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At least 595 records · Page 33

Program for Weibull Analysis of Fatigue Data

A Fortran computer program has been written for performing statistical analyses of fatigue-test data that are assumed to be adequately represented by a two-parameter Weibull distribution. This program calculates the following: (1) Maximum-likelihood estimates of the Weibull distribution; (2) Data for contour plots of relative likelihood for two parameters; (3) Data for contour plots of joint confidence regions; (4) Data for the profile likelihood of the Weibull-distribution parameters; (5) Data for the profile likelihood of any percentile of the distribution; and (6) Likelihood-based confidence intervals for parameters and/or percentiles of the distribution. The program can account for tests that are suspended without failure (the statistical term for such suspension of tests is "censoring"). The analytical approach followed in this program for the software is valid for type-I censoring, which is the removal of unfailed units at pre-specified times. Confidence regions and intervals are calculated by use of the likelihood-ratio method.

Krantz, Timothy L.↗

Development and Calibration of a Field-Deployable Microphone Phased Array for Propulsion and Airframe Noise Flyover Measurements

A new aeroacoustic measurement capability has been developed consisting of a large channelcount, field-deployable microphone phased array suitable for airframe noise flyover measurements for a range of aircraft types and scales. The array incorporates up to 185 hardened, weather-resistant sensors suitable for outdoor use. A custom 4-mA current loop receiver circuit with temperature compensation was developed to power the sensors over extended cable lengths with minimal degradation of the signal to noise ratio and frequency response. Extensive laboratory calibrations and environmental testing of the sensors were conducted to verify the design's performance specifications. A compact data system combining sensor power, signal conditioning, and digitization was assembled for use with the array. Complementing the data system is a robust analysis system capable of near real-time presentation of beamformed and deconvolved contour plots and integrated spectra obtained from array data acquired during flyover passes. Additional instrumentation systems needed to process the array data were also assembled. These include a commercial weather station and a video monitoring / recording system. A detailed mock-up of the instrumentation suite (phased array, weather station, and data processor) was performed in the NASA Langley Acoustic Development Laboratory to vet the system performance. The first deployment of the system occurred at Finnegan Airfield at Fort A.P. Hill where the array was utilized to measure the vehicle noise from a number of sUAS (small Unmanned Aerial System) aircraft. A unique in-situ calibration method for the array microphones using a hovering aerial sound source was attempted for the first time during the deployment.

Humphreys, William M., Jr.↗

Unsupervised Detection of Planetary Craters by a Marked Point Process

With the launch of several planetary missions in the last decade, a large amount of planetary images is being acquired. Preferably, automatic and robust processing techniques need to be used for data analysis because of the huge amount of the acquired data. Here, the aim is to achieve a robust and general methodology for crater detection. A novel technique based on a marked point process is proposed. First, the contours in the image are extracted. The object boundaries are modeled as a configuration of an unknown number of random ellipses, i.e., the contour image is considered as a realization of a marked point process. Then, an energy function is defined, containing both an a priori energy and a likelihood term. The global minimum of this function is estimated by using reversible jump Monte-Carlo Markov chain dynamics and a simulated annealing scheme. The main idea behind marked point processes is to model objects within a stochastic framework: Marked point processes represent a very promising current approach in the stochastic image modeling and provide a powerful and methodologically rigorous framework to efficiently map and detect objects and structures in an image with an excellent robustness to noise. The proposed method for crater detection has several feasible applications. One such application area is image registration by matching the extracted features.

Troglio, G.↗

Clutter Assessment for an Autonomous Multi-Agent Search Mission

This paper presents a method for evaluating the amount of clutter in a region where autonomous vehicles in a multi-agent system must operate based on LIDAR point cloud measurements. The point cloud is used to generate an occupancy grid which is then projected onto a 2D plane of vehicle motion, constituting an image. A series of Gaussian radial basis functions (GRBFs) is created, each centered at an occupied pixel in a 2D image, and summed together to form the clutter field. The clutter field is a representation of the density and permeability of the space at each coordinate. The clutter field is then approximated such that iso-clutter contours are simple geometric objects so that intelligent machine assets can easily query the distance between them and any given point in an environment. In this way, agents are able to determine whether to enter into or steer away from areas of interest. Each vehicle has a clutter threshold representing the clutter value of the space in which it can safely maneuver. The iso-clutter contour corresponding to a vehicle’s clutter threshold is treated as the boundary of an obstacle to be avoided. A simulation is presented where a multi-agent system is tasked with persistent observation of a cluttered area. Each vehicle in the simulation has a different clutter threshold. The vehicles use a potential field-based guidance algorithm, and an allocation of vehicles to specific regions of the space emerges.

