uVll)

2Yrui5lu 1 iLA gt

r ~(Nl-

j(q)() CIt == ltfJ~ A-x r~AiltV+ fM JY v=--Jj-=_1+( -7gt t(~ Axt f- (Y--) J5x

(Ij() )(( (~) y~ ----c---f---+--)(

(c ) CI [y rf) =- )(tN) ~ u (r~ aD) = Ax (IJvLu ~)

~ d is dRfJl~ b) XfcS)=~q Ax

I( P(

(cf) = 0liC Ashy

(0pound~d ((VW 6lt J61 vA fv J) te-ttl Ifgt ~kf llcAulc r- t6 X J ~ n-k~~

~17--- ~a COlAJiMr- --CkH) I

sk720

Rectangle

-t r= -4Tl1tfrM(oI-+tlo C4 (Jj--=- -IUr 411 Iilei-f flo

-sshy(c) 4 ~ liz [JJ-A i uI-f (i -) I~) --gt00 )

r1~c( vt lo cl-tl1 ltj( ty) cOl-~ --x ramp-~ lle ~ H -t~ t(h--e-e ~vraquoJe trr J) )( ~~~ ~d

Cve-W K4Jlc- ~ ~ ~ J-cJ ~ - 1shy (LV

~ It--) -) lvaIL6Le (- r (c-= 4)~ D ~

T[[ r - 101 I L)t0]~-e --2 ~ ) --CJo eo = Vl ----- 1 - lampl-f-l t el

~+~~

-poundshy(dv) l-- gt v sc -4 f1~ I wlt (J vlshy~u(t-J I lttk eY( Jet ~ tUltfAJ dotvgt

Car wL -( v--cN eJ wjI- ~ Ilk 01 -J (Ol t-q tshy~ M ~ 0vt

1t tre ~ S JJJcIL) ~frkcX~ 9dkn -H-~-e~ teill -ltI ~t e (~( Lla~0- ~vtd

J cloJ-UI ~ ~jVlP j lulh tCel ~11 e)

jW~tK~~) X)

(b) (l) tv lb-- ~ h-PVltA t1 ~ fAr(r) e ~IA t7(r) eler

~~~~~1 C(f-tM-7 p =Ji(rtr)I-~te =- 0 1M +1--11t--f

Ir L-~oltJ O--U ~(j~A)

r ~ (t r ((tJ ~ t C4 C Iamp)J felt A ~ ~ I~ ce Lf r-O (J-shy

rie ~ 11u ~ Ovt t-v ~r lit f oL cJ1 r( 1~ bull ~vlce r+e y~lMJ ~ c~rC-tLv

~ ) 11lt- 0LvLLr [tfl- ~J i f (ot-~ ~ t7)(-

-=-D

+(IIn4(J)-[I ~ 0

o (vr~A )

r - r V1 e- (~Jh 4 - (o) ~cI-~~ f-laquo voVl-gc )

-t r= -4Tl1tfrM(oI-+tlo C4 (Jj--=- -IUr 411 Iilei-f flo

-sshy(c) 4 ~ liz [JJ-A i uI-f (i -) I~) --gt00 )

r1~c( vt lo cl-tl1 ltj( ty) cOl-~ --x ramp-~ lle ~ H -t~ t(h--e-e ~vraquoJe trr J) )( ~~~ ~d

Cve-W K4Jlc- ~ ~ ~ J-cJ ~ - 1shy (LV

~ It--) -) lvaIL6Le (- r (c-= 4)~ D ~

T[[ r - 101 I L)t0]~-e --2 ~ ) --CJo eo = Vl ----- 1 - lampl-f-l t el

~+~~

-poundshy(dv) l-- gt v sc -4 f1~ I wlt (J vlshy~u(t-J I lttk eY( Jet ~ tUltfAJ dotvgt

Car wL -( v--cN eJ wjI- ~ Ilk 01 -J (Ol t-q tshy~ M ~ 0vt

1t tre ~ S JJJcIL) ~frkcX~ 9dkn -H-~-e~ teill -ltI ~t e (~( Lla~0- ~vtd

J cloJ-UI ~ ~jVlP j lulh tCel ~11 e)

jW~tK~~) X)

(b) (l) tv lb-- ~ h-PVltA t1 ~ fAr(r) e ~IA t7(r) eler

