Aero Vehicle Performance

7/23/2019 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*


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-


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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(: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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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;


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=


)-


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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)@


*-

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