Introduction to
`
`Automotive Powertrains
`
`
`
`Craig J. Hoff, Ph.D., P.E.
`Gregory W. Davis, Ph.D., P.E.
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`Page 1 of 49
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`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 fcmdamentals 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.
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`,4
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`H .;:..
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`Awledgemen
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`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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`Preface ................................................................................ .. 3
`Table of Contents ................................................................ .. 5
`1 Automotive Drivetrain Components and Layouts ........ .. 1 1
`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
`Driveshafis ................................................................................................ 24'
`1.2.7
`Differentials ............................................................................................ .. 25
`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................................................................. .. 3 5
`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
`Afierbody 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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`Inlfaduction to Automotive Powertruins
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`‘
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`Optimization Study ................................................................................. .. 52
`2.2.17
`Effect of Wind......................................................................................... .. 53
`2.2.18
`Complete Aerodynamic Forces of a Vehicle .......................................... .. 54
`2.2.19
`Density of Air ..........................
`............................................................. .. 55
`2.2.20
`Alternate Form for Drag Equation .......................................................... .. 57
`2.2.21
`2.3
`Rolling Resistance .......................................................................................... .. 59
`2.3.1
`Simple Model for Rolling Resistance ..................................................... .. 60
`2.3.2
`Effect of Road Surface ............................................................................ .. 61
`Effect of Temperature on Rolling Resistance ......................................... .. 61
`2.3.3
`Effect of Tire Inflation Pressure ............................................................. .. 62
`2.3.4
`Effect of Tire Speed
`........................................................................... .. 62
`2.3.5
`Effect of Tire Materials ........................................................................... .. 62
`2.3.6
`2.3.7 . Effect of Tire Slip Angle......................................................................... .. 63
`2.3.8
`Other Models for Rolling Resistance .................. .................................... .. 64
`2.4
`Coast Down Testing.......................................................................................... 64
`2.5
`Grade Resistance .................................................................................. .._ ......... .. 65
`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
`3.2
`Engine Brake Torque and Power .................................................................... .. 72
`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 Eificiency).................................... .. 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 ofFuel 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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`Automotive Drivetrain Components and Layouts
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`7
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`3.7.3
`3.8
`3.8.1
`3.8.2
`
`Part Load Performance ........................................................................... .. 86
`Other Power Systems ........................................................................................ 87
`Gasoline Direct Injection (GDI) Spark-Ignited Engines ........................ .. 87
`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
`4.2.2
`4.3
`4.3.1
`4.3.2
`4.3.3
`
`Ideal Driveline .............................. .._................................. .; ....................... 96
`Driveline Losses ...................................................................................... .. 99
`Tires (idealized Model) ................................................................................... 103
`NN Ratio (Idealized Tire) .................................................................... .. 103
`Available Tractive Power ..................................................................... .. 108
`Available Tractive Effort ...................................................................... .. 111
`
`’
`
`Actual Tractive Power and Tractive Effort........................................... .. l 15
`4.3.4
`Tires (Better Model) ..................................................................................... .. 1 18
`4.4
`Tire Forces and Moments ............................................................... .; .... .. 1 18
`4.4.1
`Tire Slip ................................................................................................ .. 1 19
`4.4.2
`NN Ratio (Better Model) ...............
`.................................................... .. 122
`4.4.3
`' Tractive Efibrt....................................................................... .; .............. .. 122
`4.4.4
`Example - Effect of Tire Slip ............................................................... .. 124
`4.4.5
`Slip Angle ............................................................................................. .. 127
`4.4.6
`The Friction Ellipse....................................................................................... .. 130
`4.5
`4.5.1
`Rolling Resistance (Revisited) .............................................................. .. 134
`4.5.2
`A Final Note on Tires ........................................................................... .. 135
`
`Move—otf Elements ................................................. .. .................................... .. 135
`4.6
`References....._.................................................................................................. 137
`4.7
`5 Gear Ratio Selection ..........
