On the Mutual Coefficient of Restitution in Two Car Collinear Collisions


 Marianna Todd
 2 years ago
 Views:
Transcription
1 //006 On the Mutual Coefficient of Restitution in Two Car Collinear Collisions Milan Batista Uniersity of Ljubljana, Faculty of Maritie Studies and Transportation Pot poorscako 4, Sloenia, EU (Jan. 006) Abstract In the paper two car collinear collisions are discussed using Newton's law of echanics, conseration of energy and linear constitutie law connecting ipact force and crush. Two ways of calculating the utual restitution coefficient are gien: one already discussed by other authors that does not include the car's stiffness and a new one based on car stiffness. A nuerical exaple of an actual test is proided.. Introduction For the odeling of the collinear car collision two ethods are usually used. The first is the socalled ipulseoentu ethod based on classical Poisson ipact theory, which replaces the forces with the ipulses ([3], [9]). The second ethod treats a car as a deforable body; so the constitutie law connecting contact force with crush is necessary. For the copression phase of ipact the linear odel of force is usually adopted and the odels differ in the way the restitution phase of collision is treated ([5], [], [], [4]). The purpose of this paper is to extend the linear force odel discussed in [] to the collinear ipact of two cars. In the quoted article it is proposed that a car is characterized by its ass, stiffness and liit elocity for peranent crush. The latter properties can be established by a fixed barrier crush test. Also, the proposed restitution odel is siple: rebound elocity is constant. The question arises as to how these
2 //006 characteristics can be incorporated into the two car collision odel since it is well known that the utual coefficient of restitution is the characteristic of ipact; i.e., it is a two car syste and not the property of an indiidual car ([], [4]). To answer the aboe question, first the wellknown theory of central ipact is specialized for collinear car collisions. The kinetic energy losses are then discussed and the restitution coefficient is related to the. The third section of the paper discusses two odels for calculating the utual restitution coefficient based on indiidual car characteristics. The last section is deoted to a description of the use of the present theory in accident reconstruction practice. The section ends with a nuerical exaple.. Two car collinear collision Consider a collinear ipact between two cars where collinear ipact refers to rearend and headon collisions. Before ipact the cars hae elocities and respectiely and after ipact they hae elocities u and u (Figure ). Figure. The two car ipact: (a) preipact elocities, (b) end of copression elocity, (c) postipact elocities
3 //006 3 In the collision phase the oeent of cars is goerned by Newton's nd and 3rd laws (Figure ). On the basis of these laws equations of otion of the cars can be written as follows d F d dt = and dt = F () where and are the asses of the cars and F is contact force. Figure. Newton's 3rd law applied to collinear ipact of two cars Following Poisson's hypothesis ([3]), the ipact is diided into two phases: copression and restitution. In the copression phase the contact force F raises and the cars are defored. The copression phase terinates when the relatie elocity of cars anishes; i.e., when cars hae equal elocity (Figure ). The copression phase () thus integrates the changes fro initial elocities to coon elocity u. This leads to the following syste of equations ( ) ( ) u = P u = P () c c where Pc τ c Fdt is copression ipulse and τ c copression tie. Fro () one 0 obtains the elocity after copression + u = + (3)
4 //006 4 and the copression ipulse ( ) Pc = + (4) In the restitution phase the elastic part of internal energy is released. Equations () are integrated fro u to the end elocities, which gies two equations for three unknowns ( ) ( ) u u = P u u = P (5) r r where Pr τ c Fdt is restitution ipulse and τ r is restitution tie. In order to sole 0 syste (5) for an unknown's postipact elocity and restitution ipulse the constitutie equation is needed. According to the Poisson hypothesis the restitution ipulse is proportional to copression ipulse P r = ep (6) c where e is the restitution coefficient. Because contact force is nonnegatie, so are copression and restitution ipulse. Fro (6) this iplies that e 0. Note. Instead of (6), one can use Newton's kineatical definition of restitution coefficient u e = u which is in the case of centric ipact without friction equialent to Poisson s definition. Howeer in the case of noncentric ipact with friction Newton's odel could lead to oerall energy increase ([0]).
