Performance of a Propeller-Vane Compared to Two Cup Anemometers
|
|
- Corey Carr
- 7 years ago
- Views:
Transcription
1 Performance of a Propeller-Vane Compared to Two Cup Anemometers Mark A. Taylor, Senior Meteorologist (mtaylor@awstruewind.com) Erik Hale, Meteorologist (ehale@awstruewind.com) Michael C. Brower, Chief Technical Officer (mbrower@awstruewind.com) AWS Truewind, LLC 3 New Karner Road Albany, New York 05 Tel: (5) 3-00 Fax: (5) Abstract A key goal of wind resource assessment is to ensure that wind speed measurements conform to known standards. Morris et al. (99) document that an RM Young Wind Monitor prop-vane sensor can record wind speeds that are as much as % lower than those measured by NRG Maximum #0 cup anemometer in turbulent settings. Their explanation is that this underspeeding is most likely the result of the prop-vane failing to point perfectly upwind with sudden direction shifts. When not pointing perfectly upwind, the propvane does not conform to its specification; the response is approximately a cosine function of the direction deviation. The results of several case studies are summarized and they provide further understanding of how the response of propeller-vane (prop-vane) anemometers differs from that of the more widely used NRG Maximum #0 and Risoe cup anemometers. We discuss the physical reasons for those differences and propose a method for converting wind speed observations from one type to the other. Introduction A key goal of wind resource assessment is to ensure that wind speed measurements conform to known standards. This study provides insights into how the response of R.M. Young 0503 propeller-vane (propvane) anemometers differs from those of the more widely used NRG Maximum #0 and Risoe P5A cup anemometers, and proposes a method for converting wind speed observations from one type to the other. According to Morris et al. (99), in non-turbulent flow from a wind tunnel, the prop-vanes and cup anemometers in their analyses recorded virtually the same speed, as is to be expected if they have been calibrated correctly. However, in their field studies, the prop-vane anemometers consistently recorded lower wind speeds. The study concluded that the prop-vane s inability to remain perfectly aligned with the horizontal wind vector under turbulent conditions was responsible. This study attempts to confirm and extend this finding using observed wind speed data from five pairs of R.M. Young prop-vane and NRG Maximum #0 cup anemometers, mounted on three masts, and three pairs of R.M. Young prop-vanes and Risoe P5A cup anemometers, mounted at different heights on the same mast. Anemometer Characteristics Cup and propeller anemometers observe the wind speed by employing an apparatus that detects the wind flow by rotating about an axis at a rate proportional to the wind speed. A propeller anemometer rotates about a horizontal axis and ideally responds only to the component of the wind velocity vector that is parallel to that
2 axis. To accurately measure the wind speed from a different direction, the propeller (impelled by an attached vane) must rotate until it faces fully into the wind. Conversely, a cup anemometer rotates on a vertical axis enabling it to measure the horizontal wind from any direction. In this study, the following three instrument models were employed to measure wind speed: the R.M. Young 0503 Wind Monitor, a prop-vane sensor, and the NRG Maximum #0 and Risoe P5A cup sensors. According to specifications published by each respective manufacturer, the anemometer starting thresholds range from less than 0. m/s (Risoe P5A) to.0 m/s (R.M. Young 0503). Another measure of anemometer sensitivity, the distance constant, indicates the length of a passing air column needed for the sensor to recover 3% of an abrupt change in speed. The Risoe model has the shortest distance constant ( m), while the NRG and R.M. Young anemometers have longer constants (3.0 m and.7 m, respectively). A shorter distance constant indicates a more rapid response to fluctuations in speed. Table summarizes the characteristics of each anemometer type. Table. Wind Measurement Instrument Specifications R.M. Young 0503 NRG Maximum #0 Risoe P5A Distance Constant.7 m (3% Recovery) 3.0 m (3% Recovery) m Default Slope / Offset 0.09 m / 0 m/s 5 m / 0.35 m/s 0.0 m / m/s Starting Threshold.0 m/s m/s < 0. m/s Monitoring Site Characteristics We chose four monitoring masts configured with side-by-side cup and R.M. Young propeller-vane anemometers. Two of these masts are located in a high-turbulence environment, while the remaining masts are located in an area characterized by moderate turbulence. Information about the sites, including the monitoring heights, anemometer types, and observed average turbulence intensities at 5 m/s are provided in Table. Table. Monitoring Site Characteristics Monitoring Mast Period of Record Monitoring Heights (m) Cup Anemometer Model Site 00 Jun 00 Sep 007 0, NRG Maximum #0 Site 00 Jan 007 Sep 007 0, 0, 0 Risoe P5A Site 003 Feb Mar 00 53, 3 NRG Maximum #0 Site 00 Feb Mar 00 53, 3 NRG Maximum #0 Mean TI at 5 m/s 9 (0 m), 0.0 ( m) 0. (0 m), 0 (0 m), 0. (0 m) 0. (53 m), 0.3 (3 m) 0. (53 m), 0.3 (3 m)
