G. L

eng,

ME

dept

, NU

S

2. S

calin

g th

e he

ight

s of t

he a

tmos

pher

e

or t

he p

robl

em o

f get

ting

up a

nd st

ayin

g up

G. L

eng,

ME

dept

, NU

S

Ref

eren

ces

•B

arne

s W. M

cCor

mic

k, “

Aer

odyn

amic

s, A

eron

autic

s, an

d Fl

ight

Mec

hani

cs, “

New

Yor

k : W

iley

, 199

5, 2

nded

.

•M

iche

l J. H

emsc

h, “

Tact

ical

Mis

sile

Aer

odyn

amic

s: G

ener

al

Topi

cs”,

Was

hing

ton,

DC

: A

mer

ican

Inst

itute

of A

eron

autic

s an

d A

stro

naut

ics ,

199

2

•G

ordo

n C

. Oat

es, “

Aer

othe

rmod

ynam

ics o

f Gas

Tur

bine

and

R

ocke

t Pro

puls

ion”

, W

ashi

ngto

n, D

C :

Am

eric

an In

stitu

te o

f A

eron

autic

s and

Ast

rona

utic

s , 1

997.

G. L

eng,

ME

dept

, NU

S

Und

erst

andi

ng th

e E

arth

’s a

tmos

pher

e

G. L

eng,

ME

dept

, NU

S

Que

stio

n: A

re th

e bo

unda

ries f

or th

e at

mos

pher

ic re

gion

s the

sa

me

ever

ywhe

re o

n th

e Ea

rth ?

No.

The

Ear

th is

not

a p

erfe

ct sp

here

.

The

Wor

ld G

eode

tic S

yste

m (W

GS)

m

odel

s the

Ear

th a

s an

obla

te sp

hero

id

equa

toria

l axi

s =

6,

378,

137.

000

m

pola

r axi

s=

6,

356,

752.

314

m

pola

r tro

popa

use

=6

kmeq

uato

rial t

ropo

paus

e=

17 k

m

G. L

eng,

ME

dept

, NU

S

Que

stio

n: I

s the

Ear

th’s

atm

osph

ere

unifo

rm ?

30A

ir te

mpe

ratu

re (o C

)

1.22

5A

ir de

nsity

(kg/

m3 )

101

325

Air

pres

sure

(N/m

2 )

20 k

m0

km

Que

stio

n:A

ny im

plic

atio

ns fo

r flig

ht v

ehic

les ?

G. L

eng,

ME

dept

, NU

S

Que

stio

n: S

o ho

w a

re th

e bo

unda

ries d

efin

ed ?

By

pres

sure

, den

sity

or

tem

pera

ture

?

Air

tem

pera

ture

falls

at a

co

nsta

nt ra

te in

the

tropo

sphe

re.

From

the

tropo

paus

e,th

e te

mpe

ratu

re re

mai

ns

cons

tant

at -

60 0 C

unt

il ≈2

0 km

abo

ve S

.L.

The

low

er st

rato

sphe

re is

th

e lim

it fo

r atm

osph

eric

fli

ght

G. L

eng,

ME

dept

, NU

S

How

hig

h ca

n ar

tille

ry g

o ?

G. L

eng,

ME

dept

, NU

S

Wha

t can

we

see

at h

igh

altit

udes

?

G. L

eng,

ME

dept

, NU

S

Mor

e co

nven

tiona

l exa

mpl

e

•R

Q-4

Glo

bal H

awk

Hig

h A

ltitu

de,

Long

End

uran

ce (H

ALE

) UA

V

•M

issi

on :

Fly

1,20

0 m

iles a

nd re

mai

n on

site

for 2

4 hr

s at 1

8km

alti

tude

•Se

nsor

suite

: El

ectro

-opt

ical

, IR

, sy

nthe

tic a

pertu

re ra

dar,

grou

nd

mov

ing

targ

et in

dica

tor.

•C

apab

ility

: sc

an 4

0,00

0 na

utic

al

squa

re m

iles (

63,0

00 k

m2 )

in 2

4 hr

s

G. L

eng,

ME

dept

, NU

S

Why

fly

at h

igh

altit

udes

?

