7- AUTOMOTIVE AERODYNAMICS

This is Part 7 of a 10 Part Series in Automotive Dynamics and Design, with an emphasis on Mass Properties. This series was intended to constitute the basis of a semester long course on the subject.

1. AUTOMOTIVE DYNAMICS, Brian Paul Wiegand, B.M.E., P.E. 1 AERODYNAMICS

2. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, GAS vs. LIQUID Brian Paul Wiegand, B.M.E., P.E 2 When a body moves through a “ fluid ” a force opposite the direction of motion is generated; this force is called “ drag ”. A force orthogonal to the direction of motion may be generated as well; this force is generally called “ lift ”. The study of such body–fluid interactions is called “ fluid mechanics ”, and when the “ fluid ” of interest is a gas such as air, then the dynamic area of study narrows down to that subset of “ fluid mechanics ” called “ aerodynamics ”. For aerodynamic drag to be generated there must be air present, and there must be relative motion between the air and a body; without air or motion there can be no drag or lift. The chief difference between aero (gas) flow and fluid (liquid) flow is that fluid (liquid) behavior is always incompressible …

3. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, NAVIER-STOKES EQUATIONS Brian Paul Wiegand, B.M.E., P.E 3 Over the course of history a great many distinguished individuals have contributed to the understanding of fluid mechanics ; Newton, Euler, Bernoulli, Navier , Stokes, and Reynolds to name just a few. The ultimate model of fluid behavior , the Navier -Stokes Equations , are so complex that a complete analytical solution can not be found …

4. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, DIMENSIONLESS INDICATORS Brian Paul Wiegand, B.M.E., P.E 4 Such “indicators” make the complex study of Fluid Mechanics more manageable as they indicate the presence of certain phases of fluid flow behavior , and whether or not two different fluid flow situations might be in the same phase and thus similar . This means that the researcher can concentrate on just certain limited behavior as much of the rest of the overwhelmingly complex nature of the situation can be disregarded per the dimensionless parameter’s indication . There are a number of such “ dimensionless indicators ”, a.k.a. “ similarity parameters ”, “ dimensionless parameters ”; like the: Reynolds Number , Mach Number , Froude Number , Weber Number , Prandtl Number … Of all of these numbers we are going to be the most concerned with just the first two…

5. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, DIMENSIONLESS INDICATOR USE Brian Paul Wiegand, B.M.E., P.E 5 For example , the Mach Number can indicate whether a gas flow is in an incompressible flow phase or not ; at Mach numbers less than 1 the flow is compressible , which means the designer need not yet be concerned with the formation of shock waves and the associated energy loss, and can focus on creating a body shape appropriate for subsonic use . Another example of the utility of a dimensionless indicator: wind tunnel testing of the aerodynamic nature of a body design by use of a scale model provides, this time of the Reynolds Number . Only when the Reynolds Number of the wind tunnel experiment is comparable in value to the Reynolds Number of the full size design can the scale model wind tunnel results have any relevance to the full scale situation.

6. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, REYNOLDS NUMBER Brian Paul Wiegand, B.M.E., P.E 6 George Gabriel Stokes (1819-1903) derived the Reynolds Number from the Navier -Stokes Equations in 1851, but it took Osborne Reynolds (1842-1912) to make its practical use apparent in 1883 … * The Reynolds Number W here: V  is the maximum velocity of the object relative to the fluid ( m/s, ft/s ) L  is a characteristic linear dimension , travelled length of the fluid ( m, ft ) μ  is the dynamic viscosity  of the fluid ( kg/( m·s ), lb-s/ft 2 ) ν is the  kinematic viscosity of the fluid: ν  =  μ / ρ ( m 2 /s, ft 2 /s ) ρ is the density  of the fluid ( kg/m 3 , lb/ft 3 /g ). * “An Experimental Investigation of the Circumstances which Determine Whether the Motion of Water in Parallel Channels shall be Direct or Sinuous and of the Law of Resistance in Parallel Channels”, 1883.

7. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, MACH NUMBER Brian Paul Wiegand, B.M.E., P.E 7 Austrian physicist and philosopher  Ernst Mach (1838-1916) published a paper in 1887 concerning the formation of “ shock waves ” by projectiles traveling at speeds greater than the speed of sound ( V p /V s > 1 )… The Mach Number Where: M  is the Mach Number . u  is the local flow velocity . c  is the speed of sound in the fluid. For a gas this is equal to (see next slide).

8. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SPEED of SOUND Brian Paul Wiegand, B.M.E., P.E 8 Where: c  is the “ speed of sound” in a gas . κ  is the “ specific heat ratio” of the gas . R is the “ specific gas constant” . T is the “ absolute temperature” . c So, an aircraft traveling at Mach 1 at 20°C (68°F) at sea level will experience shock waves just like an aircraft traveling at Mach 1 at 11,000 m (36,000 ft) altitude at −50°C (−58°F), but despite being at the same Mach Number the second aircraft is only traveling 87% as fast as the first due to the fact that the ambient conditions are quite different.

9. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SPEED of SOUND Brian Paul Wiegand, B.M.E., P.E 9 c TEMPERATURE CONVERSION: ºR = ºC * 1.8000 + 491.67

10. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SPEED of SOUND Brian Paul Wiegand, B.M.E., P.E 10 Aircraft #1 traveling at Mach 1 at 20°C (527.67°R) at sea level = Aircraft #2 traveling at Mach 1 at −50°C (401.67°R) at 36,000 ft = So the second aircraft is indeed only traveling 87% as fast as the first aircraft …

11. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS Brian Paul Wiegand, B.M.E., P.E 11 It is because fluid behavior is so complex that most problems in fluid mechanics are modeled as very limited and degenerate subsets of the ultimate reality . This means that the resultant limitations of any equations used must be borne in mind, that any exposition on fluid mechanics or some aspect thereof must necessarily be somewhat simplistic and misleading , and that any results obtained , whether by “back of the envelop” calculation or by computerized fluid dynamics ( CFD ) simulation, must still be subject to a thorough empirical validation. With that said, and the student now supposedly aware of the consequent need for caution and the requirement for humility , this segment of the Automotive Dynamics curriculum may begin in earnest…

12. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, STREAMLINES Brian Paul Wiegand, B.M.E., P.E 12 The most elemental explanation of “ streamlines ” is that such serves as an attempt to visualize the fluid flow around a body. The use of smoke, yarn tuffs, and ink in the wind tunnel as an attempt to find the streamlines is common… Ideally a streamline is a path traced out by a “mass-less” particle as it moves with the flow. Since the streamline is traced out by a moving particle, at every point along the path the velocity is tangent to the path. Since there is no normal component of the velocity along the path, mass cannot cross a streamline . The mass contained between any two streamlines remains the same throughout the flow field . We can use  Bernoulli’s Equation  to relate the pressure and velocity along the streamline. Since no mass passes through the surface of the body, the surface of the body can also be a streamline .

13. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, BERNOULLI EQUATION Brian Paul Wiegand, B.M.E., P.E 13 Daniel Bernoulli (1700-1782), developing some earlier work by Leonhard Euler (1707-1783), derived a simple but very useful equation regarding fluid flow which he published by 1738 in his book Hydrodynamica . A version of that equation may be expressed as: ½ ρ 1 V 1 2 + P 1 = ½ ρ 2 V 2 2 + P 2 This simple version of Bernoulli's equation is valid for incompressible flows  ( liquids , plus  gases  moving at low Mach Number ) where the density “ ρ ” can be taken as constant. It can be used to help interpret the meaning of streamlines realistically drawn about a body to denote the fluid flow. Essentially it says how the velocity “ V ” and the pressure “ P ” at two different points along a flow are related to each other, and that the relationship between “ V ” and “ P ” is inverse .

14. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, DRAG Brian Paul Wiegand, B.M.E., P.E 14 Aerodynamic “ drag ” comes about through a number of different mechanisms, but mainly as “ Form Drag ” and “ Skin Drag ”. To those two add “ Interference Drag ” and the trio constitutes what is called “ parasitic drag ”. Finally, there is also “ Induced Drag ”, “ Ram Drag ”, and “ Wave Drag ”. There are also a number of “ drag effects ” or qualities which affect these drag types, like “ ground effect ”. The total drag on a vehicle is the result of a very complicated interaction . The natural simplistic assumption is that the total drag , reflected in a value called the “ Coefficient of Drag ” or “ C d ”, is merely the sum of the individual drag components : C d = C dF orm + C dS kin + C d Int + C dI nd + C d Ram + C d Wav However , this is very deceptive and conducive to error due to the interaction (i.e., measured separately a 0.100 C d form plus a 0.005 C d ram might equal a total 0.130 C d due to interaction ). Parasitic Drag

15. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, FORM DRAG Brian Paul Wiegand, B.M.E., P.E 15 “ Form drag ” has to do the mass of air that is displaced as a body moves through it due to the body’s shape and size. At the front of a body moving at moderate speed the air tends to be compressed and a high pressure area develops, with the highest pressure at a location called the “ stagnation point ”, while at the rear of the body the air tends to expand and a low pressure area develops. This pressure differential times the body’s cross-sectional area constitutes the essence of form drag (actually the summation of the longitudinal pressure components over the surface area of the body constitutes the total drag force ). Note in the figure on the next slide how the absolute “ C d ” of “ force/area ” becomes the relative and dimensionless “ C d ” of general familiarity when divided by the absolute “ C d ” of a flat plate…

16. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, FORM DRAG Brian Paul Wiegand, B.M.E., P.E 16 The relative “ form drag ”, as measured by a quantity called the “ coefficient of drag ” or “ C d ”, of certain basic shapes may be illustrated as follows: ( Weight Engineer’s Handbook , Society of Allied Weight Engineers; Chula Vista, CA; 1968-1986, pg.. 10.6) * At Mach Numbers

17. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, FORM DRAG Brian Paul Wiegand, B.M.E., P.E 17 There are other chart versions which use Reynolds Number to express the limitation of applicability of the C d values… (Streeter, Victor L.; Fluid Mechanics , McGraw-Hill Book Co., NY,NY, 1966. pg. 246)

18. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, FORM DRAG 18 Then there are chart versions which are less than specific… (NASA, “ What Is Drag? ”, www.grc.nasa.gov/WWW/K-12/airplane/drag1.html ) (F1 Engineer, “ Science Behind F1 Aerodynamic Features ”, www.f1-country.com /f1-engineer/ aeorodynamics /aerodynamics.html)

19. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, FORM DRAG VARIABILITY 19 Form drag C d can be very sensitive to slenderness ratio, speed realms… Tree (C values from Munson et al., 1998) A=Tree frontal area C=0.43 if V=10 m/s (36.0 km/h, 22.4 mph) C=0.26 if V=20 m/s (72.0 km/h, 44.7 mph) C=0.20 if V=30 m/s (108 km/h, 67.1 mph) Flag (C values from Munson et al., 1998) A=DL C=0.07 if L/D =1 C=0.12 if L/D= 2 C=0.15 if L/D= 3 Thin Rectangular Plate (C from Blevins, 2003) A=DL C=1.05 if L/D= 1.0 C=1.10 if L/D= 2.0 C=1.12 if L/D= 4.0 C=1.20 if L/D= 8.0 C=1.22 if L/D=10.0 C=1.33 if L/D=17.8 C=1.90 if L/D= infinity Brian Paul Wiegand, B.M.E., P.E

20. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SKIN DRAG Brian Paul Wiegand, B.M.E., P.E 20 “ Skin drag ” has to do with the air in actual contact with the external surface area of the moving body. The magnitude of the skin area and the degree of its roughness are the primary factors in determining the amount of skin drag present. The layer or “ lamina ” in actual contact with the body’s skin tends to slow down with respect to the body until it is actually moving along with the body as an “ entrained ” or captive mass; i.e., the relative velocity is zero . The next layer of air tends to slow down due to its contact with the first layer , but will retain a velocity relative to the body just short of zero. The layer after that will also tend to slow , but to even a lesser degree, and so forth.

21. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SKIN DRAG Brian Paul Wiegand, B.M.E., P.E 21 The total number of “ lamina ” in close proximity with the body’s skin that has had its relative velocity affected by the body constitutes the “ boundary layer ”; the lamina of this boundary layer present a characteristic velocity profile such as shown in the figures on this slide. Eventually there will be a point reached where the boundary layer “ laminae ” in closest proximity to the body will have slowed down to the extent that the affected air mass has come to serve as an obstacle to the flow from upstream; this is called the “ separation point ” where the large scale turbulence of a “ wake ” sets in…

22. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, OTHER DRAG SOURCES Brian Paul Wiegand, B.M.E., P.E 22 “ Induced drag ” is a usually small (except in the case of high lift forms such as wings) drag component resulting from the generation of lift forces. The generation of drag and lift is always interconnected . “ Interference drag ” is the drag resulting from the interaction of aero flows, like that around an exterior side-mounted rear-view mirror conflicting with the flow around an automobile’s A-pillar. However, there are many other examples of such drag, some being of such particular interest as to constitute a particular type or “effect”… “ Wave drag “ is the result of a “ shock wave ” formation at supersonic speeds. “ Ram drag ” is the drag associated with induction of free atmospheric air into a vehicle interior (for cooling, combustion, etc.).

23. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, RAM DRAG Brian Paul Wiegand, B.M.E., P.E 23 “ Ram drag ” is the drag associated with induction of free atmospheric air into a vehicle interior (for cooling, combustion, etc.). AIR INLETS AND OUTLETS OF THE PORSHE 956

24. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, RAM DRAG Brian Paul Wiegand, B.M.E., P.E 24 ( Hucho , Wolf-Heinrich; Aerodynamics of Road Vehicle s , SAE R-177, Warrendale, PA, pg. 293 (small chart), pg. 201 (large figure).)

25. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, LIFT & INDUCED DRAG Brian Paul Wiegand, B.M.E., P.E 25 Bernoulli’s Equation says when the air has to go faster over the top than under the bottom there will less pressure at the top than the bottom . The pressure difference times the planform area is the resultant lift , which acts orthogonal to the chord “ A-B ”. Resolving this resultant into its components gives us the Lift and the Induced Drag … a = Angle of Attack Lift = Lift R Cos( a ) Induced Drag = Lift R Sin( a )

26. AUTOMOTIVE DYNAMICS, AERODYNAMICS Brian Paul Wiegand, B.M.E., P.E 26 BASICS, LIFT & DRAG Note the minimum drag at zero lift, which is not at α = 0; airfoil drag also has a minimum at some speed

27. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SIMPLE DRAG FORCE EQUATION Brian Paul Wiegand, B.M.E., P.E 27 Where: D = the drag force (lb) C d = the drag coefficient (dimensionless) A f = the frontal area (ft 2 ) V = the velocity (ft/sec) If “ V ” is to be in mph, then the “ 841 ” factor should be “ 391 ”.

28. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, DRAG FORCE EQUATION Brian Paul Wiegand, B.M.E., P.E 28 Where: D = the drag force (lb). C d = the drag coefficient (dimensionless). A f = the frontal area (ft 2 ). V = the velocity (ft/sec). ρ = the air & vapor mass density (slugs/ft 3 ): Where: ρ is the atmospheric pressure (lb/ft 2 ). P v is the vapor pressure (lb/ft 2 ). g is the gravitational constant (32.172 ft/s 2 ). T is the temperature (°R).

29. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, SIMPLE LIFT FORCE EQUATION Brian Paul Wiegand, B.M.E., P.E 29 Where: L = the lift force (lb) C l = the lift coefficient (dimensionless) A p = the plan area (ft 2 ) V = the velocity (ft/sec) If “ V ” is to be in mph, then the “ 841 ” factor should be “ 391 ”. PLAN AREA FRONT AREA

30. AUTOMOTIVE DYNAMICS, AERODYNAMICS BASICS, LIFT FORCE EQUATION Brian Paul Wiegand, B.M.E., P.E 30 Where: L = the lift force (lb). C l = the lift coefficient (dimensionless). A p = the plan area (ft 2 ). V = the velocity (ft/sec). ρ = the air & vapor mass density (slugs/ft 3 ): Where: ρ is the atmospheric pressure (lb/ft 2 ). P v is the vapor pressure (lb/ft 2 ). g is the gravitational constant (32.172 ft/s 2 ). T is the temperature (°R).

31. CENTER OF PRESSURE AUTOMOTIVE DYNAMICS, AERODYNAMICS Brian Paul Wiegand, B.M.E., P.E. 31 Integrating the pressure times the surface area all around the body surface determines the resultant aerodynamic force on the body. This single force acts in effect through the average location of the pressure on the surface of the object. This average location of the pressure forces is termed the  center of pressure (CP)  in much the same way that the average location of the gravitational forces on a body is termed the  center of gravity (CG) , through which acts the resultant gravitational force which is called the weight of the body. However, unlike that single force, the resultant aerodynamic force must be resolved into two component forces,   lift and drag , both of which act through the center of pressure . Another difference between the CG and the CP is that the CP will move with variation in orientation and velocity of the body with respect to the flow, whereas the CG is more fixed.

32. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 32 The aero forces acting through the CP affects automotive directional stability in two ways. The lift and drag forces will modify the normal loads on the tires, and thereby affect the directional stability “indirectly”. However, there is also a more “direct” effect… 1969 Dodge Charger @ 60 mph

33. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 33 The “ direct ” effect is what commonly comes to mind when the term “ aerodynamic directional stability ” is used; it is the stability imparted to arrows, missiles, and other such bodies moving through a fluid (air) without benefit of ground contact… And that directional stability comes about when the center of pressure is located aft of the center of gravity : “ If the vehicle becomes airborne, or if the track surface offers little traction, the effect of the contact patches may suddenly disappear or be lessened. In that case, ground vehicle stability, like aircraft stability, requires that the center of pressure be located behind the center of mass . If the vehicle develops a yaw or pitch angle, the aerodynamic forces acting at the center of pressure will be a restoring force if located behind the center of mass , but will tend to increase the yaw or pitch angle if located ahead of the center of mass , possibly leading to a spin or flip. Thus it is highly desirable to have the center of pressure located behind the center of mass .” ( Pater, Larry; “Aerodynamics: Drag, Lift, and Stability”, Design and Construction of a Land Speed Record Streamliner , www.paterstreamliner.com, 2016 )

34. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 34 However, from the same source as the previous quote the location of the CP is said to be determined by: “ An approximate, much easier, method is to use the area centroid of the projected body profile (Benson, NASA model rocketry website) as an estimate of the location of the center of pressure . This works quite well for long and thin bodies such as a streamliner body or model rocket ( but maybe not a roadster or other car ) for which the pressure variations over the surface are not large. This can be done mathematically by using area-moments to determine the geometric area centroid. Mathematics can be avoided by finding the balance point of a cardboard cutout of the projected profile, which gives a non-mathematical estimate of the location of the area centroid and thus the center of pressure... ” It’s good that the source acknowledged the possible lack of accuracy in using the body profile area centroid as an estimate of the location of the CP for “roadster or other car”; just consider the previous 1969 Dodge Charger example…

35. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E 35 …the profile area centroid would seem to pretty far aft of the known CP location; this “centroid CP” could be the CP location to use for determining the effect of a side wind gust acting at a right angle to the longitudinal axis of the vehicle, but for a strictly longitudinal air flow would be still located as shown: 1969 Dodge Charger @ 60 mph

36. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 36 The CP actually might vary in location between the illustrated location to the centroid location depending on the magnitude and direction of the air flow vector. This illustrates the fact that the CP location is a much more variable parameter than the CG location, even though that too varies with loading, free surface effect, etc. Having a CP well aft of the CG certainly promotes directional stability for an arrow or other body totally dependent on aero forces; but for a wheeled vehicle a lateral aero disturbance force would act through the centroid location shown and, if tire/suspension characteristics are the same all around , tend to cause larger slip angles at the rear than the front . That would tend to make the vehicle turn towards the disturbance force such that the resulting centrifugal reaction would be in the same direction as the aero disturbance (!), but that centrifugal reaction would also tend to even out the front-to-rear slip angle relationship thereby tending to return the vehicle to straight ahead motion (!)…Consider the consequences of a lateral aero disturbance for a number of CG / CP relationships…

37. The conventional wisdom is that the CP should be aft of the CG ; usually the CP is not far from the CG so following two cases (fwd CG and aft CG ) quite naturally present themselves: It would seem that, based on this “analysis”, the conventional wisdom doesn‘t work out as well for an aft CG car as it does for a fwd CG car. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 37

38. Now consider the exact opposite of the conventional wisdom, again for the two cases of a fwd CG and an aft CG : Neither of these two cases seem to work out very well with regard to directional stability…However, what happens if the CG and CP are not so closely coupled? AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 38

39. AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 39 It is unlikely the CG and CP would ever be quite as divergent as depicted, but to complete this “analysis” consider the two cases of a fwd and an aft CG : It would seem that a far aft CP doesn’t work out too badly for a fwd CG , but a far fwd CP for an aft CG car works out very, very poorly.