multi-agent↗

Theoretical and experimental flow fields for a supersonic cruise fighter forebody

The capability of two numerical methods to predict the flow field about a representative supersonic cruise aircraft was examined. The two codes were a small-disturbance transonic program of Boppe and a conservative form full-potential transonic program of Shankar and Szema. For the former code, comparisons were made with wind-tunnel data at Mach numbers of 0.6, 0.9, and 1.2 and angles of attack of 0 deg, 5 deg, and 10 deg (7.5 deg instead of 10 deg at a Mach number of 1.2). Predictions from the two codes were compared at a Mach number of 1.2 and an angle of attack of 7.5 deg. The comparison criteria were contours of local angle of attack, local angle of sideslip, and local Mach number. The comparisons indicated that both codes may be considered useful for design applications, depending on the degree of accuracy required by the user's solution. Both solutions show an inaccuracy in their predictions, particularly as Mach number and/or angle of attack increases, because of their lack of viscous effects and any mechanisms to predict vortex development.

Yaros, S. F.↗

Laboratory Report on the Investigation of the Flow around Two Turbine-Blade Profiles using the Interferometer Method

At the request of the Junkers Aircraft and Engine Construction Company, Engine Division, Dessau Main Plant, an investigation was made using the interferometer method on the two turbine-blade profiles submitted. The interferometer method enables making visible the differences in density and consequently the boundary layers that develop when a flow is directed on the profile. Recognition of the points on the profile at which separation of flow occurs is thus possible. By means of the interference photographs the extent of the dead-water region may be ascertained. The size of the dead-water region provides evidence as to the quality of the flow and allows a qualitative estimate of the amount of the flow losses. Interference photographs thus provide means of judging the utility of profiles under specific operating conditions and provide suggestions for possible changes of profile contours that might help to improve flow relations. Conclusions may be drawn concerning the influence of the blade-spacing ratio, the inlet-air angle, and the connection between the curvature of the profile contour and the point of separation of the flow from the profile surface.

vonVietinghoff-Scheel, K.↗

Basin-Scale Structural Features Database

The Basin-Scale Structural Features database provides spatial datasets of faults, fractures, folds, and earthquakes compiled from public, authoritative sources (e.g., U.S. Geological Survey and State Geological Surveys) and aggregated into derivative forms to support subsurface assessments. Recognizing that characterizing basin-scale structural features requires interpreting data that are often ambiguous or lack key information, the source data were evaluated using a knowledge-data framework and geospatial fuzzy logic method (Justman et al., 2020) to represent both measured (observed) and predicted (inferred or potential) structural features as derivative datasets. This workflow employs conceptual models for known structural features and predicted structural features, incorporating geospatial data to estimate potential, even with limited data. The aim is to aid and support an understanding of basin-scale features and identify potential gaps in data and knowledge. As of 4/30/2025, the database includes resources for nine sedimentary basins: Appalachian, Denver, U.S. Gulf Coast, Illinois, Michigan, Permian, Sacramento, San Joquin and Williston. The database is organized by basin and then data category: 1) Faults, fractures, folds, 2) Earthquakes, 3) Topographic, 4) Structural contours and isopachs, 5) Geophysical, and 6) Structural feature density assessment maps.

basin scale↗

Defect Localization Capabilities of a Global Detection Scheme: Spatial Pattern Recognition Using Full-field Vibration Test Data in Plates

