Introduction to
`
`Automotive Powertrains
`
`
`
`Craig J. Hoff,’ Ph.D., P.E.
`Gregory W. Davis, Ph.D., P.E.
`
`FORD 1425
`
`

`

`
`
`
`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 flie basis for developing computer models that can be used to predict vehicle ‘
`performance.
`
`Acknowledgemen
`
`
`n 5.3"
`arc;
`
`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.
`
`FORD 1425
`
`

`

`Tble Cones
`
`
`
`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 ..........................................»....... 1 1
`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 TorqueConverter 19
`1.2.3
`Manual Transmission ..................'.............................................................. 2 1
`1.2.4
`Automatic Transmissions.......................................................................... 22
`1.2.5
`Transaxles ................................................................................................. 23
`1.2.6
`Driveshafis ................................................................................................ 24 I
`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 anAutomobile.............................................‘..‘.................... 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
`
`FORD 1425
`
`

`

`Inb‘educh'on to Automotive Powertruins
`
`‘
`
`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
`GradeRes1stance ........... 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 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 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
`
`-
`
`I
`
`I
`’
`
`I
`'
`I
`i
`‘
`-
`‘
`-
`
`I
`J
`,
`
`I
`,
`.
`
`FORD 1425
`
`

`

`Automotive Drivetrain Components and Layouts
`
`7
`
`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
`
`Idea] Driveline
`
`....................... 96
`
`4.2.2
`4.3
`4.3.1
`4.3.2
`4.3.3
`
`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............................................. 1 15
`4.3.4
`Tires (Better Model) ....................................................................................... 1 18
`4.4
`Tire Forces andMoments ...... 118
`4.4.1
`Tire Slip .................................................................................................. l 19
`4.4.2
`N/V Ratio (Better Model) .................-...................................................... 122
`4.4.3
`' TractiveEfi‘ort ................ 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—Ofi'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
`
`Selecting Intermediate Gear ratios .....................................................‘..... 1 59
`Example .......................................................................................................... 168
`Select a Top Gear NN ratio.................................................................... 169
`Select a top gear ratio .............................................................................. 169
`Select an axle ratio .......................................................... ;.: ..................... 169
`Select first gear ratio ..........................‘..................................................... 1 70
`Select intermediate gear ratios ................................................................ 170
`Evaluate Gear Ratios ............................................................................... 172
`
`5.4
`
`5.5
`
`Homework ....................................................................................................... 172
`
`References.....................................................I ................................................. 173
`
`FORD 1425
`
`

`

`
`
`-._‘
`
`i i i i i i i
`
`. i
`
`Introduction to Automotive Powcrtrains
`
`6 Acceleration Performance ........................................... 175
`6.1
`Predicting Acceleration Performance ............................................................. 178
`6.2
`Power-Limited Acceleration............................................'............................... 1 80
`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
`Gradeabilityw1thaTrailer.............. 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
`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
`10.1
`Introduction..................................................................................................... 327
`
`FORD 1425
`
`

`

`Automotive Drivetrain Components and Layoufs
`
`9
`
`Torque Converters .......................................................................................... 329
`10.2
`10.2.1
`Fluid Couplings....................................................................................... 329
`10.2.2
`Torque Converters .................................................................................a. 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
`
`FORD 1425
`
`

`

`Chapter 2
`
`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 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 (TEr > 0), front wheel drive (TE; > 0) and
`four-wheel drive (TEf and TE, > 0).
`
`
`
`FORD 1425
`
`

`

`__________________1
`
`28
`
`_
`
`Introduction to Automotive Pawcrtraim-
`
`The major forces acting on the vehicle are:
`
`W
`N]; N,
`
`= Gross vehicle weight
`= Normal forces on the front and rear axles, respectively
`
`RR}; 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): 7
`
`EF, = max
`TEf+TEr—-WR—RRI—RR,—Wsin6=max
`
`(2'1)
`
`The component of the weight acting to oppose the'motion (W sin 0) is often 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-direction1s:
`-
`-
`
`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).
`
`(2.3)
`
`(2-4)
`
`RL=WR+RR+GR
`
`Solving Equation (2.2) for the acceleration of the vehicle yields:
`
`m
`
`TE~RL
`
`TE~WR—RR—GR
`a, =——— or a, =
`m
`
`This is the fundamental equation of vehicle motion.
`acceleration, ax = dV/ dt , the equation of motion becomes:
`
`Substituting the definition of
`
`(2.5)
`
`m
`
`£17K_TE—RL
`dt
`
`FORD 1425
`
`