`...................................... .. 139
`5.1
`Typical Gear Ratios Selected for Passenger Vehicles .................................. .. 143
`5.2
`A Procedure for Selecting Gear Ratios ......................................................... .. 149
`5.2.1
`Selection of a top gear N/V ratio .......................................................... .. 149
`5.2.2
`Determination of Top Gear Ratio and Axle Ratio ................................ .. 153
`5.2.3
`Low Gear Ratio Determination ............................................................. .. 154
`
`5.2.4
`5.3
`5.3.1
`5.3.2
`5.3.3
`5.3.4
`5.3.5
`5.3.6
`
`159
`Selecting Intermediate‘ Gear ratios ...................................................
`Example ........................................................................................................ .. 168
`Select a Top Gear NN ratio.................................................................. .. 169
`Select a top gear ratio ............................................................................ .. 169
`Select an axle ratio ........................................................ ..~..: ................... .. 169
`Select first gear ratio ........................
`................................................... .. 170
`Select intermediate gear ratios .............................................................. .. 170
`Evaluate Gear Ratios ............................................................................. .. 172
`
`5.4
`
`5.5
`
`Homework ..................................................................................................... .. 172
`
`References .................................................... .2 ............................................... .. 173
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`8
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`Introduction to Automotive Powcrtrains
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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
`6.6
`Examples: Power-Limited Acceleration — Automatic Transmission.............. 218
`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
`6.8.1
`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 ........................................................................... 239
`7.2
`Traction-Limited Gradeability ................................
`...................................... 247'
`7.3
`Gradeability with a Trailer .............................................................................. 251
`7.3.1
`Power-Limited Gradeability ................................................................... 251
`7.3.2
`Traction-Lirnited Gradeability ................................................................ 253
`7.4
`References .......................................... ............................................................. 258 .
`Chapter 3 ........................................................................ .. 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
`9.2
`Analysis of a Clutch........................................................................................ 310
`9.2.1
`Uniform Pressure Model ....................................................................... .. 311
`9.2.2
`Uniform Rate of Wear Model ..........................................
`.................. 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
`1 0.1
`Introduction..................................................................................................... 327
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`Automotive Drivetrain Components and Layoufs
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`9
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`Torque Converters ........................................................................................ .. 329
`10.2
`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................................................ 355
`10.5 Other Considerations ...................................................................................... 362
`10.5.1
`Transmission And Engine Oil Coolers ................................................. .. 362
`10.5.2
`Parking .............................,...................................................................... 364
`1 1 Differentials ................................................................ .. 365
`11.1
`Introduction..................................................................................................... 365
`11.2 Open Differentials ......................................................................................... .. 367
`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 .................................................................................... .. 374
`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
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`
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`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 fiee 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 (TE, > 0), fiont wheel drive (TE; > 0) and
`four-wheel drive (TEf and TE, > 0).
`
`
`
`Figure 2-1 Free body diagram of a vehicle traveling up an incline.
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`28
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`_
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`Introduction to Automotive Pawertraing
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`The major forces acting on the vehicle are:
`
`W
`
`= Gross vehicle weight
`
`Nfi N,
`
`= Normal forces on the front and rear axles, respectively
`
`RRfi RR, = Rolling resistance on the front and rear tires, which act to oppose
`the vehicle motion.
`
`TEfi TE, = Tractive effort on the fiont and rear tires, which is the force created
`by the engine at the. driving wheels propelling the vehicle forward.
`
`WR
`
`Lift
`
`the component of the
`= Wind resistance or drag, which is
`aerodynamic force that acts to oppose the motion of the vehicle.
`
`the
`component of
`the
`force, which is
`lift
`= Aerodynamic
`aerodynamic force that acts vertically relative to the motion of the
`vehicle
`-
`
`Summing the forces in the direction of vehicle motion (i.e. the x—direction): ,
`
`S
`
`ZF, =max
`TEf+TE,—-WR—RRf—RR,—Wsinl9=ma,
`
`21
`( ' )
`
`The component of the weight acting to oppose themotion (W sin 49) is oflen referred to as
`the Grade Resistance (GR). To simplify the analysis for the moment, the tractive forces
`acting on the front and rear tires (TEf and TE,, 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,
`
`(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
`: or ax :
`m
`
`ax
`
`TE~RL
`
`m
`
`(2.3)
`
`(2.4)
`
`This is the fundamental equation of vehicle motion.
