Aero Vehicle Performance
Transcript of Aero Vehicle Performance
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1
Aircraft Range
Aircraft Performance and Design
Chapter 5 Part J
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INTRODUCTION
We discussed tead! and "e#e" f"ight
Then stead! c"im$ing f"ight
We come $ac% to stead! "e#e" f"ight todiscuss t&o more #er! important
topics of A'C performance
Range(ndurance
)
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*
Range
Distance a"ong the ground co#ered in
one "oad of fue" is the range +
Consider the fo""o&ing termino"ogies ,,gross &eight of the airp"ane
,,&eight of the fue"
,,&eight of the airp"ane &ith no fue"
0W
fW
1W
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Range
At an! instant during the f"ight. the &eight of
the airp"ane /W0 is
Indeed the time rate of change of &eight is
oth dW'dt and dWf'dt are negati#e
num$ers
fWWW += 1 2531-)4
ff
Wdt
dW
dt
dW .0 =+= 2531-*4
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5
Range
Range is intimate"! connected &ith
engine performance through the C
C for PD'reciprocating engine
C for JPA
C com$ined
P
Wc
f
.
6531--7
T
W
c f
t
.
6531-57
pr
t
cVc
6*3-*7
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8
Range
Consider stead! "e#e" f"ight
Assuming stationar! atmosphere
A genera" range re"ation can $e found9
A modified e:uation 531-5 cou"d $e
dtVds
dt
dsV
=
=
6531-87
Tc
dWdt
T
dtdWc
t
f
f
t
=
/
6531-;7
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;
Range
u$stitute e:uation 531-; in 531-8
rom e:uation 531-).
(:uation 531-< $ecomes
f
t
dW
Tc
Vds = 6531-
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'D is maBimum
This condition is different for PDAsand JPAs
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1)
aBimum Range for JPA
Range e:uation for JPA is a"read!
gi#en $! e:uation 5315) in the form of
thrust specific fue" consumption
Eere maBimum range is dictated $!
the product of #e"ocit! and >'D3 >et useBamine the product
1
0lnW
W
D
L
c
VR
t
= 65315)7
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1*
aBimum Range for JPA
The product is
Thus the product is maBimum &henthe aircraft is f"!ing at maBimum
To get a more eBp"icit eBpression "et
us put e:uation 5315- into 53151
D
L
D
L
L C
C
S
W
C
C
SC
W
D
LV
2/122
==
65315-7
D
L
C
C 2/1
=1
0
W
Wt W
dW
D
L
c
VR 6531517
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1-
aBimum Range for JPA
We get
( )2/112/1
0
2/1
2/1
2/1
2/1
t
2/1
22
or21
aswrittenbecan5.155equationconstant,and,,cAssuming
21
0
1
0
1
WWC
C
ScR
W
dW
C
C
ScR
C
C
W
dW
C
C
S
W
c
R
D
L
t
W
WD
L
t
D
L
D
L
W
W t
=
=
=
6531517
6531557
6531587
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15
aBimum Range for JPA
(:uation 53158 is a simp"ified range
e:uation for a Fet,prope""ed airp"ane3rom this e:uation &e see that for
maBimum range"! at maBimum
Ea#e the "o&est possi$"e thrust C"! at high a"titude i3e3 "o& densit!
Carr! a "ot of fue"
DL CC /2/1
( )2/112/1
0
2/1
22 WWCC
ScR
D
L
t
=
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18
aBimum Range for JPA
What happens &hen densit! goes to
GeroH O$#ious"! from the e:uation
range goes to infinit! ut is that possi$"eH Isnt !our a"titude
"imited $! a$so"ute cei"ingH
o the deciding factor is Therefore maBimum range for JPA is
o$tained at a f"ight #e"ocit! for maB
DL
CC /2/1
DL CC /2/1
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1;
aBimum Range for JPA
Which means
( )
2/1
0,
max/
322/1
= S
W
C
KV
DCC DL
4/1
3
0,
2/1
3
1
4
3
=
DD
L
KCC
C
2
0, 3 LD KCC =
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N(T - >ID( AR( OPTINA>
1'D is the deciding factor
Therefore for maBimum range9"! at maB >'D
Ea#e highest possi$"e prope""er
efficienc!Ea#e "o&est possi$"e C
Carr! a "ot of fue"
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))
aBimum Range for
PD'reciprocating engine
Therefore theoretica" maBimum range
is o$tained $! f"!ing at #e"ocit! at
&hich >'D is maBimum. that is2
0, LD KCC =
( )
2/1
0,
max/
2
=
S
W
C
KV
D
DL
KCD
L
D 0,max 4
1=
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(AP>( 531=
11'@1'15Chapter 5 , PART A
)*
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(AP>( 531=
11'@1'15Chapter 5 , PART A
)-
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)5
Aircraft (ndurance
Aircraft Performance andDesign
Chapter 5 Part K
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)8
Aircraft (ndurance
(ndurance9 It is amount of time that
an airp"ane can sta! in air on one "oad
of fue" >ong endurance is Re:uirement of
sur#ei""ance airp"anes
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);
Aircraft (ndurance
rom e:uation 531-5
ince T?D. >?W in stead! "e#e" f"ight
Tc
dWdt
or
Tcdt
dW
t
f
t
f
=
=
65318-7
W
dW
cD
L
Dc
dWdt
f
tt
f 1==
6531857
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)'D. and W are%no&n throughout the f"ight. e:uation 53188 can $e
numerica""! integrated to o$tain an eBact resu"t for
the endurance
or pre"iminar! f"ight performance
==0
1
1
0
11 W
W
f
t
W
W
f
t W
dW
D
L
cW
dW
D
L
cE 6531887
1
0ln
1
1 0
1
W
W
D
L
cE
or
W
dW
D
L
cE
t
W
W
f
t
=
= 65318;7
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)=
Aircraft (ndurance for JPAs
(:uation 5318; is a"read! eBpressed in terms of
thrust PC. and it gi#es endurance for JPA
direct"!
or aBimum endurance for a JPA "! at maBimum >'D
Ea#e the "o&est possi$"e thrust C
Carr! a "ot of fue"
1
0
ln
1
W
W
D
L
cE t=65318;7
c
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N(T * >ID( AR( OPTIONA>
*@
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*1
Aircraft (ndurance for PDAs We %no& that
u$stituting in integra" e:uation 53188. &e ha#e
Using #a"ue of #e"ocit!. &e ha#e
pr
t
cVc
6*3-*7
=0
1
W
W
f
D
Lpr
WdW
CC
cVE
=
=
0
1
0
1
2/3
2/3
2
2
W
W
f
D
Lpr
W
W
f
D
LLpr
W
dW
C
C
W
S
cE
or
W
dW
C
C
W
SC
cE
65318
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*)
Aircraft (ndurance for PDAs
! ma%ing the assumption of constants. &e ha#e
aBimum endurance for a PDA corresponds to "! at maBimum
Ea#e the "o&est possi$"e C
Carr! a "ot of fue"
"! at sea "e#e" &here densit! is the "argest #a"ue
( )2/10
2/1
1
2/3
2
= WWC
CS
cE
D
Lpr
65318=7
D
L
C
C 2/3
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**
ummar!
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(AP>( 53)@
11'@1'15Chapter 5 , PART A
*-