Recently, a conceptually simple approach, based on the notion of defect energy in material space has been developed and extensively studied (from the theoretical and computational standpoints). The present study focuses on its evaluation from the viewpoint of damage localization capabilities in case of two-dimensional plates; i.e., spatial pattern recognition on surfaces. To this end, two different experimental modal test results are utilized; i.e., (1) conventional modal testing using (white noise) excitation and accelerometer-type sensors and (2) pattern recognition using Electronic speckle pattern interferometry (ESPI), a full field method capable of analyzing the mechanical vibration of complex structures. Unlike the conventional modal testing technique (using contacting accelerometers), these emerging ESPI technologies operate in a non-contacting mode, can be used even under hazardous conditions with minimal or no presence of noise and can simultaneously provide measurements for both translations and rotations. Results obtained have clearly demonstrated the robustness and versatility of the global NDE scheme developed. The vectorial character of the indices used, which enabled the extraction of distinct patterns for localizing damages proved very useful. In the context of the targeted pattern recognition paradigm, two algorithms were developed for the interrogation of test measurements; i.e., intensity contour maps for the damaged index, and the associated defect energy vector field plots.

Saleeb, A. F.↗

Physical Simulation Of Rocket Exhaust Aerodynamics Using Heated Ethane: Prototypical Experiments

An inaugural experimental investigation into the use of heated ethane as a motive fluid for subscale simulation of rocket exhaust plume aerodynamics has been conducted. A small, self-contained, hydrocarbon aerodynamics test stand was designed and fabricated for this purpose. Testing was performed on an aerodynamic system comprised of a 77:1 upper stage nozzle contour coupled with a passive second-throat supersonic diffuser, specifically selected for its known LOX/GH2 hot-fire performance and complex shock structure. Effects of ethane purity and stagnation temperature on the accuracy of flow field replication have been examined. All major flow features present in hot-fire tests were reproduced in heated ethane with start and unstart pressure ratio errors of approximately +4% and -5%, respectively. Steady-state test cell pressure ratio errors of ±0.5% were shown to be readily achievable when the stagnation temperature was well-controlled. Ambient-temperature nitrogen testing was also conducted for the purpose of direct comparison of the ethane method to conventional cold-flow techniques. However, its higher isentropic exponent prevented the diffuser from achieving start.

rocket↗

Validation Experiments of Incipient Turbulent Separation over an Axisymmetric Afterbody

Historically, the flow physics involved with most turbulent separated flows have presented fundamental challenges in validation between experimental and numerical approaches. As recognized by the CFD Vision 2030 study commissioned by NASA, validation of Reynolds-averaged Navier-Stokes (RANS) models and other scale-resolving methods for turbulent separated flow requires the support of advanced, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, a new test platform, referred to as the NASA Axisymmetric Afterbody, was designed to obtain detailed information of the flow field over a smooth body, undergoing adverse pressure gradient induced separation for a fixed Reynolds number, Re = 180,000. The parametric body offers a range of flow states from fully attached,incipient separation, to fully separated flow based on variable afterbody geometries. In an initial effort to evaluate RANS turbulence model capabilities, the present configuration of the axisymmetric model features a mild adverse pressure gradient over the contoured boattail section, inducing incipient turbulent separation. Experiments include steady pressure measurements to serve as preliminary comparisons to simulation studies, which examine the effect of variable grid domains and RANS turbulence models, in an effort to understand and evaluate the critical variability between solutions for the present configuration. Results indicate potential discrepancies may be due to the effect of the square tunnel test section walls, relatively large blockage ratio, and inconsistent reference parameters. Ongoing work will focus on the experimental campaigns to obtain surface flow visualizations and high-resolution, off-body flow field measurements using Stereoscopic Particle Image Velocimetry (SPIV) and Laser Doppler Velocimetry (LDV) techniques to provide a detailed benchmark dataset to aid turbulence modelers.

axisymmetric afterbody↗

Wing flutter boundary prediction using an unsteady Euler aerodynamic method

Modifications to an existing three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1) for the aeroelastic analysis of wings are described. These modifications, which were previously added to CFL3D Version 1.0, include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time-integration with the government flow equations. The paper gives a brief description of these modifications and presents unsteady calculations which check the modifications to the code. Euler flutter results for an isolated 45 degree swept-back wing are compared with experimental data for seven freestream Mach numbers which define the flutter boundary over a range of Mach number from 0.499 to 1.14. These comparisons show good agreement in flutter characteristics for freestream Mach numbers below unity. For freestream Mach numbers above unity, the computed aeroelastic results predict a premature rise in the flutter boundary as compared with the experimental boundary. Steady and unsteady contours of surface Mach number and pressure are included to illustrate the basic flow characteristics of the time-marching flutter calculations and to aid in identifying possible causes for the premature rise in the computational flutter boundary.

