Fahrzeug - und Windradaerodynamik

Dr.-Ing. A. Henze, Prof. Dr.-Ing. W. Schröder

Institute of Aerodynamics, RWTH Aachen University

Windradaerodynamik

High Performance Vehicles

Definition

• Sportscars:− permission for usual road traffic− High power− Suitable for every day life

• Race cars:− Only for race tracks− Competition− Prototypes− Modified standard cars

• Record cars

Different aerodynamic requirements• small drag• small lift for high velocities in curves• directional stability• driving in the slipstream • cooling of different aggregates• comfort for the driver

• Record cars− Highest velocity− Smallest fuel consumption− Largest cruising range− Special types of drive system (solar, …)

History

• „Blitzen“ Benz, 1911• 21.5 l, 200 hp, > 200 km/h• pointed cooler• slender body• pointed tail• driver + co-driver• isolated wheels

• drop shaped car, Benz, 1923• free wheels• smooth under body• l/d ~ 6.8 slender body

History

• streamlined shape• fully covered wheels• Daimler-Benz, 1937• Auto Union, 1937

History

• Mercedes 300 SLR, 1955• 24 hours of Le Mans• break flap• increase of cW from 0.44 to 1.09

http://www.uniquecarsandparts.com.au/images/heritage/mercedes_300SLR.jpg

Daimler-Benz AG

• small drag coefficient• reduced stability• limited curve velocity

Porsche Carrera 6 Langheck220 hp, 265 km/hcW = 0.33

CD Peugeot 66105 hp, 245 km/h

http://www.super-autos.net/c/cd-peugeot-66c01.jpg

History

http://www.histomobile.com/dvd_histomobile/usa/784/1965_Chaparral_2C.htm

Racing cars with wings to produce negative lift = downforce Chaparral 2C

http://www.metaphorsinmotion.com/posts/16-Jim-Hall-s-New-Chaparral-2-Chttp://www.histomobile.com/dvd_histomobile/usa/784/1965_Chaparral_2C.htm

http://www.auto-power-girl.com/high-resolution-wallpapers/porsche-celebrates-40th-anniversary-of-porsche-917/1973-porsche-917-30-sypder.jpg

Porsche 917/30, 1973. 1100 hp, 370 km/h, cW = 0.57

http://www.porsche.com/germany/sportandevents/motorsport/history/historicalgallery/?gtabindex=1&gitemindex=7

Porsche 935/78, 1978, 845 hp. 370 km/h

History

http://upload.wikimedia.org/wikipedia/commons/2/2d/Chaparral_2F_-

http://1.bp.blogspot.com/-0VPU0wW-ifs/TV7-z3hV7aI/AAAAAAAAGGM/88quDXQqg9Q/s1600/Chaparral2E.jpg

commons/2/2d/Chaparral_2F_-_Mike_Spence_-_1967.jpg

http://ashcom.homestead.com/RMH3257W.jpg

History

http://www.ddavid.com/formula1/images/lotus79b.jpghttp://www.ddavid.com/formula1/lotus79.htm

Ground effect

http://www.more.racing-history.de/Porsche_962_1988.jpeg

http://www.ddavid.com/formula1/images/lotus79b.jpghttp://www.ddavid.com/formula1/lotus79.htm

Rear wing with up to 9 elementsMaximum of 3 is allowed

History

Temporal development of the maximum lateral acceleration forlimousines, sports cars and racing cars

Record vehicles

• First vehicle > 100 km/h• Jenatzky, 1899• electric engine• l/d ~ 4• streamlined body• non optimized under carriage• non integrated driver

Golden Arrow, 1929372 km/hVertical tail wingUnderbody aerodynamics

Record vehicles

Railton Mobil Special, 1947634.4 km/h = 394.2 mph

http://other-roads.blogspot.com/2009/07/railton-napier-mobil-special-merdeka.html

http://www.motoringpicturelibrary.com/docs/hi-mpl340001197c.jpg

http://www.creativelydifferentblinds.com/BlindImages/1045.jpg

Golden Rod, 1965658.649 km/h409.3 mph

Record vehicles

Rocket driven „Blue Flame“

http://www.jetblack.co.nz/site/cms/lsr-history

Rocket driven „Blue Flame“1001,671 km/h, 1970

http://artschoolvets.com/blog/superblast/files/2009/03/the_blue_flame.jpg

http://www.jetblack.co.nz/site/cms/lsr-history

Thrust SSCSuper Sonic Car2 turbo jet engines1227.985 km/h

Transonic speeds

• Compressibility• Displacement of the force application point• Displacement of the force application point• Strong increase of the drag coefficient

