# Aircraft Performance - Drag

Size: px
Start display at page:

## Transcription

1 Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce this cefficient The drag cefficient (CD) is a nn-dimensinal parameter, but it takes int accunt every aerdynamic cnfiguratin aspect f the aircraft including large cmpnents as wing, tail, fuselage engine, and landing gear; and small elements such as rivets and antenna This cefficient has tw main parts lift-related drag cefficient r induced drag cefficient (CDi) zer-lift drag cefficient (CD). The calculatin f the first ne is nt very hard, but it takes a lng time and energy t determine the secnd part. In large transprt aircraft, this task is dne by a grup f engineers up t twenty engineers fr a time perid f up t six mnths. This calculatin is nt nly time cnsuming, but als is very sensitive, since it influences every aspect f 1 aircraft perfrmance.

2 Aircraft Perfrmance - Drag Classificatin f Drag A list f definitins f varius types f drag is presented, and then a classificatin f all f these drag frces is described Induced Drag: The drag that results frm the generatin f a trailing vrtex system dwnstream f a lifting surface with a finite aspect rati. In anther wrd, this type f drag is induced by the lift frce Parasite Drag: The ttal drag f an airplane minus the induced drag. Thus, it is the drag nt directly assciated with the prductin f lift. The parasite drag is cmpsed f drag f varius aerdynamic cmpnents

3 Aircraft Perfrmance - Drag Parasite Drag Skin Frictin Drag: The drag n a bdy resulting frm viscus shearing stresses (i.e., frictin) ver its cntact surface (i.e., skin) This drag is a functin f Reynlds number. There are mainly tw cases where the flw in the bundary layer is laminar r turbulent ver the plate A laminar bundary layer begins t develp at the leading edge and its thickness grws in dwnstream. At sme distance frm the leading edge the laminar bundary becmes unstable and is unable t suppress disturbances impsed n it by surface rughness r fluctuatins in the free stream In a distance the bundary layer usually underges a transitin t a turbulent bundary layer 3

4 Aircraft Perfrmance - Drag Parasite Drag Frm Drag (smetimes called Pressure Drag): The drag n a bdy resulting frm the integrated effect f the static pressure acting nrmal t its surface reslved in the drag directin. Unlike the skin frictin drag that results frm viscus shearing frces tangential t a bdy s surface, frm drag results frm the distributin f pressure nrmal t the bdy s surface Frm drag is based n the prjected frntal area 4

5 Aircraft Perfrmance - Drag Parasite Drag Interference Drag: The increment in drag resulting frm bringing tw bdies in prximity t each ther. Fr example, the ttal drag f a wing-fuselage cmbinatin will usually be greater than the sum f the wing drag and fuselage drag independent f each ther Trim Drag: The increment in drag resulting frm the (tail) aerdynamic frces required t trim the aircraft abut its center f gravity. Trim drag usually is a frm f induced and frm drag n the hrizntal tail Prfile Drag: Usually taken t mean the ttal f the skin frictin drag and frm drag fr a tw-dimensinal airfil sectin Cling Drag: The drag resulting frm the mmentum lst by the air that passes thrugh the pwer plant installatin fr the purpse f cling the engine Wave Drag: This drag; limited t supersnic flw; is a frm f induced drag resulting frm nn-canceling static pressure cmpnents t either side f a shck wave acting n the surface f the bdy frm which the wave is emanating 5

6 Aircraft Perfrmance - Drag Classificatin f Drag 6

7 Aircraft Perfrmance Drag Plar C D,0 is parasite drag cefficient at zer lift (a L =0) C D,i drag cefficient due t lift (induced drag) Oswald efficiency factr, e, includes all effects frm airplane C D,0 and e are knwn aerdynamics quantities f airplane C ear L C D CD, 0 CD,0 CD, i