Lee-Rausch, Elizabeth M.↗

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗

Quantification of airport community noise impact in terms of noise levels, population density, and human subjective response

The Fraction Impact Method (FIM), developed by the National Research Council (NRC) for assessing the amount and physiological effect of noise, is described. Here, the number of people exposed to a given level of noise is multiplied by a weighting factor that depends on noise level. It is pointed out that the Aircraft-noise Levels and Annoyance MOdel (ALAMO), recently developed at NASA Langley Research Center, can perform the NRC fractional impact calculations for given modes of operation at any U.S. airport. The sensitivity of these calculations to errors in estimates of population, noise level, and human subjective response is discussed. It is found that a change in source noise causes a substantially smaller change in contour area than would be predicted simply on the basis of inverse square law considerations. Another finding is that the impact calculations are generally less sensitive to source noise errors than to systematic errors in population or subjective response.

Deloach, R.↗

Comparison of central axis and jet ring coolant supply for turbine disk cooling on a SSME-HPOTP model

The test facility, test methods and results are presented for an experimental study modeling the cooling of turbine disks in the blade attachment regions with multiple impinging jets, in a configuration simulating the disk cooling method employed on the Space Shuttle Main Engine oxygen turbopump. The study's objective was to provide a comparison of detailed local convection heat transfer rates obtained for a single center-supply of disk coolant with those obtained with the present flight configuration where disk coolant is supplied through an array of 19 jets located near the disk outer radius. Specially constructed disk models were used in a program designed to evaluate possible benefits and identify any possible detrimental effects involved in employing an alternate disk cooling scheme. The study involved the design, construction and testing of two full scale rotating model disks, one plane and smooth for baseline testing and the second contoured to the present flight configuration, together with the corresponding plane and contoured stator disks. Local heat transfer rates are determined from the color display of encapsulated liquid crystals coated on the disk in conjunction with use of a computer vision system. The test program was composed of a wide variety of disk speeds, flowrates, and geometrical configurations, including testing for the effects of disk boltheads and gas ingestion from the gas path region radially outboard of the disk-cavity.

Kim, Y. W.↗

Validation Experiments for Turbulent Separation over an Axisymmetric Body of Revolution

Historically, the flow physics involved with most turbulent separated flows have presented fundamental challenges to validating numerical approaches. As recognized by the CFD Vision 2030 study commissioned by NASA, validation of Reynolds-averaged Navier-Stokes (RANS) models and other scale-resolving methods for turbulent separated flow requires data from advanced, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, a new test platform, referred to as the NASA Axisymmetric Afterbody, was designed to obtain detailed measurements of the flow field undergoing a smooth, adverse pressure gradient induced separation for a fixed Reynolds number, Re = 180,000. The parametric body offers a range of flow states progressing from fully attached, to incipient separation, and finally to small-scale separated flow based on variable afterbody geometries. In an initial effort to evaluate RANS turbulence model capabilities, the present configurations of the axisymmetric model host a mild adverse pressure gradient over the contoured boattail section, inducing incipient turbulent separation, as well as a slightly larger adverse pressure gradient, inducing a small-scale region of turbulent separation. Experiments include steady pressure measurements and 2-D PIV to provide the preliminary dataset for simulation studies, which examine the effect of variable grid domains and RANS turbulence models. This is done in an effort to understand and evaluate the critical variability between solutions for the present model configurations. Results indicate potential discrepancies may be due to the effect of the square tunnel test section walls, relatively large blockage ratio, and slight variability in reference parameters. Ongoing work will focus on higher fidelity experimental campaigns to obtain surface flow visualizations and Stereo-Particle Image Velocimetry (SPIV) to deliver higher spatial resolution of the three-dimensional flow field to aid turbulence modelers.

