COMMISSIONING THE NEW PITCH DAMPING RIG AT THE CSIR WIND TUNNEL FACILITIES
|
|
- Michael Thompson
- 6 years ago
- Views:
Transcription
1 3 RD INTERNATIONAL SYMPOSIUM ON BALLISTICS TARRAGONA, SPAIN 6-0 APRIL 007 COMMISSIONING THE NEW PITCH DAMPING RIG AT THE CSIR WIND TUNNEL FACILITIES F. Dionisio, L. Vn Zyl nd A. Stockenström 3 CSIR DPSS, PO Box 395, Pretori, South Afric Phone: , Fx: , emil: fdionisi@csir.co.z CSIR DPSS, PO Box 395, Pretori, South Afric Phone: , Fx: , emil: lvzyl@csir.co.z 3 DYNAX, PO Box 70336, The Willows, Pretori, 004, South Afric Phone: , Fx: , emil: dynx@ifric.com Session: Exterior Bllistics ABSTRACT The first phse in the estblishment of pitch dmping cpbility ws presented t the nd ISB (reference ). Following functionlity checks nd nlysis of the cquired dt from tests performed t M0.3 it ws decided to re-evlute some spects of the rig design. This pper describes the commissioning of the first rig t the CSIR s wind tunnel fcilities. In ddition, the spects for reevlution re discussed with some bsic design criteri required for follow-up work by second rig. 7
2 7 EXTERIOR BALLISTICS DESCRIPTION OF EXPERIMENTAL DESIGN In order to respect the requirement for performing pitch dmping tests t nominl incidence ngles of up to 0, test rig development focused on the concept of n oscillting frme, fitted with sting nd blnce such s to provide controlled, sinusoidl rottion of the model in the pitch plne. Motion ws effected vi wing, mounted on this frme, controlled from n externl hydrulic ctutor through drive trin system. The min technicl prmeters describing the pitch dmping test rig re s follows: Mximum Dynmic pressure = 5 kp Typicl Reynolds number =.0 x 0 6 Mch number limit, M 0.9 Commnded frequency 4 Hz (limited by rig nturl frequency) Commnded mplitude = ±.0 (structurl limits) Rig nturl frequency = 7. Hz Model mss 5 kg Mximum offset incidence 0 CALIBRATION Sensors Dt from three mesurement sensors ws cquired: reference gyro-on-chip (clibrtion shown in Figure ), 4-component lod blnce (clibrtion shown in Figure ) nd n ccelerometer with nominl sensitivity of 50mV/g.
3 Commissioning the new pitch dmping rig t the CSIR wind tunnel fcilities Sensitivity [mv/(deg/s)] 4 3 mesured mgnitude theoreticl mgnitude mesured phse theoreticl phse Phse [deg] Frequency [Hz] Figure : ADXRS300EB gyro-on-chip clibrtion NF A PM A NF B PM B Blnce output [V] Lod [kg] Figure : Lod blnce clibrtion
4 74 EXTERIOR BALLISTICS Inertil chrcteriztion The bsic ssumption used in processing the dt ws tht the inertil lods could be described by constnt reltionship: NF = PM gyro ccel The elements of the mtrix re trnsfer functions. The mtrix ws determined by oscillting the model in two independent motions with ir-off. With these results one could define: NF PM or NF PM NF PM NF PM = gyro ccel gyro ccel gyro ccel = gyro ccel Without loss of generlity, ll the mesurements were normlised by the gyro output. The results were recorded s trnsfer functions for the output signls of the mesurement sensors. The dt ws then processed by subtrcting the inertil lods, pplying the sensor trnsfer functions nd converting the blnce output to lods. The first motion nlyzed ws the sting verticl bending mode while the second ws the pitching mode. The frequency of the sting bending mode obtined ws 7.5 Hz, which mde it impossible to obtin sufficiently pure pitching motion bove 6 Hz. TEST DATA ACQUISITION AND DATA REDUCTION To check the full functionlity of the rig, low speed test cmpign ws first performed t M0.3 in the Low Speed Wind Tunnel fcility (LSWT) (see Figure 3).