8 Aircraft Perfrmance - Drag Classificatin f Drag Drag Plar 8

9 Aircraft Perfrmance - Drag Classificatin f Drag 9

10 Aircraft Perfrmance 4 Frces Acting n Airplane Mdel airplane as rigid bdy with fur natural frces acting n it Lift (L): Acts perpendicular t flight path (perpendicular t relative wind) Drag (D): Acts parallel t flight path directin (parallel t relative wind) Prpulsive Thrust (T): Fr mst airplanes prpulsive thrust acts in flight path directin Weight (W): Always acts vertically tward center f earth Apply Newtn s Secnd Law (F=ma) t curvilinear flight path Frce balance in directin parallel t flight path Frce balance in directin perpendicular t flight path 10

11 Aircraft Perfrmance Static vs Dynamic Analyses Static Perfrmance: Zer Acceleratins (dv/dt = 0) Maximum velcity Maximum rate f climb Maximum range Maximum endurance Dynamic Perfrmance: Accelerating Flight Take-ff and landing characteristics Turning flight Accelerated flight and rate f climb 11

12 Aircraft Perfrmance Level, Un-accelerated Flight Equatins f mtin reduce t very simple expressins Aerdynamic drag is balanced by thrust f engine Aerdynamic lift is balanced by weight f airplane T L D W 1

13 L D L D C C W T SC V W L SC V D T W L D T 1 1 D L W C C W T D L R T R is thrust required t fly at a given velcity in level, un-accelerated flight Ntice that minimum T R is when airplane is at maximum L/D Airplane s pwer plant must prduce a net thrust which is equal t drag Level, Un-accelerated Flight Aircraft Perfrmance

14 Aircraft Perfrmance Thrust Requirement TR fr airplane at given altitude varies with velcity Thrust required curve: TR vs V Select a flight speed V Calculate C L W 1 V C L S Calculate C D C D C D, 0 CL ear Calculate C L /C D Calculate T R This is hw much thrust engine must prduce t fly at V T R W CL C D 14

15 Aircraft Perfrmance Thrust Requirement Different pints n TR curve crrespnd t different angles f attack At b: Small q Large C L (C L ) and a (supprt W) D large 1 L W V D q SC D SC L q SC L At a: Large q Small C L and a D large 15

16 Aircraft Perfrmance Thrust Required vs Flight Velcity T T R R D q q SC D,0 SC D q q S C CL S ear D,0 C D, i Zer-Lift T R (Parasitic Drag) Lift-Induced T R (Induced Drag) Zer-Lift T R ~ V (Parasitic Drag) Lift-Induced T R ~ 1/V (Induced Drag) 16

17 Aircraft Perfrmance Thrust Required vs Flight Velcity Zer-Lift Drag = Induced Drag At minimum T R and maximum L/D 17

18 Aircraft Perfrmance Airplane Pwer Plants 18

19 Aircraft Perfrmance Thrust vs Pwer Jets Engines (turbjets, turbfans fr military and cmmercial applicatins) are usually rate in Thrust Thrust is a Frce with units (kg m/s ) Pistn-Driven Engines are usually rated in terms f Pwer Frce*velcity with units (kg m/s )*(m/s) = kg m /s 3 = Watts Usually rated in terms f hrsepwer (1 hp=550 ft lb/s = 746 W) Example: Airplane is level, un-accelerated flight at a given altitude with speed V Pwer Required, P R =T R *V 19

20 Aircraft Perfrmance Pwer Required P R vs. V qualitatively resembles T R vs. V 0

21 Aircraft Perfrmance Pwer Available 1

22 Aircraft Perfrmance Rate f Climb Prpeller Drive Engine Jet Engine Maximum R/C Occurs when Maximum Excess Pwer

23 Aircraft Perfrmance Pwer Required 3

### Introductory Thoughts

Flw Similarity By using the Buckingham pi therem, we have reduced the number f independent variables frm five t tw If we wish t run a series f wind-tunnel tests fr a given bdy at a given angle f attack,

### AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

### NGSS High School Physics Domain Model

NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

### Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data

Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed

### Kinematic transformation of mechanical behavior Neville Hogan

inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

### Kinetics of Particles. Chapter 3

Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

### Conceptual Dynamics SDC. An Interactive Text and Workbook. Kirstie Plantenberg Richard Hill. Better Textbooks. Lower Prices.