3 Data Analysis Methods The data consisted of 0-minute average wind speed, direction, and temperature readings and their standard deviations, and were received in various formats from the tower owners. All of the prop-vane anemometers were uncalibrated; the raw binary data for these sensors were converted to physical values according to the manufacturer s specified slope with no offset. The NRG Maximum #0 cup anemometers were calibrated, but the manufacturer s standard slope and offset were used to convert the raw data. The Risoe P5A cup anemometers were all calibrated, and the raw binary data were converted according to the calibration information provided with the sensors. At Site 00, the prop-vane instrument had been in operation for roughly months before the cup anemometers were installed; furthermore, the original -m cup anemometer failed shortly after its installation, calling into question its overall reliability. A new calibrated anemometer was installed almost months later. At Site 00, all instruments were installed when the tower was erected. However, the Risoe anemometer at 0 m did not become operational until months later. At Sites 003 and 00, instruments were installed on three separate occasions. The masts were initially installed with single prop-vanes at 53 m and 3 m; an additional set of prop-vanes was installed 9 months later at the same heights; the NRG Maximum #0 anemometers were installed an additional months later. For tubular monitoring towers, the impact of the tower on the wind flow is approximately symmetric on either side of the wind vector. Therefore, to minimize differential tower effects, we analyzed wind speed observations only from direction sectors that were within 0 degrees of the midpoint between each sensor pair on the upwind side. It has been documented that off-horizontal flow impacts anemometers differently. However, due to the absence of vertical anemometers on three of these masts, this phenomenon was not assessed. An experienced meteorologist examined the data for completeness and reasonableness and determined the functionality of each instrument. Each sensor pair showed satisfactory operation except for the 53-m level at Site 00, which was disqualified from the study. For all turbulence-related calculations, we only used R.M. Young-reported wind speeds between m/s and m/s, the range typically used to calibrate the NRG Maximum #0 anemometers. Finally, to avoid the potential for undetected icing of the anemometers to contaminate the data, we selected only observations between the months of May and September at Sites 00 and 00. Icing was not expected to impact Sites 003 and 00. Theory The turbulent energy in the wind flow manifests itself through variations in both the speed and direction. Longitudinal turbulence causes a change in speed, whereas lateral or transverse turbulence, which is usually of a comparable magnitude, causes a change in direction. The turbulence intensity (TI) is computed as the quotient of the standard deviation of the observed speed and the mean speed for each 0-minute period. The standard deviation of direction (DSD) provides a comparable measure of transverse turbulence. Both cup and propeller anemometers experience a lag in response to longitudinal speed changes, as indicated by their distance constants. This lag is often implicated as a cause of anemometer overspeeding. The NRG and R.M. Young anemometers have similar distance constants and therefore should experience similar degrees of such overspeeding under the same conditions. The Risoe anemometer should be somewhat less susceptible to this problem. However, in any case the impact is relatively small under most conditions. Separate analyses were run using the instrument-specific calibration slopes and offsets at Site 00. 3