5 Commissioning the new pitch dmping rig t the CSIR wind tunnel fcilities 75 Figure 3. Pitch Dmping Rig in the LSWT using the Stndrd Dynmic Model (SDM) Test results The pitch dmping derivtive results for three testing frequencies re shown in Tble. These represent the erodynmic pitch dmping moment t the instnt of mximum ngulr velocity nd minimum (or men) incidence. Tble. Pitch dmping, Nm/(rd/s) Frequency Repetition Repetition Averge One would expect resonbly constnt vlue of pitch dmping moment over the frequency rnge of to 4 Hz (k=0.0 to 0.04), which is not the cse. This is likely due to combintion of poor dt qulity, prticulrly from the built-in inertil sensors, high model mss nd low dynmic pressure. The pitch dmping coefficient pproches
6 76 EXTERIOR BALLISTICS the experimentlly determined vlue s the frequency, nd therefore the signl levels, increse. RE-EVALUATION OF THE DESIGN The wing-driven oscillting frme potentilly provides n elegnt solution to the chllenge of cquiring dynmic derivtive dt t significnt ngles of incidence. The design did, however, pose the following problems during implementtion in the Low Speed Wind Tunnel nd design review. Model inerti The model mounting to the blnce is designed for multi-functionlity, llowing xil position djustment nd controlled roll motion. A lrge mss penlty is incurred by the berings, ctutors nd structures required to provide this functionlity. The high model inerti negtively impcts the ccurcy of the dt reduction result, becuse the blnce redings re dominted by the inertil forces. Rig stiffness A reltively low nturl frequency is chieved, pproximtely 7.5 Hz. The first mode consists of the model mss pitching ginst the stiffness of the sting in bending, the cross-bem in torsion nd the two side-rms in bending. This vlue is difficult to improve upon without significntly reducing the model mss nd thereby removing the multi-functionlity. Another design restriction with respect to rig stiffness is the cross-bem running through the wing. The wing size, internl structure nd berings, limit the mximum cross-bem dimeter, resulting in excessive flexibility. Similrly, the presence of the wing behind the model determines n dequte clernce distnce. Incresing length of the sting nd side-rms decreses the inherent
7 Commissioning the new pitch dmping rig t the CSIR wind tunnel fcilities 77 stiffness of the frme. These fctors present inherent design limittions, tht link chievble stiffness to wing size. Aerodynmic pitching moment nturl frequency An erodynmic pitch plne frequency is identified by considering the nturl frequency of the rig inerti bout the centre of oscilltion with the wing erodynmic restoring moment s the spring fctor: f n = (/π) (d.q.s. C Nα /I)½ where C Nα ( = 6.3) is the wing norml force slope with respect to incidence, in rdins, d is the distnce between the wing erodynmic centre nd the rig centre of oscilltion nd I ( 5 kg m ) is the inerti of the rig bout the centre of oscilltion. It follows tht the term (d.q.s.c Nα ) yields the erodynmic stiffness resisting rottion of the rig inerti (I). The high vlues for chrcteristic length (d = 0.8 m) nd surfce re (S = m ) results in uncommonly high vlues for f n, when compred to typicl vlues for bllistic rockets, for instnce. At dynmic pressures pproching 5 kp, vlues for f n 7.5 Hz, the erodynmic nd structurl first modes converge nd resonnce occurs. This potentil filure scenrio cnnot be tolerted. In ddition the potentil dynmic pressure llowble for testing would lso be seriously limited. Flutter potentil The combintion of lrge wing nd low frequency structurl modes poses the wkwrd possibility of flutter. With most of the frme flexibility residing in the sting, there is lso the possibility of the SDM / sting system pproching flutter mode.