Cnceptual Dynamics An Interactive Text and Wrkbk Kirstie Plantenberg Richard Hill SDC P U B L I C AT I O N S Better Textbks. Lwer Prices. www.sdcpublicatins.cm Pwered by TCPDF (www.tcpdf.rg) Visit the

### Study Guide Physics Pre-Comp 2013

I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)

### Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

### Assume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected.

1 HW #3: Cnservatin f Linear Mmentum, Cnservatin f Energy, Cnservatin f Angular Mmentum and Turbmachines, Bernulli s Equatin, Dimensinal Analysis, and Pipe Flws Prblem 1. Cnservatins f Mass and Linear

### Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

### Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

### Equilibrium of Stress

Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

### Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY

Unit 43: Plant and Prcess Principles Unit cde: H/601 44 QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY 3 Understand static and namic fluid systems with

### 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes

### 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which

### Work, Energy, and Power

rk, Energy, and Pwer Physics 1 There are many different TYPES f Energy. Energy is expressed in JOULES (J 419J 4.19 1 calrie Energy can be expressed mre specifically by using the term ORK( rk The Scalar

### Surface and Contact Stress

Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated

### Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

### Q x = cos 1 30 = 53.1 South

Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is

### CLASS XI SET A PHYSICS

PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the

### ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS On cmpletin f this tutrial yu shuld be able t d the fllwing. Define viscsity

### 1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?

1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is

### Lecture 5: Equilibrium and Oscillations

Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if

### Chapter 9 Vector Differential Calculus, Grad, Div, Curl

Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields

### Chapter 5: Force and Motion I-a

Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse

### 7.0 Heat Transfer in an External Laminar Boundary Layer

7.0 Heat ransfer in an Eternal Laminar Bundary Layer 7. Intrductin In this chapter, we will assume: ) hat the fluid prperties are cnstant and unaffected by temperature variatins. ) he thermal & mmentum

### ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

### CHAPTER 6 -- ENERGY. Approach #2: Using the component of mg along the line of d:

Slutins--Ch. 6 (Energy) CHAPTER 6 -- ENERGY 6.) The f.b.d. shwn t the right has been prvided t identify all the frces acting n the bdy as it mves up the incline. a.) T determine the wrk dne by gravity

### SPH3U1 Lesson 06 Kinematics

PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

### CHAPTER 8b Static Equilibrium Units

CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but

### ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

### Solution to HW14 Fall-2002

Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

### Electric Current and Resistance

Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current

### ON THE EFFECTIVENESS OF POROSITY ON UNSTEADY COUETTE FLOW AND HEAT TRANSFER BETWEEN PARALLEL POROUS PLATES WITH EXPONENTIAL DECAYING PRESSURE GRADIENT

17 Kragujevac J. Sci. 8 (006) 17-4. ON THE EFFECTIVENESS OF POROSITY ON UNSTEADY COUETTE FLOW AND HEAT TRANSFER BETWEEN PARALLEL POROUS PLATES WITH EXPONENTIAL DECAYING PRESSURE GRADIENT Hazem Ali Attia

### bulk velocity through orifice,

150A Review Sessin Other Frictin Lsses Bernulli hf accunts fr all types f drag: is drag due t skin frictin is drag due t fittings (tabulated fractin f the velcity head) is drag due t units (a given r calculated

### Types of Gear Pg xxx. Spur Gear Teeth is parallel to axis of rotation Can transmit power between parallel shaft The simplest form for gear

[Pg / 2] Gears Objectives. 2. 3. 4. 5. Cmpute the frces exerted n gear teeth as they rtate and transmit pwer. Use apprpriate stress analyses t determine the relatinships amng the applied frces, the gemetry

