fluids

Article Some Observations on Shape Factors Influencing Aerodynamic Lift on Passenger Cars

Jeff Howell 1,*, Steve Windsor 2 and Martin Passmore 1

1 Aeronautical and Automotive Engineering, Loughborough University, Loughborough LE11 3TU, UK; [email protected] 2 Aerodynamics Department, Jaguar Land Rover, Gaydon CV35 0RR, UK; [email protected] * Correspondence: [email protected]

Abstract: The car aerodynamicist developing passenger cars is primarily interested in reducing aerodynamic drag. Considerably less attention is paid to the lift characteristics except in the case of high-performance cars. Lift, however, can have an effect on both performance and stability, even at moderate speeds. In this paper, the basic shape features which affect lift and the lift distribution, as determined from the axle loads, are examined from wind tunnel tests on various small-scale bodies representing passenger cars. In most cases, the effects of yaw are also considered. The front-end shape is found to have very little effect on overall lift, although it can influence the lift distribution. The shape of the rear end of the car, however, is shown to be highly influential on the lift. The add-on components and other features can have a significant effect on the lift characteristics of real passenger cars and are briefly discussed. The increase in lift at yaw is, surprisingly, almost independent of shape, as shown for the simple bodies. This characteristic is less pronounced on real passenger cars but lift increase at yaw is shown to rise with vehicle length.

Keywords: car aerodynamics; lift; lift distribution; wind tunnel; shape effects; yaw angle





Citation: Howell, J.; Windsor, S.; Passmore, M. Some Observations on 1. Introduction Shape Factors Influencing The primary role of the aerodynamics development engineer working on passenger Aerodynamic Lift on Passenger Cars. car design is typically to reduce drag without compromising stability or refinement. All Fluids 2021 6 , , 44. https://doi.org/ aerodynamic characteristics are affected by the shape of the car and cannot be developed 10.3390/fluids6010044 in isolation. For example, the shape factors which influence drag will also influence the parameters which have an effect on stability, including lift. Received: 29 November 2020 Aerodynamic lift has a strong effect on car stability at high vehicle speeds. In particular, Accepted: 14 January 2021 Published: 18 January 2021 the lift coefficient and lift balance (the difference between front and rear axle lift coefficients) has a pronounced effect on high-speed cornering, lane change manoeuvrability, and straight

Publisher’s Note: MDPI stays neutral line stability [1]. Lift also has an influence on crosswind sensitivity and high-speed braking with regard to jurisdictional claims in performance. In addition, high lift characteristics are associated with increased drag, published maps and institutional affil- through the vortex drag component [2], and yawing moments [3], which affect drivability iations. in windy conditions. During the car development process, the targets for the lift coefficient are set accord- ing to the stability requirements of the vehicle. These targets usually take the form of a maximum permissible lift coefficient for each axle or combinations of them. The magnitude of the limiting lift coefficients is reduced as the performance of the car increases. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Passenger car shapes are effectively imposed by the design department (styling), and This article is an open access article the car aerodynamicist must manipulate the shape to achieve the desired aerodynamic distributed under the terms and performance within the constraints set by design. The shape evolves through the devel- conditions of the Creative Commons opment process but is essentially fixed before the build process of prototypes begins. The Attribution (CC BY) license (https:// aerodynamic development prior to style sign-off, for most manufacturers, consists of a creativecommons.org/licenses/by/ mix of wind tunnel tests and computational fluid dynamics (CFD) simulations of the 4.0/). evolving shape to monitor changes and suggest modifications. Most original equipment

Fluids 2021, 6, 44. https://doi.org/10.3390/fluids6010044 https://www.mdpi.com/journal/fluids Fluids 2021, 6, x FOR PEER REVIEW 2 of 17

Fluids 2021, 6, 44 2 of 16

evolving shape to monitor changes and suggest modifications. Most original equipment manufacturers (OEMs)(OEMs) useuse small-scalesmall-scale modelsmodels forfor the initial phase of wind tunnel testing, withwith scalesscales thatthat rangerange fromfrom 20%20% toto 40%,40%, whilewhile full-sizefull-size aerodynamicaerodynamic bucksbucks areare typicallytypically used for the laterlater phase,phase, beforebefore prototypesprototypes becomebecome available.available. Various studiesstudies havehave beenbeen conductedconducted onon thethe influenceinfluence ofof shapeshape onon thethe aerodynamicaerodynamic characteristics of passenger passenger cars. cars. Carr Carr [4], [4], in in an an early early extensive extensive study, study, developed developed a simpli- a sim- plifiedfied quarter-scale quarter-scale saloon saloon car car shape shape from from a rect a rectangularangular box box and and then then explored explored the the effect effect of ofmodifying modifying most most surfaces surfaces on onthe the car car model. model. As Aswell well as asthe the configuration configuration changes, changes, the the ef- effectsfects of of sharpening sharpening individual individual edges edges of of the the car car model model were were also investigated. Carr mademade thethe observationobservation thatthat all all the the changes changes in in lift lift were were identifiable identifiable from from the the changes changes in thein the camber- cam- line—theber-line—the line line passing passing through through the centroidthe centroid of each of each cross-section, cross-section, as shown as shown in Figure in Figure1.A positive1. A positive camber camber or incidence or incidence change change generated generated an increase an increase in lift while in lift negative while negative changes hadchanges the oppositehad the opposite effect. effect.

Figure 1. Camber and incidence for car shapes.

Another extensive study of shape changes was conducted by Gilhaus and Renn [[5],5], using a 3/8th3/8th scale scale model model of of a generic hatchback car, a vehiclevehicle typetype whichwhich diddid notnot existexist whenwhen Carr’sCarr’s investigationinvestigation waswas made.made. An assessmentassessment ofof squaringsquaring individualindividual edgesedges waswas also included. The results of this study figurefigure stronglystrongly inin thethe reviewreview ofof liftlift toto bebe foundfound inin both Hucho [[6]6] and SchultzSchultz [[7].7]. Before thethe timetime whenwhen CFDCFD waswas available,available, anan attemptattempt atat liftlift andand pitchingpitching momentmoment predictionprediction forfor carcar shapesshapes waswas mademade byby MorelliMorelli [[8],8], usingusing anan elegantelegant adaptationadaptation ofof slenderslender wingwing theory.theory. InIn thisthis model,model, thethe locallocal liftlift isis aa functionfunction ofof thethe curvaturecurvature of thethe camber-line,camber-line, span, and groundground clearance.clearance. Later, butbut beforebefore CFDCFD waswas aa reliablereliable technique,technique, aa predictionprediction method forfor liftlift waswas developeddeveloped by by Carr Carr et et al. al. [9 [9],], based based on on the the geometric geometric features features of of a simple a sim- carple model.car model. This paper doesdoes notnot attempt toto predictpredict thethe liftlift characteristicscharacteristics ofof passengerpassenger cars.cars. AsAs allall aerodynamic development engineers areare aware,aware, veryvery smallsmall changes,changes, especiallyespecially inin criticalcritical regions,regions, cancan havehave aa significantsignificant effecteffect onon lift,lift, andand thisthis isis exploitedexploited byby usingusing smallsmall add-onadd-on components to tunetune thethe liftlift characteristics.characteristics. The main aim of the paperpaper isis toto makemake somesome general observations on thethe effecteffect ofof large-scalelarge-scale shapeshape changeschanges onon lift.lift. TheseThese havehave beenbeen noted over many yearsyears ofof wind tunnel testingtesting ofof a wide range of small-scale simple bodiesbodies representingrepresenting carcar shapes.shapes. InIn manymany cases,cases, thesethese effectseffects havehave notnot beenbeen previouslypreviously reported.reported. 2. Experimental Details 2. Experimental Details The data presented in this paper were acquired over a considerable period of time. This isThe not, data therefore, presented a systematic in this paper investigation, were acquired although over individuala considerable sections period may of havetime. beenThis carriedis not, therefore, out in a systematic a systematic manner. investigation, A range of although different modelsindividual have sections been used may for have the variousbeen carried investigations, out in a systematic but most ofmanner. the studies A range involve of different very simple models models have with been extensive used for flatthe surfacesvarious investigations, to make configuration but most changes of the studies simpler involve and easier very to simple understand. models The with different exten- modelssive flat are surfaces described to make in the configuration section relevant changes to their simpler use. and easier to understand. The differentOver models the time are span described considered, in the differentsection relevant wind tunnels to their have use. been used. While most of theOver studies the weretime span performed considered, using different the MIRA wind MWT tunnels (Model have Wind been Tunnel), used. While this tunnel most evolvedof the studies with timewere and performed now no longerusing the exists. MIRA Details MWT of (Model the different Wind wind Tunnel), tunnels this willtunnel be keptevolved to a with minimum time and in this now paper, no longer but the exists. references Details will of providethe different further wind details tunnels if required. will be Fromkept to a a combination minimum in of this balance paper, accuracy but the refe andrences observed will repeatability, provide further the details lift coefficients, if required. in all cases, can be considered accurate to within ±0.005. Fluids 2021, 6, x FOR PEER REVIEW 3 of 17

Fluids 2021, 6, 44 3 of 16 From a combination of balance accuracy and observed repeatability, the lift coefficients, in all cases, can be considered accurate to within ±0.005. AllAll thethe teststests reportedreported herehere werewere conductedconducted usingusing aa fixedfixed groundground simulation.simulation. WhileWhile itit isis recognisedrecognised thatthat groundground simulationsimulation hashas anan effecteffect onon liftlift measurements,measurements, thethe impactimpact onon thethe changeschanges inin liftlift duedue toto thethe upperupper bodybody shapeshape parametersparameters assessedassessed herehere isis minimalminimal andand doesdoes notnot affectaffect thethe conclusionsconclusions drawndrawn fromfrom thethe experiments.experiments. CorrectionsCorrections forfor blockage, blockage, using using the the continuity continuity method, method, [10 [10],], have have been been used used where where the windthe wind tunnel tunnel is of theis of closed-jet the closed-jet type. For type. a model For a withmodel frontal with area, frontalA, testedarea, inA, atested closed-jet in a windclosed-jet tunnel wind with tunnel working with section working area, sectionAT, the area, blockage AT, the ratio, blockageB, is givenratio, B by:, is given by:

B = A/AT (1) B = A/AT (1) and the corrected lift coefficient, CLc, is given by: and the corrected lift coefficient, CLc, is given by: CLc = CLm (1 − B)2 (2) 2 CLc = CLm (1 − B) (2) where CLm is the measured lift coefficient. where CLm is the measured lift coefficient. 3. Shape Effects 3. Shape Effects 3.1.3.1. BasicBasic BlocksBlocks AA range of very very simple simple rectangular rectangular blocks blocks were were tested tested by by Howell Howell [11]. [11 The]. The basic basic ge- geometryometry is isshown shown in inFigure Figure 2, 2with, with the the overa overallll dimensions dimensions given given in inTable Table 1.1 The. The models models are aresmall small but but provide provide data data for for a arange range of of planform planform aspect aspect ratios, ratios, thicknesses, thicknesses, and lengths.lengths. TheyThey werewere testedtested in the T3 wind wind tunnel tunnel in in the the Department Department of of Aeronautical Aeronautical Engineering Engineering at atThe The City City University, University, London. London. The Thewind wind tunnel tunnel was a was closed-jet, a closed-jet, closed-return closed-return wind tunnel wind tunnelwith an with octagonal an octagonal working working section section 1.14 m 1.14 wide m by wide 0.93 by m 0.93 high. m high.It had It a had full aspan full spanfixed fixedground ground plane plane mounted mounted 0.2 m 0.2 above m above the the wind wind tunnel tunnel floor, floor, giving giving an an area aboveabove thethe groundground planeplane ofof 0.750.75 mm22.. TheThe modelsmodels werewere mountedmounted toto anan overheadoverhead balancebalance viavia aa singlesingle longlong streamlinedstreamlined main main strut strut and and a atail tail rod. rod. Th Thee pitch pitch angle angle could could be varied, be varied, although although only onlythe data the datafor a for zero-pitch a zero-pitch angle, angle, where where the the underside underside of of the the model model is is parallel withwith thethe ground,ground, isis presentedpresented here.here. NoNo taretare correctionscorrections werewere appliedapplied toto thethe liftlift measurements.measurements. TheThe modelsmodels werewere tested at a nominal nominal test test airspeed airspeed of of 30 30 m/s, m/s, giving giving a Reynolds a Reynolds number number of 7 of × 710×5 for105 thefor 0.325 the 0.325 m long m long model, model, and andthe turbulence the turbulence intensity intensity was was 0.5%. 0.5%.

L

H z0

W

FigureFigure 2.2. SimpleSimple rectangularrectangular blocks.blocks.

TableTable 1. 1.Dimensions Dimensions ofof simplesimple rectangularrectangular blocks. blocks.

BlockBlock L (m)L (m) W (m)W (m) H (m)H (m) 1 N 0.325 0.1 0.1 1 N 0.325 0.1 0.1 22 N N 0.325 0.325 0.2 0.2 0.1 0.1 33 N N 0.325 0.325 0.3 0.3 0.1 0.1 44 N N 0.325 0.325 0.2 0.2 0.05 0.05 55 N N 0.325 0.325 0.2 0.2 0.025 0.025 66 N N 0.225 0.225 0.2 0.2 0.1 0.1 77 N N 0.425 0.425 0.2 0.2 0.1 0.1 Fluids 2021, 6, 44 4 of 16

The leading-edge radius for all models was 0.25H, where H is the block height. The ground clearance, z0, was varied from 0.0025 to 0.05 m. The boundary layer displacement thickness at the model mid-length location in the empty tunnel was 0.003 m. The variation in the lift coefficient as a function of ground clearance for the range of blocks in Table1 is shown in Figure3a. The increase in lift at small ground clearances occurs because the boundary layer development on the underside inhibits the underbody flow, but in the limit of zero ground clearance, the lift will always be positive for these simple blocks as all the Fluids 2020, 5, x FOR PEERflow REVIEW must pass over the body. 4 of 16

0.6 0.2 CL 2N 2N 1N CLH/L 1N 0.4 3N 3N 4N 0.15 4N 5N 5N 0.2 6N 6N 7N 0.1 7N

z0 (m) 0 0 0.01 0.02 0.03 0.04 0.05 0.05 -0.2 z0/√(WL) 0 -0.4 0.00 0.10 0.20 0.30

-0.05 -0.6

118 -0.8 -0.1 119 (a) (b)

120Figure 3. LiftFigure coefficient 3. Lift coefficient for the range for ofthe rectangular range of rectangular blocks as a blocks function as a of function ground clearance;of ground (clearance;a) lift coefficient (a) lift based on 121frontal area,coefficient (b) lift coefficient based on adjusted frontal area, for plan (b) lift area. coefficient adjusted for plan area.

122 For all the blocks withFor the all same the blocks thickness with and the samelength thickness the lift coefficient and length,s are the very lift similar. coefficients The are very 123 data is affected slightlysimilar. by The model data length, are affected but significantly slightly by model by model length, heig butht significantly. Adjusting by the model lift height. Adjusting the lift coefficient by the factor, H/L, which in effect gives a lift coefficient based 124 coefficient by the factor, H/L, which in effect gives a lift coefficient based on plan area, as shown in on plan area, as shown in Figure3b, greatly reduces the spread of the data. The ground 125 Figure 3(b), greatly reduces the spread of the data. The ground clearance is also non-dimensionalised clearance is also non-dimensionalised by the square root of the plan area. 126 by the square root of the plan area. This might suggest that it would be beneficial to generate lift coefficients based on plan 127 This might suggestarea ratherthat it thanwould frontal be beneficial area, but thisto generate would be lift inappropriate coefficients forbased automotive on plan developmentarea 128 rather than frontal area,as lift but is notit would the component be inappropriate of primary for automotive interest. development as lift is not the 129 component of primary interest. 3.2. Front-End Shape 130 3.2. Front End Shape 3.2.1. Leading Edge Radius Newnham [12] investigated the effect of Reynolds number on the aerodynamic char- 131 3.2.1 Leading edge radiusacteristics of simple shapes with different leading-edge radii. The model used was a 132 Newnham [12] rectangularinvestigated block the effect as shown of Reynolds in Figure number4a. The on model the aerodynamic was 0.845 m long,characteristics 0.38 m wide, and 0.39 m high. The leading-edge radius was applied equally to the upper and side leading 133 of simple shapes with different leading edge radii. The model used was a rectangular block as shown edges only and varied from 0.01 to 0.1 m in 0.01 m steps. The ground clearance was 0.06 m. 134 in Figure 4(a). The model was 0.845m long, 0.38m wide and 0.39m high. The leading edge radius was The model was mounted to an underfloor balance via four slender struts, located just 135 applied equally to the upper and side leading edges only and varied from 0.01m to 0.1m in 0.01m inboard of the model side edges and spaced longitudinally by 0.60 m, which represents a 136 steps. The ground clearancenominal was “wheelbase”. 0.06m. The No model lift corrections was mounted were to applied an underfloor for the struts. balance via four 137 slender struts, located justThe inboard model was of the tested model in the side Loughborough edges and spaced University longitudinally wind tunnel, by 0.60m, which is of the 138 which represents a nominalclosed-jet, ‘wheelbase’. open-circuit No type. lift corrections The wind were tunnel applied working for sectionthe struts. is 1.32 m high by 1.92 m 139 The model waswide tested with in the corner Loughborough fillets, giving University a tunnel wind area oftunnel 2.49 mwhich2. The is maximumof the closed wind-jet, speed is 140 open-circuit type. The50 wind m/s andtunnel the working turbulence section intensity, is 1.32m 0.2%. high by 1.92m wide with corner fillets, 141 giving a tunnel area of 2.49mFigure2. The4b maximum shows the wind overall speed lift coefficientis 50m/s and and the the turbulence nominal intensity, front and 0.2%. rear axle lift 142 coefficients, CLF and CLR, respectively, as a function of the ratio of edge radius to model 6 height. This test was conducted at0.30 a Reynolds number (based on length) of Re = 2.9 × 10 . The overall lift coefficient varies only slightlyCL with small edge radii, CL but insignificantly as the edge radius exceeds 0.04 m.0.20 The front axle lift reduces sharply CLF and the rear axle lift CLR increases sharply at low edge radii,0.10 but both only vary slightly as the edge radius exceeds 0.04 m. r/H r 0.00 H 0.00 0.10 0.20 0.30 -0.10

-0.20

-0.30

-0.40 6 ReL = 2.9 x 10 143 -0.50 144 (a) (b)

145 Figure 4. (a) Model used by Newnham [12]; (b) Lift coefficients as a function of leading edge radius. Fluids 2021, 6, 44 5 of 16

Newnham [12] also carried out an investigation on the effect of bonnet leading-edge radius using the MIRA Reference Car in the estate car configuration in the full-scale wind tunnel. The bonnet leading edge was reduced from the standard 0.152-m radius to 0.025 m. Fluids 2021, 6, x FOR PEER REVIEWFor an edge radius greater than 0.05 m, there was a negligible effect of radius on overall5 lift,of 17 but front axle lift reduced slightly while rear axle lift increased. A small effect of Reynolds number was noted.

0.30 CL CL 0.20 CLF CLR 0.10 r/H r 0.00 H 0.00 0.10 0.20 0.30 -0.10

-0.20

-0.30

-0.40 6 ReL = 2.9 x 10 -0.50 .

(a) (b)

FigureFigure 4. 4.( (aa)) Model Model used used by by Newnham Newnham [ 12[12];]; ( b(b)) Lift Lift coefficients coefficients as as a a function function of of leading-edge leading-edge radius. radius.