4 The R.M. Young anemometer, however, is uniquely susceptible to underspeeding caused by changes in wind direction. Such changes force the wind vane to constantly realign itself with the horizontal velocity vector, introducing a directional lag. Since the component of the scalar speed v that is parallel to the propeller axis is given by vcos(θ), where θ is the angle between the wind vector and the axis, it is reasonable to suppose that the degree of underspeeding over an extended period is proportional to the cosine of the standard deviation of direction. To correct for this effect and recover the free-stream speed, we propose dividing the observed wind speed by cos(dsd). Results and Discussion Dependence on Speed Plots of the cup anemometer wind speeds as a function of those observed concurrently by the R.M. Young anemometers reveal very tight correlations between the two readings. Figure contains two examples of these plots. In the first plot, it is notable that the scatter at very low speeds tends to drop below the regression line; in the other graph, the scatter at the same speeds drifts above the regression line. Site 00 0-m Speeds Site 00 0-m Speeds NRG Maximum #0 Speed (m/s) y =.057x R² = Risoe Speed (m/s) y =.005x + R² = Figure. Scatterplots of Simultaneous 0-m Wind Speeds Observed at Site 00 To show the different responses of the sensors in more detail, Figures and 3 plot the wind speed ratios between sensor pairs as a function of the wind speeds observed by the R.M. Young anemometer. Underspeeding by the R.M. Young is indicated by a ratio less than one. For anemometers with a similar response, the plots should show a tight scatter near a ratio of one at most speeds, with random scatter at speeds near the instruments cut-in. The two series of plots show decidedly different signatures, however. For the R.M. Young / NRG anemometer pairs at Site 00, the scatter in the speed ratio as a function of speed is tightly clustered at a ratio near one at speeds greater than about m/s; at lower speeds, random scatter centered near the same ratio was observed. There is, however, a hint that the scatter at low speeds may be biased toward speed ratios greater than one. The R.M. Young / Risoe anemometer pairs at Site 00 demonstrate mostly tight scatter at all speeds. However, the center point of the scatter varies with speed. At speeds greater than about m/s, the average speed ratio is nearly constant at a value near ; below m/s, the mean ratio drops slowly with declining speed until it reaches about m/s, where it drops rapidly.
5 0-m Anemometer Pair -m Anemometer Pair RM Young / NRG Speed Ratio RM Young /NRG Speed Ratio Figure. Plots of R.M. Young / NRG Wind Speed Ratio as a Function of Wind Speed at Site 00 0-m Anemometer Pair RM Young / Risoe Speed Ratio m Anemometer Pair 0-m Anemometer Pair RM Young / Risoe Speed Ratio RM Young / Risoe Speed Ratio Figure 3. Plots of R.M. Young / Risoe Wind Speed Ratio as a Function of Wind Speed 5
6 We hypothesize that the different patterns indicate that the problem of overspeeding due to longitudinal turbulence becomes worse at low speeds for sensors with relatively large distance constants. The NRG and R.M. Young sensors, both of which have large distance constants, provide similar speed readings at low speeds, despite some scatter, but the R.M. Young sensor reads significantly higher than the Risoe anemometer at speeds below 5 m/s. The different patterns may also reflect the lower cut-in speed of the Risoe anemometer, since the wind speed will more often drop below the cut-in for the NRG and R.M. Young models. Neither hypothesis could be confirmed, however. Dependence on Transverse Turbulence Turbulent energy in the horizontal wind flow manifests itself through fluctuations both along the axis of the flow (turbulence intensity - TI) and transverse to the flow (directional standard deviation - DSD). Figure provides examples of the strong linear relationship between the two. (It should be noted that turbulent energy also is present in the vertical component of the flow but is not analyzed here due to lack of vertical speed and turbulence measurements.) Site 00 -m Site 00 0 m DSD 0 0 y =.3x +.73 R² = TI DSD y = 7.57x + 39 R² = TI Figure. Plots of DSD as a Function of TI We assessed the relationship between the turbulence transverse to the horizontal wind flow and the variation between the anemometer types. Figure 5 contains scatterplots of the wind speed differences between the anemometers as a function of cos(dsd) for the NRG and Risoe sensor pairs. For both cup models, the amount of underspeeding by the RM Young anemometer increases with the transverse turbulence, and at high turbulence levels can amount to several percent, a substantial effect for wind energy. However, for the Risoe anemometer pairs, the underspeeding becomes noticeable only for cos(dsd) values greater than about (DSD <.5 o, or TI ~0.-). For the NRG pairs, the impact of turbulence is evident over the full range. We next multiplied the wind speeds reported by the R.M. Young anemometers by /cos(dsd) and plotted the adjusted speeds as a function of the cos(dsd). Figure contains separate plots for the NRG and Risoe anemometer pairs. The NRG anemometer pairs appear to confirm that transverse turbulence causes propvane underspeeding, as the slopes are not statistically different from zero for all but the -m level at Site 00. While this suggests that the DSD correction is useful, the variation of the intercepts implies that other factors are impacting the anemometer relationships.
