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`Introduction to
`Automotive Powertrains
`
`Lift
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`'L X
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`f
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`· Craig J. Hott, Ph.D., P.E.
`Gregory W. Davis, Ph.D., P.E.
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`s
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`BMW1039
`Page 1 of 49
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`Preface
`
`This book is intended for advanced engineering students and practicing automotive
`engineers who are interested in learning about the overall design of an automotive
`powertrain. It is an introductory text on the topic, but it will provide the interested reader
`with a basis for understanding the fundamentals of automotive engines and automotive
`transmissions, and more importantly how to select those components to provide the
`optimum compromise between acceleration performance, gradeability performance and
`fuel economy performance.
`The level of analysis used in the text is not particularly difficult (it is assumed that the
`reader has a good grasp of engineering mechanics), however the equations derived in the
`text become the basis for developing computer models that can be used to predict vehicle
`performance.
`
`Acknowledgements·
`
`: ... ,:1;; :~~~f
`
`The authors of this book would like to thank and to acknowledge the work and support of
`many others who have come before us. In particular, we would like to thank Dr. Colin
`Jordan for his significant contributions to the original notes from which this book was
`drawn. Finally, we would like to acknowledge the works of others who have made many
`of the original illustrations in this edition. Unfortunately, we have not yet been able to
`track down the sources of some of these works. We are working diligently to locate the
`authors and to replace illustrations as needed. This work is currently a pre-production
`work intended for educational use.
`·
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`BMW1039
`Page 2 of 49
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`Table of Contents
`
`Preface .................................................................................. 3
`Table of Contents .................................................................. 5
`1 Automotive Drivetrain Components and Layouts .......... 11
`1.1
`Typical Drivetrain Layouts ............................................................................... 11
`1.1.1
`Typical Rear Wheel Drive Configuration ................................................. 11
`1.1.2
`Typical Front Wheel Drive Configuration ................................................ 14
`1.1.3
`Rear Wheel Drive with Rear Engine ........................................................ 15
`1.1.4
`Typical Four Wheel Drive Configuration ................................................. 16
`1.1.5
`Drivetrain Packaging ................................................................................. 17
`1.2
`Driveline Components ...................................................................................... 18
`1.2.1
`Clutches ..................................................................................................... 18
`1.2.2
`Hydraulic Torque Converter ..................................................................... 19
`1.2.3 Manual Transmission ................. : .............................................................. 21
`1.2.4
`Automatic Transmissions .......................................................................... 22
`1.2.5
`Transaxles ................................................................................................. 23
`1.2.6
`Driveshafts ................................................................................................ 24 ·
`Differentials .............................................................................................. 25
`1.2. 7
`1.2.8
`Rear Axle .................................................................................................. 26
`1.3
`References ......................................................................................................... 26
`Chapter 2 .................................... · ........................................ 27
`2 Road Loads ................................................................... 27
`2.1
`Introduction ....................................................................................................... 27
`2.2
`Aerodynamic Lift and Drag .............................................................................. 29
`2.2.1
`Inviscid Flow: Euler and Bernoulli Equations ................................... ; ...... 30
`2.2.2
`Application to an Automobile ................................................................... 32
`2.2.3
`Viscid Flow: Boundary Layers .................................................... ; ............ 34
`2.2.4
`Application to an Automobile ................................................................... 35
`2.2.5
`Inviscid Flow over Bodies ........................................................................ 35
`2.2.6
`Viscid Flow over Bodies ........................................................................... 37
`2.2.7
`Application to an Automobile ................................................................... 40
`2.2.8
`Experimental Techniques .......................................................................... 40
`2.2.9
`Application to an Automobile ................................................................... 42
`2.2.10 Vortex Shedding ....................................................................................... 46
`2.2.11 Application to an Automobile ............................................ :.: .................... 46
`2.2.12 Automotive Drag Studies ...................... ~ ................................................... 47
`2.2.13 Afterbody Drag .......................................................................................... 48
`2.2.14 Wheel and Wheel Wells ............................................................................ 49
`2.2.15
`Forebody Effects ....................................................................................... 50
`2.2.16 Underbody Drag .................................... ; ................................................... 51
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`6
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`Introduction to Automotive Powertrains