40. As a final thought on the subject of automotive aerodynamic directional stability consider the following quote: “ A vehicle in an airstream is the less stable the better its shape is suited for low drag .” Dr. Wunibald Kamm , 1933* Of course, early aerodynamically shaped cars tended to be teardrop shaped with a large blunt front end and long tapering tail which placed the CP far forward . The engine tended to get placed far aft so that the air intake and exhaust would have minimum affect on the flow over the body, but this tended to result in a very aft CG location . That combination of CP and CG location we have already seen as being very unstable … AUTOMOTIVE DYNAMICS, AERODYNAMICS AERO DIRECTIONAL STABILITY Brian Paul Wiegand, B.M.E., P.E. 40 (* Hucho , Wolf-Heinrich; Aerodynamics of Road Vehicles , SAE R-177, Warrendale, PA, 1988, pg. 31.)

41. AUTOMOTIVE DYNAMICS, AERODYNAMICS MAGNUS EFFECT Brian Paul Wiegand, B.M.E., P.E. 41 …is commonly depicted as a rotating cylinder traveling against an airstream such that the rotation assists the flow over the “top” and retards the flow under the “bottom”. For such a situation of high speed, hence low pressure, on top and low speed, hence high pressure, on bottom, the classical Bernoulli result is one of lift. However, the obvious automotive application differs from this in that the wheels rotate with respect to the air- stream so as to cause “down-force”. At least the wheels would generate such down-force if they were in a free stream as opposed to being in contact with the ground plane . And if the wheels are partially enclosed within wheel-wells , then the resultant behavior has precious little left to do with the Magnus Effect…However, some people still seek to invoke it…

42. AUTOMOTIVE DYNAMICS, AERODYNAMICS WHEELS/TIRES/HOUSING EFFECT A 1996 paper presented by Pfadenhauer , Wickern , and Zwicker claims that the wheels/tires/housings account for about 35% of the total vehicle C d 1 ; BMW aerodynamicist Karlheinz Ebbinghaus corroborated this estimate of the wheels/tires/housings aero drag contribution: “ Thirty to forty percent of a car’s aerodynamic resistance is created in the wheels and housings ” 2 . It would therefore seem to be reasonable to use this figure as the basis for a crude estimation of the wheels/tires/housings impact on the aerodynamics of the basic auto body form. However, this applies only to most road cars with C d s of around 0.35 to 0.30 in value . The more streamlined the basic body form (the lower its C d ) the bigger the relative impact (+%) that the addition of tire/wheel/ wheelwells will have (and streamlined open wheel race cars with very wide wheels may be the most affected of all 3 )…. Brian Paul Wiegand, B.M.E., P.E. 42 1 Talamelli & Westin; “ Aerodynamics of Cars, Drag Reduction ”, Department of Mechanics Presentation, KTH Royal Institute of Technology, Stockholm, Sweden, slide 31. 2 Zenlea , David; “ First Drive BMW i8 ” , Automobile , pp. 12-14, November 2013, pg.14. 3 Such race cars also have open cockpits and are designed to generate large amounts of “down-force” or negative lift, and such lift generation means a large induced drag contribution to the total drag. Total C d values might be around 0.7 to 1.3 for an F1 car depending on wing angle of attack settings, etc.!!

43. ( Hucho , Wolf-Heinrich; Aerodynamics of Road Vehicles , SAE R-177, Warrendale, PA, 1988, pg. 182.) AUTOMOTIVE DYNAMICS, AERODYNAMICS WHEELS/TIRES/HOUSING EFFECT Brian Paul Wiegand, B.M.E., P.E. 43 Drag and Lift is reduced for a rotating wheel on the ground with respect to a stationary wheel just off the ground. However, drag is still high due to three pairs of trailing vortices. Experiments with a wheel just over a stationary ground plane demonstrates how C d and C l decrease with wheel rotation. The benefit of using large smooth (“Moon”) wheel covers is also demonstrated.

44. AUTOMOTIVE DYNAMICS, AERODYNAMICS WHEELS/TIRES/HOUSING EFFECT Brian Paul Wiegand, B.M.E., P.E. 44 Wheel housings further affect the Drag and Lift effect of the wheels; the smaller the housing volume “ V H “ with respect to the wheel volume “ V W “ the less the Drag and Lift generated… ( Hucho , Wolf-Heinrich; Aerodynamics of Road Vehicles , SAE R-177, Warrendale, PA, 1988, pp. 185 and 180.)