### Short notes for Heat transfer

Furier s Law f Heat Cnductin Shrt ntes fr Heat transfer Q = Heat transfer in given directin. A = Crss-sectinal area perpendicular t heat flw directin. dt = Temperature difference between tw ends f a blck

### CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,

### Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

### Physics 2010 Motion with Constant Acceleration Experiment 1

. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

### 37 Maxwell s Equations

37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut

### Study Guide: PS. 10 Motion, Forces, Work & Simple Machines DESCRIBING MOTION SPEED

DESCRIBING MOTION Distance: hw far smething has mved; SI unit meters (m) Reference pint: nn-mving bject used as a cmparisn pint t detect an bject s mtin. Displacement: the distance between the starting

### Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W

Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = 60 9. 81 =

### MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

### Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

### Homework 1 AERE355 Fall 2017 Due 9/1(F) NOTE: If your solution does not adhere to the format described in the syllabus, it will be grade as zero.

1 Hmerk 1 AERE355 Fall 217 Due 9/1(F) Name NOE: If yur slutin des nt adhere t the frmat described in the syllabus, it ill be grade as zer. Prblem 1(25pts) In the altitude regin h 1km, e have the flling

### Honors Physics Final Review Summary

Hnrs Physics Final Review Summary Wrk Dne By A Cnstant Frce: Wrk describes a frce s tendency t change the speed f an bject. Wrk is dne nly when an bject mves in respnse t a frce, and a cmpnent f the frce

### Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.

Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther

### Rigid Body Dynamics (continued)

Last time: Rigid dy Dynamics (cntinued) Discussin f pint mass, rigid bdy as useful abstractins f reality Many-particle apprach t rigid bdy mdeling: Newtn s Secnd Law, Euler s Law Cntinuus bdy apprach t

### . (7.1.1) This centripetal acceleration is provided by centripetal force. It is directed towards the center of the circle and has a magnitude

Lecture #7-1 Dynamics f Rtatin, Trque, Static Equilirium We have already studied kinematics f rtatinal mtin We discussed unifrm as well as nnunifrm rtatin Hwever, when we mved n dynamics f rtatin, the

### Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

### Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm

Faculty f Engineering and Department f Physics Engineering Physics 131 Midterm Examinatin February 27, 2006; 7:00 pm 8:30 pm N ntes r textbks allwed. Frmula sheet is n the last page (may be remved). Calculatrs

### Thermodynamics Partial Outline of Topics

Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

### Review of the Roll-Damping, Measurements in the T-38 Wind Tunnel

Internatinal Jurnal f Scientific and Research Publicatins, Vlume 3, Issue 12, December 2013 1 Review f the Rll-Damping, Measurements in the T-38 Wind Tunnel Dušan Regdić *, Marija Samardžić **, Gjk Grubr

### Chapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion.

Chapter Kinematics in One Dimensin Kinematics deals with the cncepts that are needed t describe mtin. Dynamics deals with the effect that frces have n mtin. Tgether, kinematics and dynamics frm the branch

### Practical Solutions for Reducing Rain-Wind-Induced Vibrations of Cables, in Cables-Stayed Bridges.

Internatinal Balkans Cnference n Challenges f Civil Engineering, BCCCE, 19-21 May 2011, EPOKA University, Tirana, ALBANIA. Practical Slutins fr Reducing Rain-Wind-Induced Vibratins f Cables, in Cables-Stayed

### , which yields. where z1. and z2

The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

### DESIGN OPTIMIZATION OF HIGH-LIFT CONFIGURATIONS USING A VISCOUS ADJOINT-BASED METHOD

DESIGN OPTIMIZATION OF HIGH-LIFT CONFIGURATIONS USING A VISCOUS ADJOINT-BASED METHOD Sangh Kim Stanfrd University Juan J. Alns Stanfrd University Antny Jamesn Stanfrd University 40th AIAA Aerspace Sciences