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`2.2.17 Optimization Study ........................................................ -........................... 52
`2.2.18
`Effect of Wind ........................................................................................... 53
`2.2.19 Complete Aerodynamic Forces of a Vehicle ...................................... ·!'"· 54
`2.2.20 Density of Air ............................ · ............................................................... 55
`2.2.21 Alternate Form for Drag Equation ............................................................ 57
`2.3
`Rolling Resistance ............................................................................................ 59
`2.3 .1
`Simple Model for Rolling Resistance ....................................................... 60
`2.3.2
`Effect of Road Surface .............................................................................. 61
`· 2.3.3
`Effect of Temperature on Rolling Resistance ........................................... 61
`2.3.4
`Effect of Tire Inflation Pressure ............................................................... 62
`Effect of Tire Speed .... '. ............................................................................. 62
`2.3.5
`2.3.6
`Effect of Tire Materials ............................................................................. 62
`2.3.7
`Effect of Tire Slip Angle ........................................................................... 63
`2.3.8
`Other Models for Rolling Resistance ........................................................ 64
`2.4
`Coast Down. Testing .......................................................................................... 64
`Grade Resistance ................................................................................... '. ........... 65
`2.5
`2.6
`The Proving Ground Equation .......................................................................... 66
`2.7
`References ........................... '. .............................. · ............................................... 68
`3 Power Systems ................ '. ............................................. 69
`3 .1
`Introduction to Internal Combustion Engines and Their Performance ............. 69
`3.1.1
`Spark-ignited (SI) or Gasoline Four-stroke Engines ................................ 69
`3.1.2
`Compression-ignition (DI) or Diesel Four-stroke Engines ....................... 70
`Engine Brake Torque and Power ...................................................................... 72
`3 .2
`3 .2.1
`Brake Power .............................................................................................. 73
`3.2.2
`Friction Power (FP) ................................................................................... 75
`3.2.3
`Indicated Power (IP) ................................................................................. 75
`3.2.4
`Specific Power ........................................................................................... 75
`3.2.5 Mean Effective Pressure (MEP) ............................................................... 75
`3 .3
`Efficiencies ....................................................................................................... 78
`3.3.1 Mechanical Efficiency .............................................................................. 78
`3.3.2
`Overall Thermal Efficiency (or Fuel Efficiency) ...................................... 78
`3.3.3
`Combustion Efficiency ............................................................................. 80
`3.3.4
`Thermal Efficiency (or Specific Efficiency) ............................................. 80
`3.3.5
`Specific Fuel Consumption (SFC) ............................................................ 81
`3.3.6
`Volumetric Efficiency ............................................................................... 81
`3.4
`Fuels .................................................................................................................. 81
`3.4.1
`Octane Rating ............................................................................................ 82
`3.4.2
`Decane Rating ........................................................................................... 82
`3.4.3
`Determination of Fuel Specific Gravity and Heating Value ..................... 82
`3.5
`Emissions ............................................................. ; ............................................ 82
`3.6
`Other Engine Parameters ......................................................... : .. ' ...................... 83
`3.6.1
`Mean Piston Speed (S) ....... .' ................ : ..................................................... 83
`3.6.2
`Inlet Air Velocity ...................................................................................... 83
`3.7
`Typical Engine Performance Data .................................................................... 83
`3.7.1
`Full Load Performance Comparison of SI and CI Engines ...................... 83
`3.7.2
`SAE Net Versus Gross Performance ........................................................ 86
`
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`Page 4 of 49
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`Automotive Drivetrain Components and Layouts
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`7
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`Part Load Performance ............................................................................. 86
`3.7.3
`3.8
`Other Power Systems ........................................................................................ 87
`3.8.1
`Gasoline Direct Injection (GDI) Spark-Ignited Engines .......................... 87
`3.8.2
`Electric Motors .......................................................................................... 89
`3.8.3
`Hybrid Electric Power Systems ................................................................ 90
`3.9
`References ......................................................................................................... 92
`Chapter 4 ............................................................................ 93
`4 Driveline ......................................................................... 93
`4.1
`Introduction ....................................................................................................... 93
`4.2
`Driveline ........................................................................................................... 96
`4.2.1
`Ideal Driveline ................................ _ .................................. ; ....................... 96
