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8/13/2019 Taxa_subida e Curva
1/22
G.Le
ng,M
EDept,NUS
4:C
limband
TurnPerformance
orhownim
bleistheaircraft?
8/13/2019 Taxa_subida e Curva
2/22
G.Le
ng,M
EDept,NUS
Therateofclimb(R
OC)
T
herateofclim
b(ROC)istherateat
w
hichanaircraftincreasesitsaltitude
Climbrecords
h(km)time(s)
ROC(m/s)
8/13/2019 Taxa_subida e Curva
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G.Le
ng,M
EDept,NUS
Clim
bmodel
:flightpath(climb)angle
8/13/2019 Taxa_subida e Curva
4/22
G.Le
ng,M
EDept,NUS
Resolvingforcesparallelandperpendicular
toflightpath
(velocityV)
TDW
sin
=
mdV/dt
LWco
s
=
mVd/dt
Theclimbrateisthen
d
h/dt
=
Vsin
=
or
(TD)V
=
8/13/2019 Taxa_subida e Curva
5/22
G.Le
ng,M
EDept,NUS
T
heclimbequa
tion
(TD)V
=
dh/dt
+d[V
2/(2g)]/dt
W
8/13/2019 Taxa_subida e Curva
6/22
G.Le
ng,M
EDept,NUS
Specificenergy
Thequantityo
ntherhsofth
eclimbequationcanbewrittenas:
dh/dt
+d[V
2/(2g)]/dt
= =
8/13/2019 Taxa_subida e Curva
7/22
8/13/2019 Taxa_subida e Curva
8/22
G.Le
ng,M
EDept,NUS
Example:
F104P
sc
urves
Howto
flyfrom
energy
stateAto
stateB
asfastas
possible?
A
B
Sou
rce:NASATND6398
8/13/2019 Taxa_subida e Curva
9/22
G.Le
ng,M
EDept,NUS
C
ompariso
nF4H-1v
sF15A
F4H-1
2xJ79-GE-2Aturbojets
thrust
=2x10
,350lb(2x4,693kg)
MTOW
=
54
,600lb
(24,761kg)
T/W
=
F15A
2xF100-PW-100turbofan
thrust
=
2x25,0
00lb(2x
11,2
50kg)
MTOW
=
5
6,000lb
(25,200kg)
T/W
=
8/13/2019 Taxa_subida e Curva
10/22
G.Le
ng,M
EDept,NUS
Ene
rgy-Mane
uverabilit
yTheory
DevelopedbyU
SAFColJohn
BoydatGeorgia
Te
chin1962
Th
esis:
Pr
ovedthattheF-4couldnotoutturnaMiG
-21
ex
ceptatlowaltitudeandhigh
speed
E-
Mtheorywas
appliedtothe
designofthe
F1
5andF16
USAF
ColJohnBoyd
1
927-1997
8/13/2019 Taxa_subida e Curva
11/22
8/13/2019 Taxa_subida e Curva
12/22
G.Le
ng,M
EDept,NUS
S
ustainedlevelturn
model
Lcos
=
Lsin
=
Resolving
forcesinthev
erticaland
horizontaldirections
L
:
:bankangle
d/dt:turnrate
W=
mg
8/13/2019 Taxa_subida e Curva
13/22
G.Le
ng,M
EDept,NUS
D
efinetheload
factorn
=
L/W
=
1/cos
(n>
1)
Dividingthe2
forceequations
V/gd/dt
=
tan
= =
8/13/2019 Taxa_subida e Curva
14/22
G.Le
ng,M
EDept,NUS
Theturnequationis:
d/dt
=
(g/V)(n2
-1)
Theturnradiusis:
R
=
V/d/dt
=
V2/(g(n2-1))
8/13/2019 Taxa_subida e Curva
15/22
G.Le
ng,M
EDept,NUS
E
xample:
Turnenvelope
8/13/2019 Taxa_subida e Curva
16/22
G.Le
ng,M
EDept,NUS
Exercise:
Per
formance
estimation
AssumingAhasacornervelocityof450ktsat
aloadfactorof8,whats
thetu
rnradiusand
turnrate?
AssumingBisflyingatthesame
speed,whatstheloadfactorandturn
ratef
orB?
8/13/2019 Taxa_subida e Curva
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G.Le
ng,M
EDept,NUS
Tu
rnatmax
imum
loadfactor
Question:Whatsthe
bankangle?
8/13/2019 Taxa_subida e Curva
18/22
G.Le
ng,M
EDept,NUS
lo
adfactorn=
bank
angle=
airspeedV
=
450kts=
450*0.5151
=
232m/s
tu
rnrate
= = = =
turnradius
=
V/turnrate
=
8/13/2019 Taxa_subida e Curva
19/22
G.Le
ng,M
EDept,NUS
RA
=
V2/(g(nA
21
))
RB
=
V2/(g(nB
21))
loadfactornB
= =
turnrate
= =
8/13/2019 Taxa_subida e Curva
20/22
G.Le
ng,M
EDept,NUS
Comparisonofturn
rates
8/13/2019 Taxa_subida e Curva
21/22
G.Le
ng,M
EDept,NUS
BottomLine
Highturnrat
esrequirehighloadfactors
Notes:
8/13/2019 Taxa_subida e Curva
22/22
G.Le
ng,M
EDept,NUS
V-n
Diagram