7 For the adjusted Risoe anemometer pairs, the portion of the graph where the observed speed difference was dependent on the cos(dsd) has become flat, but the slope is now reversed at low turbulence. We believe this pattern may be because the Risoe anemometer itself underestimates the scalar wind speed when the wind vector has a vertical component. Since horizontal turbulence is generally accompanied by vertical turbulence, which causes the wind vector to stray off-horizontal, the effects of transverse turbulence on the Risoe and RM Young anemometers may be comparable at low to moderate turbulence levels and therefore cancel each other. NRG Anemometer Pairs Risoe Anemometer Pairs Speed Difference (%) % 0% % % 3% % Cos (DSD) Site 00 m Site 00 0 m Site m Site m Site 00 3 m Speed Difference (%) 0% % % 3% % 5% % 7% Site 00 0 m Site 00 0 m Site 00 0 m Cos (DSD) Figure 5. Plots of Observed Speed Difference as a Function of cos(dsd) NRG Anemometer Pairs Risoe Anemometer Pairs % 0% Adjusted Speed Difference (%) 0% % % 3% % Cos (DSD) Site 00 m Site 00 0 m Site m Site m Site 00 3 m Adjusted Speed Difference (%) % % 3% % 5% % 7% Site 00 0 m Site 00 0 m Site 00 0 m Cos (DSD) Figure. Plots of Adjusted Speed Difference as a Function of cos(dsd) Summary and Conclusions In this analysis, we have compared the wind speed measurements from several R.M. Young 0503 prop-vane instruments with those of NRG Maximum #0 and Risoe P5A cup anemometers. Consistent with previously published results, the R.M. Young instruments recorded lower wind speeds with respect to the two types of cup anemometers. In general, our results suggest that the precise method for adjusting each R.M. Young anemometer to a cup anemometer standard should be determined on-site when side-by-side data are available. However, when employed for resource assessment, a single R.M. Young prop-vane is often the sole 7
8 instrument installed at a monitoring level. This situation necessitates the derivation of a turbulence-based adjustment that can be computed from the speed and direction data provided by a single instrument. We have assumed that the standard deviation of the wind direction for each 0-minute observation is a good measure of the impact of off-axis winds not observed by the R.M. Young anemometer. Based on the cosineresponse of a propeller anemometer, we multiplied the reported speeds by /cos(dsd) in order to estimate the free-stream horizontal wind speed observed by each corresponding cup anemometer. For the NRG / R.M. Young pairs, the result was to eliminate most evidence of underspeeding. Conversely, for the Risoe / R.M. Young pairs, our results suggest that the same adjustment is only applicable when the cos(dsd) was less than about (DSD >.5 o ); under lower turbulence conditions, no relationship is implied and this adjustment is, therefore, not recommended. This research has addressed the underspeeding by prop-vane anemometers associated with turbulence. It is stressed that other factors, such as differing anemometer distance constants, calibration, degradation, tower effects, and off-horizontal flow must also be analyzed in order to fully understand differences between anemometers used for wind resource assessment. These topics are the subject of continuing research at AWS Truewind. References Hunter, R.S The Accuracy of Cup Anemometer Calibration With Particular Regard to Testing Wind Turbines. Wind Engineering, ()3 3 Morris, V.R., et al. Comparison of Anemometers for Turbulence Characterization, Windpower 9, Seattle, Washington Pedersen, T.F.; Schmidt Paulsen, U., Classification of operational characteristics of commercial cupanemometers. In: Wind energy for the next millennium. Proceedings. 999 European wind energy conference (EWEC '99), Nice (FR), -5 Mar 999. Petersen, E.L.; Hjuler Jensen, P.; Rave, K.; Helm, P.; Ehmann, H. (eds.), (James and James Science Publishers, London, 999) p. -5
Adjustment of Anemometer Readings for Energy Production Estimates WINDPOWER June 2008 Houston, Texas
Adjustment of Anemometer Readings for Energy Production Estimates WINDPOWER June 2008 Houston, Texas Matthew Filippelli, Julien Bouget, Michael Brower, and Dan Bernadett AWS Truewind, LLC 463 New Karner
More informationSandia National Laboratories New Mexico Wind Resource Assessment Lee Ranch