### Space Shuttle Ascent Mass vs. Time

Space Shuttle Ascent Mass vs. Time Backgrund This prblem is part f a series that applies algebraic principles in NASA s human spaceflight. The Space Shuttle Missin Cntrl Center (MCC) and the Internatinal

### Sodium D-line doublet. Lectures 5-6: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments

Lectures 5-6: Magnetic diple mments Sdium D-line dublet Orbital diple mments. Orbital precessin. Grtrian diagram fr dublet states f neutral sdium shwing permitted transitins, including Na D-line transitin

### GAUSS' LAW E. A. surface

Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric

### Professional Development. Implementing the NGSS: High School Physics

Prfessinal Develpment Implementing the NGSS: High Schl Physics This is a dem. The 30-min vide webinar is available in the full PD. Get it here. Tday s Learning Objectives NGSS key cncepts why this is different

### ( ) + θ θ. ω rotation rate. θ g geographic latitude - - θ geocentric latitude - - Reference Earth Model - WGS84 (Copyright 2002, David T.

1 Reference Earth Mdel - WGS84 (Cpyright, David T. Sandwell) ω spherid c θ θ g a parameter descriptin frmula value/unit GM e (WGS84) 3.9864418 x 1 14 m 3 s M e mass f earth - 5.98 x 1 4 kg G gravitatinal

### Suggested reading: Lackmann (2011), Sections

QG Thery and Applicatins: Apprximatins and Equatins Atms 5110 Synptic Dynamic Meterlgy I Instructr: Jim Steenburgh jim.steenburgh@utah.edu 801-581-8727 Suite 480/Office 488 INSCC Suggested reading: Lackmann

### Study Group Report: Plate-fin Heat Exchangers: AEA Technology

Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery

### Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell

6.5 Natural Cnvectin in Enclsures Enclsures are finite spaces bunded by walls and filled with fluid. Natural cnvectin in enclsures, als knwn as internal cnvectin, takes place in rms and buildings, furnaces,

### 205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3

ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at

### = m. Suppose the speed of a wave on a string is given by v = Κ τμ

Phys101 First Majr-11 Zer Versin Sunday, Octber 07, 01 Page: 1 Q1. Find the mass f a slid cylinder f cpper with a radius f 5.00 cm and a height f 10.0 inches if the density f cpper is 8.90 g/cm 3 (1 inch

### (1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f

1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments

### Design and Analysis of Gas Turbine Blade by Potential Flow Approach

V. Vijaya kumar et al Int. Jurnal f Engineering Research and Applicatins RESEARCH ARTICLE OPEN ACCESS Design and Analysis f Gas Turbine Blade by Ptential Flw Apprach V. Vijaya Kumar 1, R. Lalitha Narayana

### Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

### CHAPTER 4 Dynamics: Newton s Laws of Motion /newtlaws/newtltoc.html

CHAPTER 4 Dynamics: Newtn s Laws f Mtin http://www.physicsclassrm.cm/class /newtlaws/newtltc.html Frce Newtn s First Law f Mtin Mass Newtn s Secnd Law f Mtin Newtn s Third Law f Mtin Weight the Frce f

### Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects

Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential

### Lecture 7: Damped and Driven Oscillations

Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and

### Trigonometry, 8th ed; Lial, Hornsby, Schneider

Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the

### Coupled Inductors and Transformers

Cupled nductrs and Transfrmers Self-nductance When current i flws thrugh the cil, a magnetic flux is prduced arund it. d d di di v= = = dt di dt dt nductance: = d di This inductance is cmmnly called self-inductance,

### Computational modeling techniques

Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

### Chapter 23 Electromagnetic Waves Lecture 14

Chapter 23 Electrmagnetic Waves Lecture 14 23.1 The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic

### NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

r NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 1930 AN ANALYSIS OF THE EFFECT OF LIFT-DRAG RATIO AND STALLING SPEED ON LANDING-FLARE CHARACTERISTICS By J. Calvin Lvell and Stanley Lipsn v

### Phys101 Second Major-061 Zero Version Coordinator: AbdelMonem Saturday, December 09, 2006 Page: 1

Crdinatr: AbdelMnem Saturday, December 09, 006 Page: Q. A 6 kg crate falls frm rest frm a height f.0 m nt a spring scale with a spring cnstant f.74 0 3 N/m. Find the maximum distance the spring is cmpressed.