Figure 4b shows the overall lift coefficient and the nominal front and rear axle lift 3.2.2. Front-End coefficients, CLF and CLR, respectively, as a function of the ratio of edge radius to model height.The This MIRA test Variable was conducted Geometry at Model a Reynolds (VGM) number was used (based to explore on length) the effect of Re of = front-end 2.9 × 106. shapeThe overall on the lift aerodynamic coefficient varies characteristics only slightly of a simplewith small car shape.edge radii, This but model insignificantly as tested for as this exercise is shown in Figure5. It is 1.003 m long, 0.413 m wide, and 0.344 m high, with the edge radius exceeds 0.04 m. The front axle lift reduces2 sharply and the rear axle lift aincreases wheelbase sharply of 0.667 at low m and edge a frontalradii, but area both of 0.114only vary m . Allslightly edges as had the aedge radius radius of 0.030 exceeds m, except for the rearmost trailing edges, which were sharp. The ground clearance for the body 0.04 m. was 0.05 m. The front-end shapes comprised a series of 1-box shapes, shown in blue in the Newnham [12] also carried out an investigation on the effect of bonnet leading-edge figure, where the windscreen angles ranged from vertical, 90◦, to 25◦. Note that the angles radius using the MIRA Reference Car in the estate car configuration in the full-scale wind are measured from horizontal, which is non-standard. Three notched front-ends were also tunnel. The bonnet leading edge was reduced from the standard 0.152-m radius to 0.025 tested, as shown in red in the figure. All the windscreen and bonnet angles are given in m. For an edge radius greater than 0.05 m, there was a negligible effect of radius on overall Table2. The model had tumblehome and was tested in two rear-end configurations, a lift, but front axle lift reduced slightly while rear axle lift increased. A small effect of Reyn- squareback and notchback, as shown by the grey dotted line in Figure5. For the notchback, Fluids 2021, 6, x FOR PEER REVIEW olds number was noted. 6 of 17 the backlight slope is 25◦ and the small boot extension gives an effective backlight angle of 21◦. Roughness strips could be added to the underfloor and the model was tested without 3.2.2. Front-End cooling airflow simulation. The MIRA Variable Geometry Model (VGM) was used to explore the effect of front- end shape on the aerodynamic characteristics of a simple car shape. This model as tested for this exercise is shown in Figure 5. It is 1.003 m long, 0.413 m wide, and 0.344 m high, with a wheelbase of 0.667 m and a frontal area of 0.114 m2. All edges had a radius of 0.030 m, except for the rearmost trailing edges, which were sharp. The ground clearance for the body was 0.05 m. The front-end shapes comprised a series of 1-box shapes, shown in blue in the figure, where the windscreen angles ranged from vertical, 90°, to 25°. Note that the angles are measured from horizontal, which is non-standard. Three notched front-ends were also tested, as shown in red in the figure. All the windscreen and bonnet angles are given in Table 2. The model had tumblehome and was tested in two rear-end configura- tions, a squareback and notchback, as shown by the grey dotted line in Figure 5. For the Figure 5. MIRA VG Model. Figurenotchback, 5. MIRA the backlight VG Model. slope is 25° and the small boot extension gives an effective back- light angle of 21°. Roughness strips could be added to the underfloor and the model was Tabletested without2. Windscreen/bonnet cooling airflow simulation.angles for MIRA VGM. The investigation was conducted in the MIRA MWT and for this test was in open-jet open-return Modelform. The Type wind tunnel nozzle was Windscreen 2.0 m wide by Angle° 1.0 m high. The nominalBonnet Angle° airspeed was 27 m/s, giving a Reynolds number, based on90 length, of 1.9 × 106. The turbu- - lence intensity was 1.2%. The wheels were mounted on small60 pads, which were flush with - the wind tunnel floor and connected to an underfloor balance. 1-box 45 - 35 - 25 - 30 19 Notched front 35 17 40 15

Figure 6a shows the overall lift coefficient at zero yaw for the range of different front- end shapes as defined by the windscreen angle. The data for the squareback shape are shown for a smooth and rough underfloor condition, while the notchback geometry was only tested with a rough underfloor. The 1-box shapes are shown by the solid symbols and the open symbols denote the notched front shapes.

0.40 1 C 90 SQB 90 NB C L L0 0.9 60 SQB 60 NB 0.35 45 SQB 45 NB 0.8 35 SQB 35 NB 0.30 0.7 25 SQB 25 NB 0.25 SQB Rough floor 1-box 0.6 SQB Smooth floor Notch front 0.20 0.5 NB Rough floor Rough underfloor

0.15 0.4 0.3 0.10 0.2 0.05 0.1 Windscreen Angle Yaw Angle 0.00 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 (a) (b) Figure 6. (a) Lift coefficient at 0° yaw as a function of windscreen angle for the range of front-end shapes; (b) Lift coefficient at yaw for the squareback and notchback shapes.

Figure 6b shows the overall lift coefficient as a function of yaw angle for the square- back and notchback configurations with a rough floor. Except for the cases with a vertical windscreen, the lift increase with yaw is essentially independent of the front-end shapes tested. Comparing the notchback shapes against those with a squareback, the lift increase is similar up to a yaw angle of 10° but is reduced noticeably at higher yaw angles. Figure 7a shows the front and rear axle lift coefficients as a function of windscreen angle. For the 1-box shapes, the front axle lift increases linearly with windscreen angle, while the rear axle lift coefficients reduce. For the notched front-end shapes, however, the front and rear axle lift coefficients remain almost constant. The variation in the 1-box lift coefficients is explained by the movement of the roof header. Suction peaks will occur at Fluids 2021, 6, 44 6 of 16

Table 2. Windscreen/bonnet angles for MIRA VGM.

Model Type Windscreen Angle◦ Bonnet Angle◦ 90 - 60 - 1-box 45 - 35 - 25 - 30 19 Notched front 35 17 40 15

The investigation was conducted in the MIRA MWT and for this test was in open-jet open-return form. The wind tunnel nozzle was 2.0 m wide by 1.0 m high. The nominal airspeed was 27 m/s, giving a Reynolds number, based on length, of 1.9 × 106. The turbulence intensity was 1.2%. The wheels were mounted on small pads, which were flush with the wind tunnel floor and connected to an underfloor balance. Figure6a shows the overall lift coefficient at zero yaw for the range of different front- end shapes as defined by the windscreen angle. The data for the squareback shape are shown for a smooth and rough underfloor condition, while the notchback geometry was only tested with a rough underfloor. The 1-box shapes are shown by the solid symbols and the open symbols denote the notched front shapes. Fluids 2020, 5, x FOR PEER REVIEW 6 of 16

1 0.40 CL 90 SQB 90 NB CL0 0.9 60 SQB 60 NB 0.35 45 SQB 45 NB 0.8 35 SQB 35 NB 0.30 0.7 25 SQB 25 NB

0.25 SQB Rough floor 1-box 0.6 SQB Smooth floor Notch front 0.20 0.5 NB Rough floor Rough underfloor 0.4 0.15 0.3 0.10 0.2 0.05 0.1 Windscreen Angle Yaw Angle 0.00 0 183 10 20 30 40 50 60 70 80 90 0 5 10 15 20 184 (a) (b)

Figure185 6. (a) LiftFigure coefficient 6. (a) at 0 Lift◦ yaw coefficient as a function at 0° of windscreenyaw as a function angle for of the windscreen range of front-end angleshapes; for the ( brange) Lift coefficientof front at186 yaw for theend squareback shapes. (b) and Lift notchback coefficient shapes. at yaw for the squareback and notchback shapes.

187 Figure 6(b) showsFigure the6 overallb shows lift the coefficient overall lift as coefficient a function as of a functionyaw angle of yawfor the angle squareback for the squareback and 188 notchback configurationsand notchback with a configurations rough floor. Except with afor rough the cases floor. with Except a vertical for the windscreen cases with the a lift vertical 189 increase with yawwindscreen, is essentially the independent lift increase withof the yaw front is end essentially shapes tested. independent Comparing of the the front-end notchback shapes 190 shapes against tested.those with Comparing a squareback, the notchback the lift increase shapes againstis similar those up withto a yaw a squareback, angle of 10°, the liftbut increaseis ◦ 191 reduced noticeablyis similar at higher up toyaw a yaw angles. angle of 10 but is reduced noticeably at higher yaw angles. 192 Figure 7(a) showsFigure the 7fronta shows and therearfront axle lift and coefficient rear axles lift as coefficientsa function of as windscreen a function angle. of windscreen For 193 the 1-box shapesangle. the front For theaxle 1-box lift increases shapes, linearly the front with axle windscreen lift increases angle, linearly while with the windscreenrear axle lift angle, 194 coefficients reduce.while For the the rear notched axle lift front coefficients end shapes reduce., however, For the the notched front and front-end rear axle shapes, lift coefficients however, the 195 remain almost constant.front and The rear variation axle lift coefficientsin the 1-box remain lift coefficients almost constant. is explained The by variation the movement in the 1-box of lift 196 the roof header.coefficients Suction peaks is explained will occur by atthe the movementextreme front of theend roof of the header. car and Suction on the peaks roof header will occur. at the extreme front-end of the car and on the roof header. As the windscreen angle reduces, 197 As the windscreen angle reduces the front edge suction will increase and the suction at the roof the front-edge suction will increase and the suction at the roof header will decrease. For 198 header will decrease. For the front header forward of the front axle the lift at the front axle will be the front header forward of the front axle, the lift at the front axle will be enhanced. This 199 enhanced. This combination will increase front axle lift and reduce lift at the rear axle. In the case of combination will increase front axle lift and reduce lift at the rear axle. In the case of the 200 the notched front ends, a positive pressure occurs at the base of the windscreen, which tends to notched front-ends, a positive pressure occurs at the base of the windscreen, which tends 201 increase with increasingto increase windscreen with increasing angle. windscreen angle.

0.90 0.40 90 CLF 90 CLR 60 CLF 60 CLR CLF, CLR CLF0, CLR0 45 CLF 45 CLR 0.30 0.70 35 CLF 35 CLR 25 CLF 25 CLR

0.20 0.50 SQB Rough underfloor 0.10 0.30 Windscreen Angle 0.00 10 20 30 40 50 60 70 80 90 0.10 -0.10 SQB Rough floor CLF 0 5 10 15 20 -0.10 -0.20 SQB Smooth floor CLR Yaw Angle NB Rough floor Notch front 202 -0.30 -0.30 203 (a) (b) 204 Figure 7. (a) Front and rear axle lift coefficient at 0° yaw as a function of windscreen angle for 205 the range of front end shapes. (b) Front and rear axle lift coefficients as a function of yaw angle for 206 the squareback shape with a rough underfloor.

207 Figure 7(b) shows the front and rear axle lift coefficients as a function of yaw angle for the 208 squareback configuration with a rough floor. The front axle lift is shown by the open symbols and a 209 dashed line, while the rear axle lifts are shown by the solid symbols and lines. As with the overall lift 210 coefficients shown in Figure 6(b), the variation of axle lift with yaw is similar for all windscreen 211 angles, except for the vertical front end case. For the squareback model shown, the lift increase with 212 yaw is slightly greater at the front axle than it is at the rear. Fluids 2020, 5, x FOR PEER REVIEW 6 of 16

1 0.40 CL 90 SQB 90 NB CL0 0.9 60 SQB 60 NB 0.35 45 SQB 45 NB 0.8 35 SQB 35 NB 0.30 0.7 25 SQB 25 NB

0.25 SQB Rough floor 1-box 0.6 SQB Smooth floor Notch front 0.20 0.5 NB Rough floor Rough underfloor 0.4 0.15 0.3 0.10 0.2 0.05 0.1 Windscreen Angle Yaw Angle 0.00 0 183 10 20 30 40 50 60 70 80 90 0 5 10 15 20 184 (a) (b) 185 Figure 6. (a) Lift coefficient at 0° yaw as a function of windscreen angle for the range of front 186 end shapes. (b) Lift coefficient at yaw for the squareback and notchback shapes.