45. AUTOMOTIVE DYNAMICS, AERODYNAMICS BARGE BOARDS, SIDE BOARDS Brian Paul Wiegand, B.M.E., P.E. 45 ( Dimitriadis , Greg; “ Vehicle Aerodynamics, Lecture 4: Fast Cars ”, Université de Liége , Aeroelasticity and Experimental Aerodynamics Research Group (AEA), Department of Aerospace and Mechanical Engineering , 2014 )

46. AUTOMOTIVE DYNAMICS, AERODYNAMICS DRAFTING EFFECT In NASCAR racing a practice known as “ drafting ”, a.k.a. “ slipstreaming ”, wherein one car follows closely in the wake of another, has long been known to reduce the aerodynamic drag of both vehicles. The exact effect depends very much on the aerodynamic sophistication of the vehicles involved, the relative size of those vehicles, and the distance ( proximity ), measured in car lengths, between the vehicles. Brian Paul Wiegand, B.M.E., P.E. 46 ( Hucho , Wolf-Heinrich (Ed.); Aerodynamics of Road Vehicles , SAE R-177, Warrendale, PA, pg. 208.)

47. AUTOMOTIVE DYNAMICS, AERODYNAMICS VORTEX EFFECT Brian Paul Wiegand, B.M.E., P.E. 47 Whenever there is a pressure differential generated by the passage of a body through a fluid the tendency of nature to equalize that differential results in some lateral flow around the body causing swirling flow motions that represent a large energy loss and further drag…

48. AUTOMOTIVE DYNAMICS, AERODYNAMICS VORTEX, TURBULENCE GENERATORS Brian Paul Wiegand, B.M.E., P.E. 48 Although turbulence and vortices are generally something to be avoided, ironically such can actually be used to reduce drag, but just when used on a smaller scale. When airflow in the boundary layer begins to slow down to the point of separation, small scale roughness or, even more efficiently certain structures, can induce turbulent and/or vortex flow within the boundary layer lamina. This transverse flow serves to bring an influx of energy to the layers nearest the body surface, speeding those layers up and delaying separation. This results in a reduced wake and an overall decrease in drag…at least in the higher speed ranges: (Shapiro, Archer H .; Shape and Flow , The Fluid Dynamics of Drag , Doubleday & Co., Garden City, NY, 1961, pg. 170.)

49. AUTOMOTIVE DYNAMICS, AERODYNAMICS WINGS Brian Paul Wiegand, B.M.E., P.E. 49 1928 1967 Wings had been used early in automotive history to provide down-force to ensure traction, but their most extensive and notable automotive use came in the form of the huge “high wings” used in racing during the 1960’s. The wings were mounted so high in an attempt to move them up out of the disturbed air flow and thereby increase their effectiveness. For a wing, the total  drag coefficient, C d  is equal to the base drag coefficient at zero lift,  C do ,  plus the induced drag coefficient  C di : C d = C do + C di

50. AUTOMOTIVE DYNAMICS, AERODYNAMICS WINGS Brian Paul Wiegand, B.M.E., P.E. 50 Modern wing usage as in Formula 1 involve the use of a front wing and an aft wing, spread apart as far as possible to maximize their effect as “tuning” devices for longitudinal normal load distribution and CP location. Front wings operate in an extreme ground effect situation and are readily affected by vehicle pitch motions. The rear wing is often designed to act in symbiosis with a device located in the rear underbelly called a “ diffuser ”. CP CP CP

51. AUTOMOTIVE DYNAMICS, AERODYNAMICS ENDPLATES, FENCES Brian Paul Wiegand, B.M.E., P.E. 51 Fences are just barriers intended to direct airflow in desired directions. Endplates are just big fences commonly found at wing tips in an effort to impede trailing vortex formation; it could be said that such are an attempt to maintain a 2-dimensional flow.

52. AUTOMOTIVE DYNAMICS, AERODYNAMICS GROUND EFFECTS There is a paper by a Prof. Debojyoti Mitra , of the Sir Padampat Singhania University, which allows quantification of the relation between ground clearance and C d / C L as per the following charts; n ote an example vehicle with a 102 inch wheelbase undergoing a 1 inch reduction in ground clearance sees a C d reduction of 183 counts and a C L increase of 319 counts : Brian Paul Wiegand, B.M.E., P.E. 52

53. AUTOMOTIVE DYNAMICS, AERODYNAMICS GROUND EFFECTS Brian Paul Wiegand, B.M.E., P.E. 53 Shawn Buckley of the University of California at Berkeley was an early researcher of underside aerodynamics of vehicles. Buckley had been the designer of the first high-mounted wing used on an Indy racer, the Jerry Eisert “Bat Car” of 1966. By 1969 Buckley was investigating how, by shaping a car's underside so that the air speed there would increase, the pressure could be reduced generating a negative lift. His resulting test vehicles had a  venturi -shaped channel on the underside which was sealed by flexible side skirts from intrusion by “outside” air flow. Buckley would also investigate how flow separation on the undersurface channel was influenced by boundary layer suction and underbody surface divergence. Much of Buckley’s work would not only influence Lotus, but Chaparral (Jim Hall), March (Robin Herd), Brabham (Gordon Murray), and others. Later, as a mechanical engineering professor at MIT, Buckley would work with Lotus on the development of the Lotus 78.