~~~~~1 C(f-tM-7 p =Ji(rtr)I-~te =- 0 1M +1--11t--f

Ir L-~oltJ O--U ~(j~A)

r ~ (t r ((tJ ~ t C4 C Iamp)J felt A ~ ~ I~ ce Lf r-O (J-shy

rie ~ 11u ~ Ovt t-v ~r lit f oL cJ1 r( 1~ bull ~vlce r+e y~lMJ ~ c~rC-tLv

~ ) 11lt- 0LvLLr [tfl- ~J i f (ot-~ ~ t7)(-

-=-D

+(IIn4(J)-[I ~ 0

o (vr~A )

r - r V1 e- (~Jh 4 - (o) ~cI-~~ f-laquo voVl-gc )

-sshy(c) 4 ~ liz [JJ-A i uI-f (i -) I~) --gt00 )

r1~c( vt lo cl-tl1 ltj( ty) cOl-~ --x ramp-~ lle ~ H -t~ t(h--e-e ~vraquoJe trr J) )( ~~~ ~d

Cve-W K4Jlc- ~ ~ ~ J-cJ ~ - 1shy (LV

~ It--) -) lvaIL6Le (- r (c-= 4)~ D ~

T[[ r - 101 I L)t0]~-e --2 ~ ) --CJo eo = Vl ----- 1 - lampl-f-l t el

~+~~

-poundshy(dv) l-- gt v sc -4 f1~ I wlt (J vlshy~u(t-J I lttk eY( Jet ~ tUltfAJ dotvgt

Car wL -( v--cN eJ wjI- ~ Ilk 01 -J (Ol t-q tshy~ M ~ 0vt

1t tre ~ S JJJcIL) ~frkcX~ 9dkn -H-~-e~ teill -ltI ~t e (~( Lla~0- ~vtd

J cloJ-UI ~ ~jVlP j lulh tCel ~11 e)

jW~tK~~) X)

(b) (l) tv lb-- ~ h-PVltA t1 ~ fAr(r) e ~IA t7(r) eler

~~~~~1 C(f-tM-7 p =Ji(rtr)I-~te =- 0 1M +1--11t--f

Ir L-~oltJ O--U ~(j~A)

r ~ (t r ((tJ ~ t C4 C Iamp)J felt A ~ ~ I~ ce Lf r-O (J-shy

rie ~ 11u ~ Ovt t-v ~r lit f oL cJ1 r( 1~ bull ~vlce r+e y~lMJ ~ c~rC-tLv

~ ) 11lt- 0LvLLr [tfl- ~J i f (ot-~ ~ t7)(-

-=-D

+(IIn4(J)-[I ~ 0

o (vr~A )

r - r V1 e- (~Jh 4 - (o) ~cI-~~ f-laquo voVl-gc )

-poundshy(dv) l-- gt v sc -4 f1~ I wlt (J vlshy~u(t-J I lttk eY( Jet ~ tUltfAJ dotvgt

Car wL -( v--cN eJ wjI- ~ Ilk 01 -J (Ol t-q tshy~ M ~ 0vt

1t tre ~ S JJJcIL) ~frkcX~ 9dkn -H-~-e~ teill -ltI ~t e (~( Lla~0- ~vtd

J cloJ-UI ~ ~jVlP j lulh tCel ~11 e)

jW~tK~~) X)

(b) (l) tv lb-- ~ h-PVltA t1 ~ fAr(r) e ~IA t7(r) eler