187 Figure 6(b) shows the overall lift coefficient as a function of yaw angle for the squareback and 188 notchback configurations with a rough floor. Except for the cases with a vertical windscreen the lift 189 increase with yaw is essentially independent of the front end shapes tested. Comparing the notchback 190 shapes against those with a squareback, the lift increase is similar up to a yaw angle of 10°, but is 191 reduced noticeably at higher yaw angles. 192 Figure 7(a) shows the front and rear axle lift coefficients as a function of windscreen angle. For 193 the 1-box shapes the front axle lift increases linearly with windscreen angle, while the rear axle lift 194 coefficients reduce. For the notched front end shapes, however, the front and rear axle lift coefficients 195 remain almost constant. The variation in the 1-box lift coefficients is explained by the movement of 196 the roof header. Suction peaks will occur at the extreme front end of the car and on the roof header. 197 As the windscreen angle reduces the front edge suction will increase and the suction at the roof 198 header will decrease. For the front header forward of the front axle the lift at the front axle will be Fluids 2021199, 6, 44 enhanced. This combination will increase front axle lift and reduce lift at the rear axle. In the case of 7 of 16 200 the notched front ends, a positive pressure occurs at the base of the windscreen, which tends to 201 increase with increasing windscreen angle.

0.90 0.40 90 CLF 90 CLR 60 CLF 60 CLR CLF, CLR CLF0, CLR0 45 CLF 45 CLR 0.30 0.70 35 CLF 35 CLR 25 CLF 25 CLR

0.20 0.50 SQB Rough underfloor 0.10 0.30 Windscreen Angle 0.00 10 20 30 40 50 60 70 80 90 0.10 -0.10 SQB Rough floor CLF 0 5 10 15 20 -0.10 -0.20 SQB Smooth floor CLR Yaw Angle NB Rough floor Notch front 202 -0.30 -0.30 203 (a) (b)

Figure204 7. (a) FrontFigure and rear 7. (a) axle Front lift coefficient and rear at axle 0◦ yaw lift ascoefficient a function at of 0° windscreen yaw as a angle function for the of range windscreen of front-end angle shapes. for (b)205 Front andthe rear range axle of lift front coefficients end shapes. as a function (b) Front of yaw and angle rear foraxle the lift squareback coefficients shape as witha function a rough of underfloor. yaw angle for 206 the squareback shape with a rough underfloor. Figure7b shows the front and rear axle lift coefficients as a function of yaw angle for 207 Figure 7(b)the shows squareback the front configuration and rear axle with lift a coefficient rough floor.s as The a function front axle of lift yaw is shown angle for by the open 208 squareback configurationsymbols and with a dasheda rough line,floor. while The front the rear axle axle lift is lifts shown are shown by the byopen the symbols solid symbols and a and 209 dashed line, whilelines. the As rear with axle the lifts overall are shown lift coefficients by the solid shown symbols in Figure and lines.6b, the As variation with the overall of axle lift with 210 coefficients shownyaw in is Figure similar 6(b), for all the windscreen variation of angles, axle lift except with for yaw the is vertical similar for front-end all windscreen case. For the 211 angles, except forsquareback the vertical model front shown, end case. the For lift increasethe squareback with yaw model is slightly shown, greater the lift at increase the front wi axleth than 212 yaw is slightly greaterit is at theat the rear. front axle than it is at the rear. 3.3. Rear-End Shape Fluids 2021, 6, x FOR PEER REVIEW 3.3.1. Roof Slope/Backlight Angle 8 of 17

The Windsor Body, shown in Figure8a, has been used for many years to investigate many fundamental aspects of car aerodynamics. The model represents an approximately quarter-scalevortices, both lower-mediumof which increase hatchback. with slant It hasangl thee. At same the overallcritical dimensionsangle, the edge as the vortices well- knowncannot maintain Ahmed Body, an attached with length flow at 1.044 the slant m, width trailing 0.389 edge m, and and the height, separation 0.289 m,for givingthe base a frontalflow moves area offrom 0.112 the m slant2. For trailing the purposes edge to ofthe generating slant leading front edge. and In rear this lift post-critical coefficients, state, the wheelbasethe base pressure is 0.668 acts m and on the mid-wheelbase slant surface isand at halfso the the lift model does not length. quite All revert theleading to the square- edges areback well value. rounded Almost with all athe radius variation of 0.05 in m,lift except occurs the at the roof rear leading axle edge,because which of the has proximity a radius of 0.20the slant m. All leading the remaining edge to the edges rear are axle sharp. position.

0.8

CL CL CLF 0.6 CLR

0.4

0.2

0.0 0 5 10 15 20 25 30 35 40

Slant Angle O -0.2 (a) (b)

Figure 8. (a) Windsor Body;Body; ((b)) VariationVariation inin liftlift coefficientscoefficients asas aa functionfunction ofof rearrear slantslant angle.angle.

ItThe has effect been of tested yaw angle with on a range lift for of the rear range slant of angles, slant angles representing is shown roof in Figure slope 9a. at lowFor anglesall the subcritical and backlight slant angle angles, at higher from 0° angles. to 30°, Slant the increase angles range in lift from coefficient 0◦, for with the squareback yaw angle shape,is very to similar. 40◦. The For slant the length immediate is kept post-critical constant at 0.222slant mangles, to give however, a fixed aspect the initial ratio oflift 1.75 in- forcrease all thewith slant yaw surfaces. is much Thelarger. wind At tunnelhigher usedyaw forangles, the teststhe trend reported with here yaw was reverts the MIRAto the MWTtrends in at open-jetlower slant configuration, angles. This as suggests described that in the Section flow on3.2.2 the. This backlight and subsequent at these high testing slant angles is switching from a separated to an attached flow condition, as the yaw angle in- creases. At a 40° slant angle, the lift increase with yaw is similar to that for the sub-critical slant angles, which suggests that the flow always remains separated at yaw.

0.8 0 20 32.5 0.8 5 25 35 CL ∆CL15 10 27.5 40 CL 15 30 CLF 0.6 0.6 CLR

0.4 0.4

0.2 0.2

0.0 0.0 0 5 10 15 20 0 5 10 15 20 25 30 35 40

Yaw Angle O Slant Angle O -0.2 -0.2 (a) (b) Figure 9. Lift coefficient for the Windsor Body. (a) Lift as a function of yaw angle for all slant angles; (b) Increase in lift coefficient at 15° yaw angle as a function of slant angle.

This data are summarized in Figure 9b, which shows the increase in lift coefficient between yaw angles of 0° and 15° as a function of slant angle for overall lift and the front and rear axle components. There is a small increase in the lift rise with yaw for the sub- critical slant angles, but the plot shows the large jump in the lift increase with yaw for the slant angles which are just above the critical angle. The rear axle lift rise follows a similar pattern, while the front axle lift increase remains almost constant.

Fluids 2021, 6, 44 8 of 16

of the Windsor Body was carried out at a nominal airspeed of 27 m/s, with a Reynolds number, based on length, of 2.0 × 106. The ground clearance was 0.050 m. The model is connected to the underfloor balance via thin plates, flush with the model sides, in the nominal wheel locations. No lift corrections were applied for the model supports. The effect of slant angle on the overall lift coefficient and the front and rear axle lift coefficients at 0◦ yaw angle are shown in Figure8b. Lift increases linearly with slant angle from 0◦ to 27.5◦, but at 30◦, there is a dramatic loss of lift. For slant angles up to the critical angle, the lift is generated at the slant leading edge and on the slant sides beneath the edge vortices, both of which increase with slant angle. At the critical angle, the edge vortices cannot maintain an attached flow at the slant trailing edge and the separation for the base flow moves from the slant trailing edge to the slant leading edge. In this post-critical state, the base pressure acts on the slant surface and so the lift does not quite revert to the squareback value. Almost all the variation in lift occurs at the rear axle because of the proximity of the slant leading edge to the rear axle position. The effect of yaw angle on lift for the range of slant angles is shown in Figure9a. For all the subcritical slant angles, from 0◦ to 30◦, the increase in lift coefficient with yaw angle is very similar. For the immediate post-critical slant angles, however, the initial lift increase with yaw is much larger. At higher yaw angles, the trend with yaw reverts to the trends at lower slant angles. This suggests that the flow on the backlight at these high slant angles is switching from a separated to an attached flow condition, as the yaw angle increases. At a 40◦ slant angle, the lift increase with yaw is similar to that for the sub-critical slant angles, which suggests that the flow always remains separated at yaw. Fluids 2020, 5, x FOR PEER REVIEW 8 of 16

0.8 0 20 32.5 0.8 5 25 35 CL ∆CL15 10 27.5 40 CL 15 30 CLF 0.6 0.6 CLR

0.4 0.4

0.2 0.2

0.0 0.0 0 5 10 15 20 0 5 10 15 20 25 30 35 40

Yaw Angle O Slant Angle O 250 -0.2 -0.2 251 (a) (b)

252Figure 9. Lift coefficientFigure 9. Lift for coefficient the Windsor for Body.the Windsor (a) Lift Body. as a function (a) Lift as of a yaw function angle of for yaw all angle slant angles;for all slant (b) Increase angles. in lift ◦ 253coefficient at 15(b) yawIncrease angle in as lift a coefficient function of at slant 15° angle.yaw angle as a function of slant angle.