54. The Lotus 79 was developed as an attempt to get more effective ground effect, now with the assistance of David Williams of the Cranfield Institute of Technology. Williams helped set up instrumented studies of the “ ground effect ” downforce in order to discover the exact nature of the phenomenon that Lotus was trying to tame. The main problem at the time was that changes in vehicle speed, attitude, and ground clearance would vary the pressure and cause the CP to move about affecting vehicle behavior; these were effects not observable in the more idealized environment of the wind tunnel. The vertical fluctuations and increased down-load required much stiffer springing, which in turn caused increased shock and vibration resulting in structural failure and driver discomfort. AUTOMOTIVE DYNAMICS, AERODYNAMICS GROUND EFFECTS Brian Paul Wiegand, B.M.E., P.E. 54

55. AUTOMOTIVE DYNAMICS, AERODYNAMICS GROUND EFFECTS Brian Paul Wiegand, B.M.E., P.E. 55 Part of the vertical fluctuation problem stemmed from the difficulty in maintaining an adequate “seal” with the side skirts due to ground surface and ride height variation. Movable skirts that could flex in response to the track contour were banned by the FIA in 1981.

56. AUTOMOTIVE DYNAMICS, AERODYNAMICS DIFFUSERS Brian Paul Wiegand, B.M.E., P.E. 56 Current Formula 1 regulations require that the under-body between the axle lines be absolutely flat, and that no side skirts be used to “seal off” the under-side to prevent a lateral in-flow. This prevents the extensive sculpting of the underside to generate negative pressure zones as had been the case previous. However, this gave rise to the development of what came to be known as a “ diffuser ” just aft of the rear axle line. Diffusers constitute a shaping of the aft end such as to act as an “extractor” sucking out the air from under the car and thereby increasing velocity and lowering the pressure, resulting in “ downforce ”.

57. addition of the vertical ‘fences’ to the diffuser help to optimize the efficiency by restoring smooth air flow. AUTOMOTIVE DYNAMICS, AERODYNAMICS DIFFUSERS Brian Paul Wiegand, B.M.E., P.E. 57 Toyota TF109. The role of the diffuser on a racing car is to speed the airflow up underneath the car, reducing its pressure, creating a greater difference in pressure between the upper and lower surfaces of the car. The diffuser increases in volume along its length, creating a void that has to be filled by the air passing under the body. The resulting venturi effect means that the flow is accelerated through the throat of the diffuser , creating the desired low pressure, after which the flow is gradually returned to the same velocity at which it started. The angle or slope of the diffuser is very important; the diffuser must have a gradual slope to avoid flow separation from its roof and sides. The

58. SPOILERS Brian Paul Wiegand, B.M.E., P.E. 58 AUTOMOTIVE DYNAMICS, AERODYNAMICS For road cars a front spoiler is often positioned under, or integrated into, the front bumper. In regular passenger vehicle use, the focus is often on directing the airflow into the engine bay for cooling purposes. When used in racing, the spoiler is designed to improve the drag coefficient of the body and to generate down force, at least at the front axle, by diverting air flow from going underneath the vehicle. For dedicated race cars, such as Formula 1 vehicles, front end aerodynamics depend on front wings and splitters in lieu of spoilers. Rear spoilers tend to be found on road cars, or racing versions thereof, and are generally situated on the aft end of the rear deck. The intent is to alter the aft airflow mainly for the purpose of reducing rear axle lift. However, sometimes the rear spoiler can also be used to reduce drag as well, depending on the specific aerodynamic situation.

59. AUTOMOTIVE DYNAMICS, AERODYNAMICS SPILTTERS Brian Paul Wiegand, B.M.E., P.E. 59 A splitter , like a front spoiler or air dam, is also located toward the front leading edge of a vehicle body. However, it is on, and even constitutes, the exact leading edge and is horizontal in orientation. The intent is once again to direct more air up and over (and possibly into the radiator) the vehicle as opposed to underneath. However, a splitter tends to be effective only at relatively high speeds, and since it is so low on the vehicle, and projecting forwards, it may pose a practical problem for road vehicles (curbs, bump stops, etc.)

60. AUTOMOTIVE DYNAMICS, AERODYNAMICS DAMS Brian Paul Wiegand, B.M.E., P.E. 60 The difference between an air flow dam and a front spoiler is mainly that a dam is larger and more vertical in orientation than a front spoiler. Otherwise they are pretty much the same in that their function is to divert airflow so as to minimize flow going under the vehicle, thereby reducing drag and front end lift. (Simanaitis, Dennis; “ Our Day in the Tunnel: Dam the Wind, Full Speed Ahead ”, Road & Track , August 1982, pp. 48-50.)