Validation↗

In-Situ Detection of Process-Induced Porosity During Cure of Out-of-Autoclave Composites

Composite materials offer unique benefits in aerospace applications, including high strength-to-weight ratio, and are becoming increasingly used by industry manufacturers. Current manufacturing and processing methods can lead to defects in the composites, which are identified after fabrication using inspection methods. This study utilized a high-temperature ultrasonic inspection system to detect process-induced porosity in an out-of-autoclave (OOA) composite panel during cure. In order to perform ultrasonic scans in-situ during cure, the system needed to be able to operate at oven temperatures up to 200 °C. There are no commercially available ultrasonic scanning systems that can operate continuously at these temperatures, so an enclosure was fabricated to insulate the ultrasonic system in the curing oven. The enclosure housed a MISTRAS® motorized X-Y raster scanner and contact transducer (Olympus® X2002). The Olympus® X2002 contact transducer is a continuous high-temperature delay line transducer with a center frequency of 2.25 MHz. In order to prevent the inside of the enclosure from reaching high temperatures, a sparge pipe inside the cooling enclosure was connected to a liquid nitrogen (LN2) tank outside of the oven via insulated hoses. The cooling system was automatically controlled by a temperature controller that was programmed to open a solenoid valve along the hose at 31 ℃ and close at 28 ℃ inside the cooling enclosure. When the solenoid valve was open, LN2 would flow from the LN2 tank and vaporize prior to reaching cooling enclosure. A U-shaped sparge pipe had holes drilled along its length to uniformly introduce cold nitrogen gas into the cooling enclosure. This prevented the motors from ever reaching the maximum desired operating temperature of 38 ℃. In the bottom of the enclosure, the tool plate was placed with the composite facing the outside of the enclosure, exposing it to the temperatures of the oven. The tool plate was 63.5 mm thick borosilicate glass, which was chosen for its low ultrasonic attenuation and moderate thermal conductivity. A thin layer of ultrasonic couplant was placed on the tool plate. The transducer sent and received ultrasonic waves through the tool plate into the composite. A MISTRAS® Remote UT System performed all wave generation, analog to digital conversion, and data acquisition and processing. The transducer was connected directly to the Remote UT System via a high-temperature BNC cable (CD International, RG-316). Polyimide insulated copper wire was used to connect the scanner to a 2-axis motor drive, which was connected to the Remote UT System. The motor drive and Remote UT System were located outside the industrial oven. A diagram of the ultrasonic system is shown in Figure 1. Figure 1: Diagram of ultrasonic in-situ defect detection system. In this study, a porosity gradient was introduced into the carbon fiber reinforced polymer (CFRP) composite through a misfit of the part and caul plate. A 24-ply quasi-isotropic ([0/90, ±45]12S) composite panel was laid up using Newport® AS4C-M/NB321 out-of-autoclave (OOA) plain weave (PW) prepreg (42% resin content, 195 g/m2). The first 16 plies were 203 mm × 203 mm. Ply drops were incorporated into the panel by decreasing the length of plies 17-24. The sizes of each ply are included in Table 1. All plies were centered along their length (x-axis) creating a trapezoidal type cross-section. Table 1: Ply sizes Plies Length (mm) Width (mm) 1-16 203 203 17-18 102 203 19-20 85 203 21-22 68 203 23-24 51 203 A 15-5 stainless steel caul plate (Size: 203 × 203 × 1.2 mm) was placed on the laminate. The composite and caul plate were vacuum bagged to the tool plate. Per the product datasheet, Newport 321 can be cured between 121 °C and 149 °C, depending on service temperature, with a hold for 90-120 minutes. Based on prior thermal testing of the cooling enclosure, the desired composite temperature cycle could be attained when the air temperature of the oven was ramped to 160 °C at a rate of 1.7 °C/min with a 3 hour hold. The extended hold was not necessary to cure the composite, but did allow for additional scans at the cure temperature during preliminary testing. The composite panel was under vacuum pressure for the entire cure cycle. Under vacuum, the caul plate deformed causing high and low pressure regions. The low-pressure regions formed high porosity in the composite part. The ultrasonic data collected showed that the inspection system was able to monitor the evolution of porosity within the composite throughout the cure cycle. Fifty scans of a 203 mm × 51 mm (8 in. × 2 in.) area of the composite were completed throughout the cure cycle. The scan speed was set to 43 mm/s in the x-direction and 36 mm/s in the y-direction, with a 1.0 mm/pixel resolution in both directions. Each scan took approximately five minutes to complete. Figure 2 shows C-scan amplitude data (top view) from one scan during the cure cycle. The color map indicates the maximum amplitude (%) measured with a time gate that contains reflections from the back surface (furthest from the transducer in contact with the caul plate) of the composite. Because porosity in the composite increases the ultrasonic attenuation in the composite part, a higher amplitude (red) indicates low porosity and a lower amplitude (blue) indicates high porosity. The regions where the caul plate was applying increased pressure (center and ends of the panel) resulted in reduced porosity, whereas the ply drop regions had reduced pressure and thus had higher porosity. Figure 2: Amplitude C-scan (top view) of OOA composite from one scan during the 160 °C temperature hold. Higher amplitude (red) indicates low porosity. Lower amplitude (blue) indicates high porosity. A B-scan is a two-dimensional image plotting the ultrasonic signals from a single y-position at every x-location of the composite panel. The travel time (μs) of the ultrasonic wave (representing the through-thickness location) is plotted along the y-axis, and the ultrasonic wave signal is represented as a contour map. Based on the B-scan data, the location of the defects with respect to the composite thickness was able to be determined. The ply drop regions had high porosity near the front (tool plate) surface of the composite (Figure 3). Figure 3: B-scan (cross-section view) of OOA composite from one scan during the 160 °C temperature hold. Using the data obtained from amplitude C-scans and B-scans throughout the cure cycle, the high and low porosity regions within the composite laminate were detected and localized with high spatial resolution. This paper will discuss the evolution of porosity content in the OOA composite during cure. OOA tests aided the transition of this system to an autoclave, which is the primary method of curing aerospace-grade thermoset composites.