254 This data is summarizedThis data in areFigure summarized 9(b), which in shows Figure the9b, increase which shows in lift thecoefficient increase between in lift coefficient yaw between yaw angles of 0◦ and 15◦ as a function of slant angle for overall lift and the 255 angles of 0° and 15° as a function of slant angle for overall lift and the front and rear axle components. front and rear axle components. There is a small increase in the lift rise with yaw for the 256 There is a small increase in the lift rise with yaw for the sub-critical slant angles, but the plot shows sub-critical slant angles, but the plot shows the large jump in the lift increase with yaw 257 the large jump in the lift increase with yaw for the slant angles which are just above the critical angle. for the slant angles which are just above the critical angle. The rear axle lift rise follows a 258 The rear axle liftsimilar rise follows pattern, a while similar the pattern, front axle while lift increase the front remains axle lift almost increase constant. remains almost 259 constant. 3.3.2. Slant Aspect Ratio 260 3.3.2 Slant aspect ratioThe effect of the slant surface aspect ratio on the lift and drag characteristics of the 261 The effect ofWindsor the slant Bodysurface has aspect alsobeen ratio investigatedon the lift and by drag Howell characteristics and Le Good of [the2]. Windsor The aspect Body ratio, AR, 262 has also been investof theigated slant by surface Howell is and defined Le Good, as: [2]. The aspect ratio, AR, of the slant surface is AR = W2/A (3) 263 defined as: S where AS is the area and W is the span or, in this case, the width of the slant surface, 2 264 as shown in Figure 10a. ForAR the = rectangularW /AS slant surface for this body, the aspect(3) ratio

265 where AS is the areabecomes and W the is ratio, the span,W/L Sor, where in thisL Scase,is the the slant width length. of the slant surface, as shown in 266 Figure 10(a). For the rectangular slant surface for this body the aspect ratio becomes the ratio, W/LS, 267 where LS is the slant length. 268 The effect of slant aspect ratio on the lift coefficient increase with slant angle is shown in Figure 269 10(b). Aspect ratios from 1.25 to 1.75 were tested in the MIRA MWT when it was a closed-jet wind 270 tunnel with a working section, 2.0m wide by 1.0m high. Also shown is the results of a test by Pavia, 271 [13], who tested a short chamfer on the roof trailing edge of a Windsor Body in the Loughborough 272 University Wind Tunnel. Details of this wind tunnel have been given in section 3.2.1. In all cases the 273 ground clearance was 0.050m and the data has been corrected for blockage. The data is presented as 274 the increase in lift from the squareback configuration to account for wind tunnel and model mounting 275 differences. 276 0.60

ΔCL AR 1.25 0.50 AR 1.75 AR 2.25 φ 0.40 AR 8.64

0.30

0.20 W

0.10

Slant Angle 0.00 0 5 10 15 20 25 30 35 40

277 (a) (b) Fluids 2021, 6, x FOR PEER REVIEW 9 of 17

3.3.2. Slant Aspect Ratio The effect of the slant surface aspect ratio on the lift and drag characteristics of the Windsor Body has also been investigated by Howell and Le Good [2]. The aspect ratio, AR, of the slant surface is defined as:

AR = W2/AS (3)

where AS is the area and W is the span or, in this case, the width of the slant surface, as shown in Figure 10a. For the rectangular slant surface for this body, the aspect ratio be- comes the ratio, W/LS, where LS is the slant length. The effect of slant aspect ratio on the lift coefficient increase with slant angle is shown in Figure 10b. Aspect ratios from 1.25 to 1.75 were tested in the MIRA MWT when it was a closed-jet wind tunnel with a working section 2.0 m wide by 1.0 m high. Also shown are the results of a test by Pavia [13], who tested a short chamfer on the roof trailing edge of a Windsor Body in the Loughborough University Wind Tunnel. Details of this wind tun- nel have been given in Section 3.2.1. In all cases, the ground clearance was 0.050 m and the data have been corrected for blockage. The data are presented as the increase in lift Fluids 2021, 6, 44 9 of 16 from the squareback configuration to account for wind tunnel and model mounting dif- ferences.

0.60

ΔCL AR 1.25 0.50 AR 1.75 AR 2.25 φ 0.40 AR 8.64

0.30

0.20 W

0.10

Slant Angle 0.00 0 5 10 15 20 25 30 35 40 (a) (b)

FigureFigure 10.10. ((aa)) Windsor Windsor Body Body showing showing slant slant surface; surface; (b) ( Variationb) Variation in lift in coefficients lift coefficients with slantwith angleslant angle for different for different aspect ratiosaspect. ratios. The effect of slant aspect ratio on the lift coefficient increase with slant angle is shown in FigureFigure 10 b.10b Aspect shows ratios that lift from increases 1.25 to 1.75approximately were tested linearly in the MIRA with MWTslant angle when for it wasa sig- a closed-jetnificant range wind of tunnel slant angles with a and working the slope section reduces 2.0 m as wide aspect by ratio 1.0 mincreases. high. Also The shown two mod- are theels with results the of lowest a test byaspect Pavia ratios [13], (i.e., who the tested long aest short slant chamfer lengths) on have the roof near trailing identical edge critical of a Windsorangles where Body the in theflow Loughborough on the backlight University is effectively Wind Tunnel.stalled. This Details angle of thisreduces wind as tunnel slant havelength been is reduced. given in Section 3.2.1. In all cases, the ground clearance was 0.050 m and the data have been corrected for blockage. The data are presented as the increase in lift from the3.3.3. squareback Edge Rounding configuration to account for wind tunnel and model mounting differences. FigureThe Windsor 10b shows Body thatwas liftalso increases tested in an approximately alternative form, linearly known with as slantthe Tumblehome angle for a significantmodel, which range is shown of slant in angles Figure and 11a. the The slope model reduces has exactly as aspect the ratiosame increases. side view, The but two the modelsupper body with surface the lowest is inclined aspect inwards, ratios (i.e., a feature the longest called slant tumblehome, lengths) have at an near angle identical of 15°. critical angles where the flow on the backlight is effectively stalled. This angle reduces as

slant length is reduced.

3.3.3. Edge Rounding The Windsor Body was also tested in an alternative form, known as the Tumblehome Fluids 2021, 6, x FOR PEER REVIEW model, which is shown in Figure 11a. The model has exactly the same side view, but10 of the 17

upper body surface is inclined inwards, a feature called tumblehome, at an angle of 15◦.

0.6

CL Windsor body 0.5 Tumblehome model

0.4

0.3

0.2

0.1

Slant Angle 0 Standard Tumblehome 0 102030405060 -0.1 (a) (b)

Figure 11. ((aa)) Windsor Windsor Body and and Tumblehome model showing cross-section; cross-section; ( (bb)) Variation Variation in lift coefficients coefficients with slant angle for standard Winsor Body and the Tumblehome model.model.

TheThe split split line line between between upper upper and and lower lower side side surfaces surfaces is shown is shown by bythe thegrey grey line linein the in sidethe sideview view drawing drawing of Figure of Figure 11a. All11a. the All lead theing-edge leading-edge radii were radii the were same the as same on the as stand- on the ardstandard model, model, but the but longitudinal the longitudinal edges, edges, as well as as well the asside the and side leading and leading edges edgesof the ofslant the surface,slant surface, have a have radius a radius of 0.025 of 0.025m, instead m, instead of being of being sharp. sharp. This Thismodel model was wastested tested in the in MIRAthe MIRA MWT MWT in closed-jet in closed-jet configuration configuration and andblockage blockage corrections corrections have have been been applied. applied. A comparison of the variation in lift coefficient with slant angle for the standard Windsor Body and Tumblehome model is shown in Figure 11b. The slope for the Tum- blehome model is significantly less than that for the standard body, but the maximum lift coefficient occurs at a considerably higher slant angle. The reduction in lift that occurs at slant angles higher than that for maximum lift is less precipitous and of lower magnitude than for the standard body. As with the Windsor Body the front axle lift is approximately constant for all slant angles and almost all of the lift variation with slant angle occurs at the rear axle. Figure 12 shows the increase in lift coefficient at yaw as a function of slant angle for the Tumblehome model. The increase in lift, ΔCL, is the change in lift between yaw angles of 0° and 15°. The increase in lift is fairly constant for slant angles from 5° to 35°. The slight reduction in lift rise with yaw as the slant angle increases is consistent with the behaviour noted in Figure 6b comparing squareback and fastback variants of the VGM model, but it differs from that shown for the sharp-edged Windsor Body. As shown by the Windsor Body, the lift rise with yaw is increased for post-critical slant angles. While for the Wind- sor Body, this increase is over a narrow range of slant angles, with the Tumblehome model, the lift increase with yaw rises to a peak when the slant angle is between 50° and 60°, the limit of the available data, but persists over a wider range of slant angles.

0.4 0.6 R = 0 r = 0

ΔCL R = 0.10m r = 0 ∆CL15 CL R = 0.20m r = 0 CLF 0.5 0.3 CLR R = 0.20m r = 0.05m R = 0.20m r = 0.10m 0.4 0.2

0.3

0.1 0.2

Slant Angle 0.0 0.1 0 102030405060 Slant Angle 0 -0.1 0 5 10 15 20 25 30 35 40 (a) (b) Figure 12. (a) Lift coefficient increase for the Tumblehome model at 15° yaw; (b) Effect of slant edge radii on lift of Windsor Body at 0° yaw. Fluids 2021, 6, x FOR PEER REVIEW 10 of 17

0.6

CL Windsor body 0.5 Tumblehome model

0.4

0.3

0.2

0.1

Slant Angle 0 Standard Tumblehome 0 102030405060 -0.1 (a) (b) Figure 11. (a) Windsor Body and Tumblehome model showing cross-section; (b) Variation in lift coefficients with slant angle for standard Winsor Body and the Tumblehome model.

The split line between upper and lower side surfaces is shown by the grey line in the side view drawing of Figure 11a. All the leading-edge radii were the same as on the stand- ard model, but the longitudinal edges, as well as the side and leading edges of the slant Fluids 2021, 6, 44 10 of 16 surface, have a radius of 0.025 m, instead of being sharp. This model was tested in the MIRA MWT in closed-jet configuration and blockage corrections have been applied. A comparison of the variation in lift coefficient with slant angle for the standard WindsorA comparison Body and ofTumblehome the variation model in lift coefficientis shown within Figure slant 11b. angle The for slope the standard for the Wind-Tum- blehomesor Body model and Tumblehome is significantly model less is than shown that in for Figure the standard 11b. The body, slope but for the the maximum Tumblehome lift coefficientmodel is significantly occurs at a lessconsiderably than that forhigher the standardslant angle. body, The but reduction the maximum in lift that lift coefficient occurs at slantoccurs angles at a considerably higher than higherthat for slant maximum angle. lift The is reduction less precipitous in lift that and occurs of lower at slant magnitude angles thanhigher for than the standard that for maximum body. As liftwith is the less Windsor precipitous Body and the of front lower axle magnitude lift is approximately than for the constantstandard for body. all Asslant with angles the Windsorand almost Body all theof the front lift axle variation lift is approximately with slant angle constant occurs for at theall slantrear axle. angles and almost all of the lift variation with slant angle occurs at the rear axle. Figure 12 shows the increase in lift coefficientcoefficient at yaw as a function of slant angle for the Tumblehome model.model. TheThe increaseincrease inin lift,lift, ∆ΔCCLL, is the change in lift between yaw angles ◦ ◦ ◦ ◦ of 0° 0 andand 15°. 15 . The The increase increase in lift is fairly constant for slant angles fromfrom 55° toto 3535°.. The slight reduction in lift rise with yaw as the slant an anglegle increases is consistent with the behaviour noted in Figure Figure 66bb comparing squareback and and fastback fastback variants variants of of the the VGM VGM model, model, but but it differsit differs from from that that shown shown for for the the sharp-edged sharp-edged Windsor Windsor Body. Body. As As shown shown by by the Windsor Body, thethe liftlift riserise withwith yawyaw is is increased increased for for post-critical post-critical slant slant angles. angles. While While for for the the Windsor Wind- sorBody, Body, this increasethis increase is over is a over narrow a narrow range of range slant angles,of slant with angles, the Tumblehomewith the Tumblehome model, the ◦ ◦ model,lift increase the lift with increase yaw rises with to yaw a peak rises when to a the peak slant when angle the is slant between angle 50 is andbetween 60 , the50° limit and 60°,of the the available limit of data,the available but persists data, over but ape widerrsists rangeover a ofwider slant range angles. of slant angles.