`4.2.2
`Driveline Losses ........................................................................................ 99
`4.3
`Tires (Idealized Model) ................................................................................... 103
`NN Ratio (Idealized Tire) ...................................................................... 103
`4.3.1
`4.3.2
`Available Tractive Power ....................................................................... 108
`4.3 .3
`Available Tractive Effort ........................................................................ 111
`4.3.4
`Actual 1_'ractive Power and Tractive Effort ............................................. 115
`4.4
`Tires (Better Model) ....................................................................................... 118
`4.4.1
`Tire Forces and Moments ................................................................ : ...... 118
`4.4.2
`Tire Slip .................................................................................................. 119
`NN Ratio (Better Model) ....................................................................... 122
`4.4.3
`4.4.4
`Tractive Effort ........................................................................ ; ................ 122
`4.4.5
`Example-Effect of Tire Slip ................................................................. 124
`4.4.6
`Slip Angle ............................................................................................... 127
`4.5
`The Friction Ellipse ......................................................................................... 130
`4.5.1
`Rolling Resistance (Revisited) ................................................................ 134
`A Final Note on Tires ............................................................................. 135
`4.5.2
`4.6 Move-off Elements .................................................. : ...................................... 135
`4.7
`References ....................................................................................................... 137
`5 Gear Ratio Selection .................................................... 139
`5 .1
`Typical Gear Ratios Selected for Passenger Vehicles .................................... 143
`5.2
`A Procedure for Selecting Gear Ratios ........................................................... 149
`Selection of a top gear NN ratio ............................................................ 149
`5 .2.1
`Determination of Top Gear Ratio and Axle Ratio .................................. 153
`5.2.2
`5 .2.3
`Low Gear Ratio Determination ............................................................... 154
`5.2.4
`Selecting Intermediate Gear ratios .................................................... : ..... 159
`5.3
`Example .......................................................................................................... 168
`5.3.l
`Select a Top GearNN ratio .................................................................... 169
`5.3.2
`Select a top gear ratio .............................................................................. 169
`5.3.3
`Select an axle ratio .......................................................... :.: ..................... 169
`5.3.4
`Select first gear ratio ......................... : ..................................................... 170
`5.3.5
`Select intermediate gear ratios ................................................................ 170
`5.3.6
`Evaluate Gear Ratios ............................................................................... 172
`5 .4
`Homework ....................................................................................................... 172
`5.5
`References ..................................................... : ................................................. 173
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`8
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`Introduction to Automotive Powertrains
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`6 Acceleration Performance ......................... : ................. 175
`6.1
`Predicting Acceleration Performance ............................................................. 178
`6.2
`Power-Limited Acceleration ........................................................................... 180
`6.3
`Power-Limited Acceleration - Calculation Procedure ........... : ....................... 188
`6.4
`Examples: Power-Limited Acceleration- Manual Transmission .................. 190
`6.5
`Acceleration - Automatic Transmission ......................................................... 209
`6.5.1
`Torque Converter Basics ......................................................................... 209
`6.5.2 Matching of the engine and torque converter ......................................... 212
`Examples: Power-Limited Acceleration-Automatic Transmission .............. 218
`6.6
`6.7
`Dynamic Axle Loads ................................................. : .................................... 224
`6. 7.1
`Special Case: Static Loads on Level Ground without a Trailer .............. 228
`6. 7 .2
`Determining the Location of the Vehicle CG ......................................... 228
`6.7.3
`Low-Speed Acceleration ......................................................................... 230
`6.8
`Traction-Limited Acceleration ........................................................................ 232
`6.8.l Maximum Possible Acceleration ............................................................ 232
`6.8.2
`Actual Maximum Acceleration- Low Speed; ........................................ 235
`6.8.3
`Traction Limited Acceleration- Example .............................................. 237
`6.9
`Final Comments .............................................................................................. 238
`. 7 Gradeability Performance ............................................ 239
`7 .1
`Power-Limited Gradeability ........................................................................... 23 9
`7.2
`Traction-Limited Gradeability .................................. · ...................................... 247
`7.3
`Gradeability with a Trailer ............................................................... : .............. 251
`7.3.1
`Power-Limited Gradeability ................................................................... 251
`7.3.2
`Traction-Limited Gradeability ................................................................ 253
`7.4
`References ....................................................................................................... 258 .