5 //006 5 The total ipulse is P= Pc + Pr so by using (4) and (6) P= ( + e) Δ + (7) Soling (5) and (6) and taking into account (4) gies the well known forulas (see for exaple [3], [9]) for the cars postipact elocities ( + ) e = Δ = Δ u u e + + ( + ) e = + Δ = + Δ u u e + + (8) where Δ =. The aboe equations can be used for calculation of postipact elocities if preipact elocities are known, asses of cars are known and, in addition, the restitution coefficient is known. 3. Energy consideration At car ipact the kinetic energy is dissipated. Applying the principle of conseration of energy one obtains, after copression, ( + ) u + = +Δ E (9) where Δ E is axial kinetic energy lost (or axial energy absorbed by crush). By using (3) one has E Δ = + Δ (0)
6 //006 6 Siilarly, by applying the principle of conseration of energy to the oerall ipact process u u + = + +Δ E () one finds the well known forula for total kinetic energy lost (see for exaple [9]) Δ E = ( e ) + Δ () Since, by the law of therodynaics, ΔE 0, it follows fro () that e. Now, fro (0) and () one has ( ) gien by ([9]) Δ E = e Δ E, so the utual restitution coefficient is ΔE e = = ΔE a ΔE ΔE 0 (3) where ΔE0 ΔE Δ E is the rebound energy. The forula obtained is the basis for relating the utual coefficient of restitution e with the restitution coefficients obtained for indiidual cars in the fixed barrier test. 4. The utual coefficient of restitution Let T be a barrier test elocity of a first car and T a barrier test elocity of a second car. Let these elocities be such that the axial kinetic energy lost can be written as T T Δ E = + (4) and in addition the rebound energy can be written as (see [7])
7 //006 7 e T e T Δ E0 = + (5) The utual restitution coefficient is therefore fro (3), (4) and (5), by using (0), e = e + e T T T+ T (6) For the odel of the barrier test proposed in [] the restitution coefficients of cars are e in, 0 = T 0 and e = in, T (7) where 0 and 0 are liited ipact elocities where all the crush is recoerable ([]). The task is now to deterine appropriate test elocities of cars which satisfy (4). 4. Model A. Let T be the barrier test elocity (or barrier equialent elocity [6]) of the first car for the sae crush as in a two car ipact and T the barrier test elocity for the sae crush for the second car. Then the test elocities for the sae crush ust satisfy relations ([], [6]) T kδ = and T kδ = (8) where k and k are stiffness of the cars and δ and δ are actual axial dynaics crush of the cars. Fro (8) one has
8 //006 8 = k δ and k = T δ (9) T On the other hand, fro (0), (4) and (8) it follows that kδ k δ Δ E = Δ = + + (0) Defining oerall axial crush δ δ + δ and taking into account the law of action and reaction kδ = kδ one obtains δ k δ δ k = = δ k+ k k+ k () Substituting () into (0) yields Δ kδ Δ E = = () where is syste ass and k is syste stiffness, gien by kk k + k + k (3) Fro () one has δ = Δ and therefore fro (9) the required test elocities are k (see also [6]) k k = Δ and = Δ (4) T T k k
9 //006 9 Substituting (4) into (4) leads to identity proides the required utual restitution coefficient = + and substituting it into (6) k k k e = ke k + ke + k (5) This equation for the calculation of e has (to the author s knowledge) not yet been published. Knowing the ass and stiffness of the cars and Δ one can calculate test elocities fro (4), restitution of indiidual cars fro (7), the utual restitution coefficient fro (5) and postipact elocities fro (8). 4. Model B. This odel does not include cars stiffness and it's based on (0) and (4) only. Equating (0) and (4) results in the equation Δ = + (6) T T for two unknowns. To sole it one could set = = (7) T 0 T where 0 is a new unknown elocity. Substituting (7) into (4) one obtains after siplification ( ) ( ) + = 0 0 0, so 0 = + + (8) This is in fact the elocity of the centre of the ass of colliding cars. Substituting (8) into (7) yields unknown test elocities
10 //006 0 ( ) ( ) = = T T + + (9) Note that in calculation of restitution coefficients (7) the absolute alues of test elocities should be used. Substituting (9) into (6) gies the utual restitution coefficient e = e + e + (30) This forula was deried by different arguents of Howard et al ([7]) and is also quoted by Watts et al ([5]). 4.3 Copartent of the odels Coparing (4) and (5) one finds that test elocities of both odels are the sae if stiffness is proportional to the ass; i.e., k = k 0 and k = k 0 where k 0 is a constant. While the test elocities of the odels differ, the utual restitution coefficient differs only in the case when just one car is crushed peranently, since when T 0 and T 0 then both e = e = so by (5) or (30) it follows e = and when T > 0 and T > 0 then substituting (7) and appropriate test elocities into (5) or (30), and taking (0) into account, yields e = + Δ 0 0 (3)
11 //006 Note that (3) can not be used directly for calculating the utual restitution coefficient in adance since the classification of ipactfully elastic, fully plastic or ixed depends on test elocities. At last the question arises as to which odel is ore physically justified. While Model A has a sound physical base connecting test elocities with crushes, Model B requires soe additional analysis. It turns out that it can be interpreted as follows. The copression ipulse (4), can be written by using (3) as Pc = Δ. Using () one could define test elocities of indiidual cars as elocities resulting at the end of the copression phase in a fixed barrier test as the sae ipulse as in an actual two car collision; i.e., P = Δ = = (3) c T T Fro this equation, test elocities gien already by (9) result. Now by (6) restitution ipulse is Pr = epc = e Δ, so by (5) and (3) one ust hae e Δ = e = e. But this can be fulfilled only in the special case when e T T = e, and consequently, by (30), when e= e. This consequence raises a doubt about Model B s adequacy for general use. 4.4 Exaples The aboe forulas were ipleented into the spreadsheet progra (Table ).As the exaple, a full scale test (test no. 7) reported by Cipriani et al ([4]) was executed. In this test the bullet car ade ipact with the rear of the target car at a elocity of 5 /s or 8 k/h. The ass of the cars and their stiffness was taken fro the report; howeer, the liit speed was taken to be 4 k/h for both cars ([]). The result of the calculation is shown in Table. The calculated elocity difference for the target car is 4.8 k/h, which differs fro that easured (3.9 /s or 4.0 k/h) by about 5%. The calculated elocity change for the bullet car is.3 k/h and the easured one was.9 /s or 0.4 k/h. The discrepancy is thus about 7%. If one takes the liit speed to be 3 k/h,