0.4 0.6 R = 0 r = 0

ΔCL R = 0.10m r = 0 ∆CL15 CL R = 0.20m r = 0 CLF 0.5 0.3 CLR R = 0.20m r = 0.05m R = 0.20m r = 0.10m 0.4 0.2

0.3

0.1 0.2

Slant Angle 0.0 0.1 0 102030405060 Slant Angle 0 -0.1 0 5 10 15 20 25 30 35 40 (a) (b)

Figure 12. ((a) Lift Lift coefficient coefficient increase for the Tumblehome modelmodel atat 1515°◦ yaw; (b) Effect of slant edge radii on lift of Windsor Windsor Body at 00°◦ yaw. It is unclear whether it is the edge rounding or the tumblehome which creates the significantly different lift characteristics at high slant angles between the Windsor Body and the Tumblehome model. Measurements were taken on the Windsor Body with rounded edges on the slant surface for a limited range of slant angles from 25◦ to 40◦. These tests were conducted at 0◦ yaw. The increase in lift coefficient, relative to the squareback configuration, is shown in Figure 12b for various combinations of edge radii. The radius on the slant leading edge is denoted by R and the radius of the side edges by r. With the side edges kept sharp and the slant leading-edge radius, R = 0.10 m, the lift is essentially the same as for the sharp-edged body but the critical angle is slightly less and the post-critical lift is increased. On increasing the leading-edge radius to R = 0.20 m, the lift coefficient is approximately constant for all slant angles, suggesting that the flow is always separated on the slant for the tested slant angles. With the leading-edge radius of 0.20 m, side edge radii of 0.05 and 0.10 m were applied. As the edge radius is increased, the increase in lift with slant angle and the maximum lift is reduced but the critical angle is increased above a slant angle of 40◦, the maximum slant angle tested. This shows that it is the edge rounding which is primarily responsible for the changes shown in Figure 11 for the Tumblehome model. It is possible that these results will be affected by Reynolds number.

3.3.4. Notchback The Windsor Body has also been tested with boot extensions to create a notchback geometry. The basic geometry is sketched in Figure 13a. All trailing edges were sharp, as Fluids 2021, 6, 44 11 of 16

were the roof trailing edge and the backlight side edges. The underfloor was flat to the boot trailing edge and the upper surface of the boot extension was always flat. The backlight angle is denoted by ϕ and an effective backlight angle, ϕEff, is defined by the angle of an imaginary line joining the roof trailing edge and the boot trailing edge to the horizontal. Fluids 2021, 6, x FOR PEER REVIEW 12 of 17 This model was tested in the MIRA MWT at the time it was a closed-jet wind tunnel and blockage corrections have been applied.

0.50 CL 40 deg bl 35 deg bl 0.40 30 deg bl 25 deg bl φ 0.30 20 deg bl

φ Eff No boot 0.20

0.10

0.00 0 5 10 15 20 25 30 35 40

φ Eff -0.10 (a) (b)

FigureFigure 13.13. ((aa)) WindsorWindsor BodyBody withwith bootboot extensions;extensions; (b)) LiftLift coefficientcoefficient asas aa functionfunction ofof effectiveeffective slantslant angleangle forfor aa rangerange ofof backlightbacklight angles.angles.

FigureAn attempt 13b showsto rationalise the lift coefficientthe lift of the as booted a function Windsor of the Body effective in relation backlight to the angle stand- for theard rangebody is of shown backlight in Figure angles, 14. where Because the backlightthe boot length is denoted extends by bl.the The body, backlight the lift anglescoeffi- ◦ ◦ varycients from are based 20 to on 40 theand plan all area the data,and denoted with very by few CL′. exceptionsThe increase where in lift the coefficient backlight relative angle isto justthe post-critical,squareback body are within is denoted an envelope by ΔCL′, formed and in byFigure the bootless14a, it is configuration,presented as a (i.e., ratio the to effectivethe lift coefficient backlight increase angle = for the the backlight standard angle). unbooted This body implies with that the the same addition backlight of aangle, boot always reduces the lift. ΔCL0′, for the pre-critical backlight angles, 20°–30°. Figure 14a shows that the lift increase for theThe notchback boot trailing configuration edge was relative located to in the 0.010-m squareback steps case both isrearwards approximately and upwardsgiven by: from the slant surface trailing edge. Although not directly identified on the graph, these initial small incremental changes to theΔC standardL′/ΔCL0′ = body(φEff/φ with)2 pre-critical slant angles show(4) a significantFor the reduction booted configurations in lift. For larger where boot the sizes, backlight a significant angle body would of thenormally data shows be post- lift increasing approximately linearly with effective backlight angle and at the same rate as for critical, a reference lift coefficient cannot be defined. Figure 14b shows that the increase in the standard bootless body with backlight angle. It is also apparent that the addition of a the lift coefficient for the notchback configurations where the flow is attached to the boot, boot to the post-critical backlight angles of 35◦ and 40◦ can make the separated flow from indicated by the data within the red boundary, is approximately given by: the roof trailing edge reattach to the boot surface and generate comparable lift coefficients to the pre-critical configurations. ΔCL′ = ΔCL0′′ − k (5) An attempt to rationalise the lift of the booted Windsor Body in relation to the standard where, in this case, ΔCL0′′ is the increase in the lift coefficient for an unbooted configuration body is shown in Figure 14. Because the boot length extends the body, the lift coefficients with the same backlight angle as the effectiv0e backlight angle for the booted case. It can are based on the plan area and denoted by CL . The increase in lift coefficient relative to the also be seen from Figure 14b that the0 critical angle between the attached and separated squareback body is denoted by ∆CL , and in Figure 14a, it is presented as a ratio to the lift backlight flow is less than the critical angle for the unbooted configurations. 0 coefficient increase for the standard unbooted body with the same backlight angle, ∆CL0 , ◦ ◦ 1.00 for the pre-critical backlight angles,0.16 20 –30 . Figure 14a shows that the lift increase for the 40 deg bl ΔCL'/ΔCL0' notchback 30 deg bl configuration relative to the squarebackΔCL' case is approximately given by: 0.90 0.14 35 deg bl 25 deg bl CL' based on plan area based on plan area 0.80 0 0 2 20 deg bl ∆C0.12L /∆CL0 = (ϕEff/ϕ) (4) 0.70 For the booted configurations0.10 where the backlight angle would normally be post- 0.60 critical, a reference lift coefficient cannot be defined. Figure 14b shows that the increase in 0.50 the lift coefficient for the notchback0.08 configurationsNo boot where the flow is attached to the boot, 0.40 indicated by the data within the red0.06 boundary, is approximately given by: 0.30 0 0.04∆CL = ∆CL0” − k (5) 0.20 0.02 0.10 ΔC '/ΔC ' = (φ /φ)2 L L0 Eff φ /φ Eff φ Eff 0.00 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40 (a) (b) Figure 14. Lift coefficient increase for the notchback configurations relative to the squareback case for (a) pre-critical back- light angles, 20°–30°; (b) post-critical backlight angles, 35° and 40°.

Fluids 2021, 6, 44 12 of 16

where, in this case, ∆CL0” is the increase in the lift coefficient for an unbooted configuration with the same backlight angle as the effective backlight angle for the booted case. It can also be seen from Figure 14b that the critical angle between the attached and separated Fluids 2020, 5, x FOR PEER REVIEWbacklight flow is less than the critical angle for the unbooted configurations.12 of 16

1.00 0.16 40 deg bl ΔCL'/ΔCL0' 30 deg bl ΔCL' 0.90 0.14 35 deg bl 25 deg bl CL' based on plan area based on plan area 0.80 20 deg bl 0.12 0.70 0.10 0.60

0.50 0.08 No boot

0.40 0.06 0.30 0.04 0.20 0.02 0.10 ΔC '/ΔC ' = (φ /φ)2 L L0 Eff φ /φ Eff φ Eff 0.00 0.00 374 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40

375 (a) (b) Fluids 2021, 6, x FOR PEER REVIEW 13 of 17 376 FigureFigure 14. Lift 14. Lift coefficient coefficient increase increase for thefor notchbackthe notchback configurations configurations relative relative to the to the squareback squareback case case for for (a) pre-critical ◦ ◦ ◦ ◦ 377 backlight(a) pre angles,-critical 20 backlight–30 ;(b) post-criticalangles, 20° backlight- 30° (b) post angles,-critical 35 andbacklight 40 . angles, 35° and 40°.