~~~~~1 C(f-tM-7 p =Ji(rtr)I-~te =- 0 1M +1--11t--f

Ir L-~oltJ O--U ~(j~A)

r ~ (t r ((tJ ~ t C4 C Iamp)J felt A ~ ~ I~ ce Lf r-O (J-shy

rie ~ 11u ~ Ovt t-v ~r lit f oL cJ1 r( 1~ bull ~vlce r+e y~lMJ ~ c~rC-tLv

~ ) 11lt- 0LvLLr [tfl- ~J i f (ot-~ ~ t7)(-

-=-D

+(IIn4(J)-[I ~ 0

o (vr~A )

r - r V1 e- (~Jh 4 - (o) ~cI-~~ f-laquo voVl-gc )

-1shy(c)

f

~ 4 ~1k ~ ---L--L-L-~-~()Arr~r~oQ Ue(=- (~J~t-

vNr-vc-1 VI-f J (t7VreJ ~~ ~ tVJI MI~ltif(~x~ r 0- )

~ Co lt t Irzky ~ IJ ryfL ltI 1t4 -mz (Il lj (Ier~ (CI-)

~ cg I tV hlC I4J k ((]V--C crltJtgt 11 -) IVhlu ~r v--e k r--tA d l He J (PJlpt-=-o ) lt Th J

ti 5~ Lr J( C(Vr) r--QII 1 vN r( t - ~(M =V7 ~ - kiH(pYJJ t-vk li=e eLrAurJ( bl(~~Q

WJcAe

f I OI(1rdtI - - - -11]Jr ~~

E0 - 3

)tf-euroA h --~-U J-fC(-J ~ 1iAJ I~ ~vJj Jll~v

4 (1) CVki c4J laquo~hkt- ct fot~ tvthi tGz amp~-U 7Le

~rvUr( J-tff ~ I r--QJeJvf

~ fI ampX h ~r~ T) FO f--~ LHi ~ ce (II VII gt0 VI(O Iltgt IIe r--7o ep-UIr--~J fJt-eJ

Ikllt (oltL l lt-fq I -or( p IAJ (I it-v ~l f-~1 h lt-J -7ff vc-if

(11 (1 ~o vgt 0 - li- Vce veYOL -

4 b~1t- C9Ae

J fv-e--VI I r t lLv fj j~L -gt

~t(dlAR) t--oW~ Ik V~) 10 rCJtcAr- ~IJv) l-~ r-ryU ) r-t1 tvY c--A 1)Lv) (JiftJ Jrt-elfJ

(19 )(iWw le vJ1 y~ 0 J ~ j-V) hr-efJwf1nWI(j Jk ~I~-v ~~cgt- Imiddot

~~ f- Vja -~(Z1t)vX JX II

Alc- vdlt ~ ~ i ~ =-0 - il7)~Oq ~v= (~Jt _ 1 I Jshyltgt-tgtl LltO I v ~ f~J=0 ~ tl L 0Jf

JRJ]Q ~ ~ ~ =0 ~ -) i1 ~ ~ ~ f rJi f - U-z

r ( iAV2V lArcYv v-J c~ fL~6-U -

-~--(ii) + ltv ([- (r-tvv t4e CJcgtj) lttk v Q llk h7

tnlbmiddot1e -1 clMvd---v 6~ ~ctCJ ~

(CtW 1 fk vel ~ ~~ ~ f(~Y)

- rsect L+r I Y fs-()1J ==- fht f( ~f )Jr v v y v

0l II P A =) 11 =) ~- ~ (A f) If )I 4--( d1 J~ ( )

(A 3l-- === f ( ~l( )