12 //006 then the calculated alue of elocity change for the bullet car is 3.6 k/h, differing fro that easured by about %, and the calculated alue of elocity change for the target car is 0.4, which actually atches the easured alue.. Table. Spreadsheet progra for calculation of postipact elocities Full scale test 7 of Cipriani et al ([4]) Vehicle Vehicle ass kg stiffness kn/ liit elocity k/h 4 4 ipact elocity k/h 8 0 Delta V k/h 8.00 elocity after copression k/h 7.8 syste ass kg syste stiffness kn/ test elocity k/h test restitution restitution 0.45 post ipact elocity k/h Delta V k/h Maxial crush Residual crush Accident Reconstruction In a real car accident the proble is not to deterine postipact elocities but usually the opposite; i.e., to calculate the preipact elocities. For deterining preipact elocities, howeer, the postipact elocities deterined fro skidarks should be known. If only the peranent crushes of cars are known then only the elocity changes for indiidual cars in an accident can be calculated. If the characteristics of cars are knowni.e., ass, stiffness and liit elocitythen the proble is soled as follows. Let δ r be residual crush of the first ehicle. The axial crush, then, is ([])
13 //006 3 δ = δ + δ (33) r 0 where the recoerable part of crush is calculated as δ 0 = 0. The axial crush of k the second car can be calculated in the sae way or fro Newton s 3rd law as δ k = δ (34) k The axial energy lost at ipact is then calculated fro Δ E =Δ E +Δ E (35) kδ where Δ E = and fro (), kδ Δ E =. The preipact elocity difference is thus, ΔE Δ = (36) To calculate elocity changes of indiidual ehicles the first test elocities are calculated by (8) ΔE ΔE = = (37) T T Fro (7) the restitution coefficient for indiidual cars are calculated and fro (5) the utual coefficient of restitution. Fro (8) the elocity differences of indiidual cars at ipact are ( + e) ( + ) e Δ = u = Δ Δ = u = Δ + + (38)
14 //006 4 The aboe forulas were prograed into a spreadsheet progra (Table ). As the exaple, the car to car test described by Kerkhoff et al ([8]) is considered. In this test the test car (bullet) struck the rear of the stationary car (target) at a speed of 40.6 ph or 65 k/h. The actual easured Δ was.6 ph or 36. k/h. As can be seen fro Table, the calculated alue Δ for the bullet car is 36. k/h; i.e., the discrepancy between actual and calculated alue is 0.% and the calculated ipact elocity 64.4 k/h differs fro the actual by.3 %. Note that the deforation of the stationary car was not reported, so (34) is used for calculation of its axial dynaic crush. The liit speed for both cars was taken to be 4 k/h ([]). The discrepancy of calculated alues in the preious case is so inial because the actual low ipact elocity tests were used for deterination of stiffness. If one used for the calculation the default alues of CRASH stiffness and appropriate calculated liit elocity for class cars the discrepancy would increase (Table 4). Thus, in this case the calculated elocity change of the bullet car is 38.5 k/h, which differs fro the actual change by about 6% and the calculated Δ is 5. k/h, differing by about 0%. Table. Spreadsheet progra for calculation of elocity differences at ipact. Car to car test no by Kerkhoff et al ([8]) Vehicle Vehicle ass kg Data stiffness kn/ liit speed k/h crush 0.6? recoerable crush axial crush syste ass kg syste stiffness kn/ ax energy lost kj test elocity k/h test restitution restitution 0. Delta V k/h
15 //006 5 References [] M. Batista, A Note on Linear Force Model in Car Accident Reconstruction [] R.M.Brach. Friction, Restitution, and Energy Loss in Planar Collisions Trans ASME, Journal of Applied Mechanics, 5, 6470, 984 [3] R.M.Brach, R.M.Brach. A Reiew of Ipact Models for Vehicle Collision. SAE Paper [4] A. L. Cipriani. F. P. Bayan, M. L. Woodhouse, A. D. Cornetto, A. P. Dalton, C. B. Tanner, T. A. Tibario, E. S. Deyerl. Lowspeed Collinear Ipact Seerity: A Coparison between FullScale Testing and Analytical Prediction Tools with Restitution Analysis, SAE Papers [5] R.I.Eori. Analytical Approach to Autoobile Collisions. SAE Papers [6] P.V.Hight, D.B.LentKoop, R.A.Hight. Barrier Equialent Velocity, Delta V and CRASH3 Stiffness in Autoobile Collisions. SAE Papers [7] R.P.Howard, J.Boar, C.Bare. Vehicle Restitution Response in Low Velocity Collisions. SAE Paper 9384 [8] J.F.Kerkhoff, S.E.Hisher, M.S.Varat, A.M.Busenga, K.Hailton. An Inestigation into Vehicle Frontal Ipact Stiffness, BEV and Repeated Testing for Reconstruction. SAE Paper [9] R.H.Macillan, Dynaics of Vehicle Collision, Inderscience Enterprise Ltd. 983 [0] M.T.Manson. Mechanics of Robotic Manipulation. MIT Press,00, pp.4 [] R.R.McHenry. A Coparison of Results Obtained with Different Analytical Techniques for Reconstruction of Highway Accidents. SAE Papers [] R.R.McHenry, B.G.McHenry, Effects of Restitution in the Application of Crush Coefficients, SAE [3] E.W.Routh. The Eleentary Part of A Treatise on the Dynaics of a Syste of Rigid Bodies. Doer Publications, 960 [4] S.Tany, The Linear ElasticPlastic Vehicle Collision, SAE 9073 [5] A.J.Watts, D.R.Atkinson, C.J.Hennessy. Low Speed Autoobile Accidents. Lawyers & Judges Publishing Copany, Tuscon, AZ, 999
and that of the outgoing water is mv f
Week 6 hoework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign ersions of these probles, arious details hae been changed, so that the answers will coe out differently. The ethod to find the solution is
More informationLecture L9  Linear Impulse and Momentum. Collisions
J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9  Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,
More informationE k = ½ m v 2. (J) (kg) (m s 1 ) FXA KINETIC ENERGY (E k ) 1. Candidates should be able to : This is the energy possessed by a moving object.