3.4. Roof Curvature 378 3.4. Roof Curvature 3.4. Roof Curvature Curved roof profiles have been added to the standard flat roof Windsor Body. All 379 Curved roof profiles have been added to the standard flat roof Windsor Body. All Curved roof profilesadd-on have been roofroof sectionssectionsadded to werewere the thethestandard samesame lengthlength flat roof andand Windsor eacheach hadhad body. aa constantconstant All add radiusradius-on ofofroof curvaturecurvature asas 380 section were the same length and each had a constant radius of curvature as shown in Figure 15(a). shownshown inin FigureFigure 1515a.a. The maximum thicknessthickness ofof thethe add-onadd-on roofroof sectionsection isis denoteddenoted byby zzGG. 381 The maximum thickness TheTheof the trailingtrailing add-on edgeedge roof ofof section thethe roofroof is bowdenotedbow sectionsection by z waswaG. Thes alignedaligned trailing withwith edge thethe of leadingleading the roof edgeedge bow ofof thethe slantslant 382 section was aligned withsurface.surface. the leading The leadingedge of edgethe slant of the surface. roof bow The waswas leading fairedfaired edge intointo thethe of frontthefront roof surfacesurface bow ofof was thethe roofroof withwith 383 faired into the front surfacetape.tape. The of the slant roof edges with were tape. allall sharpsharpThe slantforfor thethe edges data presented. were all Thesharp effect for on the the data lift coefficientcoefficient 384 presented. The effect on theas a l ift function coefficient of slant as a angle function for the of rangeslant angle of roof for curvaturescurvatures the range isis of shownshown roof curvaturesinin FigureFigure 1515b. b. TheThe liftlift 385 is shown in Figure 15(b).coefficientscoefficients The lift coefficients are, inin thisthis case,are,case, in allall this basedbased case, onon thetheall based frontalfrontal on areaarea the ofof frontal thethe standardstandard area of bodybody the withwith aa flatflat roofroof asas thisthis isis aa measuremeasure ofof thethe liftlift increase.increase. 386 standard body with a flat roof as this is a measure of the lift increase.

387 0.70 Flat roof CL' zR = 0.005m 0.70 Flat roof 0.60 zR = 0.010m CL' zR = 0.005m zR = 0.015m 0.60 zR = 0.010m 0.50 zR = 0.020m zR = 0.015m 0.50 0.40 zR = 0.020m

0.40 zR Roof bow height 0.30

zR Roof bow height 0.30 0.20

0.20 0.10 Slant Angle 0.10 0.00 0 5 10 15 20 25 30 35 40 Slant Angle 0.00 -0.10 0 5 10 15 20 25 30 35 40 (a) -0.10 (b) 388 FigureFigure 15.15. ((aa)) WindsorWindsor(a Body )Body with with roof roof curvature; curvature; ( b )(b Variation) Variation in liftin lift coefficients coefficients with with(b slant) slant angle angle for range for rang of roofe of curvatures.roof curva- tures. 389 Figure 15. (a) Windsor BodyIf with the coefficientsroof curvature were; (b) basedVariation on of actual lift coefficients frontal area, with the slant increments angle for would still be 390 positive,If the but coefficients smaller.range of roof Thewere curvatures lift based increase on. actual arising frontal from area, the roofthe increments curvature increaseswould still with be increasingpositive, but slant smaller. angle. The With lift the increase exception arising of the from smallest the roof bowcurvature case, theincreases introduction with in- of 391 If the coefficients wereroofcreasing based curvature slant on actualangle. also shifts Withfrontal the the area critical exception the angle increments of higher.the smallest would roof still bow be case,positive, the introduction but of 392 smaller. The lift increase roofarising curvature from the also roof shifts curvature the critical increases angle higher. with increasing slant angle. With 393 the exception of the smallest roof bow case the introduction of roof curvature also shifts the critical 394 angle higher. 4. Discussion 4.1. Shape and Drag 395 4. Discussion As stated in the Introduction, the primary task of the car development aerodynami- cist is to reduce drag without compromising stability. For most passenger cars, this will 396 4.1. Shape and Drag always prioritise drag over lift, but it cannot mean that lift is ignored. In an ideal devel- opment process, shape changes which reduce drag would also result in desirable overall 397 As stated in the Introduction,lift and distribution the primary of lift, task but ofthis the rarely car occurs development in practice aerodynamicist and compromises is to will be re- 398 reduce drag without compromisingquired. If the stability. reader isFor interested most passenger in the dr carsag effects this will from always the shape prioritise changes drag discussed in 399 over lift, but it cannot meanthis that paper, lift isthey ignored. can be In found an ideal in developmentthe following processreferences. shape The changes drag of which the rectangular blocks was discussed in [11]; the effect on drag for front-end rounding in [12]; the influ- ence on drag of front-end design on the MIRA VGM and the effect of slant angle on the standard Windsor Body in Howell et al. [14]; the effect of slant aspect ratio on drag can be found in [2]; the effect of slant surface edge rounding for the Tumblehome model and the Windsor Body on drag was discussed in Howell [15]; and for the effects of adding a boot and roof curvature on Windsor Body drag, see Howell [16].

4.2. Other Lift Factors and Considerations With current Design trends, lift characteristics are relatively benign, although the achievement of a beneficial lift balance can be more problematic, but the potential for high lift coefficients is apparent from the results in this paper. Although many cars will not be driven at high speed as they operate in countries with speed restrictions, they have a high performance capability and can potentially be driven at their maximum speed. The result Fluids 2021, 6, 44 13 of 16

4. Discussion 4.1. Shape and Drag As stated in the Introduction, the primary task of the car development aerodynamicist is to reduce drag without compromising stability. For most passenger cars, this will always prioritise drag over lift, but it cannot mean that lift is ignored. In an ideal development process, shape changes which reduce drag would also result in desirable overall lift and distribution of lift, but this rarely occurs in practice and compromises will be required. If the reader is interested in the drag effects from the shape changes discussed in this paper, they can be found in the following references. The drag of the rectangular blocks was discussed in [11]; the effect on drag for front-end rounding in [12]; the influence on drag of front-end design on the MIRA VGM and the effect of slant angle on the standard Windsor Body in Howell et al. [14]; the effect of slant aspect ratio on drag can be found in [2]; the effect of slant surface edge rounding for the Tumblehome model and the Windsor Body on drag was discussed in Howell [15]; and for the effects of adding a boot and roof curvature on Windsor Body drag, see Howell [16].

4.2. Other Lift Factors and Considerations With current Design trends, lift characteristics are relatively benign, although the achievement of a beneficial lift balance can be more problematic, but the potential for high lift coefficients is apparent from the results in this paper. Although many cars will not be driven at high speed as they operate in countries with speed restrictions, they have a high performance capability and can potentially be driven at their maximum speed. The result is that all cars must meet the lift targets regardless of the market that they operate in. Typically, for a passenger car with reasonable performance, overall lift coefficients should not exceed 0.2 and the difference between front and rear axle lift coefficients should be less than 0.1. Where possible, the lift targets should be achieved through the basic shape and not rely on add-ons for cost and aesthetic reasons. Only high-performance derivatives would then require add-ons if necessary to meet their more restrictive lift requirements. In general, the influence of lift is realised as a comfort parameter in that with good lift characteristics, the car feels better to drive. However, there are occasions where the influence becomes a safety issue. A safety critical situation only arises at very high speed and occurs, for example, where the aerodynamic lift on an axle of a car at yaw due to a crosswind approaches the mass on the axle. The reduced tyre grip can allow a dynamic yaw angle to develop, exacerbating the lift and creating an unstable situation. This could, potentially, happen with high rear lift on a lightly loaded rear axle, i.e., a front engine car, or with high front lift on a lightly loaded front axle, but, fortunately, such an event is extremely rare. The results shown in this paper suggest that overall lift is fairly insensitive to major shape changes, except at the rear of the car. However, only upper body shape changes have been considered; the area of the car for which design has the major influence and a consequence of this insensitivity is that the aerodynamics development engineer cannot significantly alter the lift characteristics by modifying the style. However, the aerodynamic lift on passenger cars is not similarly insensitive and lift can be affected by many other components and features. These factors are discussed below. It is not an exclusive list, but includes most of the major influences. The efficient placement for a cooling pack is in the front of the car. In this location, the cooling airflow has a significant effect on lift as the engine bay becomes pressurised. This increases front axle lift, but also decreases rear axle lift. The change is crudely dependent on the size of the open intake. Cars have progressively adopted aerodynamically refined underfloors, predominantly for drag reduction. Lift is also reduced, but the lift distribution is dependent on the detail floor design. When underfloors were rough, a diffuser section between the rear axle and the rear bumper had little effect, but with the trend to better underfloor design, a diffuser can reduce overall lift with the load concentrated at the rear axle. Fluids 2021, 6, 44 14 of 16

This trend has also seen the once ubiquitous bib spoiler beneath the front bumper become increasingly redundant. This simple aerodynamic aid was a very cheap and effec- tive way to reduce drag, by reducing the flow energy passing over the rough underfloor, but it also reduced lift substantially and improved cooling airflow. The bib spoiler also deflected air away from the front wheels, reducing wheel drag, and this function is now performed by wheel spoilers mounted at the front edge of the wheelarch. These reduce the pressure inside the wheelarch, reducing lift. With regard to wheels and tyres, wider tyres tend to increase lift, while open wheel designs reduce lift by relieving the pressure between the wheels. Spoilers at the rear of passenger cars are used to control drag and lift, as discussed in [1]. For hatchbacks with an upright tailgate, a spoiler at the top of the tailgate will reduce drag if angled downwards, but increase lift, although this squareback shape in general has low rear axle lift. For fastback shapes and saloon cars, where the airflow is attached to the boot, a spoiler at the boot trailing edge or a boot mounted aerofoil will reduce lift. The change to drag will depend on the height of the boot in relation to the optimum. Lift is also affected by other factors. With regard to the ride height of the car, lift is not significantly changed with ground clearance over the normal operating range for cars, but lift is strongly affected by pitch attitude. For a negative (nose-down) pitch angle, front axle lift is reduced and rear axle lift increased slightly, giving a reduction in overall lift. All the wind tunnel tests reported in this paper were conducted using a fixed ground surface, which was the normal procedure for all automotive aerodynamics testing at the time many of the experiments were undertaken. As the paper only considers changes in upper body shape, this is acceptable. Extensive testing to establish the effects of using a moving belt for ground simulation have been carried out with both the Windsor Body [17] and the MIRA VGM model [18], in the MIRA MWT. In [17], Howell measured lift and drag on the Windsor Body, with a range of diffuser and backlight angles, using a moving and stationary belt. In [18], Howell and Hickman used the MIRA VGM with a range of different rear-end shapes, with and without cooling airflow and underbody roughness to investigate the effects of moving and stationary belt ground simulation on lift and drag. Although the trends for lift were very similar, there were differences in absolute values, but both studies show that the effects of ground simulation would not be significant for the shape changes explored in this paper.