8 78 EXTERIOR BALLISTICS GENERAL SAFETY CONSIDERATIONS The high potentil energy ssocited with the lrge wing leds to sitution where it is difficult to gurntee sfety. Potentilly criticl scenrios include controller runwy, wing instbility nd ero-mechnicl resonnce. Conclusion of review It is concluded tht the design, lthough inherently promising, should be modified to ddress sfety concerns nd, if possible, extend the currently limiting prmeters of operting frequency, dynmic pressure nd model inerti. DESIGN CRITERIA FOR SECOND RIG The oscillting frme is still regrded s the nswer to chieving pitch dmping testing t significnt ngles of incidence. A redesign of the frme nd ctution method is being conducted with the following in view: Investigte direct ctution, possibly hydrulic or electricl, to eliminte the need for lrge wing inside the test section. Increse the frme nturl frequency by optimising with respect to frme member stiffness, frme shpe, frme mss nd model mss. Achievement of pure sinusoidl motion is priority. It is n importnt criterion in the selection of n ctution method nd / or peripherl systems to fcilitte this function. One option under considertion is to implement mechnicl spring resistnce, to mke use of the nturl sinusoidl motion resulting from spring-nd-inertil system. Due to the poor qulity of cquired dt from the build in sensors, lser mesurement techniques re going to be investigted.
9 Commissioning the new pitch dmping rig t the CSIR wind tunnel fcilities 79 Decrese model nd blnce block mss to the fullest extent, s limited by structurl sfety nd mnufcturbility. The design im is for mss of less thn 4 kg. The structurl design gol is to chieve 8 Hz operting frequency nd 30 kp dynmic pressure (double the current test limits, for both prmeters). The offset incidence requirement is 0, with n oscilltion bout the nominl of ±3. Preliminry design results indicte fir level of fesibility. The frme inerti, ctuted t the stted frequency nd mplitude levels, become driver design prmeter. With the wing-driven design, the erodynmic force is vilble t such n excess tht it ws not concern. The frme needs to be optimised for low mss (inerti) nd drg (frontl size) on the one hnd nd stiffness on the other, in order to converge on solution tht stisfies the contrdicting requirements. REFERENCES. F Dionisio, Estblishing Pitch Dmping Testing Cpbility t CSIR Defencetek. nd Interntionl Symposium on Bllistics, 4-8 November 005, Vncouver Cnd
Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More informationINVESTIGATION ON THE MODEL OF VORTEX-INDUCED
The Seventh Asi-Pcific Conference on Wind Engineering, November 8-1, 9, Tipei, Tiwn ABSTRACT INVESTIGATION ON THE MODEL OF VORTEX-INDUCED VIBRATIONS OF RECTANGULAR SUPER HIGH-RISE BUILDINGS Hi-Yng Wu 1
More informationFlexible Beam. Objectives
Flexile Bem Ojectives The ojective of this l is to lern out the chllenges posed y resonnces in feedck systems. An intuitive understnding will e gined through the mnul control of flexile em resemling lrge
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationMotion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons
n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.
More information1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon
2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)
More informationPhysics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018
Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.