Uzr [ v ---c I L( + k uJI(()rcxl CR

I

fcJ Y ==-[c1tplLY (WitcjJ c~c~ruJ-middot) 1(-4- IF clt+

-(Ushy

s ~) 11e (rxJ I1tC~(c~-ej- ~ ~ltbd iT k Lolo-R e~~(tv-e (Le c6 cJf~c( 6]

ct(r) 1noI t = ttl (d -~o(r) -61 (YJ )e fJruT (T

+ (0 ~ IntI Q= (Lln-f) A TIJT gtltvfWMI-I tA)-iu

~ce ike ~ l~~middot~ -( ~~I~ 1(q= ~ ) ifUlC

r (y) ~l - d (lt) - rJ~ (()-n-1i coO

Q

(1) Eti~hc (~l ~~Y)~r (1-f)1~ nq)~r gt ~

1) Rt-JV CJA) Lf WJ (V)= J rl[ ~ ~ r -gttaf cent shy~ 4rr Cit rshy

-J __________ g T=- 5 UV e ~~6 qIcent

bull 0lt t~5 Csd-~~ 1r ((-t( r-PftA

- A ~ - ro (~J r- ampA - e eft) J f bet 1 U ltJU I I

uo~ rsect ~ 01 - oI~( l() - rQ ~ - - shy

11f c(-() ~ 4~fS T (7 r-J~t-

10 d) t- ( 0-k ~ t-ltv k cpound1iIYf vev() eli r Cltgt~ (~ C (()-=coj-tLlJl IJfl7r( fCC ( )

N (if )ck CC- JYpt ( lN71 t-Wi Jt-VtV (J (I af l-c~

~ ((inti ~ft CCN-~ I4-(( hv~ Jr- o-e C6-tJ-Pv tshy

-(1 shy

(-i ~ ) rCVl Je ( ctL) rf vtVltJo- ~tW~ ue dVlV-tA l~ VWt-f )(c~th- cJM~~ - - ~ Jictr-cLU(

(d ) LoCJ Cl

h (01- (0 -G ) laquoLfj ~

C~jy-pv Cshy

-J2shy

c

J) ~tr--e

)~l N~

(~ )

til v t 1D (t) ck--c (PCJ- 0 (X D) -1 5 rlvt

It ()(0) - J rr(7lt ~ AIlt I lrr(X- x I)

o ~

00

cA I 4H 01 IE-e II (iA u 1 C JJr y 17--- tCI7 Shi e- ~

x= r 0+ (oJ amp) J

(1)lt ~ -Co Sh e- ~ f)L

X=-o I (1~ IT ~=c J amp-0

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-~--(ii) + ltv ([- (r-tvv t4e CJcgtj) lttk v Q llk h7

tnlbmiddot1e -1 clMvd---v 6~ ~ctCJ ~

(CtW 1 fk vel ~ ~~ ~ f(~Y)

- rsect L+r I Y fs-()1J ==- fht f( ~f )Jr v v y v

0l II P A =) 11 =) ~- ~ (A f) If )I 4--( d1 J~ ( )

(A 3l-- === f ( ~l( )

Uzr [ v ---c I L( + k uJI(()rcxl CR

I

fcJ Y ==-[c1tplLY (WitcjJ c~c~ruJ-middot) 1(-4- IF clt+

-(Ushy

s ~) 11e (rxJ I1tC~(c~-ej- ~ ~ltbd iT k Lolo-R e~~(tv-e (Le c6 cJf~c( 6]

ct(r) 1noI t = ttl (d -~o(r) -61 (YJ )e fJruT (T

+ (0 ~ IntI Q= (Lln-f) A TIJT gtltvfWMI-I tA)-iu

~ce ike ~ l~~middot~ -( ~~I~ 1(q= ~ ) ifUlC

r (y) ~l - d (lt) - rJ~ (()-n-1i coO

Q

(1) Eti~hc (~l ~~Y)~r (1-f)1~ nq)~r gt ~

1) Rt-JV CJA) Lf WJ (V)= J rl[ ~ ~ r -gttaf cent shy~ 4rr Cit rshy

-J __________ g T=- 5 UV e ~~6 qIcent

bull 0lt t~5 Csd-~~ 1r ((-t( r-PftA

- A ~ - ro (~J r- ampA - e eft) J f bet 1 U ltJU I I

uo~ rsect ~ 01 - oI~( l() - rQ ~ - - shy

11f c(-() ~ 4~fS T (7 r-J~t-

10 d) t- ( 0-k ~ t-ltv k cpound1iIYf vev() eli r Cltgt~ (~ C (()-=coj-tLlJl IJfl7r( fCC ( )