Lift has been avoided for all speedsBut, during sound transmission the negative pressureunder the vehicle becomes positive.Subsonic: acceleration � underpressureSupersonic: oblique shock �overpressureCan lead to instability

Other record aims

• Optimized cW• reach a given vmax with a fixed type of drive system

− Diesel engine− Wankel engine− Turbo engine− Turbo diesel− Solar mobile

• minimize fuel consumption• maximize cruising range for a given amount of fuel

C111 Mercedes Benz, 1978cW = 0.18l/h = 4.94 (relatively large)Integrated wheels

• ARVW Aerodynamic Research Volkswagen, 1982• l/h = 5.93, cW = 0.15• Face area A = 0.73 m2

• 173 hp 360 km/h• 13.6l/100km Diesel

Other record aims

• “Sparmobil” 1982, Volkswagen• cW = 0.15, A =0.32• 1491.3 km with one l Diesel• average velocity: 16.9 km/h

• One-liter car• three wheels• l/h = 3.56/1.1 = 3.2• cW = 0.159, A = 1 m2

• 2 Persons• 237 km, 95 km/h, 0.99 l Diesel/100km

Other record aims

http://www.autoplenum.de/Bilder/P/p0014821/OPEL/OPEL-Speedster-2-0-Turbo--2003-2005-.jpg

http://www.netcarshow.com/opel/2002-eco_speedster_concept/1024x768/wallpaper_02.htm

• good agreement for drag• bad agreement for lift

• Diesel 1.3 l CDTL, 110 hp, Common-Rail injection• vmax = 250 km/h• 2.5 l/ 100km

Solar mobile

• Long laminar length• Spirit of Biel-Bienne, university in Switzerland• A= 1.1 m2

• cW = 0.105• solar surface 7.9 m2

• Flying dutchman• University Delft, Rotterdam• 3010 km• average velocity 96.8 km/h• vmax : 110 km/h

Sports Cars

Before the war• Large coolers• separated mud guards• not aerodynamically optimized

http://www.kompressor-club.de/fahrzeuge.htm

• Rudolf Caracciola, winner at mille miglia, 1931

Example: Mercedes-Benz 720 SSK, 1928A = 1.57 m2 , cW = 0.91, 180 km/h

• Rudolf Caracciola, winner at mille miglia, 1931• road race in north italy• weight saving: 125 kg

DKW based on F8, 1939Streamlined chassisOnly 3 exemplars

Sports Cars

• Porsche 356, 1948• open version• cW = 0.46, A = 1.41 m2

• Porsche 356 A, 1950• closed version• cW = 0.28, A = 1.68 m2

• cA = 0.26, relatively high,but not very important, becausethe max. speed was not so high(140 km/h)

Sports Cars

Front spoiler, rear spoiler also for production cars

Porsche 911 Turbo, 1983300 hp260 km/hcW = 0.4A = 1.87 m2

http://www.elferhelfer.com/Galerie/1983gal/magic/1983_turbo_magic.htm

http://www.conceptcarz.com/view/photo/5282,762/1987-Porsche-959_photo.aspx

Results from racing aerodynamicsare used also in sports production cars.• Porsche 959, 1987• Integrated rear spoiler• covered underbody• cW = 0.31• A = 1.92 m2

Sports Cars

Rear spoiler can be moved out automatically at higher speeds

• Ferrari F60 “Enzo”• Ferrari F60 “Enzo”• Adjustable front diffuser• movable rear spoiler�Balance can be controlled

at different velocities

Vehicle classes – 3 groups

1.) Free wheels• Formula 1• formula 3• formula 3000• Indy racing league (IRL)• Champ Cars (CART)

2.) touring cars• Deutsche Tourenwagen-Masters (DTM)• European touring car cup (ETTC)• …• Base model are production limousines or coupes• allowed modification depends on the racing class

3.) Long distance cars• 2 hours sprint race• 24 hours Le Mans• …• divided in subclasses

− Prototypes− Grand Touring

Vehicle classes

Formula 1 Mercedes McLaren, 2005Formula 1 Mercedes McLaren, 2005Dalara IRL, short oval, 2003

Dalara Indianapolislong oval

Dalara Formula 3, 2001

Vehicle classes

Abt Audi TTR, 2002, won DTMAudi R8, 2002, won Le Mans

Generic sports serial car for comparison• A = 2 m2

• cw = 0.33• cA = 0• m = 1400 kg• P = 500 hP

Vehicle classes

• generic car− P/m = 0.25 kW/kg− vmax = 320 km/h

• Formula 3 − similar power-mass ratio− less power � less vmax

• DTM: − higher power-mass ratio − worse drag � less vmax

• Long distance car• Long distance car− good power mass ratio− optimized for high average vel.