More informationSolutions to Supplementary Problems
Solutions to Supplementry Problems Chpter 8 Solution 8.1 Step 1: Clculte the line of ction ( x ) of the totl weight ( W ).67 m W = 5 kn W 1 = 16 kn 3.5 m m W 3 = 144 kn Q 4m Figure 8.10 Tking moments bout
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationReview of Calculus, cont d
Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationShear and torsion interaction of hollow core slabs
Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction
More informationOn the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou
On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationINTRODUCTION. The three general approaches to the solution of kinetics problems are:
INTRODUCTION According to Newton s lw, prticle will ccelerte when it is subjected to unblnced forces. Kinetics is the study of the reltions between unblnced forces nd the resulting chnges in motion. The
More informationFlutter frequency based on bending - torsion coupling theory
Flutter frequency bsed on bending - torsion coupling theory *ZHENG Xin ¹, LIU Yu-Bin¹, CHEN Pu, SHEN Feng 3,ZHANG Sheng-Jun 3,nd FU Xing-Rong ¹ 1 College of Wter Conservncy nd Civil Engineering, Chin Agriculturl
More informationDESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM
Interntionl Journl of Automotive Technology, Vol. 18, No. 3, pp. 499 504 (2017) DOI 10.1007/s12239 017 0049 x Copyright 2017 KSAE/ 096 13 pissn 1229 9138/ eissn 1976 3832 DESIGN OF FERRITE MAGNET CFSM
More informationDriving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d
Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGI OIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. escription
More informationFactors affecting the phonation threshold pressure and frequency
3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch
More informationUsing air lines as references for VNA phase measurements
Using ir lines s references for VNA phse mesurements Stephen Protheroe nd Nick Ridler Electromgnetics Tem, Ntionl Physicl Lbortory, UK Emil: Stephen.protheroe@npl.co.uk Abstrct Air lines re often used
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More information1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt
More information99/105 Comparison of OrcaFlex with standard theoretical results
99/105 Comprison of OrcFlex ith stndrd theoreticl results 1. Introduction A number of stndrd theoreticl results from literture cn be modelled in OrcFlex. Such cses re, by virtue of being theoreticlly solvble,
More information25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses
More informationFirst Law of Thermodynamics. Control Mass (Closed System) Conservation of Mass. Conservation of Energy
First w of hermodynmics Reding Problems 3-3-7 3-0, 3-5, 3-05 5-5- 5-8, 5-5, 5-9, 5-37, 5-0, 5-, 5-63, 5-7, 5-8, 5-09 6-6-5 6-, 6-5, 6-60, 6-80, 6-9, 6-, 6-68, 6-73 Control Mss (Closed System) In this section
More informationEstimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor
Glyndŵr University Reserch Online Conference Presenttion Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor Kornilin, D.V., Kudryvtsev,
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationVorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen
Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:
More informationSage Model Notes LoudspeakerVoicecoil.stl
Sge Model Notes LoudspekerVoicecoil.stl D. Gedeon 24 June 2012 A model of voice-coil type liner ctutor commonly used for driving loudspekers. A circulr coil moves xilly bck nd forth within rdil mgnetic
More informationDuality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.
Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we
More informationESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability
ESCI 343 Atmospheric Dynmics II Lesson 14 Inertil/slntwise Instbility Reference: An Introduction to Dynmic Meteorology (3 rd edition), J.R. Holton Atmosphere-Ocen Dynmics, A.E. Gill Mesoscle Meteorology
More informationModeling and Controller Design for the Air-to-Air Missile Uncertain System
Interntionl ournl of Computer (IC) ISSN 07-45 (Print & Online) Globl Society of Scientific Reserch nd Reserchers http://ijcjournl.org/ Modeling nd Controller Design for the Air-to-Air Missile Uncertin
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 8 The Force Method of Anlysis: Bems Version CE IIT, Khrgpur Instructionl Objectives After reding
More informationFEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS
XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University
More information7.2 The Definite Integral
7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where
More informationForces from Strings Under Tension A string under tension medites force: the mgnitude of the force from section of string is the tension T nd the direc
Physics 170 Summry of Results from Lecture Kinemticl Vribles The position vector ~r(t) cn be resolved into its Crtesin components: ~r(t) =x(t)^i + y(t)^j + z(t)^k. Rtes of Chnge Velocity ~v(t) = d~r(t)=
More informationAPPROXIMATE INTEGRATION
APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be