KINETIC ENERGY (E k ) 1 Candidates should be able to : This is the energy possessed by a oing object. Select and apply the equation for kinetic energy : E k = ½ 2 KINETIC ENERGY = ½ x MASS x SPEED 2 E
More informationKinetic Molecular Theory of Ideal Gases
ecture /. Kinetic olecular Theory of Ideal Gases ast ecture. IG is a purely epirical law  solely the consequence of eperiental obserations Eplains the behaior of gases oer a liited range of conditions.
More informationImagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut.
A Resource for Freestanding Matheatics Qualifications Iagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut. Suppose both had a speed of
More information4 Impulse and Impact. Table of contents:
4 Impulse and Impact At the end of this section you should be able to: a. define momentum and impulse b. state principles of conseration of linear momentum c. sole problems inoling change and conseration
More informationUse of extrapolation to forecast the working capital in the mechanical engineering companies
ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL 2014. Vol. 1. No. 1. 23 28 Use of extrapolation to forecast the working capital in the echanical engineering copanies A. Cherep, Y. Shvets Departent of finance
More informationProblem Set 1: Solutions
PH 253 / LeClair Fall 213 Proble Set 1: Solutions 1. Daily proble due 23 Aug 213: How fast ust a rocket trael relatie to the earth so that tie in the rocket slows down to half its rate as easured by earthbased
More informationWork, Energy, Conservation of Energy
This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and nonconservative forces, with soe
More informationCOMBINING CRASH RECORDER AND PAIRED COMPARISON TECHNIQUE: INJURY RISK FUNCTIONS IN FRONTAL AND REAR IMPACTS WITH SPECIAL REFERENCE TO NECK INJURIES
COMBINING CRASH RECORDER AND AIRED COMARISON TECHNIQUE: INJURY RISK FUNCTIONS IN FRONTAL AND REAR IMACTS WITH SECIAL REFERENCE TO NECK INJURIES Anders Kullgren, Maria Krafft Folksa Research, 66 Stockhol,
More informationCalculusBased Physics I by Jeffrey W. Schnick
Chapter Matheatical Prelude Calculusased Physics I by Jeffrey W. Schnick cbphysicsia8.doc Copyright 005008, Jeffrey W. Schnick, Creatie Coons Attribution ShareAlike License 3.0. You can copy, odify,
More informationAnswer: Same magnitude total momentum in both situations.
Page 1 of 9 CTP1. In which situation is the agnitude of the total oentu the largest? A) Situation I has larger total oentu B) Situation II C) Sae agnitude total oentu in both situations. I: v 2 (rest)
More informationLinear Graph Modeling: OnePort Elements 1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING.5 Adanced Syste Dynaics and Control Linear Graph Modeling: OnePort Eleents Introduction In the preious handout Energy and Power
More informationPhys101 Lectures 14, 15, 16 Momentum and Collisions
Phs0 Lectures 4, 5, 6 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 9,,3,4,5,6,7,8,9. Page Moentu is a vector:
More information( C) CLASS 10. TEMPERATURE AND ATOMS
CLASS 10. EMPERAURE AND AOMS 10.1. INRODUCION Boyle s understanding of the pressurevolue relationship for gases occurred in the late 1600 s. he relationships between volue and teperature, and between
More informationPlane Trusses. Section 7: Flexibility Method  Trusses. A plane truss is defined as a twodimensional
lane Trusses A plane truss is defined as a twodiensional fraework of straight prisatic ebers connected at their ends by frictionless hinged joints, and subjected to loads and reactions that act only at
More informationComputers and Mathematics with Applications. The evaluation of barrier option prices under stochastic volatility
Coputers and Matheatics with Applications 64 () 34 48 Contents lists aailable at SciVerse ScienceDirect Coputers and Matheatics with Applications journal hoepage: www.elseier.co/locate/cawa The ealuation
More informationChapter 13 Simple Harmonic Motion
We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances. Isaac Newton 13.1 Introduction to Periodic Motion Periodic otion is any otion that
More informationMh1: Simple Harmonic Motion. Chapter 15. Motion of a SpringMass System. Periodic Motion. Oscillatory Motion
Mh1: Siple Haronic Motion Chapter 15 Siple block and spring Oscillatory Motion Exaple: the tides, a swing Professor Michael Burton School of Physics, UNSW Periodic Motion! Periodic otion is otion of an
More informationThe Velocities of Gas Molecules
he Velocities of Gas Molecules by Flick Colean Departent of Cheistry Wellesley College Wellesley MA 8 Copyright Flick Colean 996 All rights reserved You are welcoe to use this docuent in your own classes
More information2. The acceleration of a simple harmonic oscillator is zero whenever the oscillating object is at the equilibrium position.
