* Cruise fABgit - Pouoer Requived
Basicals.pouer is a Product Df thuSt
uire Tnto
yelouty Preay Treay
Replace os Preq
Drag
DXV
C
wefght XxCpCo thiis Expression Says about
CL
Telationship lFE Co-efffuent f drag o-etfiiert
: Expiessíon
Fxom Ift e,n LLfu. ^CL
Hhis y2
from this
y2
2L
2
V=
2L
2W
Cs Pe Ctuse ond.
Pseq, = DV
W Co
2W
|2w co2
use
Take of,
A
Lo
L=W
Duerg cruise Aight.
T =D
Prey d
G, 3/2
cOnstaut
"It Shouws that pouEY requr ed for the couse fght deperd's
aiciatt waght , density, using area aerodyramic
Co-crriien t Ca l c) it implies
3/2
inversely p1opostioral CL
pouer Yequred
CD
Note :- i) Fox minimum poweY
rguirermentc
h
masdniSed
Speed must
i. C at the particular aïrcaft
t
produn
foni
ko balance .the weight So therefore.op
CL
must be
maumised.
P availabie
Prcgurd
Vfor
Pp min
Vna
Caise FIht Concition ;.
The velouty fox min pouey YeQre.
’ Powes Tequred is product of drag 4 veloty
’ From drag eqn D Capiessed a S
S
using arêa
using
Co
Coo t
kcL Drag polar
Co is the drag Coeffiient; CD due to the skin
Sfn fricHon
pYeSSure duag.
k induced drag facor
CL = Ift Co -effident
Co = Coo t
CL
AARC
e = Osuoal d effiCaerscy effect
Chous mach fet (an oing produe cusirg ing).
AR' Apect satio
s
oing spa)
ATea.
DV
TRAC,
C,
vs
(
RAe
ARe
w
2
RAe
AARe
C
RA
2
g'vsRA
2
fvsn ARe
2h2
JVS AARe
Pabaite cod
This epressfon says Qbout paer raü~ed has two
Component
Coo payasite coeffilent
ushich incoease
oi th Wa.
Kinduced crag Co-effiaeht
de Cvases uorth V,
Pouer requised is a Combinakion Parasite ontibutcn
e induced drog
contoibufion
# Fight Dyramics
1, Arcraft Pexfonance
i Couisig light petosmance
hanaeuvaing FIight pevfoimance
2-Stabilty
DDO
$ Cortsol
longitucliral stality
iv, Latexal E disect Stabilitý
V, Dyramic Stability.
"Range :
the total distance an aiscraft Can tsavel on a gi ven
fuel tank.
Enduronce :
ancgatt to Stay in as foY
TOtad tíme taken for the ofsCxaet
the qiven tank of fuel.
" Rate
of cimb:
The tate .of change of altude of an aiscat in Aight.
* This value, of
Cu CosTeSponds to Ci ot mac effiaency
* light Stabil ity ! Contol deal $ oith hordling ualities
of. an aurcaft nder the influence Of .ecteral OY
itesnal force
* Míssfon ole Of an aTcrat
Lotes :when ascKaAt can
CTuse
ind sigrnal due to woeather
Takeoff
Landing
o is the pllch aliti
od, targle of atalk
VW=Rc
Horiantal
Let, Ve AîN relative vel o&ty
X6
Body Aced a-aus
ds : Staßiity axis - aés adong th e air
velocity [vJ
body fxed zau's
Stabfty ois
¢ horisontal.
AOA defin ed as le blw
oiplare pftch'al tude zle blus
'
kou0t
.
: Flight path
vetical vel
Vn
le blw
hoyigantal
Comp a so knoon
as Rate of dinh
Hosaontal vel comp
¢ : Thiust force inclination defined as zle biw
trust ine of acion.
(n his díag tam dh :0)
*] Cvuise : Ejuatia of Motion
’ Consíder aitcraft is subieted to aerodynamic force,
grvi toutforal force, propu sive foce for case ght the
aisCraft fs Shid to be steady lev ight.
Negieting the change în mass (id con Sumpton)
ma
dt
v
Yadu s
DYa
wt Com poneat
’.