More informationTemperature influence compensation in microbolometer detector for image quality enhancement
.26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More informationA027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More informationComparison of the Design of Flexural Reinforced Concrete Elements According to Albanian Normative
ISBN 978-93-84422-22-6 Proceedings of 2015 Interntionl Conference on Innovtions in Civil nd Structurl Engineering (ICICSE'15) Istnbul (Turkey), June 3-4, 2015 pp. 155-163 Comprison of the Design of Flexurl
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationPractical exercise 7. Surge tank
Prcticl exercise 7. Surge tnk Introduction Surge tnk is used t hydro power plnts for reduction of wter hmmer tht occurs t closing of the turbine inlet vlve. In this exercise we will mesure mss osciltions
More informationP 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)
1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this
More informationE S dition event Vector Mechanics for Engineers: Dynamics h Due, next Wednesday, 07/19/2006! 1-30
Vector Mechnics for Engineers: Dynmics nnouncement Reminders Wednesdy s clss will strt t 1:00PM. Summry of the chpter 11 ws posted on website nd ws sent you by emil. For the students, who needs hrdcopy,
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More information5.7 Improper Integrals
458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the
More information1 Module for Year 10 Secondary School Student Logarithm
1 Erthquke Intensity Mesurement (The Richter Scle) Dr Chrles Richter showed tht the lrger the energy of n erthquke hs, the lrger mplitude of ground motion t given distnce. The simple model of Richter
More informationTHE IMPORTANCE OF INCLUDING ELASTIC PROPERTY OF PENSTOCK IN THE EVALUATION OF STABILITY OF HYDROPOWEWR PLANTS
6 th IAHR Interntionl Meeting of the Workgroup on Cvittion nd Dynmic Problems in Hydrulic Mchinery nd Systems, September 9-, 05, jubljn, Sloveni THE IMPORTANCE OF INCUDING EASTIC PROPERTY OF PENSTOCK IN
More informationThe Regulated and Riemann Integrals
Chpter 1 The Regulted nd Riemnn Integrls 1.1 Introduction We will consider severl different pproches to defining the definite integrl f(x) dx of function f(x). These definitions will ll ssign the sme vlue
More informationLABYRINTH SEALS DYNAMIC COEFFICIENTS AND CRITICAL SPEED RESEARCH BASED ON CHILDS MODEL
Abstrct LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL M Wensheng, Hung Hi, Feng Guoqun AVIC Shenyng Aeroengine eserch Institute, Shenyng, Chin Keywords:lbyrinth sels, dynmics
More informationProbability-Based Seismic Assessments: Implementing Wide-Range Nonlinear Dynamic Analysis Methods
Probbility-Bsed Seismic Assessments: Implementing Nonliner Dynmic Anlysis Methods Ftim Jlyer Postdoctorl Scholr University of Rome L Spienz Cliforni Institute of Technology (CIT) Outline A brief Introduction
More informationAnalysis for Transverse Sensitivity of the Microaccelerometer
Engineering, 009, 1, 196-00 doi:10.436/eng.009.1303 Published Online November 009 (http://www.scirp.org/journl/eng). Anlsis for Trnsverse ensitivit of the Microccelerometer Abstrct Yu LIU 1,,3, Guocho
More informationVadose Zone Hydrology
Objectives Vdose Zone Hydrology 1. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Drcy s lw is useful in region A. Some knowledge of
More informationLecture 19: Continuous Least Squares Approximation
Lecture 19: Continuous Lest Squres Approximtion 33 Continuous lest squres pproximtion We begn 31 with the problem of pproximting some f C[, b] with polynomil p P n t the discrete points x, x 1,, x m for
More informationEnergy Consideration
Energy Considertion It hs been noted tht the most common brkes employ friction to trnsform the brked system's mechnicl energy, irreversibly into het which is then trnsferred to the surrounding environment
More informationFLEXOELECTRIC ACTUATION AND VIBRATION CONTROL OF RING SHELLS
Proceedings of the ASME 5 Interntionl Design Engineering Technicl Conferences & Computers nd Informtion in Engineering Conference IDETEC/CIE 5 August -5, 5, Boston, Msschusetts, USA DETC5-47994 FLEXOELECTRIC
More informationLecture XVII. Vector functions, vector and scalar fields Definition 1 A vector-valued function is a map associating vectors to real numbers, that is
Lecture XVII Abstrct We introduce the concepts of vector functions, sclr nd vector fields nd stress their relevnce in pplied sciences. We study curves in three-dimensionl Eucliden spce nd introduce the
More informationBend Forms of Circular Saws and Evaluation of their Mechanical Properties
ISSN 139 13 MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No. 1. 5 Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology,
More informationEstimation of Binomial Distribution in the Light of Future Data
British Journl of Mthemtics & Computer Science 102: 1-7, 2015, Article no.bjmcs.19191 ISSN: 2231-0851 SCIENCEDOMAIN interntionl www.sciencedomin.org Estimtion of Binomil Distribution in the Light of Future
More informationA sequence is a list of numbers in a specific order. A series is a sum of the terms of a sequence.