• IRL cars:− very good power mass ratio− highest velocity due to small drag

on ovals• Formula 1

− highest power mass ratio− slightly smaller vmax

Power vs. mass for typical race cars and for serialgeneric sports car

Vehicle classes

• generic car− typical values for good sports cars

• Formula 3− similar drag but higher down force− much better in curves and

during breaking• DTM

− much higher drag area then the generic car (generic car is thebase of DTM)

Down force x area vs. drag x area for typical race cars and for serial generic sports car

E: Efficiency = Lift/Drag

base of DTM)− Reglement

� prescribes rear wing geom.� variations are not allowed

− higher power mass ratio• IRL

− long oval: drag is similar toserial sports car, high lift, lateralaccel.: 3.5 g

− short oval: values are 2 timeshigher, accel.: 4.5 g

Vehicle classes

• Formula 1− drag between the IRL cars− higher efficiency− high flexibility− strong lateral accel: 3 g− longitudinal accel while

breaking: 4g• Long distance cars

− drag similar to Formula 1 cars− optimized for the high speed

Down force x area vs. drag x area for typical race cars and for serial generic sports car

E: Efficiency = Lift/Drag

− optimized for the high speedrace track in Le Mans

− less accelerations than inFormula 1

Vehicle classes

Longitudinal and lateral accelerations for typical race cars

Race tracks

• Monza: 75 % full load• Monte Carlo

− slowest curve, 40 km/h− wavy surface � no ground effect possible− higher down force with front and rear wing� higher drag

• Optimization of the values for drag and lift• Changes during the race are allowed between

small limits• generic race track (3 curves and 3 long lanes)• generic race track (3 curves and 3 long lanes)• variation of curve radii and length• longer straight lanes � lower lift• large curve radius � higher liftbut the drag should not be too large (box stop)

• „Handling“• ability to brake• ability to überholen• tyres• gasoline

Aerodynamics, performance, driving behaviour

Drag force is proportional to cw and front faceMinimization of both leads to conflicts• Reglement

− free wheels− minimal dimensions of components

Cooling systemWidth of tyres

Example:m = 1100 kg, mass ratio front/rear = 47/53m = 1100 kg, mass ratio front/rear = 47/53A = 2 m2,cAV = -0.45, cAH = -0.55

Assumption:Highest gearVery long straight road > 2000 m

Vmax as a function of the drag coefficient and the engine power

Low drag and high power � v maxAt low power: increase of drag by a factor of 3� reduction of vmax about 28.2 %

At high power: increase of drag by a factor of 3� Reduction of vmax about 30.2 %

More power for a cooler engine (in between limits)But, more cooling power � higher drag

higher velocity for 450 hP at cw = 0.5if increase of power is > 7 hP, at an increase of cw of0.01

Aerodynamics, performance, driving behaviour

Same example on HockenheimringLength of straight road: 1050 m

Lines of constant vmax are much steeperPower is more important

higher velocity for 450 hP at cw = 0.5if increase of power is > 6.2 hP, at an increase of cw of0.01

Aerodynamics, performance, driving behaviour

Fuel consumption as a functionof drag and power

�Volume of tank, number of refuel stops (if allowed)� mass of fuel influences the total mass of the car

Total time for a single lapSlope of lines of constant lap time dependson the power

The power in different classes is more or lessimportant

Aerodynamics, performance, driving behaviour

Lift force as a function of the velocityLift force as a function of the velocity

The aerodynamic forces are in the same orderof magnitude as the static forces� Influence on the stability in curves ar at side winds

Lateral acceleration for the generic car with standard race tyres as function of lift and drag(influences the curve velocity

is only a function of lift coefficient

Aerodynamics, performance, driving behaviour

Curve velocity as function lift and drag

Slight influence of the drag forceSmaller drag � higher velocity at the beginningof the curve � stronger braking� Larger curve radius � slightly higher velocity in the curve at the same acceleration

Lap time as function of lift and drag

Cw / cL = 0.3/0.5 has the same result as 0.9/2.0

Optimum ratio depends on the operating point

For higher drag more variation of lift is necessary for the same optimization of the laptime than for lower drag