`acceleration, ax = dV/ dz‘ , the equation of motion becomes:
`
`Substituting the definition of
`
`£I£_TE—RL
`dt
`m
`
`(2.5)
`
`_-_--______.______1
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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(t).
`
`Altemately, alternately the acceleration can be defined as ax = VdV/dS, so that the
`
`equation of motion is:
`
`~
`
`dV_TE—RL
`dS
`m
`
`(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 detennine 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:
`
`ZF), = ma
`y
`+N +Lzfi—Wcos6=ma
`7‘
`J’
`
`Nf
`
`(2.8)..
`
`This equation (along with another equation found by summing moments) is important in
`detennining 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:
`
`a =——
`
`(2.9)
`
`where R is the radius of curvature of the road surface. On a flat road R ~—> 00 and a, = 0.
`However, on hills and bumps this acceleration term can be substantial.
`Further
`discussion of these equations will be put off until Chapter 4.
`
`,
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`I
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`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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`-
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`Introduction to Automotive Powgrtrains
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`
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`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 (CFD) 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 lnviscid Flow: Euler and Bernoulli Equations
`
`Leonhard Euler (1707-1783) and his one-time roommate Daniel Bernoulli (1700—1782)
`developed
`the
`foundations
`for modern
`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 F H4 = 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:
`
`—a—E=—p Vi’:
`as
`- 6s
`
`'
`
`x
`
`(2.10)
`
`n-direction: 93: p E
`
`an
`
`R
`
`(2.11)
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`Road Loads
`
`3 1
`
`Increasing Pressure
`
`
`
`Increasing Pressure
`
`Figure 2-3 Streamlines in a flow field.
`
`where p is the static pressure, V is the fluid velocity, p is 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:
`
`2
`2
`£51--V—;-=&+V2
`p2p2
`
`A
`
`(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 / 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:
`
`pm = p+
`
`/0V’
`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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`Introduction to Automotive Powertrains
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`2.2.2 Application to an Automobile
`The Euler and Bernoulli equations have direct application to automotive aerodynamics.
`Reconsider Figure 2-2. It can be seen that:
`0 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.)
`
`0 The curvature of the streamlines indicate:
`
`0 High pressure at the bumper.
`
`0 Low pressure at the leading edge of the hood.
`
`0 High pressure at the base of the windshield
`0 Low pressure over the roof. (Contributing greatly to
`good place for a sunroof.)
`
`but making it a
`
`Actual pressure measurements taken along the centerline of a Vehicle are shown in
`Figure 2-4 and confirm the. expected results.
`
`“P
`
`1-0
`
`0 IASIIINI (No Mr}
`0 Hum. UP
`
` '-‘_!I'.lIlIle1|IllII.‘!!_'.
`
`u.'.gur_-_.-_:,-
`
`PRESSURE COEFIICIEIIIS PLOTIID NORMAI 1'0 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
`aerodynamics) by defining the pressure coefficient:
`
`in
`
`C =p_pco
`P
`1/ZPV2
`
`.
`
`I
`
`(2.14)
`
`Where pm is the static pressure measured in the free stream (essentially the atmospheric
`
`pressure).
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`Figure 2-5 CFD Studies showing pressure acting on a vehicle (Roettger).
`
`In
`Figure 2-5 shows the pressures acting on a vehicle as predicted by a CFD study.
`Figure 2—5(a) the pressures are mapped on to the surface of the vehicle using a color map
`(which is admitted difficult to read in a black and white reproduction). The darker (red)
`colors on the front facia and along the base of the windshield indicates high pressure.
`The light (blue) color along the front edge of the hood and along the A—pillars indicates
`low press