`Chapter 8 .......................................................................... 259
`8 Fuel Economy Performance ........................................ 259
`8.1
`Engine Fuel Consumption ............................................................................... 259
`8.2 WOT Fuel Economy ....................................................................................... 264
`8.3
`POT Fuel Economy ......................................................................................... 266
`8.3.1
`Example Problem .................................................................................... 267
`8.4
`Corporate Average Fuel Economy (CAFE) .................................................... 277
`8.5
`Vehicle Emissions Performance ..................................................................... 289
`8.6
`Selecting Powertrain Components .................................................................. 294
`9 Manual Transmissions ................................................. 299
`9 .1
`Clutch Systems ................................................................................................ 299
`Analysis of a Clutch ........................................................................................ 310
`9.2
`9 .2.1
`Uniform Pressure Model. ........................................................................ 311
`9.2.2
`Uniform Rate ofWearModel ............................................... : .................. 312
`9.3 Manual Transmission Gearboxes .................................................................... 315
`9.3.1
`Operation of a Constant Mesh Transmission .......................................... 321
`9.3.2
`Typical Overdrive Transmission ............................................................. 324
`10 Automatic Transmissions ............................................. 327
`10.1
`Introduction ..................................................................................................... 327
`
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`Automotive Drivetrain Components and Layouts
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`9
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`10.2 Torque Converters .......................................................................................... 329
`10.2.1
`Fluid Couplings ....................................................................................... 329
`10.2.2 Torque Converters ................................................................................... 332
`10.3 Planetary (Epicyclic) Gear Trains ................................................................... 340
`10.3.1 Kinematics of a Planetary Gear Train ..................................................... 342
`10.3.2
`Speed and Torque Ratios for Simply Planetary Gear Trains .................. 342 .
`10.3.3
`Summary of Equations for Simply Planetary Gear Sets and Example ... 345
`10..3 .4 Compound Planetary Gearsets ................................................................ 346
`10.4 Control Elements ............................................................................................ 347
`10.4.1 Control of a Simple Planetary Gearset.. .................................................. 354
`10.4.2 Example -Allison AT540 Transmission ..................... h ......................... 355
`10.5 Other Considerations ...................................................................................... 362
`10.5.1
`Transmission And Engine Oil Coolers ................................................... 362
`10.5.2 Parking .............................. _ ...................................................................... 364
`11 Differentials .................................................................. 365
`11.1
`Introduction ...................................................................................................... 365
`11.2 Open Differentials ..................... · ...................................................................... 3 67
`11.2.1 Vehicle traveling in a straight line .......................................................... 368
`11.2.2 Vehicle Turning .................................................. : ................................... 370
`11.3 Limited Slip Differentials ................... : .................................... : ...................... 373
`11.4 Locking Differentials ...................................................................................... 3 7 4
`11.5 Planetary gear set as a Differential .................................................................. 375
`Table of Figures ................................................................ 377
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`-Chapter 2
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`2 Road Loads
`
`The fundamental forces acting on the automobile will discussed in this chapter. These
`forces include the road load forces (wind resistance, rolling resistance, and grade
`resistance) and the tractive forces available at the wheels from the power plant and
`transmission.
`
`2.1 Introduction
`A free body diagram of a vehicle traveling up an incline is shown in Figure 2-1. The
`FBD allows for the case of rear wheel drive (TEr > 0), front wheel drive (TE1 > 0) and
`four-wheel drive (TE1and TEr > 0).
`
`Figure 2-1 Free body diagram of a vehicle traveling up an incline.
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`28
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`Introduction to Automotive Powertrains
`
`The major forces acting on the vehicle are:
`= Gross vehicle weight
`W
`= Normal forces on the front and rear axles, respectively
`Nj; Nr
`RR1, RRr = Rolling resistance on the front and rear tires, which act to oppose
`the vehicle motion.