4.3. Influence of Camber-Line The concept of a camber-line and its influence on changes in lift was advanced in the Introduction. It would be interesting to see if the suggestion that changes in lift can be explained by changes in camber and incidence is supported by the results presented in this paper. For the front-end shape changes, with the exception of the vertical windscreen case, the incidence is identical and the camber is very similar, implying negligible change in lift, which is shown by the data. In the case of the rear-end shape changes, an increasing slant angle increases both camber and incidence, which suggests that lift will increase, as shown by the results for pre-critical slant angles. It should be noted, however, that the lift is enhanced by the slant edge vortices, which are not considered in the simple theory. For the notchback configurations, raising the boot trailing edge reduces camber and incidence, implying lift reduction, which is what occurs. Extending the boot rearwards, however, creates negligible change in both camber and incidence, which implies no change in lift, but the data show a reduction in lift. For increasing roof curvature, camber is increased while incidence is unchanged, which suggests a lift increase, as shown by the data. In general, the theory seems to apply but there are exceptions. It should be remem- bered that it is essentially a 2D concept and the effect of side edges are not considered. In addition, it assumes attached flow and cannot account for separations. Post-critical rear slant angles and notchback configurations with extensive separated flow from the roof trailing edge are outside its scope. Fluids 2021, 6, 44 15 of 16

4.4. Lift at Yaw It is surprising that lift is insensitive to some major shape changes, but it is more remarkable that lift increase with yaw is very similar for almost all the configurations investigated in this paper. The lift at yaw data for a saloon car model with extensive configuration changes reported by Carr [4] show a similar result. The only significant exceptions were for the introduction of squared edges in certain areas of the body. For the same reasons discussed in Section 4.2 above, the results presented in this paper do not mean that all cars will have the same lift increase characteristics at yaw. Some small components and local changes to edge conditions can have an effect on lift at yaw by the action of flow interference and separation. However, from full-scale tests on a wide range Fluids 2021, 6, x FOR PEER REVIEW 16 of 17 of cars, shown in Figure 16, it can be seen that, even with this variability, the increase in lift at yaw is broadly similar.

0.50 ΔCL15 0.45 MPV 0.40 Hatch 0.35 Estate SUV 0.30 Saloon 0.25 Sports

0.20

0.15

0.10

0.05 Length, L (m) 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 FigureFigure 16.16.Lift Lift increaseincrease atat 1515°◦ yawyaw angleangle forfor aa widewide rangerange ofof passengerpassenger cars.cars.

AllAll thethe wind wind tunnel tunnel tests tests were were conducted conducte ind the in MIRA the MIRA Full Scale Full Wind Scale Tunnel Wind (FSWT)Tunnel and(FSWT) represent and represent a consistent a consiste dataset.nt dataset. The data The are data for are approximately for approximately 80 cars 80 of cars different of dif- typesferent and types are and essentially are essentially the same the dataset same as data usedset in as the used study in of the side study force of by side Howell force and by PanigrahiHowell and [19 Panigrahi]. The tunnel [19]. is The a fixed tunnel ground is a windfixed ground tunnel and wind the tunnel tests were and the conducted tests were at aconducted nominal wind at a nominal speed of wind 27 m/s. speed The of plot27 m/s. shows The the plot increase shows inthe lift increase from 0 in◦ to lift 15 from◦ yaw 0° angleto 15° as yaw a function angle as of aoverall function car of length. overall Length car length. is one Length parameter is one that parameter was not significantlythat was not variedsignificantly in any varied of the investigationsin any of the investigations reported in this reported paper, in except this paper, for the except basic rectangularfor the basic blocks,rectangular which blocks, were notwhich tested were at not yaw. tested at yaw. AlthoughAlthough therethere isis aa broadbroad spreadspread ofof data,data, theythey suggestsuggest thatthat thethe increaseincrease inin thethe liftlift 2 coefficientcoefficient at at yaw yaw is is increased increased with with length length, as2, shownas shown by theby the dashed dashed lines. lines. As the As coefficientthe coeffi- iscient based is based on frontal on frontal area, then, area, the then, lift the rise lift is increasedrise is increased with height with andheight width, and butwidth, width but varieswidth insignificantlyvaries insignificantly for all thefor all cars the tested. cars te Thested. data The have data nothave been not interrogatedbeen interrogated for any for shapeany shape features features other other than than the the overall overall vehicle vehicl dimensions,e dimensions, but but the the high high lift lift outliers outliers in in FigureFigure 16 16 are are allall carscars withwith post-criticalpost-critical backlights. backlights. 5. Conclusions 5. Conclusions The effect of large-scale upper body shape changes on the aerodynamic lift of passen- The effect of large-scale upper body shape changes on the aerodynamic lift of pas- ger cars has been investigated in small-scale wind tunnel tests on a range of simple bodies. senger cars has been investigated in small-scale wind tunnel tests on a range of simple Large-scale shape changes in the front of a car have a negligible effect on overall lift, bodies. although the lift balance between front and rear axles varies. Large-scale shape changes in the front of a car have a negligible effect on overall lift, Lift is strongly influenced by the shape of the upper rear body. In particular, increasing although the lift balance between front and rear axles varies. the slant angle of the roof or backlight increases lift and is enhanced through the action of Lift is strongly influenced by the shape of the upper rear body. In particular, increas- the edge vortices. Modifications to the leading and side edges of the surface can have a significanting the slant effect. angle of the roof or backlight increases lift and is enhanced through the action of theFor edge the vortices. basic shapes Modifications tested in thisto the paper, leading a simple and side relationship edges of the has surface been established can have a betweensignificant notchback effect. and fastback geometries for bodies where the airflow is attached to the boot surface.For the basic shapes tested in this paper, a simple relationship has been established between notchback and fastback geometries for bodies where the airflow is attached to the boot surface. In general, for most of the cases in this study, changes in lift are qualitatively deter- mined by changes to the camber-line. The increase in lift at yaw is surprisingly insensitive to shape change for the large- scale shape changes investigated in this paper. This has some support from full-scale wind tunnel tests on real cars. In reality, lift is affected by factors other than upper body shape and can be manipu- lated by small features and components which modify separation points or create inter- ference effects.

Author Contributions: formal analysis, J.H., S.W.; investigation, S.W., J.H., M.P.; writing—original draft preparation, J.H.; writing—review and editing, J.H., M.P., S.W.; supervision, M.P.; All authors have read and agreed to the published version of the manuscript. Fluids 2021, 6, 44 16 of 16

In general, for most of the cases in this study, changes in lift are qualitatively deter- mined by changes to the camber-line. The increase in lift at yaw is surprisingly insensitive to shape change for the large- scale shape changes investigated in this paper. This has some support from full-scale wind tunnel tests on real cars. In reality, lift is affected by factors other than upper body shape and can be ma- nipulated by small features and components which modify separation points or create interference effects.

Author Contributions: Formal analysis, J.H., S.W.; investigation, S.W., J.H., M.P.; writing—original draft preparation, J.H.; writing—review and editing, J.H., M.P., S.W.; supervision, M.P.; All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: The data are mostly available on request from the corresponding author except for that which is commercially sensitive. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Howell, J.P.; Le Good, G.M. The Influence of Aerodynamic Lift on High Speed Stability. SAE Tech. Pap. 1999, 1, 0651. 2. Howell, J.P.; Le Good, G.M. Effect of Backlight Aspect Ratio on Vortex and Base Drag for a Simple Car-Like Shape. SAE Tech. Pap. 2008, 1, 0737. 3. Howell, J.P.; Baden Fuller, J. A Relationship between Lift and Lateral Aerodynamic Characteristics for Passenger Cars. SAE Tech. Pap. 2010, 1, 1025. 4. Carr, G.W. The Aerodynamics of Basic Shapes for Road Vehicles. Part 2: Saloon Car Bodies; MIRA Report No. 1968/9; MIRA: Nuneaton, UK, 1968. 5. Gilhaus, A.M.; Renn, V.E. Drag and Driving Stability Related Aerodynamic Forces and their Interdependence—Results of Measurements on 3/8-Scale Basic Car Shapes. SAE Tech. Pap. 1986, 95, 1047–1062. 6. Hucho, W.-H. (Ed.) Aerodynamics of Road Vehicles, 4th ed.; SAE R-177; SAE International: Warrendale, PA, USA, 1998; ISBN 0-7680-0029-7. 7. Schütz, T. (Ed.) Aerodynamics of Road Vehicles, 5th ed.; SAE R-430; SAE International: Warrendale, PA, USA, 2016; ISBN 978-0-7680-7977-7. 8. Morelli, A. Theoretical Method for Determining the Lift Distribution on a Vehicle; FISITA Congress: Tokyo, Japan, 1964. 9. Carr, G.W.; Atkin, P.D.; Somerville, J. An Empirically Based Prediction Method for Car Aerodynamic Lift and Side Force. In Proceedings of the RAeS Vehicle Aerodynamics Conference, Loughborough University, Loughborough, UK, 18–19 July 1994. 10. Carr, G.W. Wind Tunnel Blockage Corrections for Road Vehicles; MIRA Report No. 1971/4; MIRA: Nuneaton, UK, 1971. 11. Howell, J.P. Force and Wake Characteristics of Simple Bluff Bodies in Ground Proximity. In Proceedings of the ASME Conference—Aerodynamics of Transportation, Niagara Falls, NY, USA, 18–20 June 1979. 12. Newnham, P.S. The Influence of Real World Turbulence on the Aerodynamic Optimisation of Bluff Body Road Vehicles. Ph.D. Thesis, Loughborough University, Loughborough, UK, 2007. 13. Pavia, G. Characterisation of the Unsteady Wake of a Squareback Road Vehicle. Ph.D. Thesis, Loughborough University, Loughborough, UK, 2019. 14. Howell, J.; Passmore, M.; Windsor, S. A Drag Coefficient for Test Cycle Application. SAE Tech. Pap. 2018, 1, 0742. [CrossRef] 15. Howell, J.P. Shape Features which Influence Crosswind Sensitivity. In Proceedings of the Ride and Handling Conference, Birmingham, UK, 15–17 November 1993; Paper C466/036/93. IMechE: London, UK, 1993. 16. Howell, J. Shape and Drag. In Euromotor: Using Aerodynamics to Improve the Properties of Cars; FKFS: Stuttgart, Germany, 1998. 17. Howell, J.P. The Influence of Ground Simulation on the Aerodynamics of Simple Car Shapes with an Underfloor Diffuser. In Proceedings of the RAeS Vehicle Aerodynamics Conference, Loughborough University, Loughborough, UK, 18–19 July 1994. 18. Howell, J.P.; Hickman, D. The Influence of Ground Simulation on the Aerodynamics of a Simple Car Model. SAE Tech. Pap. 1997, 1, 970134. 19. Howell, J.; Panigrahi, S. Aerodynamic Side Forces on Passenger Cars at Yaw. SAE Tech. Pap. 2016, 1, 1620.