•Je

t stre

am :

fast

mov

ing

curr

ent o

f air

at a

ltitu

des o

f le

vels

of 1

0-15

km

cau

sed

by

tem

pera

ture

diff

eren

ces.

•Ty

pica

lly O

(103 )

km

long

, O

(102 )

km

wid

e, a

nd a

few

km

th

ick.

•W

ind

spee

ds fr

om 5

5 km

/h to

12

0 km

/h c

ausi

ng a

ir tu

rbul

ence

G. L

eng,

ME

dept

, NU

S

Scal

ing

of a

erod

ynam

ic fo

rces

Aer

odyn

amic

forc

es o

n a

fligh

t veh

icle

scal

e as

:

Aer

odyn

amic

forc

e ∝

ρV

2

Not

e th

e de

pend

ence

on

V2

G. L

eng,

ME

dept

, NU

S

For m

issi

les,

ther

e ar

e tw

o im

porta

nt a

erod

ynam

ic fo

rces

Axi

al fo

rce

A=

½ ρ

V2

S C

A

Nor

mal

forc

eN

=½ρ

V2

S C

N

V

Thes

e fo

rces

are

alig

ned

with

the

mis

sile

bod

y an

d no

t the

vel

ocity

G. L

eng,

ME

dept

, NU

S

The

sym

bols

are

:

S:

refe

renc

e ar

ea (m

2 ) e

.g. m

issi

le c

ross

sect

ion

area

CA

:ax

ial f

orce

coe

ffic

ient

(non

dim

ensi

onal

)

CN

:no

rmal

forc

e co

effic

ient

(non

dim

ensi

onal

)

½ ρ

V2

:dy

nam

ic p

ress

ure

( N/m

2 )

G. L

eng,

ME

dept

, NU

S

Equi

vale

ntly

we

can

repr

esen

t the

aer

odyn

amic

s for

ces a

s lif

tand

dra

gfo

rces

alig

ned

with

the

velo

city

Lift

forc

eL

=½

ρV

2S

CL

Dra

g fo

rce

D=

½ρ

V2

S C

D

V

G. L

eng,

ME

dept

, NU

S

Ex

: Est

imat

e C

Lfo

r the

AG

M 6

5

Flig

ht c

ondi

tions

mas

s:

300

kg

spee

d:

320

m/s

altit

ude:

sea

leve

l

diam

eter

: 0.

3048

m

G. L

eng,

ME

dept

, NU

S

sea

leve

l ⇒

S

=

For l

evel

flig

ht,

CL

= = =

G. L

eng,

ME

dept

, NU

S

Ex

: Spe

ed/a

ltitu

de v

aria

tion

for v

ertic

al la

unch

AM

M

Sea

Wol

fA

ster

G. L

eng,

ME

dept

, NU

S

1

23

4

Que

stio

n : E

stim

ate

the

term

inal

vel

ocity

to e

ngag

e a

targ

et a

t sea

le

vel

G. L

eng,

ME

dept

, NU

S

At 1

0 km

,

At S

.L 0

km

,

.

G. L

eng,

ME

dept

, NU

S

Aer

odyn

amic

flow

par

amet

ers

Mis

sile

/pro

ject

ile a

irspe

eds c

an ra

nge

from

100

–10

3m

/s

For t

his r

ange

of s

peed

s, ai

rflo

w c

hara

cter

istic

s are

det

erm

ined

by

2 im

porta

nt p

aram

eter

s :

1. R

eyno

lds n

umbe

r Re

2. M

ach

num

ber

M

G. L

eng,

ME

dept

, NU

S

Rey

nold

s num

ber

1. A

ir is

“st

icky

” o

r vis

cous

2. F

rom

the

mis

sile

’s v

iew

poin

t, th

e ai

r at t

he su

rfac

e is

stat

iona

ry

V =

mis

sile

airs

peed

norm

al

dire

ctio

n

mis

sile

surf

ace

G. L

eng,

ME

dept

, NU

S

3. T

he th

in re

gion

whe

re th

e ai

r flo

w b

uild

s up

its sp

eed

is

calle

d th

e bo

unda

ry la

yer.