CHAPTER : Vibrations and Waes Answers to Questions The acceleration o a siple haronic oscillator is zero wheneer the oscillating object is at the equilibriu position 5 The iu speed is gien by = A k Various
More informationDELTAV AS A MEASURE OF TRAFFIC CONFLICT SEVERITY
DELTAV AS A MEASURE OF TRAFFIC CONFLICT SEVERITY Steen G. Shelby Senior Research Engineer, Econolite Control Products, Inc., Tucson, AZ, USA, eail: sshelby@econolite.co Subitted to the 3 rd International
More informationHonors Physics. Momentum Review
Honors Physics Moentu Review Nae Date. A freight car of ass 0,000 kg oves along a frictionless level railroad track with a constant speed of 5 /s. What is the oentu of the car A. 30,000 kg /s B. 3,000
More informationFundamentals of Microelectronics
Fundaentals of Microelectronics H Why Microelectronics? H2 Basic Physics of Seiconductors H3 Diode ircuits H4 Physics of Bipolar Transistors H5 Bipolar plifiers H6 Physics of MOS Transistors H7 MOS plifiers
More informationChapter 8: Newton s Third law
Warning: My approach is a soewhat abbreviated and siplified version of what is in the text, yet just as coplete. Both y treatent and the text s will prepare you to solve the sae probles. Restating Newton
More informationAnalyzing Methods Study of Outer Loop Current Sharing Control for Paralleled DC/DC Converters
Analyzing Methods Study of Outer Loop Current Sharing Control for Paralleled DC/DC Conerters Yang Qiu, Ming Xu, Jinjun Liu, and Fred C. Lee Center for Power Electroni Systes The Bradley Departent of Electrical
More informationThe Mathematics of Pumping Water
The Matheatics of Puping Water AECOM Design Build Civil, Mechanical Engineering INTRODUCTION Please observe the conversion of units in calculations throughout this exeplar. In any puping syste, the role
More informationTHREEPHASE DIODE BRIDGE RECTIFIER
Chapter THREEPHASE DIODE BRIDGE RECTIFIER The subject of this book is reduction of total haronic distortion (THD) of input currents in threephase diode bridge rectifiers. Besides the reduction of the
More informationPure Bending Determination of StressStrain Curves for an Aluminum Alloy
Proceedings of the World Congress on Engineering 0 Vol III WCE 0, July 68, 0, London, U.K. Pure Bending Deterination of StressStrain Curves for an Aluinu Alloy D. TorresFranco, G. UrriolagoitiaSosa,
More informationExperience with WinterKennedy coefficients on hydraulic identical units
IGHEM 014 The 10 th International conference on hydraulic efficiency easureents Itajuba, Brasil Septeber 16 th  18 th, 014 XXXXXX Experience with WinterKennedy coefficients on hydraulic identical units
More informationPhysics 211: Lab Oscillations. Simple Harmonic Motion.
Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.
More informationThe Virtual Spring Mass System
The Virtual Spring Mass Syste J. S. Freudenberg EECS 6 Ebedded Control Systes Huan Coputer Interaction A force feedbac syste, such as the haptic heel used in the EECS 6 lab, is capable of exhibiting a
More informationSimple Harmonic Motion
SHM1 Siple Haronic Motion A pendulu, a ass on a spring, and any other kinds of oscillators ehibit a special kind of oscillatory otion called Siple Haronic Motion (SHM). SHM occurs whenever : i. there
More information412C The area under the process curve, and thus the boundary work done, is greater in the constant pressure case. Note: for an ideal gas,
Hoework solutions 4C The area under the process cure, and thus the boundary work done, is greater in the constant pressure case. Note: for an ideal gas, Boundary work for constant pressure is entire yellow
More informationAnalysis of the purchase option of computers
Analysis of the of coputers N. Ahituv and I. Borovits Faculty of Manageent, The Leon Recanati Graduate School of Business Adinistration, TelAviv University, University Capus, RaatAviv, TelAviv, Israel
More informationPERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO
Bulletin of the Transilvania University of Braşov Series I: Engineering Sciences Vol. 4 (53) No.  0 PERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO V. CAZACU I. SZÉKELY F. SANDU 3 T. BĂLAN Abstract:
More informationLesson 44: Acceleration, Velocity, and Period in SHM
Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it akes sense that the object will accelerate. In Physics 20 you are only required to explain
More informationThe Fundamentals of Modal Testing
The Fundaentals of Modal Testing Application Note 2433 Η(ω) = Σ n r=1 φ φ i j / 2 2 2 2 ( ω n  ω ) + (2ξωωn) Preface Modal analysis is defined as the study of the dynaic characteristics of a echanical
More informationVersion 001 test 1 review tubman (IBII201516) 1
Version 001 test 1 review tuban (IBII01516) 1 This printout should have 44 questions. Multiplechoice questions ay continue on the next colun or page find all choices before answering. Crossbow Experient
More informationLecture L263D Rigid Body Dynamics: The Inertia Tensor
J. Peraire, S. Widnall 16.07 Dynaics Fall 008 Lecture L63D Rigid Body Dynaics: The Inertia Tensor Version.1 In this lecture, we will derive an expression for the angular oentu of a 3D rigid body. We shall
More informationAll you wanted to know about Formulae and Graphs (but were afraid to ask!)