`TE1, TEr = Tractive effort on the front and rear tires, which is the force created
`by the engine at the driving wheels propelling the vehicle forward.
`= Wind resistance or drag, which is the component of the
`aerodynamic force that acts to oppose the motion of the vehicle.
`= Aerodynamic
`the component of the
`is
`lift force, which
`aerodynamic force that acts vertically relative to the motion of the
`vehicle
`
`Lift
`
`WR
`
`Summing the forces in the direction of vehicle motion (i.e. the x-direction): .
`
`Z:Fx =max
`TE1 +TEr-WR-RR1 -RRr-WsinB=max
`
`(2.1)
`
`The component of the weight acting to oppose the motion ( W sin B) is ofterr referred to as
`the Grade Resistance (GR). To simplify the analysis for the moment, the tractive forces
`acting on the front and rear tires (TE1and TEr, respectively) can be combined into a single.
`force (TE). With these changes, the equation of motion in the x-direction is:
`
`TE-WR-RR-GR=ma X
`
`(2.2)
`
`The wind resistance, rolling resistance, and grade resistance all oppose the motion of the
`vehicle and are commonly referred to as the road load (RL).
`
`Solving Equation (2.2) for the acceleration of the vehicle yields:
`
`RL=WR+RR+GR
`
`TE-WR-RR-GR
`ax=
`m
`
`or ax=
`
`TE-RL
`m
`
`(2.3)
`
`(2.4)
`
`This is the fundamental equation of vehicle motion. Substituting the definition of
`acceleration, ax = dV I dt, the equation of motion becomes:
`
`dV TE-RL
`= - - -
`m
`dt
`
`(2.5)
`
`,,~,·-,,=, Jf'>
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`Road Loads
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`29
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`Equation (2.5) can be integrated once to determine the velocity of the vehicle over time,
`V(t). Integrating the result with respect to time once again will yield the position of the
`vehicle over time, S(~.
`
`Alternately, alternately the acceleration can be defined as ax = V dV / dS, so that the
`equation of motion is:
`
`VdV = TE-RL
`m
`dS
`
`(2.6)
`
`Equation (2.6) can be integrated once to find V(S). This form is particularly useful for
`studying vehicle-passing maneuvers, where the goal is to determine the distance needed
`for one vehicle to pass another vehicle.
`.
`Finally, if the vehicle is traveling at a constant speed (a = 0), Equation (2.4) · can be
`rearranged:
`
`TE=RL
`
`(2.7)
`
`This indicates that when a vehicle is traveling with constant velocity, the tractive effort
`required is equal to the road load.
`
`Returning to the free body diagram, the forces can be summed in the y-direction to yield:
`
`I,F y =may
`
`NJ +N +Lift-WcosB=ma
`r
`y
`
`(2.8}
`
`This equation (along with another equation found by summing moments) is important in
`determining the normal forces acting on the tires. The normal forces are directly related
`to the maximum tractive effort that can be developed by the tires. On a solid road the
`acceleration in the y-direction will be given by:
`v2
`a - -
`R
`y
`
`(2.9)
`
`where R is the radius of curvature of the road surface. On a flat road R-+ oo and ay = 0.
`However, on hills and bumps this acceleration term can be substantial. Further
`discussion of these equations will be put off until Chapter 4.
`
`2.2 Aerodynamic Lift and Drag
`Automotive vehicles move along the ground, but also through the air. The vehicle must
`push the air out of the way as it passes. The air in turn exerts both lift and drag forces on
`the vehicle. Automakers spend considerable time and money testing vehicles in wind
`tunnels to improve the aerodynamic characteristics of the vehicle. Figure 2-2 shows
`
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`30
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`Introduction to Automotive Powertrains
`
`Figure 2-2 Streamlines over an automobile (Gillespe, 1992).
`
`streamlines passing over an actual vehicle in a full-size windtunnel. Smoke has been
`used to visualize the fluid streamlines.