Sandia National Laboratories New Mexico Wind Resource Assessment Lee Ranch Data Summary and Transmittal for September December 2002 & Annual Analysis for January December 2002 Prepared for: Sandia National
More informationSummarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
More informationEVALUATION OF ZEPHIR
EVALUATION OF ZEPHIR A. Albers Deutsche WindGuard Consulting GmbH, Oldenburger Straße 5, D-31 Varel, Germany E-mail: a.albers@windguard.de, Tel: (++9) ()51/9515-15, Fax: : (++9) ()51/9515-9 Summary Since
More informationGerman Test Station for Remote Wind Sensing Devices
German Test Station for Remote Wind Sensing Devices A. Albers, A.W. Janssen, J. Mander Deutsche WindGuard Consulting GmbH, Oldenburger Straße, D-31 Varel, Germany E-mail: a.albers@windguard.de, Tel: (++9)
More informationCOMPARISON OF LIDARS, GERMAN TEST STATION FOR REMOTE WIND SENSING DEVICES
COMPARISON OF LIDARS, GERMAN TEST STATION FOR REMOTE WIND SENSING DEVICES A. Albers, A.W. Janssen, J. Mander Deutsche WindGuard Consulting GmbH, Oldenburger Straße, D-31 Varel, Germany E-mail: a.albers@windguard.de,
More informationSuccessful Implementation of an Alternative Co-located Transfer Standard Audit Approach: Continuous Deployment of CTS Wind Sensors on a Tall Tower
Successful Implementation of an Alternative Co-located Transfer Standard Audit Approach: Continuous Deployment of CTS Wind Sensors on a Tall Tower Kirk Stopenhagen Vorticity Consulting LLC Redmond, WA
More informationEFFECTS OF COMPLEX WIND REGIMES ON TURBINE PERFORMANCE
EFFECTS OF COMPLEX WIND REGIMES ON TURBINE PERFORMANCE Elisabeth Rareshide, Andrew Tindal 1, Clint Johnson, AnneMarie Graves, Erin Simpson, James Bleeg, Tracey Harris, Danny Schoborg Garrad Hassan America,
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
More informationCorrelation key concepts:
CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationThe Point-Slope Form
7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationExperiment 7: Forces and Torques on Magnetic Dipoles
MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics 8. Spring 5 OBJECTIVES Experiment 7: Forces and Torques on Magnetic Dipoles 1. To measure the magnetic fields due to a pair of current-carrying
More informationCritical Limitations of Wind Turbine Power Curve Warranties
Critical Limitations of Wind Turbine Power Curve Warranties A. Albers Deutsche WindGuard Consulting GmbH, Oldenburger Straße 65, D-26316 Varel, Germany E-mail: a.albers@windguard.de, Tel: (++49) (0)4451/9515-15,
More informationCASE HISTORY #2. APPLICATION: Piping Movement Survey using Permalign Laser Measurement System
CASE HISTORY #2 APPLICATION: Piping Movement Survey using Permalign Laser Measurement System EQUIPMENT: Dresser-Clark Hot Gas Expander (Turbine), 60-inch Inlet Flange HISTORY: Piping support modifications
More informationSolving Equations Involving Parallel and Perpendicular Lines Examples
Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines
More informationDiagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
More informationAnalytical Test Method Validation Report Template
Analytical Test Method Validation Report Template 1. Purpose The purpose of this Validation Summary Report is to summarize the finding of the validation of test method Determination of, following Validation
More information2. Simple Linear Regression
Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationAccurate Air Flow Measurement in Electronics Cooling
Accurate Air Flow Measurement in Electronics Cooling Joachim Preiss, Raouf Ismail Cambridge AccuSense, Inc. E-mail: info@degreec.com Air is the most commonly used medium to remove heat from electronics
More informationUSE OF REMOTE SENSING FOR WIND ENERGY ASSESSMENTS
RECOMMENDED PRACTICE DNV-RP-J101 USE OF REMOTE SENSING FOR WIND ENERGY ASSESSMENTS APRIL 2011 FOREWORD (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, property
More informationAcceleration Introduction: Objectives: Methods:
Acceleration Introduction: Acceleration is defined as the rate of change of velocity with respect to time, thus the concepts of velocity also apply to acceleration. In the velocity-time graph, acceleration
More informationDefinition: A vector is a directed line segment that has and. Each vector has an initial point and a terminal point.
