aircraft stability and control Assignment

7/29/2019 aircraft stability and control Assignment

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Longitudinal Static Stability

Set aspect ratio of wing ARw = 12

Given wing span b = 2.8 m

Wing area At sea level take-off:

Sizing of horizontal tail Take off speed V = 1.2 =

From Xfoil plotter, Assume elliptical lift distribution, for finite wing is as follows: To enable the UAV has enough stick fixed degree of longitudinal static stability, static margin is

set to be 0.15.

Assume chord of horizontal stabilizer to be 45% of wing chord,


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From Xfoil plotter,

Length of fuselage Assuming the wing aerodynamic centre is located at quarter of the fuselage measured from nose.

Assuming the fuselage is a symmetrical hemispheric tube. The fuselage contribution to

longitudinal static stability is analysed using Multhopps method as follows:

station x wf x d/d wf2*(d/d)x

1 0.102 0.155 0.357 1.250 0.003

2 0.102 0.155 0.306 1.300 0.003

3 0.102 0.155 0.255 1.400 0.003

4 0.102 0.155 0.102 3.200 0.008

5 0.245 0.155 0.123 0.084 0.000

6 0.245 0.155 0.368 0.251 0.001

7 0.245 0.155 0.613 0.418 0.002

8 0.245 0.155 0.858 0.585 0.003

9 0.245 0.155 1.103 0.752 0.004

sum 0.0298


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Most forward CG limit using servo limit

From Xfoil plotter, ;

station x wf a0w wf2(a0w+it) x

1 0.207 0.155 -12.86 -0.064

2 0.207 0.155 -12.86 -0.064

3 0.207 0.155 -12.86 -0.064

4 0.207 0.155 -12.86 -0.064

5 0.207 0.155 -12.86 -0.064

6 0.207 0.155 -12.86 -0.064

7 0.207 0.155 -12.86 -0.064

8 0.207 0.155 -12.86 -0.064

9 0.207 0.155 -12.86 -0.064

Sum -0.577 From figure 2.12(Nelson), k2-k1=0.944

( )

Plot the above and equation to get


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From graph:

Moment equation: In trimmed flight, :

Assume 1 deg of elevator deflection changes the horizontal tail angle of attack by 0.4 deg, =0.4

From figure 2.21 (Nelson),

For =0.4, ; therefore

y = -0.15x - 0.0486-0.4

-0.2

0

0 0.5 1 1.5 2 2.5

C

m

CL

Cm vs CL


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From the data of the servo used, operating travel is 60deg, therefore maximum available

elevator deflections Most forward cg location ( ) Therefore, permissible cg range: between 0.168c and 0.467c from wing leading edge.

Without servo control With servo control

Most forward CG 0.317c 0.168c

Cruising at 2000ft at 60 km/h:

Sizing of horizontal tail

From Xfoil plotter, Assume elliptical lift distribution, for finite wing is as follows:

To enable the UAV has enough stick fixed degree of longitudinal static stability, static margin is

set to be 0.15.


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Assume chord of horizontal stabilizer to be 37.775% of wing chord,

From Xfoil plotter, Length of fuselage Assuming the wing aerodynamic centre is located at quarter of the fuselage measured from nose.Assuming the fuselage is a symmetrical hemispheric tube. The fuselage contribution to



1 0.102 0.155 0.357 1.250 0.003

2 0.102 0.155 0.306 1.300 0.003

3 0.102 0.155 0.255 1.400 0.003

4 0.102 0.155 0.102 3.200 0.0085 0.245 0.155 0.123 0.082 0.000

6 0.245 0.155 0.368 0.245 0.001

7 0.245 0.155 0.613 0.408 0.002

8 0.245 0.155 0.858 0.571 0.003

9 0.245 0.155 1.103 0.734 0.004

sum 0.0295


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From Xfoil plotter, ;

station x wf a0w wf2(a0w+it) x

1 0.207 0.155 -13.12 -0.065

2 0.207 0.155 -13.12 -0.065

3 0.207 0.155 -13.12 -0.065

4 0.207 0.155 -13.12 -0.065

5 0.207 0.155 -13.12 -0.065

6 0.207 0.155 -13.12 -0.065

7 0.207 0.155 -13.12 -0.065

8 0.207 0.155 -13.12 -0.065

9 0.207 0.155 -13.12 -0.065

Sum -0.588 From figure 2.12(Nelson), k2-k1=0.944

( )


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From graph:

Moment equation: In trimmed flight, : Assume 1 deg of elevator deflection changes the horizontal tail angle of attack by 0.4 deg, =0.4



y = -0.15x - 0.0448-0.4

-0.2

0

0 0.5 1 1.5 2 2.5

Cm

CL

Cm vs CL


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Cruising at 5000ft at 80 km/h:

Sizing of horizontal tail

From Xfoil plotter, Assume elliptical lift distribution, for finite wing is as follows:


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To enable the UAV has enough stick fixed degree of longitudinal static stability, static margin isset to be 0.15.