`

`Road Loads
`
`29
`
`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, 80‘).
`
`Alternately, alternately the acceleration can be defined as ax = VdV/dS, so that the
`
`equation of motion is:
`
`~
`
`(2-6)
`
`m
`
`Vd—V— TE— KL
`dS
`
`Equation (2.6) can be integrated once to find V(S). This form18 particularly useful for
`studying vehicle-passing maneuvers, where the goalIS 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:
`_
`
`This indicates that when a vehicleIS traveling with constant velocity, the tractive effort
`required18 equal to the road load.
`
`TE =RL
`
`(2.7)
`
`Returning to the free body diagram, the forces can be summed in the y-direction to yield:
`
`2
`
`Fy=a
`my
`
`Nf
`
`+N +Lz’fi—Wcos0=ma
`7‘
`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:
`
`a =—
`
`(2.9)
`
`where R is the radius of curvature of the road surface. On a flat road R v) 00 and 61,, = 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 vehiclesin wind
`tunnels to improve the aerodynamic characteristics of the vehicle. Figure 2-2 shows
`
`FORD 1425
`
`

`

`30
`
`_
`
`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 (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 Inviscid 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 2 ma , or more specifically F HL == 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:
`
`92 = —p Vi]—
`as
`' as
`
`'
`
`X
`
`n direction'
`.
`
`V2
`~63 -
`6n p R
`
`(2.10)
`
`(2 11)
`
`FORD 1425
`
`

`

`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:
`
`firfizzfifl”?
`p2p2
`
`(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:
`
`(2.13)
`
`W 2
`
`pm =p+
`
`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.
`
`FORD 1425
`
`

`

`32
`
`Introduction to Automotive Powerlrains
`
`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.)
`
`o 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 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.
`
`3?
`
`1.0
`
`o mum: (no m;
`0 34m. up
`
` v-lelllllle1IIIIII3993
`
`I...’ll':_.'_!.-
`
`PRESSURE COEFFICIENIS PLOTIED NORM“ 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
`
`
`P‘P
`C =
`°°
`p V2sz
`
`l
`
`1
`
`2.14
`
`(
`
`)
`
`Where pa, is the static pressure measured in the free stream (essentially the atmospheric
`
`pressure).
`
`FORD 1425
`
`

`

`Road Loads
`
`3 3
`
`
`
`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 pressures. These pressures are consistent with the expectations from reading the
`streamline patterns (shown Figure 2-5 (c) and (d)).
`The use of CFD tools allows the affects of the vehicle to be seen in more complete
`detail.
`In Figure 2—5(b) the pressure field along a plane through the centerline of. the
`vehicle is visualized using a color map. The high pressure build-up in front of the vehicle
`and along the base of the Windshield is indicated with a dark red color. The lower
`pressure region along the front edge of the hood and all over the roof of the vehicle is
`indicated with dark blue shading. (Trust me.)
`
`FORD 1425
`
`

`

`A
`W.'x
`
`
`
`
`rL.41.L_..a.
`
`34
`
`Introduction [0 Automotive Powertrains
`
`2.2.3 Viscid Flow: Boundary Layers
`
`Ludwig Prandtl (1875-1953) proposed the existence of the boundary layer in 1905, a
`concept that is considered by many to be the greatest single discovery in the history of
`fluid mechanics. Prandtl showed that the effects of fluid viscosity on a flow field were
`concentrated in a thin region (called the boundary layer) near a surface. A fluid element
`touching the surface will stick to the surface (called the no-slip boundary condition) and
`in turn this slows down the fluid particles near it. This effect propagates away from the
`surface in a process referred to as boundary layer growth.
`The growth of the boundary layer as fluid flows over a flat plate is shown in Figure
`2-6. At first the fluid in the boundary layer flows in orderly layers (laminar). As the
`fluid moves long the