All you wanted to know about Forulae and Graphs (but were afraid to ask!) o be able to carry out practical investigations in Physics you ust understand the following: 1. What variables are you investigating
More informationSinusoidal Approximation in the Analysis of TwelvePulse Output Voltage Type Rectifiers
th INTERNATIONA SYPOSIU on POWER EECTRONICS  Ee 9 XV eñunarodni sipoziju Energetsa eletronia Ee 9 NOVI SAD, REPUBIC OF SERBIA, October 8 th  th, 9 Sinusoidal Approxiation in the Analysis of TwelePulse
More informationExperimental and Theoretical Modeling of Moving Coil Meter
Experiental and Theoretical Modeling of Moving Coil Meter Prof. R.G. Longoria Updated Suer 010 Syste: Moving Coil Meter FRONT VIEW Electrical circuit odel Mechanical odel Meter oveent REAR VIEW needle
More informationEngineered Solutions To Help Prevent LCD Failures
Engineered Solutions To Help Prevent LCD Failures By Bruce Chew Senior Applications Engineer EAR Specialty Coposites Indianapolis, Indiana ENGINEERED SOLUTIONS TO HELP PREVENT LCD FAILURES A liquid crystal
More informationFUTURE LIFETABLES BASED ON THE LEECARTER METHODOLOGY AND THEIR APPLICATION TO CALCULATING THE PENSION ANNUITIES 1
ACA UNIVERSIAIS LODZIENSIS FOLIA OECONOMICA 250, 20 Agnieszka Rossa * FUURE LIFEABLES BASED ON HE LEECARER MEHODOLOGY AND HEIR APPLICAION O CALCULAING HE PENSION ANNUIIES Suary. In the paper a new recursie
More informationThe Kinetic Model of Gases
Franziska Hofann, Stephan Steinann February 0, 2007 The Kinetic Model of Gases Introduction The rando otion of perfect gases can be described by kinetic theory. Based on a siple odel pressure, igration,
More informationarxiv:0805.1434v1 [math.pr] 9 May 2008
Degreedistribution stability of scalefree networs Zhenting Hou, Xiangxing Kong, Dinghua Shi,2, and Guanrong Chen 3 School of Matheatics, Central South University, Changsha 40083, China 2 Departent of
More informationPREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW
PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW ABSTRACT: by Douglas J. Reineann, Ph.D. Assistant Professor of Agricultural Engineering and Graee A. Mein, Ph.D. Visiting Professor
More informationMotorcycle AccidentProne Types at Intersections and Innovative Improvement Design Guideline
Motorcycle AccidentProne Types at Intersections and Innovative Iproveent Design Guideline Hsu,TienPen a, KuLin Wen b a,b Departent of Civil Engineering, National Taiwan University, Taipei, 6, Taiwan
More informationQuality evaluation of the modelbased forecasts of implied volatility index
Quality evaluation of the odelbased forecasts of iplied volatility index Katarzyna Łęczycka 1 Abstract Influence of volatility on financial arket forecasts is very high. It appears as a specific factor
More informationProject Evaluation Roadmap. Capital Budgeting Process. Capital Expenditure. Major Cash Flow Components. Cash Flows... COMM2501 Financial Management
COMM501 Financial Manageent Project Evaluation 1 (Capital Budgeting) Project Evaluation Roadap COMM501 Financial Manageent Week 7 Week 7 Project dependencies Net present value ethod Relevant cash flows
More informationExercise 4 INVESTIGATION OF THE ONEDEGREEOFFREEDOM SYSTEM
Eercise 4 IVESTIGATIO OF THE OEDEGREEOFFREEDOM SYSTEM 1. Ai of the eercise Identification of paraeters of the euation describing a onedegreeof freedo (1 DOF) atheatical odel of the real vibrating
More informationHW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:
HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:
More informationModelling of Thermal Behavior NDoped Silicon Resistor
Journal of Sensor Technology, 0,, 337 http://dx.doi.org/0.436/jst.0.309 Published Online Septeber 0 (http://www.scirp.org/journal/jst) Modelling of Theral Behavior NDoped Silicon Resistor Fouad Kerrour,
More informationCPU Animation. Introduction. CPU skinning. CPUSkin Scalar:
CPU Aniation Introduction The iportance of realtie character aniation has greatly increased in odern gaes. Aniating eshes ia 'skinning' can be perfored on both a general purpose CPU and a ore specialized
More informationLesson 13: Voltage in a Uniform Field
Lesson 13: Voltage in a Unifor Field Most of the tie if we are doing experients with electric fields, we use parallel plates to ensure that the field is unifor (the sae everywhere). This carries over to
More informationPhys 207. Announcements. Hwk 6 is posted online; submission deadline = April 4 Exam 2 on Friday, April 8th. Today s Agenda
Phys 07 Announceents Hwk 6 is posted online; subission deadline = April 4 Ea on Friday, April 8th Today s Agenda Review of Work & Energy (Chapter 7) Work of ultiple constant forces Work done by gravity
More informationProcess chosen to calculate entropy change for the system
Chapter 6 Exaple 6.33 3.  An insulated tank (V 1.6628 L) is divided into two equal parts by a thin partition. On the left
More informationHomework 8. problems: 10.40, 10.73, 11.55, 12.43
Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks
More informationChapter #7 Giancoli 6th edition Problem Solutions
Chapter #7 Giancoli 6th edition Problem Solutions ü Problem #8 QUESTION: A 9300 kg boxcar traveling at 5.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s.
More informationOnline Bagging and Boosting
Abstract Bagging and boosting are two of the ost wellknown enseble learning ethods due to their theoretical perforance guarantees and strong experiental results. However, these algoriths have been used
More informationMachine Learning Applications in Grid Computing
Machine Learning Applications in Grid Coputing George Cybenko, Guofei Jiang and Daniel Bilar Thayer School of Engineering Dartouth College Hanover, NH 03755, USA gvc@dartouth.edu, guofei.jiang@dartouth.edu
More informationInternational Journal of Management & Information Systems First Quarter 2012 Volume 16, Number 1
International Journal of Manageent & Inforation Systes First Quarter 2012 Volue 16, Nuber 1 Proposal And Effectiveness Of A Highly Copelling Direct Mail Method  Establishent And Deployent Of PMOSDM Hisatoshi
More informationExample: Suppose that we deposit $1000 in a bank account offering 3% interest, compounded monthly. How will our money grow?