N (if )ck CC- JYpt ( lN71 t-Wi Jt-VtV (J (I af l-c~

~ ((inti ~ft CCN-~ I4-(( hv~ Jr- o-e C6-tJ-Pv tshy

-(1 shy

(-i ~ ) rCVl Je ( ctL) rf vtVltJo- ~tW~ ue dVlV-tA l~ VWt-f )(c~th- cJM~~ - - ~ Jictr-cLU(

(d ) LoCJ Cl

h (01- (0 -G ) laquoLfj ~

C~jy-pv Cshy

-J2shy

c

J) ~tr--e

)~l N~

(~ )

til v t 1D (t) ck--c (PCJ- 0 (X D) -1 5 rlvt

It ()(0) - J rr(7lt ~ AIlt I lrr(X- x I)

o ~

00

cA I 4H 01 IE-e II (iA u 1 C JJr y 17--- tCI7 Shi e- ~

x= r 0+ (oJ amp) J

(1)lt ~ -Co Sh e- ~ f)L

X=-o I (1~ IT ~=c J amp-0

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-(Ushy

s ~) 11e (rxJ I1tC~(c~-ej- ~ ~ltbd iT k Lolo-R e~~(tv-e (Le c6 cJf~c( 6]

ct(r) 1noI t = ttl (d -~o(r) -61 (YJ )e fJruT (T

+ (0 ~ IntI Q= (Lln-f) A TIJT gtltvfWMI-I tA)-iu

~ce ike ~ l~~middot~ -( ~~I~ 1(q= ~ ) ifUlC

r (y) ~l - d (lt) - rJ~ (()-n-1i coO

Q

(1) Eti~hc (~l ~~Y)~r (1-f)1~ nq)~r gt ~

1) Rt-JV CJA) Lf WJ (V)= J rl[ ~ ~ r -gttaf cent shy~ 4rr Cit rshy

-J __________ g T=- 5 UV e ~~6 qIcent

bull 0lt t~5 Csd-~~ 1r ((-t( r-PftA

- A ~ - ro (~J r- ampA - e eft) J f bet 1 U ltJU I I

uo~ rsect ~ 01 - oI~( l() - rQ ~ - - shy

11f c(-() ~ 4~fS T (7 r-J~t-

10 d) t- ( 0-k ~ t-ltv k cpound1iIYf vev() eli r Cltgt~ (~ C (()-=coj-tLlJl IJfl7r( fCC ( )

N (if )ck CC- JYpt ( lN71 t-Wi Jt-VtV (J (I af l-c~

~ ((inti ~ft CCN-~ I4-(( hv~ Jr- o-e C6-tJ-Pv tshy

-(1 shy

(-i ~ ) rCVl Je ( ctL) rf vtVltJo- ~tW~ ue dVlV-tA l~ VWt-f )(c~th- cJM~~ - - ~ Jictr-cLU(

(d ) LoCJ Cl

h (01- (0 -G ) laquoLfj ~

C~jy-pv Cshy

-J2shy

c

J) ~tr--e

)~l N~

(~ )

til v t 1D (t) ck--c (PCJ- 0 (X D) -1 5 rlvt

It ()(0) - J rr(7lt ~ AIlt I lrr(X- x I)

o ~

00

cA I 4H 01 IE-e II (iA u 1 C JJr y 17--- tCI7 Shi e- ~

x= r 0+ (oJ amp) J

(1)lt ~ -Co Sh e- ~ f)L

X=-o I (1~ IT ~=c J amp-0

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-(1 shy

(-i ~ ) rCVl Je ( ctL) rf vtVltJo- ~tW~ ue dVlV-tA l~ VWt-f )(c~th- cJM~~ - - ~ Jictr-cLU(