### 3. Mass Transfer with Chemical Reaction

8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,

### AEROELASTIC GALLOPING OF TALL STRUCTURES IN SIMULATED WINDS PETER P. SULLIVAN. B.S., Colorado State University Fort Collins, Colorado

AEROELASTIC GALLOPING OF TALL STRUCTURES IN SIMULATED WINDS by PETER P. SULLIVAN B.S., Clrad State University Frt Cllins, Clrad A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE

### Exam #1. A. Answer any 1 of the following 2 questions. CEE 371 October 8, Please grade the following questions: 1 or 2

CEE 371 Octber 8, 2009 Exam #1 Clsed Bk, ne sheet f ntes allwed Please answer ne questin frm the first tw, ne frm the secnd tw and ne frm the last three. The ttal ptential number f pints is 100. Shw all

### Module 4: General Formulation of Electric Circuit Theory

Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

### Physics 1200 Mechanics, Kinematics, Fluids, Waves

Physics 100 Mechanics, Kinematics, Fluids, Waes Lecturer: Tm Humanic Cntact inf: Office: Physics Research Building, Rm. 144 Email: humanic@mps.hi-state.edu Phne: 614 47 8950 Office hurs: Tuesday 3:00 pm,

### Lecture 24: Flory-Huggins Theory

Lecture 24: 12.07.05 Flry-Huggins Thery Tday: LAST TIME...2 Lattice Mdels f Slutins...2 ENTROPY OF MIXING IN THE FLORY-HUGGINS MODEL...3 CONFIGURATIONS OF A SINGLE CHAIN...3 COUNTING CONFIGURATIONS FOR

### Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations

STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.

### BASIC DIRECT-CURRENT MEASUREMENTS

Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard

### Compressibility Effects

Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

### Increasing Heat Transfer in Microchannels with Surface Acoustic Waves*

Increasing Heat Transfer in Micrchannels with Surface Acustic Waves* Shaun Berry 0/9/04 *This wrk was spnsred by the Department f the Air Frce under Air Frce Cntract #FA87-05-C-000. Opinins, interpretatins,

### 5 th grade Common Core Standards

5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin

### L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.

ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake

### Lecture 2: Single-particle Motion

Lecture : Single-particle Mtin Befre we start, let s l at Newtn s 3 rd Law Iagine a situatin where frces are nt transitted instantly between tw bdies, but rather prpagate at se velcity c This is true fr

### AP Physics Laboratory #4.1: Projectile Launcher

AP Physics Labratry #4.1: Prjectile Launcher Name: Date: Lab Partners: EQUIPMENT NEEDED PASCO Prjectile Launcher, Timer, Phtgates, Time f Flight Accessry PURPOSE The purpse f this Labratry is t use the

### EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016

OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a

### Chapter 32. Maxwell s Equations and Electromagnetic Waves

Chapter 32 Maxwell s Equatins and Electrmagnetic Waves Maxwell s Equatins and EM Waves Maxwell s Displacement Current Maxwell s Equatins The EM Wave Equatin Electrmagnetic Radiatin MFMcGraw-PHY 2426 Chap32-Maxwell's

### Subject: KINEMATICS OF MACHINES Topic: VELOCITY AND ACCELERATION Session I

Subject: KINEMTIS OF MHINES Tpic: VELOITY ND ELERTION Sessin I Intrductin Kinematics deals with study f relative mtin between the varius parts f the machines. Kinematics des nt invlve study f frces. Thus