.(Refes di ag tam fo wrdexstanding )
of
where 2F., Surmmation ot
au forces though eut the
aircrat to v at elative vel
OF LIaY fOCeS thiough ourcsatt ah
elative
vel
Considein9
Sub
ea
¿ Fi,
(9)$()
T Ccos o -
-wsfn o =0.
T=D
Le w
* Cuise Afght
’ Thxust veguired Drag Polar
Consider an aiplong in steody leve ight at a Vel
hen, thyAt to be delvexed by the engine to bolance he
dvag Can be ortter aS :
of ar
= D
v.s. Co
oroq Cotfient
S
using spa
= D= 9S.Cp .
By Combining egafion of motions
Ciui se iqht
Can be
thsE equives o
expre ssed as funtion:
aciod ton.
effiency
Tre,
asodyramc effliency
Co
The diag Coefficient Can be expsestl as
Considoing skin i Pressuse dog
Cp Co t kCL
> Parasite d'iag:
it iydepae
2 SHin DIag + PxeSSuhe dag
’
ma
Co
Litt CoPe£ient k= Indu ccol dra y.
Lit - ca 9 Yati o.
t0 ind man Lift - Dxag otio oiffexcnat e C by o
-()
Msing denomingtor ule.
CDo+ka
2
Cb)'of N
> (Go+kce) d(a)- (ca) Coo t kCL"
dcL
(Gotker}
Cbo + kc-2kcL2 =0
Coo - kCL'=0.
Coo
This value of G CorrEbpondls
to
at mox Cffiqency .
kcL
* To detesmin e
drag @ max effiuency .
Co maL =
CDo + keL
Co ma SC
= Cbo + k
Co ma
2 CD0
Ratio of
()
2
’
from 6)
B
mar.
2 Cbo
( Coo)
k
2 CDO .
yramie effdency Emox (max . 1/kCo,
Vaiation of C, ith cp
(c
lp.o6
Cbo
Co
*) Typfcal Vahiations of C
Co 'u.Tt AoA Ps shoun
fig O Silaly, a tyecal Vosfation of afeo wy
|:51
(So) Olo
O.5
CDO
10
2. Manaeuvering Flfght Pesfoutionce
* Ronge: It is the totad ogt of distonce tavell
oith one oad of fuel
Consoley
" Wo'
ed
of airaft (It ndudes
Gross t
wt of aíT gaft.4 fuel aUt.
.
w w t of
the
as croaft wirt ful tor)
wt of fuel.
cwt of arCYaft
we
ohen the fuel tank
is em pty
We + We
0Total wt of
Since w is deceasing duing
also deCIea Sing wrt time.
ght therefor e w is
wt fue.How ate.
-dwr
dt
auT CYaft.
dt
engine pertomance
Since ange is Connected aorth the
though speitc fuel Consup on.
" SFC
fs
umt of
thsust o t
the uel consuming
" StC for Psopeller diven arCraft can be
be, written as
P = Shaft pouoeY.
For Tet airCraft
TSFC
Ct =
by
We
oriting TSFC in terms ofC
Can wsite:
CL
Ct = CVoo
Pr :
op elleh
vdocity.
Novo ,consdex an airplane in
în Steocy leel tÙhi
tet
s :
hotiaon tal dStance Coves ed
vee Strea
Vo
Ovex the
veloy
ds
veÍ
afs
tne
ds
VodtA
From TSFC
C
-wsube i n
4
Ct. = -dwt
de
dt
-o8Sub, a3) In
CtT
d6 =
Now teplaang dOf chich is equal to dw
duof
dw
ds
-Voo
dw
CtT
Ct ThiustsFc
mulflyand divde' by a 6 h 9lhgoat o}
Ct
ds
-Veo
T
dw
(L- w t p ) t
Ct
Inteqiaing using bourdaby condion
R=o
R= S
Initial
Pinal
W= Wo
W We
R
- Vas L
Ct
D
we
dw
Wo
(-) 3imits Chang es the itea
R = Vao
Ct
we
for set dríven arcsaft
Breguet Rarnge Bquatfon.