`In recent years there has been considerable effort to solve aerodynamics problems
`using Computational Fluid Dynamics (CPD) techniques. The techniques work very well
`in the aerospace industry, where the vehicle moves through only one medium (air) and
`have an 'aerodynamic' shape. Automobiles with their blunt shape (which leads to a large
`wake region) and the complex interactions between the air, vehicle, and ground have
`proven to be very difficult to model accurately. Also, automotive aerodynamics is
`greatly affected by the presence of other vehicles. Cars rarely travel through 'clean' air,
`as planes do.
`To understand the aerodynamic forces on the automobile, it is necessary to review a
`bit of fluid mechanics.
`2.2.1
`Inviscid Flow: Euler and Bernoulli Equations
`Leonhard Euler (1707-1783) and his one-time roommate Daniel Bernoulli (1700-1782)
`developed
`the
`foundations
`for modem aerodynamic
`theory
`( among other
`accomplishments). Although the equations apply only to inviscid flow, the equations
`have been shown to be valid in the areas of viscid flow fields that are not near a solid
`surface. Figure 2-3 shows three arbitrary streamlines in a flow field. The Euler
`Equations for inviscid fluid motion are developed by applying Newton's second law
`( F = ma , or more specifically FI¥= pa) to a fluid element at a point on the streamline.
`Assuming steady flow and neglecting gravity forces the Euler equations are found to
`
`be:
`
`s-direction:
`
`n-direction:
`
`ap =-p(vav)
`. as
`as
`ap =p(V'J
`an
`
`R
`
`(2.10)
`
`(2.11)
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`31
`
`Increasing Pressure
`
`Increasing Pressure
`
`Figure 2-3 Streamlines in a flow field.
`
`where pis the static pressure, Vis the fluid velocity, pis the fluid density, and R is the
`radius of curvature for the streamline at the location. The Bernoulli equation is found by
`integrating equation (2.10) along the streamline. For can incompressible fluid
`( p = constant) the result is:
`
`A, V;_2 Pi V/
`-+-=-+-
`2
`2
`p
`p
`
`(2.12)
`
`The Bernoulli equation essentially says that, under the assumed conditions, a particle
`traveling along a streamline has a constant level of energy ( often referred to as "head").
`More . specifically, when the kinetic energy ( V2 I 2) goes up, the pressure energy
`(generally referred to as flow work) has to go down (and vice versa).
`When the flow is brought to a stop, all the energy will be in the form of pressure
`energy and a maximum pressure will be reached. The location in the flow field where
`this occurs is called the stagnation point. The stagnation pressure is:
`
`pV2
`Pstag = p+-
`-
`2
`
`(2.13)
`
`The Euler n-equation is usually used simply as written (2.11 ). An examination of the
`equation reveals that the acceleration of the particle in the n-direction ( V2
`/ R ) can never
`be negative, meaning that the pressure must increase radially outward across the curved
`streamlines (i.e. in the positive n-direction). This fact has been noted Figure 2-3.
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`32
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`Introduction to Automotive Powertrains
`
`2.2.2 Application to an Automobile
`Th~ Euler and Bernoulli equations hav~ direct application to automotive aerodynamics .
`Reconsider Figure 2-2. It can be seen that:
`
`• There is a stagnation streamline on the front bumper; we expect high pressure
`there. (Note: This would be a good place to put the inlet to the radiator.)
`
`• The curvature of the streamlines indicate:
`
`o High pressure at the bumper.
`
`o Low pressure at the leading edge of the hood.
`
`o High pressure at the base of the windshield
`
`o Low pressure over the roof. (Contributing greatly to lift, but making it a
`good place for a sunroof.)
`
`Actual pressure measurements taken along the centerline of a vehicle are shown in
`Figure 2-4 and confirm the expected results.
`
`1.0 Cp
`
`o.o
`
`• !ASfllNE (HO LIi'}
`o 34111111. UP
`
`PRESSURE COEFFICIENTS PLOTTED NORMAL TO SURFACE
`
`Figure 2-4 Pressure measurements along the centerline of an automobile (Gillespe, 1992).
`
`The pressures in the figure have been non-dimensionalized (as is typical in
`aerodynamics) by defining the pressure coefficient:
`
`C = p-p""
`p YzpV 2
`
`(2.14)
`
`Where p