Tyler B. Hudson↗

Micromechanics-Based Structural Analysis (FEAMAC) and Multiscale Visualization within Abaqus/CAE Environment

A unified framework is presented that enables coupled multiscale analysis of composite structures and associated graphical pre- and postprocessing within the Abaqus/CAE environment. The recently developed, free, Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software couples NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with Abaqus/Standard and Abaqus/Explicit to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. The Graphical User Interfaces (FEAMAC-Pre and FEAMAC-Post), developed through collaboration between SIMULIA Erie and the NASA Glenn Research Center, enable users to employ a new FEAMAC module within Abaqus/CAE that provides access to the composite microscale. FEA IAC-Pre is used to define and store constituent material properties, set-up and store composite repeating unit cells, and assign composite materials as sections with all data being stored within the CAE database. Likewise FEAMAC-Post enables multiscale field quantity visualization (contour plots, X-Y plots), with point and click access to the microscale i.e., fiber and matrix fields).

Arnold, Steven M.↗

Evaluation of data obtained from atmospheric laser Doppler velocimeter

The Doppler lidar velocimeter produces a variety of kinds of data. Besides the line of sight velocity components, there are the reflected amplitudes and the Doppler widths. Computer graphics software for displaying these data was produced. Different methods of presentation are needed for the various items. A picture was produced as pictures are often the best way to gain understanding. The individual lidar scans form a crosshatch pattern. Thus one-dimensional measurements fit together to form a two-dimensional whole. A pair of velocity measurements at a point combine to form a wind measurement with direction and magnitude. This gives a forest of wind vectors. The goal is to find a recognizable pattern to these trees. Often it is necessary to show only part of the information. That is, show only the wind direction not its magnitude or reduce the wind to streamlines of air flow. In other cases data are reduced to contour plots. Just enough contour lines are included to show the picture described.

Keck, T. S.↗