Core Module Revision Sheet The C exm is hour 30 minutes long nd is in two sections. Section A (36 mrks) 8 0 short questions worth no more thn 5 mrks ech. Section B (36 mrks) 3 questions worth mrks ech.
More informationV. DEMENKO MECHANICS OF MATERIALS LECTURE 6 Plane Bending Deformation. Diagrams of Internal Forces (Continued)
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 6 Plne ending Deformtion. Digrms of nternl Forces (Continued) 1 Construction of ending Moment nd Shering Force Digrms for Two Supported ems n this mode of loding,
More informationVadose Zone Hydrology
Objectives Vdose Zone Hydrology. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Wter storge in unsturted soil Minerl surfces hve uneven
More informationCHAPTER 4a. ROOTS OF EQUATIONS
CHAPTER 4. ROOTS OF EQUATIONS A. J. Clrk School o Engineering Deprtment o Civil nd Environmentl Engineering by Dr. Ibrhim A. Asskk Spring 00 ENCE 03 - Computtion Methods in Civil Engineering II Deprtment
More informationEffects of peripheral drilling moment on delamination using special drill bits
journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment
More informationBest Approximation. Chapter The General Case
Chpter 4 Best Approximtion 4.1 The Generl Cse In the previous chpter, we hve seen how n interpolting polynomil cn be used s n pproximtion to given function. We now wnt to find the best pproximtion to given
More informationStudy on the Calculation of Magnetic Force Based on the Equivalent Magnetic Charge Method
Avilble online t www.sciencedirect.com Physics Procedi 4 () 9 97 Interntionl Conference on Applied Physics nd Industril Engineering Study on the Clcultion of Mgnetic Force Bsed on the Equivlent Mgnetic
More informationCONTROL OF VIBRATION WITH DYNAMIC ABSORBER
CONTROL OF VIBRATION WITH DYNAMIC ABSORBER Ry Beebe Senior Lecturer Monsh University School of Applied Sciences nd Engineering Ry.Beebe@eng.monsh.edu.u Summry: High beting vibrtion ws evident in the structure
More informationCalculus of Variations
Clculus of Vritions Com S 477/577 Notes) Yn-Bin Ji Dec 4, 2017 1 Introduction A functionl ssigns rel number to ech function or curve) in some clss. One might sy tht functionl is function of nother function
More informationIn-Class Problems 2 and 3: Projectile Motion Solutions. In-Class Problem 2: Throwing a Stone Down a Hill
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 In-Clss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the
More informationPhys 7221, Fall 2006: Homework # 6
Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 3-7 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which
More informationJob No. Sheet 1 of 8 Rev B. Made by IR Date Aug Checked by FH/NB Date Oct Revised by MEB Date April 2006
Job o. Sheet 1 of 8 Rev B 10, Route de Limours -78471 St Rémy Lès Chevreuse Cedex rnce Tel : 33 (0)1 30 85 5 00 x : 33 (0)1 30 5 75 38 CLCULTO SHEET Stinless Steel Vloristion Project Design Exmple 5 Welded
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationPhysics 207 Lecture 7
Phsics 07 Lecture 7 Agend: Phsics 07, Lecture 7, Sept. 6 hpter 6: Motion in (nd 3) dimensions, Dnmics II Recll instntneous velocit nd ccelertion hpter 6 (Dnmics II) Motion in two (or three dimensions)
More informationSelection of bearing type
Selection of ering type Aville spce... 35 Lods... 37 Mgnitude of lod... 37 Direction of lod... 37 Mislignment... 40 Precision... 40 Speed... 42 Quiet running... 42 Stiffness... 42 Axil displcement... 43
More informationapproaches as n becomes larger and larger. Since e > 1, the graph of the natural exponential function is as below
. Eponentil nd rithmic functions.1 Eponentil Functions A function of the form f() =, > 0, 1 is clled n eponentil function. Its domin is the set of ll rel f ( 1) numbers. For n eponentil function f we hve.