# This eg,uatfon s faluenced by G# diog atio, iarge
en is nvessel y proportional to TSFC
Rarge s directly proportional to free stream
veloty of alc .
* It is
al so intuenced by
nHal am t of fucl loodel.
Fo Propeller diven aïciaft
from
R Voo,
Ct.
8y Yepocng
Ct CVao
LPr
pr
C
Ct
R=
Lpr
dn, Wo
We
* Range eq" for propeller dsiven arcrat
* Range d pYopelte.
f+ drag tatio
. t is infuenced by
Porge fs inversely poporional to the SFC.
aoa um arge et popclier Aicraft) :
AS, Jt dhven Rounge ea is :
R= Voo
L nn
D
Ct
Wo
We
to get rmar Yange geneal forn :
We need VeoJmar
v s.c
as, L
2
Voo
2
o
=
2W
Jo SCL
mutiplyL on both sfdes
L
Voo
D
Veo
2w
Cp
C
Soo SCL C
Voo
2w. C ,
Cp
Subtituting in Brêuget eonn
R
2 w
t
R
SooS
CpiijVe
2w
los
cp we
ASSuroing Ct, Soo s.clto ahe Con stant s.
R
dw
Cp
we
2
2
We
Endusnce is the aNount Of time that ean aplone
Can Stoy in aus on 1 load of fuel.
- We
know that thiust Speuffc fuel conSuoptfon
Ct : -WA
-dwp
oltT
olt
-dwt
Ct
tor a 6t ea dy 9 CTuise Hight LN
L- $ T= D
.. dt := -duf
Ct
dt
-odt
Ct
w=Wo.
Integrating the above eqn for Ts0
To
T- E
W We
Wo
dt
We
Ct
+
Ct
Wo
.1
D
we
Now fo Propley diven azcyatt endusance
We
Ct
dw
W
6w
Ct
we
duw
C Voo
Pr
We
Ct
Subs eite
C.Vag
2Pr
2W
JWe-wo
Pr 2
Jwe
w
we
CD.
Cp
CL
2
2W
C
LI
No
Cvo
we
Wo
Giding Pfght
when an araoft
arcaft lying
lying Such that pouwer vui ed is
loge than the pouoe auai lable t uî descent athes
no powes that
than cimbing in this STtuaton these s
flrght is knoon as gding Aight 0x unaccelesate fght.
"The foxce diogam for uipouwExeol fight
RaofDestcent
L
WCOS
D
wn e
For eqyuilibium gbdé angle
Sioe
cOSe
tan
The gfdle angte ie
Lie cbag rabo
is strietly aa Aurction Lt
The hohe, the L/ the shal lowey the glide angle, so
it is înve,sely pIotioral.
Turn Radus in Level Flight
a level tun retess to a tuon
where the aivcraft mantoins a Constont altitude. The
Turn Radius R oith the tusn Yate w,depehcs on
orSpeed Qnd bank angle Thtsefoxe force acting on
the aîplane.
Hlight , Path
TOP Vicw of
hoiRontal plane.
No
Top View,
Hoigortal plane
Front view
LCos
mg
og cos
0.
Centsipetal force
2
2
Cos
9 tân
gtang
this is tuin aus.
e l s h s
3. Static Longitudinal Stability
vertfcalax's (ya)
Primy Contsol Surfoces
Roll -
AlíeronS
-datealas
pitch - Elevatoy
Lptteh)
yaw - Rudder.
longitudial
Degree of Freedom
ais (Rol)
4.TYanslationa - f|b, u/p, S-S
2- Rotational
Roll, pitch, ya
Nomenclatuse tor anfoil :
TE
max
mascchosd lioe
Aerodyhamic Centze :
is the point along the astoi
momevent does not
about uohich the pitchsng
with respet to argle of attack
AC
k
vasy
Ac
h'gh AoA
aífoil about
It is the
along the
Apoint
* Centes of Pressuse ; due
to
about i t is 3 xo
ement
moV
the
chich
pOlnt of (ift .
Center ot pesswe
otl Changes it's pos?tion when
the angle of attack Charges .
Aexoky nonic chavacterices
AoA
wei ht
" Lift
DYng
Thust
AC
Moment
i!
0