4. T

he R

eyno

lds n

umbe

r is a

mea

sure

of t

he im

porta

nce

of

this

vis

cous

eff

ect

Re=

(pre

ssur

e fo

rces

) / (v

isco

us fo

rces

)

=(ρ

V2 )

/ (µ

V /

L)

=V

L/ν

L : r

efer

ence

leng

thµ

: coe

ffic

ient

of v

isco

sity

ν=

µ/ρ

: ki

nem

atic

visc

osity

G. L

eng,

ME

dept

, NU

S

Ex

: W

hat a

re ty

pica

l mis

sile

Rey

nold

s num

bers

?U

sing

the

AG

M-6

5 at

S.L

.

V

: 32

0 m

/sL

: 0.

3048

m (d

iam

eter

)ν

: 1.

4607

x 1

0-5m

2 /s (

kine

mat

icvi

scos

ity fo

r air

at S

.L.)

Re=

V L

/ ν

G. L

eng,

ME

dept

, NU

S

The

Mac

h nu

mbe

r1.

Air

is c

ompr

essi

ble.

2. A

mov

ing

mis

sile

dis

turb

s the

surr

ound

ing

air

3.Th

ese

dist

urba

nces

e.g

. pre

ssur

e va

riatio

ns, t

ake

a fin

ite ti

me

to p

ropa

gate

at t

he sp

eed

of so

und

thro

ugh

the

surr

ound

ing

air

4. T

he M

ach

num

ber m

easu

res t

he im

porta

nce

of th

is

com

pres

sibi

lity

effe

ct.

M=

airs

peed

/ (s

peed

of s

ound

)

=V

/ a

G. L

eng,

ME

dept

, NU

S

Exa

mpl

e :

Dis

turb

ance

pro

paga

tion

M <

1

Con

side

r the

dis

tanc

es tr

avel

led

by th

e di

stur

banc

e an

d th

e m

issi

le in

1s

dist

ruba

nce

0

mis

sile

G. L

eng,

ME

dept

, NU

S

Exa

mpl

e :

Dis

turb

ance

pro

paga

tion

M >

1

Con

side

r the

dis

tanc

es tr

avel

led

by th

e di

stur

banc

e an

d th

e m

issi

le in

1s

dist

ruba

nce

mis

sile

V0

θ

sin θ

= a

/V=

1/M

G. L

eng,

ME

dept

, NU

S

So fo

r M >

1, t

here

is a

dis

cont

inui

ty in

the

flow

fiel

d “s

een”

by

the

mis

sile

Air

prop

ertie

s lik

e pr

essu

re, t

empe

ratu

re a

nd d

ensi

ty c

hang

es

shar

ply

acro

ss th

e di

scon

tinui

ty o

r sho

ck Schl

iere

nph

oto

of sh

ock

wav

es

Ligh

t is r

efra

cted

di

ffer

ently

bec

ause

of

chan

ges i

n ai

r den

sity

G. L

eng,

ME

dept

, NU

S

The

shap

e of

the

shoc

k w

ave

depe

nds o

n th

e sh

ape

of th

e ob

ject

Shoc

ks c

reat

ed b

y hi

gh sp

eed

fligh

t can

be

anno

ying

....

G. L

eng,

ME

dept

, NU

S

Effe

cts o

f a sh

ock

(son

ic b

oom

)

On

the

grou

nd

On

hum

ans

G. L

eng,

ME

dept

, NU

S

Con

dens

atio

n du

e to

sudd

en c

hang

es in

air

tem

pera

ture

and

pre

ssur

e

G. L

eng,

ME

dept

, NU

S

Cla

ssifi

catio

n of

flow

reg

imes

via

spee

d

•M

< 0

.8

subs

onic

inco

mpr

essi

ble

aero

dyna

mic

s

•0.

8 <

M <

1.2

trans

onic

loca

lized

com

pres

sibi

lity

effe

cts

•1.

2 <

M <

5su

pers

onic

com

pres

sibl

e ae

rody

nam

ics

•M

> 5

hype

rson

icae

rody

nam

ic h

eatin

g