AeroII_33PropellerTheoryII

8/17/2019 AeroII_33PropellerTheoryII

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Aero II

Lecture 33 Propellers IIJ. E. Brandenburg

EAS 3101Spring 2007


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• Stall Speed E a!ple• Si!ple Propeller E a!ple• Propeller design

• "o!e#or$ %&

Agenda


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Stall Speed

L

L

L

AC W

V

LW Weight AC L

V

AC V L

∞∞

∞∞

∞∞

=

===

=

ρ

ρ

ρ

2

22

1 2


4/33

Stall Speed

' L

α

αL(0

' L)*a


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Stall Speed

Max L stall

L

AC W

V

AC W

V

LW Weight

−∞

∞∞

=

=

==

ρ

ρ

2

2


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Stall Speed E a!ple

• A #ing design +as a !a i!u! ' L (2.3 atα(20 o #it+ ,ull ,laps e tended and a #ingarea o, - !eters s uared.

• /+e aircra,t +as a ,ull loaded #eig+t o,1000 g

• +at is its stall speed at rlando airport4 sea le5el ρair (1.2 $g6! 3


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Stall Speed

[ ]

mphm

mkg xmkg x

mkg x

xm xmkg

mkgx x

AC

W V

Max L stall

80sec628

sec61079.861078.2

sec6108.1-

3.2-62.1

sec6-.:100022

261222

261

1

23

261

23

2

≅=

−=−=

==−∞ ρ


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Stall Speed E a!ple

• Suppose pre5ious aircra,t +as added 900$go, cargo and is no# a !ass o, 1900 g

• Suppose it no# is landing at Albu uer ue at1800 !eters altitude +at is its ne# stallspeed

4 sea le5el ρair (1.2 $g6! 3


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Stall Speed

[ ]

mphm

mkg xmkg x

mkg x

xm xmokg

mkgx x

AC

W V

mkg xkmkmmkg

Max L stall

air

:0sec63-

sec6109-:.1610-9.1

sec61079.2

3.2-6.1

sec6-.:190022

60.1-37.2.1:68.1e p462.1

261223

261

1

29

261

23

2

33

==

−=−=

==

==−=

−∞ ρ

ρ


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Propellers

'essna S$;+a#$)a +ig+l; opti!i


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Propeller sections

β Blade pitc+angle

β

β

β


12/33

Propeller /+eor;

φ φ α β φ

α

β

sincos D LT

attack of angle

angle pitch

−=−=

=

=


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Propeller /+eor;

∞∞ ==

=

==

==

V P

T V T P

AvailableThrust T

Available Power P efficiency

ngine from Power P P P

A A A A

A

A

A

η

η


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Propeller 'alculation• e can !odel a propeller as +a5ing an a5erage pitc+ angle o, β(30 o and

pro,ile o, =A'A 291& and total area o, 0.9! 2• I, #e +a5e t+e propeller turning at n(90rps and it +as a dia!eter o,

2!eters its a5erage rotational 5elocit; is> rot(?69 2 π n(128!6sec

• At 1&0!p+ 4 88!6sec #e +a5e angle φ(tan )14886128 (27 o

• /+e a5erage angle o, attac$ on t+e propeller blade is t+usα = β − φ = 30o−27o = 3o

• /+e total a5erage 5elocit; seen b; t+e propeller is>(4> rot2 @>2 162 ( 41&-78@93&8 162(192!6sec


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Propeller 'alculation

tonsk! ! x ! xT

mmmkg T

mmmkg T

AV D LT

A

A

A

A

o

&.07.9107.9214.102.2

214.sec6192462.14&.0

&394.9.0sec6921462.14&.0

.9&4.01.-:4.84.

2

1sincos

27

39

223

223

2

≅==

==

=+=−=

=

ρ φ φ

φ


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B-3&00

913

7&.1101.3

101.3107.9sec688

2

&3

=⇒=

=

=

=

===

P P hp power engine

hp P

kW hpkW x P

W x ! x xmVT P

A

A

A

A A


19/33

Propeller at /a$eo,,

• Cor ta$eo,, t+e propeller is not so e,,icient• Assu!e sa!e rotational 5elocit; #it+ no

c+ange in pitc+


20/33

Propeller 'alculation• e can !odel a propeller as +a5ing an a5erage pitc+ angle o, β(30 o

and pro,ile o, =A'A 291& and total area o, 0.9! 2• I, #e +a5e t+e propeller turning at n(-0rps ,or ta$eo,, 4,ull t+ottle

and it +as a dia!eter o, 2!eters its a5erage rotational 5elocit; is> rot(?69 2 π n(2&1!6sec

• At 33!p+ 4 9.9!6sec #e +a5e angle φ(tan )1419.&62&1 (.08o

• /+e a5erage angle o, attac$ on t+e propeller blade is t+us

α = β − φ = 30o

−.06o

≅ 30o

• /+e total a5erage 5elocit; seen b; t+e propeller is>(4> rot2 @>2 162 ( 483001@210 162(2&1!6sec


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α=30ο, ' L≅1.2 ' ?≅.012


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tonsk! ! m xT

mm xmkg T

mmmkg T

AV D LT

A

A

A

A

o

-.11-9-.0sec6103.848.0

2.149.0sec6103.8462.14&.0

2.149.0sec62&1462.14&.0

.0.00.142.14

2

1sincos

0

229

22293

223

2

≅==

==

=+=−=

≅

ρ φ φ

φ


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70&0039-

39-

7&.1108.2

108.210-.1sec6&.19

2

&9

===

===

===

P P hphp

hp P

kW hpkW x P

W x ! x xmVT P

A

A

A

A A

η


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Propeller /+eor;

nDV

" ratio A#vance "

spee# tip propeller V D

rotationof fre$uencyangular n

tip

∞==

×==

==

22

2

ω

π ω


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0:.2sec6-0sec6&.19

D

-2.2sec690

sec688D

22

2

==

==

==

×==

==

∞

mm

" takeoff

mm

" cruise

nD

V " ratio A#vance "

spee# tip propeller V D

rotationof fre$uencyangular n

tipω

π ω


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Propeller /+eor;

η

β1 β2


27/33

ing Spoiler


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?ucted ,an

A propeller s+roud increases e,,icienc; b;eli!inating 5orte s+edding ,ro! propeller tips


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?ucted ,an


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?ucted ,an

/urbo,an engine


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?ucted ,ans


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prop,ans


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"o!e#or$ %&

• 1430 pts Cor t+e aircra,t described earlier #+at ist+e stall speed ,or an o5erloaded plane o, 1800$g

!ass A. at rlando B. on t+e Siac+in Flacier4 9$! altitude• 2. 430 pts Cor t+e propeller described earlier A.

#+at is t+e t+rust ,or n(80rps and >(28-!p+ B.#+at is t+e e,,icienc; '. s$etc+ t+e cur5e o,

propeller e,,icienc; using t+e pre5ious t#o points.

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