Aerodynamics, performance, driving behaviour

Balance = ratio of forces on front and rear axes

Aerodynamic, static and total balance

BalAero = cAV / cA

Forces and balance of a typical racing carStatic balance 0.45c AV = -0.4, cAH = -0.6

Forces and balance of a typical serial car

Static balance = 0.55c AV = 0.05, c AH = 0.1

At 350 km/h: 0.578

c AV = -0.4, cAH = -0.6At 350 km/h: 0.424At higher velocity: tendence to understeering(only for good race drivers)

Aerodynamics, performance, driving behaviour

Typical situation during a race

1. Acceleration on the straight longroad, higher downforces, bothdistances decrease

2. Between accelerating and braking, abrupt load change, front axisdistance decreases, rear axis isunloaded, distance increases

Distance of front and rear axes to the ground• momentum during braking and acceleration • Brake � additional force onto the front axis• tendency to oversteering• ground effect can change • decreasing front axis distance � increasing balance• decreasing rear axis distance � decreasing balance

unloaded, distance increases3. Deceleration, smaller velocity,

smaller down forces, both distancesincrease

4. Between braking and accelerating, front axis is unloaded, rear axis isloaded

Strong changes of the balance at 2 and 4

Aerodynamics, performance, driving behaviour

• Stable balance is important• before the first road test• define target values for static and aerodynamic balance• not only lap time and efficiency• „Rebalancing“

Assumption: increase of down force on the front axis without a change of the drag coefficient• positive, since the efficiency is increased (point 1)• aerodynamic balance moves to the front axis � tendency to oversteer• more down force on the rear axis (increase of the angle of attack)• rear wing polar curve• increase of drag (point 2)• slightly worse lap time

Aerodynamics, performance, driving behaviour

HockenheimHigher efficiency = better lap timeincrease of lift = increase of drag�constant efficiency� Better lap time

Le Mans = fast curves, very long staright roadsIncrease of lift = increase of drag�Increase of lap time� lower drag coefficient

Generic race car: 600 hP, 1000 kg, 2 m2

typical for LeMans

Aerodynamics, performance, driving behaviour

• Data from windtunnel � polar curve• Change of front wing, rear wing• Additional aerodynamic parts• no change of balance• slope of the polar is not constant• highest efficiency E = 2.45 for cW = 0.59 and cL = 1.45, lap time = 213.5 secs• best lap time = 211 secs for cW = 0.46 and cL = 1.05, E = 2.28

Aerodynamics, performance, driving behaviour

Lift and drag for side slip angles ( < 10°)

Large and small end plates(stabilizing by moving the pressurepoint rearwards

Critical velocity: lift > weight< 45°front axis, v < 300 km/hj> 120°: rear axis is critical

Aerodynamics, performance, driving behaviour

• shorter distances than in usual traffic

• higher velocity for the follwing car due to the smaller v

∞

• drag reduction also for the leading car

Driving in lee

• drag reduction also for the leading car (increase of base pressure)• following car with lift on the front axis loses lift � oversteering• following car with down force on the front axis lose down force � understeering• leading car with down force on the rear axis loses down force � oversteering

Aerodynamics of constructional elements

Basical body• drop shaped body• classical sportscar, flat nose, blunted tail• serial cars

Influence of the nose shape• minimum for drag• decrease of lift

Higher nose if a front wing is included

Aerodynamics of constructional elements

Tail: very long droplet-like shapeKamm-tail: cut-off without remarkable increase of drag

Basical form is more or less defined by the reglement

Wings

Function: Creation of down force• horizontal projection• profile (including flaps)• winglets, end plates

Aspect ratio

Aerodynamics of constructional elements

Lift vs. Angle of attack for twoSymmetric and two asymmetric profiles

Typical configuration of a rear wing in DTM

Aerodynamics of constructional elements

Lift vs drag without (upper) and with (lower) flap

Pressure distribution on a curved wing with anAdditional flap

Induced dragthe free vortices consume kinetic energy

Gurney flap

Two additional counter-rotating vortices plus de-viation

Additional lift and drag

Efiiciency is usually worse tha for the wing, but can be positive for the balance of the total the balance of the total car

Ground effect

Principle of ground effect

• Maximum lift coefficient• separation in the diffusor• growing of boundary layers

Lift, drag and pitching moment Schematic of a „ground effect“ car

Diffuser

Components of liftas function of h1 / H

Lift as function of N / h1

Diffuser

Drag reduction as functionOf ride height and area ratio

Drag reduction as function of the dimensionless Length