(d ) LoCJ Cl

h (01- (0 -G ) laquoLfj ~

C~jy-pv Cshy

-J2shy

c

J) ~tr--e

)~l N~

(~ )

til v t 1D (t) ck--c (PCJ- 0 (X D) -1 5 rlvt

It ()(0) - J rr(7lt ~ AIlt I lrr(X- x I)

o ~

00

cA I 4H 01 IE-e II (iA u 1 C JJr y 17--- tCI7 Shi e- ~

x= r 0+ (oJ amp) J

(1)lt ~ -Co Sh e- ~ f)L

X=-o I (1~ IT ~=c J amp-0

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-J2shy

c

J) ~tr--e

)~l N~

(~ )

til v t 1D (t) ck--c (PCJ- 0 (X D) -1 5 rlvt

It ()(0) - J rr(7lt ~ AIlt I lrr(X- x I)

o ~

00

cA I 4H 01 IE-e II (iA u 1 C JJr y 17--- tCI7 Shi e- ~

x= r 0+ (oJ amp) J

(1)lt ~ -Co Sh e- ~ f)L

X=-o I (1~ IT ~=c J amp-0

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

_J--~------lt l~l ~~

ltv 9

J~1 ~01[ =lLoJe1 I I shy

I ~~amp I

-13-shy

7 ~~) I ct +00150 -001)10 [1JltJll -- tdot 3~

_____

() ~ ) j ~~ 1Joe-k(6)le ~--tr i

i f I

lt~~f~~ 1) It( e 0) I I

I

2

3

I

I

-G )

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

7middot (q I

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

[h) -ISshyItmiddot 1 ~ 7(z-) dvlt rvz ~ ~~ u ~y

e f~~l-~)ci( = f (2~~4n(H-Y7l) JA( D D

f lt =~[ (z1-If 1+-~~ ) _] It) cl1

= ~~[If-~ ~ 3+ ~ It- jS r== r ( I f-I -f -f) 30~1gt- gt ~ 15

ef~= 2 15 -

7 ~ efi ~1 f1 i [Ubz-l l1~fvJ ttr ~=-o ~l ~I JcTr fic

J

=-~tf (t- VI) ~ 2tf cf1r c-O J

__-----~ t

8) ~ (eI) fx == ~ t jfr) tHNgt w-e cyvt1gtK

jltlct ~O) l=-iP ~ ( 5 d)( VtJyen

- J[gtf01 fgtJ =ft)Jl-AX cr

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-IL-Solutions (The pictures are from the lecture handout)

a) Hatchback (the picture is of an estate but the rear flow is the same) The flowfield is dominated by flow separation at the upper edge of the rear window and the whole base flow I ss d

Saloon In a well-designed saloon car the flow stays attached along the rear window and

at the of the boot lid

Fastback In a fastback car the flow remains attached al

However this typically leads to two large counter-rotating vortices (for a bonus point)

-(jshy

b) bull Hatchback Large separation (at the roof line) but maximum internal volume (good

for short cars) Not the best drag coefficient because of the large separation bull Fastback Attached flow along the rear window but possibly with strong vortices

Not good for volume (boot space) but good to excellent drag coefficient Can have a lot of lift though which may require spoilers in performance cars

bull Saloon Attached flow along rear window and the boot lid Separation at rear of boot lid Can have vortices (but not as strong as fastback) Decent use of space through classical boot If well designed this can give very low drag values

c) The angle of the rear window slope is crucial At a slope of around 30degrees the flow changes from attached to separated

O04-----------r-------Fastback

90

k I

009 018 027

036 045

Typical angles for well-designed fastback shaped cars are around 20degrees

d) There is usually a degree of boattailing to reduce the base area and recover some pressure This means that the roofline drops slightly before the rear window and that the sides of the car are brought in

In addition a distinct separation lip can help to slightly improve the base pressure (and thus reduce drag)

New contour

~d 71~~nw~ VW-Golf I (Rabbit)

~ --2 Co

1000

~ Detail A ~ Centreline cross-sectlon