Finance 111 Finance We have to work with oney every day. While balancing your checkbook or calculating your onthly expenditures on espresso requires only arithetic, when we start saving, planning for retireent,
More informationComputer Simulation of Staged MotorcycleVehicle Collisions Using EDSMAC4
HVEWP3 Computer of Staged MotorcycleVehicle Collisions Using EDSMAC4 Eric Deyerl Dial Engineering Louis Cheng Applied BioMechanics ABSTRACT The use of computer simulation to analyze motorcycleintovehicle
More informationBase excitation of the glass mount X
Actie Vibration Isolation of RearView Mirrors ased on Piezoceraic Double Spiral Actuators.T. Kletz,2, J. Melcher 2, M. Sinapius,2 TU raunschweig, Institute of Adaptronics and unction Integration  IA
More informationThis paper studies a rental firm that offers reusable products to price and qualityofservice sensitive
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol., No. 3, Suer 28, pp. 429 447 issn 523464 eissn 5265498 8 3 429 infors doi.287/so.7.8 28 INFORMS INFORMS holds copyright to this article and distributed
More informationIf E is doubled, A will be increased by a factor of 2. That is ANew = 2 AOld. Old Old New New
OSCILLAIONS 4 Q4.. Reason: here are any exaples in daily life, such as a ass hanging fro a spring, a tennis ball being volleyed back and forth, washboard road bups, a beating heart, AC electric voltage,
More informationAn Innovate Dynamic Load Balancing Algorithm Based on Task
An Innovate Dynaic Load Balancing Algorith Based on Task Classification Hongbin Wang,,a, Zhiyi Fang, b, Guannan Qu,*,c, Xiaodan Ren,d College of Coputer Science and Technology, Jilin University, Changchun
More informationOpenGamma Documentation Bond Pricing
OpenGaa Docuentation Bond Pricing Marc Henrard arc@opengaa.co OpenGaa Docuentation n. 5 Version 2.0  May 2013 Abstract The details of the ipleentation of pricing for fixed coupon bonds and floating rate
More informationThe Concept of the Effective Mass Tensor in GR. The Equation of Motion
The Concept of the Effective Mass Tensor in GR The Equation of Motion Mirosław J. Kubiak Zespół Szkół Technicznych, Gruziąz, Polan Abstract: In the papers [, ] we presente the concept of the effective
More informationCRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS
641 CRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS Marketa Zajarosova 1* *Ph.D. VSB  Technical University of Ostrava, THE CZECH REPUBLIC arketa.zajarosova@vsb.cz Abstract Custoer relationship
More informationRick Galdos, Forensic Engineering 1
Impact and Damage Analyses of Motor Vehicle Accidents Commonly Asked Questions P.O. Box 10635 Tampa, Florida 33679 rgaldos@tampabay.rr.com General Overview Basic Terms in accident reconstruction and injury
More informationOnline Appendix I: A Model of Household Bargaining with Violence. In this appendix I develop a simple model of household bargaining that
Online Appendix I: A Model of Household Bargaining ith Violence In this appendix I develop a siple odel of household bargaining that incorporates violence and shos under hat assuptions an increase in oen
More informationAP Physics. Chapter 9 Review. Momentum et. al.
AP Physics Chapter 9 Review Moentu et. al. 1. A 2000kg truck traveling at a speed of 3.0 akes a 90 turn in a tie of 4.0 onds and eerges fro this turn with a speed of 4.0. What is the agnitude of the average
More informationTHE COLLISION PHENOMENON BETWEEN CARS
THE COLLISION PHENOMENON BETWEEN CARS What is the role of the mass in a headon collision between two vehicles? What is the role of speed? What is the force produced by each of the two vehicles? Here are
More informationSolution of Saint Venant's Equation to Study Flood in Rivers, through Numerical Methods.