More informationNon-Linear & Logistic Regression
Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More informationThe Atwood Machine OBJECTIVE INTRODUCTION APPARATUS THEORY
The Atwood Mchine OBJECTIVE To derive the ening of Newton's second lw of otion s it pplies to the Atwood chine. To explin how ss iblnce cn led to the ccelertion of the syste. To deterine the ccelertion
More informationCHM Physical Chemistry I Chapter 1 - Supplementary Material
CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion
More information12. DYNAMIC ANALYSIS. Force Equilibrium is Fundamental in the Dynamic Analysis of Structures 12.1 INTRODUCTION
12. DYNAMIC ANALYSIS Force Equilibrium is Fundmentl in the Dynmic Anlysis of Structures 12.1 INTRODUCTION { XE "Newton's Second Lw" }All rel physicl structures behve dynmiclly when subjected to lods or
More informationPOLYPHASE CIRCUITS. Introduction:
POLYPHASE CIRCUITS Introduction: Three-phse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in three-phse system is constnt rther thn pulsting nd three-phse
More informationCMDA 4604: Intermediate Topics in Mathematical Modeling Lecture 19: Interpolation and Quadrature
CMDA 4604: Intermedite Topics in Mthemticl Modeling Lecture 19: Interpoltion nd Qudrture In this lecture we mke brief diversion into the res of interpoltion nd qudrture. Given function f C[, b], we sy
More informationAP Calculus Multiple Choice: BC Edition Solutions
AP Clculus Multiple Choice: BC Edition Solutions J. Slon Mrch 8, 04 ) 0 dx ( x) is A) B) C) D) E) Divergent This function inside the integrl hs verticl symptotes t x =, nd the integrl bounds contin this
More informationSynoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?
Synoptic Meteorology I: Finite Differences 16-18 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationPart I: Basic Concepts of Thermodynamics
Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry
More informationPlate Theory. Section 11: PLATE BENDING ELEMENTS
Section : PLATE BENDING ELEMENTS Plte Theor A plte is structurl element hose mid surfce lies in flt plne. The dimension in the direction norml to the plne is referred to s the thickness of the plte. A
More informationTheoretical foundations of Gaussian quadrature
Theoreticl foundtions of Gussin qudrture 1 Inner product vector spce Definition 1. A vector spce (or liner spce) is set V = {u, v, w,...} in which the following two opertions re defined: (A) Addition of
More informationLecture 1. Functional series. Pointwise and uniform convergence.
1 Introduction. Lecture 1. Functionl series. Pointwise nd uniform convergence. In this course we study mongst other things Fourier series. The Fourier series for periodic function f(x) with period 2π is
More informationSupporting Online Material for
Correction: 1 December 007 www.sciencemg.org/cgi/content/full/318/5857/1750/dc1 Supporting Online Mteril for Mott Trnsition in VO Reveled by Infrred Spectroscopy nd Nno- Imging M. M. Qzilbsh,* M. Brehm,
More informationApplications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More informationCONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD
CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD Svetozár Mlinrič Deprtment of Physics, Fculty of Nturl Sciences, Constntine the Philosopher University, Tr. A. Hlinku, SK-949 74 Nitr, Slovki Emil:
More informationMinimum Energy State of Plasmas with an Internal Transport Barrier
Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University
More informationPlate Theory. Section 13: PLATE BENDING ELEMENTS
Section : PLATE BENDING ELEENTS Wshkeic College of Engineering Plte Theor A plte is structurl element hose mid surfce lies in flt plne. The dimension in the direction norml to the plne is referred to s
More information