin, and a small dorsal fin. The enlarged vertical tail involved only a slight increase in total vertical-tail area from 23.73 to 26.58 square feet but a relatively much larger increase in geometric aspect ratio from 1.24 to 1.73 based on height and area above the horizontal tail. At the request of the Air Material Command, Army Air Forces, flight tests were made to determine the effect of these modifications and of some combinations of these modifications on the directional stability and control characteristics of the airplane, In all, six different vertical-tail. configurations were investigated to determine the lateral and directional oscillation characteristics of the airplane, the sideslip characteristics, the yaw due to ailerons in rudder-fixed rolls from turns and pull-outs, the trim changes due to speed changes; and the trim changes due to power changes. Results of the tests showed that the enlarged vertical tail approximately doubled the directional stability of the airplane and that the pilots considered the directional stability provided by the enlarged vertical tail to be satisfactory. Calculations based on sideslip data obtained at an indicated airspeed of 300 miles per hour showed that the directional stability of the airplane with the original vertical tail corresponded to a value of 0(sub n beta) of -0.00056 whereas for the enlarged vertical tail the estimated va1ue of C(sub n beta) was -0.00130, The ventral fin was found to increase by a moderate amount the directional stability of the airplane with the original vertical tail for smal1 sides1ip angles at low speeds but little consistent change in directional stability was effected by the ventral fin at higher speeds, The effectiveness of the ventral fin was generally much less when used with the enlarged vertical tail than when used with the original vertical tail. The ventral and dorsal fins were found to be very effective in eliminating rudder-force reversals which occurred in low-speed, high-engine-power, sideslipped conditions of flight . Sideslip tests at two altitudes for approximately the sane engine power and indicated airspeed showed that a small decrease in static directional stability occurred with increasing altitude and this decrease in stability was attributed to the increased propeller blade angles required at high altitudes. The variations of rudder pedal force with indicated airspeed using normal rated power and a constant rudder tab setting through the speed range were desirably small for all the configurations tested. The rudder pedal force changed by about 50 pounds for a power change from engine idling power, to normal rated power and this pedal force change was largely independent of airspeed or of vertical-tail configuration for the various configurations tested.
Within the linear regime of mechanical and electrical responses, it is commonly accepted that direct and converse piezoelectric coefficients should be the same. However, we observed a consistently higher converse d 31 (∼54 pm/V) than the direct d 31 (∼42 pC/N) for a quenched, stretched, annealed, and electrically poled poly(vinylidene fluoride-co-trifluorethylene) [P(VDF-TrFE)] 52/48 mol.% sample (abbreviated as coP-52/48QSAP). On the contrary, the direct and converse d 31 values were the same for coP-65/35QSAP and coP-55/45QSAP. Small-angle X-ray scattering results showed that coP-52/48QSAP had a higher amount of relaxor-like secondary crystals (SCs) in the oriented amorphous fraction (OAF) (SC OAF ) than coP-55/45QSAP and coP-65/35QSAP. To explain the experimental observation, we performed molecular dynamics (MD) simulation of the pure PVDF (without TrFE) to estimate direct and converse piezoelectricity for the PVDF OAF. Based on the MD simulation, the direct d 31 had a plateau value around 350 pC/N for the transverse (i.e., along the chain direction) strain up to 1 %, whereas the simulated converse d 31 could be lower (for electric field E < 0.8 MV/m), equal (for E = 0.8 MV/m), or higher (for E > 0.8 MV/m) than the direct d 31 , depending on the poling electric field. From the MD simulation, both mechano-electrostriction and electrostatic interaction were identified in the OAF as the driving force for enhanced piezoelectricity in ferroelectric PVDF. In conclusion, when ferroelectric domains were formed in the OAF by electric poling, the simulated converse d 31 became higher than the direct d 31 . Combining both experimental and MD simulation results, the higher converse d 31 than direct d 31 for coP-52/48QSAP was understood qualitatively.
This handbook sets forth in two parts, Master List of Management Directives and Index to NASA Management Directives, the following information for the guidance of users of the NASA Management Directives System. Chapter 1 contains introductory information material on how to use this handbook. Chapter 2 is a complete master list of agencywide management directives, describing each directive by type, number, effective date, expiration date, title, and organization code of the office responsible for the directive. Chapter 3 includes a consolidated numerical list of all delegations of authority and a breakdown of such delegation by the office or center to which special authority is assigned. Chapter 4 sets forth a consolidated list of all NASA handbooks (NHB's) and important footnotes covering the control and ordering of such documents. Chapter 5 is a consolidated list of NASA management directives applicable to the Jet Propulsion Laboratory. Chapter 6 is a consolidated list of NASA regulations published in the Code of Federal Regulations. Chapter 7 is a consolidated list of NASA regulations published in Title 14 of the Code of Federal Regulations. Complementary manuals to the NASA Management Directives System are described in Chapter 8. The second part contains an in depth alphabetical index to all NASA management directives other than handbooks, most of which are indexed by titles only.