6.1 Vectors in the Plane PreCalculus 6.1 VECTORS IN THE PLANE Learning Targets: 1. Find the component form and the magnitude of a vector.. Perform addition and scalar multiplication of two vectors. 3.
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationExample SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross
CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal
More informationVirtual Met Mast verification report:
Virtual Met Mast verification report: June 2013 1 Authors: Alasdair Skea Karen Walter Dr Clive Wilson Leo Hume-Wright 2 Table of contents Executive summary... 4 1. Introduction... 6 2. Verification process...
More informationPhysics 221 Experiment 5: Magnetic Fields
Physics 221 Experiment 5: Magnetic Fields August 25, 2007 ntroduction This experiment will examine the properties of magnetic fields. Magnetic fields can be created in a variety of ways, and are also found
More informationWind Resource Assessment for BETHEL, ALASKA Date last modified: 2/21/2006 Compiled by: Mia Devine
813 W. Northern Lights Blvd. Anchorage, AK 99503 Phone: 907-269-3000 Fax: 907-269-3044 www.akenergyauthority.org Wind Resource Assessment for BETHEL, ALASKA Date last modified: 2/21/2006 Compiled by: Mia
More informationRelationships Between Two Variables: Scatterplots and Correlation
Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)
More informationUnit 9 Describing Relationships in Scatter Plots and Line Graphs
Unit 9 Describing Relationships in Scatter Plots and Line Graphs Objectives: To construct and interpret a scatter plot or line graph for two quantitative variables To recognize linear relationships, non-linear
More informationChapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
More informationDetermining Polar Axis Alignment Accuracy
Determining Polar Axis Alignment Accuracy by Frank Barrett 7/6/008 Abstract: In order to photograph dim celestial objects, long exposures on the order of minutes or hours are required. To perform this
More informationFigure 1.1 Vector A and Vector F
CHAPTER I VECTOR QUANTITIES Quantities are anything which can be measured, and stated with number. Quantities in physics are divided into two types; scalar and vector quantities. Scalar quantities have
More informationLetter Report No. 100413407CRT-004 Project No. G100413407
3933 US Route 11 Cortland, NY 13045 Telephone: (607) 753-6711 Facsimile: (607) 753-1045 www.intertek.com Letter Report No. 100413407CRT-004 Project No. G100413407 Mr. Steve Turek Phone: 952-447-6064 Wind
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares
More informationTurbulence assessment with ground based LiDARs
Turbulence assessment with ground based LiDARs E.T.G. Bot June 214 ECN-E--14-43 Acknowledgement The LAWINE project is partially funded by the Dutch government in the framework of TKI Wind op Zee. Abstract
More informationLaboratory Report Scoring and Cover Sheet
Laboratory Report Scoring and Cover Sheet Title of Lab _Newton s Laws Course and Lab Section Number: PHY 1103-100 Date _23 Sept 2014 Principle Investigator _Thomas Edison Co-Investigator _Nikola Tesla
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationDATA VALIDATION, PROCESSING, AND REPORTING
DATA VALIDATION, PROCESSING, AND REPORTING After the field data are collected and transferred to your office computing environment, the next steps are to validate and process data, and generate reports.
More informationINTRODUCTION TO ERRORS AND ERROR ANALYSIS
INTRODUCTION TO ERRORS AND ERROR ANALYSIS To many students and to the public in general, an error is something they have done wrong. However, in science, the word error means the uncertainty which accompanies
More informationPower Performance Measured Using a Nacelle-mounted LiDAR
Power Performance Measured Using a Nacelle-mounted LiDAR R. Wagner, M. Courtney, T. F. Pedersen; DTU Wind Energy, Risø Campus, Roskilde, Denmark R. Wagner External Article English Introduction Wind turbine
More informationPre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationExercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationA wind turbine is a machine for converting the kinetic energy in wind into mechanical energy.