Assume chord of horizontal stabilizer to be 30.48% of wing chord, From Xfoil plotter, Length of fuselage Assuming the wing aerodynamic centre is located at quarter of the fuselage measured from nose.

Assuming the fuselage is a symmetrical hemispheric tube. The fuselage contribution to



1 0.102 0.155 0.357 1.250 0.003

2 0.102 0.155 0.306 1.300 0.003

3 0.102 0.155 0.255 1.400 0.0034 0.102 0.155 0.102 3.200 0.008

5 0.245 0.155 0.123 0.080 0.000

6 0.245 0.155 0.368 0.241 0.001

7 0.245 0.155 0.613 0.401 0.002

8 0.245 0.155 0.858 0.561 0.003

9 0.245 0.155 1.103 0.722 0.004

sum 0.0293


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From Xfoil plotter,

; station x wf a0w wf2(a0w+it) x

1 0.207 0.155 -13.51 -0.0672 0.207 0.155 -13.51 -0.067

3 0.207 0.155 -13.51 -0.067

4 0.207 0.155 -13.51 -0.067

5 0.207 0.155 -13.51 -0.067

6 0.207 0.155 -13.51 -0.067

7 0.207 0.155 -13.51 -0.067

8 0.207 0.155 -13.51 -0.067

9 0.207 0.155 -13.51 -0.067

Sum -0.606


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From figure 2.12(Nelson), k2-k1=0.944

( )


From graph:

Moment equation:

In trimmed flight, :

Assume 1 deg of elevator deflection changes the horizontal tail angle of attack by 0.4 deg, =0.4

y = -0.15x - 0.0437-0.4

-0.3

-0.2

-0.1

0

0 0.5 1 1.5 2 2.5

Cm

CL

Cm vs CL


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Summary for size of horizontal tailplane and most forward CG position with servo control

Wing aspect ratio AR 12

Wing area S 0.653 m2

Wing span b 2.8 m

Wing chord 0.2333m

Flight condition Sea level take

off

Cruise at 2000ft

at 60km/h

Cruise at 5000ft

at 80km/h

Horizontal tail volume ratio VH 0.731 0.720 0.708

Aspect ratio of horizontal tail ARt 7.74 10.69 15.98

Area of tailplane St(m2) 0.0854 0.0831 0.0808

Chord of tailplane ct(m) 0.105 0.0881 0.0711

Span of tailplane bt(m) 0.813 0.942 1.136

Area of elevator Se (m2) 0.0171 0.0166 0.0162

Chord of elevator ce (m) 0.0210 0.0176 0.0142

XNP/c 0.467 0.456 0.452

Xcg/c (without servo control) 0.317 0.306 0.302

Xcg/c (with servo control at

maximum deflection of elevator)

0.168 0.170 0.189


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Directional Static Stability

At sea level take-off: Take off speed

= 1.2

=

Use AXI4130/20 motor with 1311 prop and 30RC1700 battery.

The motor has the following characteristics:

Effeciency = 0.86;

Pout=782W

The dynamic thrust supplied is calculated as shown:

Set the spanwise between two engines = 1.4 m

One engine is off, therefore it creates yawing moment.

Yawing moment due to asymmetric thrust:

Assume chord of vertical tail to be 50% of wing chord: From Xfoil plotter,

Assume 1 deg of rudder deflection changes the fin angle of attack by 0.4 deg, =0.4

Assume fuselage is hemispheric tube,


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By referring to figure 2.29 in textbook (Nelson), By referring to figure 2.30 in textbook (Nelson),

(1)

(2) (3) (4)Substitute equation 2,3, and 4 into 1 yielding:


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Cruising at 2000ft at 60km/h:= Use AXI4130/20 motor with 1311 prop and 30RC1700 battery.


Effeciency = 0.86;

Pout=782W





Assume chord of vertical tail to be 40% of wing chord:

From Xfoil plotter, Assume 1 deg of rudder deflection changes the fin angle of attack by 0.4 deg, =0.4


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(1)



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Cruising at 5000ft at 80km/h:= Use AXI4130/20 motor with 1311 prop and 30RC1700 battery.