Electric thrusters typically require a power processing unit (PPU) to convert the spacecraft provided power to the voltage-current that a thruster needs for operation. Testing has been initiated to study whether an arcjet thruster can be operated directly with the power produced by solar arrays without any additional conversion. Elimination of the PPU significantly reduces system-level complexity of the propulsion system, and lowers developmental cost and risk. The work aims to identify and address technical questions related to power conditioning and noise suppression in the system and heating of the thruster in long-duration operation. The apparatus under investigation has a target power level from 400-1,000 W. However, the proposed direct-drive arcjet is potentially a highly scalable concept, applicable to solar-electric spacecraft with up to 100's of kW and beyond. A direct-drive electric propulsion system would be comprised of a thruster that operates with the power supplied directly from the power source (typically solar arrays) with no further power conditioning needed between those two components. Arcjet thrusters are electric propulsion devices, with the power supplied as a high current at low voltage; of all the different types of electric thruster, they are best suited for direct drive from solar arrays. One advantage of an arcjet over Hall or gridded ion thrusters is that for comparable power the arcjet is a much smaller device and can provide more thrust and orders of magnitude higher thrust density (approximately 1-10 N/sq m), albeit at lower I(sub sp) (approximately 800-1000 s). In addition, arcjets are capable of operating on a wide range of propellant options, having been demonstrated on H2, ammonia, N2, Ar, Kr, Xe, while present SOA Hall and ion thrusters are primarily limited to Xe propellant. Direct-drive is often discussed in terms of Hall thrusters, but they require 250-300 V for operation, which is difficult even with high-voltage solar arrays. The arcjet requires under 100 V, which is more in-line with what is easily possible with a solar array. Direct-drive of an electric propulsion system confers the advantage of reducing or eliminating the power processing unit (PPU) that is typically needed to convert the spacecraft-provided power to the voltage and current needed for thruster operation. Since the PPU is typically the most expensive piece of an electric thruster system, from both a fabrication and qualification standpoint, its elimination offers the potential for major reductions in system cost and risk. The design of the arcjet built for this effort was based on previous low power (1 kW class) arcjets. It has a precision machined 99.95% pure tungsten anode which also serves as the nozzle. The anode constrictor region is 1 mm (0.040-in) diameter and 1 mm (0.040-in) long. The cathode is a tungsten welding electrode doped with LaO2; its tip was precision ground to a 30◦ angle ending in a blunt end. The two electrodes are separated by a boron-nitride insulator which also serves as the propellant injection manifold; it ends in six small holes which introduce the propellant gas in the diverging section of the nozzle, directly adjacent to the cathode. The electrodes and insulator are housed in a stainless-steel outer-body, with a Macor insulator at the mid-plane to provide thermal isolation between the front and back halves of the device. The gas seals were made using Grafoil gaskets. Figure 1A shows the assembled thruster in the vacuum chamber; figure 1B shows the thruster in operation on argon at a flow rate of 676 sccm (20 mg/s). Initial testing was conducted in a 3.5-ft diameter vacuum chamber; the ultimate pressure reached during quasi-steady operation of the thruster was about 330 millitorr. The thruster was powered with a high-current, 0-100A, 15 kW power supply. The discharge was initiated with a high-voltage (approximately 10 kV) spark initiator that was isolated from the supply by a stack of diodes. The testing indicated that an operating point exists within the I-V characteristics that is compatible with direct-drive solar-electric operation; for a flow rate of 20 mg/s (argon) the arc could be sustained at a voltage of about 20 V and a current of 25 A (500W).
Infrasound (acoustic waves below 20 Hz) can be used to detect, locate and quantify activity in the atmosphere such as volcanic eruptions and anthropogenic explosions. Attempts to quantify volcanic eruption parameters such as exit velocity, plume height and mass flow rate using infrasound data depend strongly on assumptions of the acoustic source type. Infrasonic sources may produce omnidirectional or directional wavefields, while propagation effects, such as interaction with topography, can induce further wavefield directivity that is measured by field instrumentation. Limited sampling of these wavefields can hinder our ability to infer the underlying source, and thus our understanding of the eruption characteristics. Equivalent sources are often used to represent acoustic source mechanisms and resultant wavefields. In this study, we review equivalent acoustic sources as they pertain to infrasonic scale and wavelengths commonly encountered in very local (<5 km range) geophysical field deployments. We highlight the equivalent infrasonic bipole source that can be induced by ground-reflection of an elevated monopole; we are not aware of any prior infrasound studies that use the bipole source concept. We use analytical and numerical methods to explore source directivity of monopole, dipole and bipole ground-reflected sources at infrasonic frequencies as well as the additional directivity complications introduced by interactions with topography. We illustrate that for typical volcano-infrasound wavelengths, increasing height above the ground as well as increasing source frequency leads to increased wavefield directivity. Numerical modelling using a simple omnidirectional monopole source embedded in topography further illustrates that both horizontal and vertical infrasound directionality can be induced by topography at the distance scales appropriate for local volcano infrasound monitoring. Information summarized in this analytical and numerical exploration of infrasound directivity may be used to help guide future volcano-infrasound field deployments intended to estimate source parameters or quantify wavefield directivity. Analytic solutions for simple whole-space or half-space atmospheres provide useful formulations for planning or initially analysing geophysical field-scale experimental data; however, especially at very local distances from the source (<5 km), 3-D simulations are necessary to account for complex topography commonly encountered in volcano-infrasound applications.
In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.
The paper shows that the experimentally observed close alignment of magnetic field minimum variance direction with the average magnetic field for Alfven waves in the solar wind is consistent with theoretically predicted properties of plane large amplitude Alfven waves in the MHD approximation. The theoretical properties of these Alfven waves constrain the time averaged magnetic field to cluster around the direction of minimum variance, which is aligned with the wave normal. Thus, spacecraft magnetometer observations in the solar wind of minimum variance directions strongly peaked about the average magnetic field direction are consistent with plane large amplitude Alfven waves which have wave normals aligned with the directions of minimum variance. This does not imply that geometrical hydromagnetic calculations for Alfven wave propagation direction in the solar wind are incorrect, but there is a discrepancy between geometrical hydromagnetics theory and observations that IMF minimum variance directions tend to be aligned with the ideal Parker spiral instead of the radial direction.