Type of Turbines Page 1 Turbines A wind turbine is a machine for converting the kinetic energy in wind into mechanical energy. mills Turbines If the mechanical energy is used directly by machinery, such
More informationMagnetometer Realignment: Theory and Implementation
Magnetometer Realignment: heory and Implementation William Premerlani, Octoer 16, 011 Prolem A magnetometer that is separately mounted from its IMU partner needs to e carefully aligned with the IMU in
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationUSING SIMULATED WIND DATA FROM A MESOSCALE MODEL IN MCP. M. Taylor J. Freedman K. Waight M. Brower
USING SIMULATED WIND DATA FROM A MESOSCALE MODEL IN MCP M. Taylor J. Freedman K. Waight M. Brower Page 2 ABSTRACT Since field measurement campaigns for proposed wind projects typically last no more than
More informationCALL VOLUME FORECASTING FOR SERVICE DESKS
CALL VOLUME FORECASTING FOR SERVICE DESKS Krishna Murthy Dasari Satyam Computer Services Ltd. This paper discusses the practical role of forecasting for Service Desk call volumes. Although there are many
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationSIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS. J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID
SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID Renewable Energy Laboratory Department of Mechanical and Industrial Engineering University of
More informationMaximum Range Explained range Figure 1 Figure 1: Trajectory Plot for Angled-Launched Projectiles Table 1
Maximum Range Explained A projectile is an airborne object that is under the sole influence of gravity. As it rises and falls, air resistance has a negligible effect. The distance traveled horizontally
More informationLecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation
Lecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation Display and Summarize Correlation for Direction and Strength Properties of Correlation Regression Line Cengage
More informationPrelab Exercises: Hooke's Law and the Behavior of Springs
59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically
More informationChapter 11: r.m.s. error for regression
Chapter 11: r.m.s. error for regression Context................................................................... 2 Prediction error 3 r.m.s. error for the regression line...............................................
More informationINFLUENCES OF VERTICAL WIND PROFILES ON POWER PERFORMANCE MEASUREMENTS
Abstract INFLUENCES OF VERTICAL WIND PROFILES ON POWER PERFORMANCE MEASUREMENTS U. Bunse, H. Mellinghoff DEWI GmbH, Ebertstr. 96, D 26382 Wilhelmshaven e mail: u.bunse@dewi.de The IEC 61400 12 1 [1] and
More informationLinear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares
Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects
More informationDetermination of g using a spring
INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative
More informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
More informationCorrelation and Regression
Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look
More informationWe are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries?
Statistics: Correlation Richard Buxton. 2008. 1 Introduction We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Do
More informationIndustry Environment and Concepts for Forecasting 1
Table of Contents Industry Environment and Concepts for Forecasting 1 Forecasting Methods Overview...2 Multilevel Forecasting...3 Demand Forecasting...4 Integrating Information...5 Simplifying the Forecast...6
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationEXPERIMENTAL ERROR AND DATA ANALYSIS
EXPERIMENTAL ERROR AND DATA ANALYSIS 1. INTRODUCTION: Laboratory experiments involve taking measurements of physical quantities. No measurement of any physical quantity is ever perfectly accurate, except
More information2) The three categories of forecasting models are time series, quantitative, and qualitative. 2)
Exam Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Regression is always a superior forecasting method to exponential smoothing, so regression should be used
More informationSection 14 Simple Linear Regression: Introduction to Least Squares Regression
Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship
More informationA Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion
A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for
More informationa. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F
FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all
More informationCalibration of the MASS time constant by simulation
Calibration of the MASS time constant by simulation A. Tokovinin Version 1.1. July 29, 2009 file: prj/atm/mass/theory/doc/timeconstnew.tex 1 Introduction The adaptive optics atmospheric time constant τ
More informationWhat Can We Learn by Disaggregating the Unemployment-Vacancy Relationship?
What Can We Learn by Disaggregating the Unemployment-Vacancy Relationship? No. 1- Rand Ghayad and William Dickens Abstract: The Beveridge curve the empirical relationship between unemployment and job vacancies
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationForecaster comments to the ORTECH Report
Forecaster comments to the ORTECH Report The Alberta Forecasting Pilot Project was truly a pioneering and landmark effort in the assessment of wind power production forecast performance in North America.
More informationCourse Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.
SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationPennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
More information11.1. Objectives. Component Form of a Vector. Component Form of a Vector. Component Form of a Vector. Vectors and the Geometry of Space
11 Vectors and the Geometry of Space 11.1 Vectors in the Plane Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. 2 Objectives! Write the component form of
More informationIndex-Velocity Rating Development for Rapidly Changing Flows in an Irrigation Canal Using Broadband StreamPro ADCP and ChannelMaster H-ADCP
Index-Velocity Rating Development for Rapidly Changing Flows in an Irrigation Canal Using Broadband StreamPro ADCP and ChannelMaster H-ADCP HENING HUANG, RD Instruments, 9855 Businesspark Avenue, San Diego,
More information4. Answer c. The index of nominal wages for 1996 is the nominal wage in 1996 expressed as a percentage of the nominal wage in the base year.
Answers To Chapter 2 Review Questions 1. Answer a. To be classified as in the labor force, an individual must be employed, actively seeking work, or waiting to be recalled from a layoff. However, those
More informationMSc in Autonomous Robotics Engineering University of York
MSc in Autonomous Robotics Engineering University of York Practical Robotics Module 2015 A Mobile Robot Navigation System: Labs 1a, 1b, 2a, 2b. Associated lectures: Lecture 1 and lecture 2, given by Nick
More informationSintermann discussion measurement of ammonia emission from field-applied manure
Sintermann discussion measurement of ammonia emission from field-applied manure Jan Huijsmans, Julio Mosquera and Arjan Hensen 9 April 2013 During the1990 s the measurement methods for ammonia (NH 3 )
More informationDigital Energy ITI. Instrument Transformer Basic Technical Information and Application
g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER
More informationMATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics
More informationAdvanced nacelle anemometry and SCADA-data, analysis techniques and limitations. Frank Ormel Chief Specialist in Product Integration Vestas
Advanced nacelle anemometry and SCADA-data, analysis techniques and limitations Frank Ormel Chief Specialist in Product Integration Vestas Outline Introduction State of the art Advanced methods Nacelle
More informationAlgebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
More informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationExperiment #1, Analyze Data using Excel, Calculator and Graphs.
Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationOptimum proportions for the design of suspension bridge
Journal of Civil Engineering (IEB), 34 (1) (26) 1-14 Optimum proportions for the design of suspension bridge Tanvir Manzur and Alamgir Habib Department of Civil Engineering Bangladesh University of Engineering
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationSpring Force Constant Determination as a Learning Tool for Graphing and Modeling
NCSU PHYSICS 205 SECTION 11 LAB II 9 FEBRUARY 2002 Spring Force Constant Determination as a Learning Tool for Graphing and Modeling Newton, I. 1*, Galilei, G. 1, & Einstein, A. 1 (1. PY205_011 Group 4C;
More informationData Analysis on the ABI PRISM 7700 Sequence Detection System: Setting Baselines and Thresholds. Overview. Data Analysis Tutorial
Data Analysis on the ABI PRISM 7700 Sequence Detection System: Setting Baselines and Thresholds Overview In order for accuracy and precision to be optimal, the assay must be properly evaluated and a few
More information11.6 EVALUATING SODAR PERFORMANCE AND DATA QUALITY IN SUBARCTIC WESTERN ALASKA. Cyrena-Marie Druse * McVehil-Monnett Associates
11.6 EVALUATING PERFORMANCE AND DATA QUALITY IN SUBARCTIC WESTERN ALASKA Cyrena-Marie Druse * McVehil-Monnett Associates 1. INTRODUCTION In September 28, a Sonic Detection and Ranging () antenna and two
More informationExperimental Uncertainties (Errors)
Experimental Uncertainties (Errors) Sources of Experimental Uncertainties (Experimental Errors): All measurements are subject to some uncertainty as a wide range of errors and inaccuracies can and do happen.
More informationStatistical Rules of Thumb
Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN
More informationAP Physics 1 and 2 Lab Investigations
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
More informationFacebook Friend Suggestion Eytan Daniyalzade and Tim Lipus
Facebook Friend Suggestion Eytan Daniyalzade and Tim Lipus 1. Introduction Facebook is a social networking website with an open platform that enables developers to extract and utilize user information
More informationScatter Plots with Error Bars
Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each
More informationVOLU-probe/SS. Stainless Steel Pitot Airflow Traverse Probes. Accurate airflow measurement for demanding applications
VOLU-probe/SS Stainless Steel Pitot Airflow Traverse Probes Accurate airflow measurement for demanding applications VOLU-probe/SS The VOLU-probe/SS Stainless Steel Pitot Airflow Traverse Probe is ideally
More information