Effeciency = 0.86;

Pout=782W





Assume chord of vertical tail to be 32.35% of wing chord:

From Xfoil plotter, Assume 1 deg of rudder deflection changes the fin angle of attack by 0.4 deg, =0.4


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(1)



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Size of vertical tailplane with one engine out and crosswind of 20km/h

Flight condition Sea level take

off

Cruise at 2000ft

at 60km/h

Cruise at 5000ft

at 80km/h

Vertical tail volume ratio Vvt 0.0572 0.0410 0.0237

Aspect ratio of vertical tail ARvt 5.93 6,53 5.72

Area of vertical tailplane Svt(m2) 0.0807 0.0569 0.0326

Chord of vertical vertical tailplane

cvt(m)

0.117 0.0933 0.0754

Span of vertical tailplane bvt(m) 0.692 0.610 0.432


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Longitudinal Dynamics

Sea level take off

Assuming the flight is at low speed (M

and the flight is in zero angle of attack (straight

and level).


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[

]

det(sI-A)=0

The solutions yield the eigenvalues:


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Phugoid mode:

Short period

Cruise at 2000ft at 60km/h:

det(sI-A)=0



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Oscillation characteristics:

Cruising at 5000ft at 80km/h:

det(sI-A)=0


Oscillation characteristics:


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By approximation

Parameter Obtained:

m q U Thrust S Cd Cl Cdo Clo

sea

level

10 108.8

7

13.33

2

58.655

87

1.225 0.6532

4

0.8247

87

1.3794

3

0.8796

43

0.6

200

0 ft

10 160.6

2

16.67 46.910

62

1.007 0.6532

4

0.5132

49

1.0733

11

0.5464

59

0.6

500

0 ft

10 260.0

7

22.22 35.193

52

0.736

4

0.6532

4

0.2963

59

0.8260

84

0.3160

32

0.6

Cla Cma c Lf Iy

4.319 -0.616 0.233 1.87 2.91

4.5189 -0.64627 0.233 1.87 2.66

4.5972 -0.65838 0.233 1.87 2.34

Sea level:

Phugoid mode

Xu = -(CD + 2CDO)/Um

= -(0.824 + 2(0.879))/(13.32*10)=-1.3784

Zu = -(Cl + 2Clo)/Um

= -(1.379 + 2(0.6))/(13.32*10)

= -1.3759

Wph = = 1.006

Sph = -Xu/(2Wph)

=-(-1.3784)/(2(1.006))

= 0.685

Short mode

Zw=-(Cla+Cdo)(q*S)/(U*m)

=-(4.319 +0.879)(108.87*0.653)/(13.32*10)

=--2.7732

Mw=Cma(q*S*c)/(U*Iy)

=(-0.616)( 108.87*0.653*0.233)/(13.32*2.91)

=-0-0.26


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Mq=-lf*Cla(lf/U)*q*S/Iy

=-1.87*(4.319)(1.87/13.32)(108.87*0.653)/( 2.91)

=-27.7

Wnsp= = =8.966

Ssp=-(Mq+U*Mw+Zw)/(2Wnsp)

=-(-27.7+13.32*-0.263+-2.773)/(2*8.966)

=1.896

2000ft


= -(0.513 + 2(0.879))/(16.67*10)

=-1.01


= -(1.073 + 2(0.6))/(16.67*10)

= -1.431

Wph =

= 1.0917Sph = -Xu/(2Wph)

=-(-1.01)/(2(1.0917))

= 0.551

Short mode

Zw=-(Cla+Cdo)(q*S)/(U*m)

=-(4.518 +0.5464)(169.62*0.653)/(16.67*10)

=-3.188

Mw=Cma(q*S*c)/(U*Iy)

=(-0.64)( 160.62*0.653*0.233)/(16.67*2.66)

=-0.502

Mq=-lf*Cla(lf/U)*q*S/Iy

=-1.87*(4.518)(1.87/16.67)(160.62*0.653)/( 2.66)

=-37.3


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Wnsp= = =11.17

Ssp=-(Mq+U*Mw+Zw)/(2Wnsp)

=-(-37.3+16.67*-0.356+-3.1882)/(2*11.17)=2.0776

5000ft


= -(0.296 + 2(0.3160))/(22.2*10)

=-0.70985


= -(0.826 + 2(0.6))/(22.2*10)

= -1.545

Wph = = 0.826

Sph = -Xu/(2Wph)

=-(-0.7098)/(2(0.826))

= 0.4291

Lateral-Directional Dynamics


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Since the UAV is symmetrical, therefore


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det(sI-A)=0



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Cruising at 2000ft at 60km/h

det(sI-A)=0


,

,

,

Cruising at 5000ft at 80km/h

det(sI-A)=0


,

, ,


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Summary

Sea level take-off Cruise at 2000ft at

60km/h

Cruise at 5000ft at

80km/h

Longitudinal

motion

0.293 4.02s

eriod 10.73s

0.375 Lateral-directional

motion

eriod

, , , , , ,

aircraft stability and control Assignment

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