61. AUTOMOTIVE DYNAMICS, AERODYNAMICS THE HISTORICAL DIALECTIC Brian Paul Wiegand, B.M.E., P.E. 61 The history of automotive aerodynamics would have been of interest to Georg Wilhelm Friedrich Hegel (1770-1831) as it constitutes a perfect example of the historical dialectic wherein the spirit of man drives ever onward in an uneven progress toward knowledge. The struggle involved many steps forward, followed by a few steps back, as many individuals contributed to the progress, even those whose efforts would seem wasted, who turned left or right from the straight path and ran into dead ends. Some of the contributors were rational and educated, others were more driven by sheer imagination. Some were conservative and retiring, and others were flamboyant and self-promoting. Some acquired the recognition they deserve, others fell into obscurity. The following constitutes just a few of the physical milestones that mark the irregular progress of the science of automotive aerodynamics…

62. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 62 1899 La Jamais Content By Camille Jenatzy

63. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 63 1906 “The Rocket” LSR By Stanley Steamer Co. 1903 1907

64. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 64 1914 Alfa Romeo For Count Ricotti

65. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 65 1923 Tropfenwagen by Edmund Rumpler C d = 0.28

66. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 66 1922 North -Lucas

67. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 67 1922-1936 Paul Jaray Jaray's designs for Tatra, Fiat Balilla , Maybach and Audi C d = 0.29

68. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 68 1923 Automobilul Aerodinamic Perfect by Aurel Persu C d = 0.22

69. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 69 1926 Rear/Mid-Engine by Emile Claveau 1956

70. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 70 1932 Bergholt Streamline by Fred Bergholt

71. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 71 1934 Chrysler Airflow By Carl Breer , Fred Zeder , and Owen Skelton C d = 0.50 to 0.55

72. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 72 1934 Dymaxion by Buckminster Fuller 1933 *A Cd of 0.131 was obtained based on a simplified CAD model of the Dymaxion car which contains no internal engine bay or HVAC flow. Also absent are the suspension geometries and bodywork detail (hinges, louvers etc). Other simplifications include basic wheels and wheel arches. C d = 0.25*

73. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 73 1934 McQuay-Norris “Tear Drop Test Car # 9”

74. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 74 1934-36 Tatra T77, T77a, & T87 by Hans Ledwinka T87 C d = 0.36 T77a T77a C d = 0.33 Erich Übelacker (1899-1977)

75. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 75 1935 Streamliner by Robert Gougeon

76. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 76 1935 Rier - McCaslin

77. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 77 1936 Stout Scarab

78. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 78 1936 Dolphin by André Dubonnet André Dubonnet at the wheel of the Dolphin. At his side, his chief engineer Gustav Chedru .

79. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 79 1938 Lewis Aeromobile by Paul Lewis 1937

80. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 80 1938 Phantom Corsair by Rust Heinz

81. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 81 1938-39 Kamm-Wagen K3 by Dr. Wunibald Kamm C d = 0.37 K-3 K-1

82. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 82 1938 Xenia by André Dubonnet

83. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 83 1939 Schlörwagen by Karl Schlör C d = 0.19

84. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 84 1947 TASCO by Gordon Buehrig

85. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 85 (Actually there was a series of twin-boom cars with varying types of tail fin configurations and different engine sizes) 1948 TARF GILERA BY PIERRO TARUFFI

86. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 86 1953 BAT 5 Alfa Romeo by Bertone C d = 0.23

87. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 87 1954 BAT 7 Alfa Romeo by Bertone C d = 0.19

88. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 88 1955 BAT 9 Alfa Romeo by Bertone

89. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 89 1956 Morelli M1000 by Alberto Morelli

90. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 90 C d = 0.23 1960 Pinninfarina X by Alberto Morelli

91. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 91 1962 TVR Ultra Low Drag by Frank Costin 1970 Amigo 1959 Marcos

92. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 92 1976 Pinninfarina CNR/PF by Alberto Morelli C d =0.20

93. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 93 1983 Aero 2002 by GM C d = 0.14

94. HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 94 1996 General Motors EV-1 C d = 0.19 AUTOMOTIVE DYNAMICS, AERODYNAMICS 1990 “Impact”

95. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL EXAMPLES Brian Paul Wiegand, B.M.E., P.E. 95 2002 Volkswagen 1L C d = 0.159 2015 XL1

96. AUTOMOTIVE DYNAMICS, AERODYNAMICS HISTORICAL TRENDS Brian Paul Wiegand, B.M.E., P.E. 96 FIAT Production Cars

97. ALWAYS REMEMBER THAT IN AERODYNAMICS TWO PLUS TWO SOMETIMES EQUALS FIVE, OR THREE, OR…AERODYNAMIC BEHAVIOR IS COMPLEX AND REPLETE WITH SYNERGISTIC INTERACTIONS … SUGGESTED FOR FURTHER STUDY… * Streeter, Victor L.; Fluid Mechanics , McGraw-Hill Book Co., NY,NY, 1966. * Morelli , Albert; “A New Aerodynamic Approach to Advanced Automobile Basic Shapes” , SAE Paper 2000-01-0491, Warrendale, PA, 2000. * Pershing, Bernard (Ed.); The Aerodynamics of Sports & Competition Automobiles , Proceedings of the 1968 AIAA Symposium, Vol. 7, Western Periodicals, Hollywood, CA, 1969. * Gleason, Mark, and Gary Romberg, Glen Scharpf ; Automotive Aerodynamics , Progress in Technology Series, Vol. 16, SAE PT-78/16, Warrendale, PA, 1978. * Hucho , Wolf-Heinrich (Ed.); Aerodynamics of Road Vehicles , SAE R-177, Warrendale, PA, 1998. AUTOMOTIVE DYNAMICS, AERODYNAMICS CONCLUSION Brian Paul Wiegand, B.M.E., P.E. 97