Hydrology Days 005 Solution of Saint Venant's Equation to Study Flood in Rivers, through Nuerical Methods. Chagas, Patrícia Departent of Environental and Hydraulics Engineering, Federal University of Ceará
More informationKinetic energy dissipated by the moving rower. Revised September 2009 homepage
Kinetic energy dissipated by the oving rower. Revised Septeber 2009 hoepage Introdction The boat is oving throgh the water and the rower is oving on the seat with respect to the boat. Better: rower and
More informationThe Research of Measuring Approach and Energy Efficiency for Hadoop Periodic Jobs
Send Orders for Reprints to reprints@benthascience.ae 206 The Open Fuels & Energy Science Journal, 2015, 8, 206210 Open Access The Research of Measuring Approach and Energy Efficiency for Hadoop Periodic
More informationADJUSTING FOR QUALITY CHANGE
ADJUSTING FOR QUALITY CHANGE 7 Introduction 7.1 The easureent of changes in the level of consuer prices is coplicated by the appearance and disappearance of new and old goods and services, as well as changes
More informationHalf Cycle Pairs Method for Harmonic Analysis of Cycloconverter Voltage Waveform
213 International Conference on Open Source Systes and Technologies (ICOSST) Half Cycle Pairs Method for Haronic Analysis of Cycloconerter Waefor Naeed Ashraf 1, Athar Hanif 2, Uar Farooq 3, Muhaad Usan
More informationFuzzy Sets in HR Management
Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 Fuzzy Sets in HR Manageent Blanka Zeková AXIOM SW, s.r.o., 760 01 Zlín, Czech Republic blanka.zekova@sezna.cz Jana Talašová Faculty of Science, Palacký Univerzity,
More information 265  Part C. Property and Casualty Insurance Companies
Part C. Property and Casualty Insurance Copanies This Part discusses proposals to curtail favorable tax rules for property and casualty ("P&C") insurance copanies. The syste of reserves for unpaid losses
More informationELECTRIC SERVO MOTOR EQUATIONS AND TIME CONSTANTS
ELECIC SEO MOO EQUAIONS AND IME CONSANS George W. Younkin, P.E. Life FELLOW IEEE Industrial Controls Consulting, Div. Bulls Eye Marketing, Inc Fond du c, Wisconsin In the analysis of electric servo drive
More informationMarkov Models and Their Use for Calculations of Important Traffic Parameters of Contact Center
Markov Models and Their Use for Calculations of Iportant Traffic Paraeters of Contact Center ERIK CHROMY, JAN DIEZKA, MATEJ KAVACKY Institute of Telecounications Slovak University of Technology Bratislava
More informationAnalyzing Spatiotemporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy
Vol. 9, No. 5 (2016), pp.303312 http://dx.doi.org/10.14257/ijgdc.2016.9.5.26 Analyzing Spatioteporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy Chen Yang, Renjie Zhou
More informationA CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS
A CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS Isaac Zafrany and Sa BenYaakov Departent of Electrical and Coputer Engineering BenGurion University of the Negev P. O. Box
More informationA magnetic Rotor to convert vacuumenergy into mechanical energy
A agnetic Rotor to convert vacuuenergy into echanical energy Claus W. Turtur, University of Applied Sciences BraunschweigWolfenbüttel Abstract Wolfenbüttel, Mai 21 2008 In previous work it was deonstrated,
More informationAirline Yield Management with Overbooking, Cancellations, and NoShows JANAKIRAM SUBRAMANIAN
Airline Yield Manageent with Overbooking, Cancellations, and NoShows JANAKIRAM SUBRAMANIAN Integral Developent Corporation, 301 University Avenue, Suite 200, Palo Alto, California 94301 SHALER STIDHAM
More informationEvaluating Inventory Management Performance: a Preliminary DeskSimulation Study Based on IOC Model
Evaluating Inventory Manageent Perforance: a Preliinary DeskSiulation Study Based on IOC Model Flora Bernardel, Roberto Panizzolo, and Davide Martinazzo Abstract The focus of this study is on preliinary
More information8. Spring design. Introduction. Helical Compression springs. Fig 8.1 Common Types of Springs. Fig 8.1 Common Types of Springs
Objectives 8. Spring design Identify, describe, and understand principles of several types of springs including helical copression springs, helical extension springs,, torsion tubes, and leaf spring systes.
More informationStandards and Protocols for the Collection and Dissemination of Graduating Student Initial Career Outcomes Information For Undergraduates
National Association of Colleges and Eployers Standards and Protocols for the Collection and Disseination of Graduating Student Initial Career Outcoes Inforation For Undergraduates Developed by the NACE
More informationChapter 11 Relative Velocity
Chapter 11 Relatie Velocity 11 Relatie Velocity Vector add like ector, not like nuber. Except in that ery pecial cae in which the ector you are adding lie along one and the ae line, you can t jut add the
More informationChapter 21. The Kinetic Theory of Gases
Chapter The Kinetic Theory of Gases CHAPTER OUTLINE. Molecular Model of an Ideal Gas. Molar Specific Heat of an Ideal Gas.3 Adiabatic Processes for an Ideal Gas.4 The Equipartition of Energy.5 The Boltzann
More informationSoftware Quality Characteristics Tested For Mobile Application Development
Thesis no: MGSE201502 Software Quality Characteristics Tested For Mobile Application Developent Literature Review and Epirical Survey WALEED ANWAR Faculty of Coputing Blekinge Institute of Technology
More informationAcceleration is defined as the change in velocity over a change in time, so we can rewrite Eq. 1 as: Eq. 3
Conseration of Linear Momentum (COLM) ade Bartlett, PE Presented at the 005 Pennsylania State Police Annual Reconstruction Conference, updated 9SEP05 INTRODUCTION Conseration of Linear Momentum is one
More informationDesign of Model Reference Self Tuning Mechanism for PID like Fuzzy Controller
Research Article International Journal of Current Engineering and Technology EISSN 77 46, PISSN 347 56 4 INPRESSCO, All Rights Reserved Available at http://inpressco.co/category/ijcet Design of Model Reference
More informationProperties of Pure Substances
ure Substance roperties o ure Substances A substance that has a ixed cheical coposition throuhout is called a pure substance such as water, air, and nitroen. A pure substance does not hae to be o a sinle
More informationAn Expert Decision Support System for Crisis Management. Boumediene Belkhouche Reda Bakeer Salah AlSaleh
An Expert Decision Support Syste for Crisis Manageent Bouediene Belkhouche Reda Bakeer Salah AlSaleh EECS Departent Tulane University New Orleans, LA 70118 (504) 8623372 (phone) (504) 8623293 (fax)
More informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More information