Flight Dynamics Prakul Complete.docx11111111111111111111111

8/4/2019 Flight Dynamics Prakul Complete.docx11111111111111111111111

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Ministry of Education and Science of Ukraine

National Aerospace University Kharkov Aviation Institute

Named after N.E Zhukovsky KhAI

Chair No.101

Course Project:

Flight dynamics

Calculation of aerodynamic characteristics aircraft

AERI-0000-0000-FD

Student: Mittal Prakul

Group: 10E4-1

Checked by:Prof-Ovcharov

Kharkov 2010


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CONTENT

1. Introduction. 32. Technical data 43. Calculation of aircraft aerodynamic characteristics 74. DETERMINATION OF AVAILABLE THRUST 105. GRAPH OF Cy max AGAINST MACH NUMBER 116. Polar Graph 127. Graph of Thrust vs Mach Number 138. Maximum and Minimum Flight Speed with Altitude 159. Determination of service ceiling 1610.Calculation of Power Altitude 1911.Rate of Climb Of the Aircraft 2012.Barograms of Climb 2313.Take-Off Characteristics of the Airplane 2514.Landing Characteristics of Airplane 2715.Conclusion 28


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Introduction:

Flight dynamics is the science of the aircraft motion in airspace by the

action of external forces applied to it.

Flight dynamics is, on the whole, a combination of three classical

branches of science, such as solid mechanics, fluid and gas mechanics

and mathematics.

The earlier project was dedicated to the calculation of aerodynamic

characteristics of the designed aircraft and presentation of the general

view of the aircraft with all of its parameters.

This project will present the flight dynamics of the aircraft which is the

science of aircraft motion in airspace by the action of external forces

applied to it.

With these characteristics we can determine performance parameters of

the aircraft and loads acting on its structure during flight in turbulent

conditions or during manoeuvring.

Analyzing flight dynamics helps the designers to countercheck and

perfect all their preliminary design work proceeding flight tests. Some of

the calculated parameters include:

Thrust: Available and required

Static and ballistic ceiling, Rate of climb, Barogram of climb and

longitudinal moment of the whole aircraft.


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2 Technical data

1.Take off mass - - 17666.67 kg2.

Cruising speed - - 850 km/hr3.Gross Wing area - S - 43.806

4.Wing span - L - 18.8 m5.Wing root chord - - 3.6 m6.Wing tip chord - - 1.06 m7.Mean Aerodynamic chord - - 2.6 m8.Aspect ratio - - 89.Taper ratio - - 3.4210. Fuselage length - - 19.06 m11. Fuselage diameter - - 2.3 mMass characteristics

Take off (preliminary) mass of aircraft m0 = 17666.67 kgs.

For flight dynamics calculations, we assume the decrement in the take off

mass as a result of fuel consumption during take off process, so mass of

aircraft considered for flight dynamics calculation is given as:

M= m0(o.9) =(17666.67)(0.9) =15900kgs.

Aerodynamic Parameters for Take- off and Landing mode:

M = 0

Cya

0 0.2 0.4 0.6 0.8 1.0

1.2 1.3157

(Cya max)


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Take-off flap angle = Landing flap angle =

() ()

() ()


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= = = =Calculation of aircraft aerodynamic characteristics

This includes determinetion of kinematics parameters of motion of mass center of an

aircraft depending on external forces acting on it.

Cya Calculation

Cxa = C xo + AC ya2

Cya =

g = 9.8 m/s2

qH =

v=(0.2,0.3,0.4,0.5,0.6,0.8,1.2) 330 m/s

m = 0.9.m0 m0 = take-off mass

Lift to drag ratio,

K=

Required thrust of the airplane

Preq =


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Calculated data for according to International Standard Atmosphere isas follows.

Height 0 3 6 11 Km

1.225 0.909 0.68 0.365

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cxo 0.02144 0.02079 0.02036 0.02004 0.01978 0.01955 0.01934

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

A 0.05166 0.05161 0.05154 0.05144 0.05131 0.05124 0.05105

Cyamax 1.31557 1.28705 1.25365 1.21535 1.17217 1.12410 1.07114

At H = 0

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cya

1.25383 0.55726 0.31346 0.20061 0.13931 0.10235 0.07836

Cxa

0.103 0.037 0.025 0.022 0.021 0.020 0.020

K

12.2141072 15.13597799 12.3291633 9.073314884 6.7056049 5.095566 3.9873056

Preq

12757.38184 10294.67864 12638.3296 17173.44007 23237.282 30579.533 39079.029


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At H=3

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cya 1.811777242 0.8052343

0.45294431

1

0.28988435

9

0.201308

6

0.147900

2

0.113236

1

Cxa

0.19157585 0.05478404

0.03145387

2

0.02486265

5

0.022349

3

0.021150

8

0.020464

6

K9.45723192

1 14.6983368

14.4002721

3

11.6594291

5

9.007359

3

6.992636

2

5.533270

4

Pre

q

16476.2829

9

10601.2014

5

10820.6308

8

13364.2931

7

17299.19

1

22283.44

6

28160.56

6

At H=6

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cya 2.689937466

1.19552776

3

0.67248436

7

0.43038999

5

0.298881

9

0.219586

7

0.168121

1

Cxa 0.396459546

0.095715483

0.044798203

0.030668517

0.0254335

0.0230707

0.0218129

K6.78489770

8

12.4904323

2

15.0114137

5 14.0336098

11.75148

6

9.517988

7

7.707411

3

Pre

q

22965.71534

12475.15102

10380.10357 11103.3463

13259.602

16371.109

20216.909


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At H=11

M 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cya 5.595150973

2.48673376

6

1.39878774

3

0.89522415

6

0.621683

4 0.456747

0.349696

9

Cxa 1.641353206

0.34245823

1

0.12364353

3

0.06364536

8

0.041940

8

0.032519

6

0.027822

8

K

3.40886468

7.26142209

2

11.3130684

2

14.0658178

2

14.82287

4

14.04529

3

12.56871

8

Pre

q

45710.2419

8

21458.6106

5

13773.4541

7

11077.9217

7

10512.13

4 11094.11

12397.44

8

DETERMINATION OF AVAILABLE THRUST

Pav = Po

Po = Maximum thrust available=61000 N

= 0.75 = (H, M)

H = 0

M 0.2 0.4 0.6 0.8

0.9 0.88 0.89 0.94

Pav54900 53680 54290 57950

H = 3

M 0.2 0.4 0.6 0.8

0.75 0.72 0.742 0.78

Pav45750 43920 45262 47580

H = 6

M 0.2 0.4 0.6 0.8


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0.58 0.56 0.572 0.6

Pav35380 34160 34892 36600

H = 11

M 0.2 0.4 0.6 0.8

0.38 0.37 0.38 0.393

Pav23180 22570 23180 23973

GRAPH OF Cy max AGAINST MACH NUMBER

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cya,C

yama

x

Mach

Cya0

Cya3

Cya6

Cya11

Cymax


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Polar Graph

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Cya

Cxa

Polar Graph

H=0

H=3

H=6

H=11


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Graph of Thrust vs Mach Number

Maximum and Minimum Flight Speed with Altitude

H M max M min V max (m/s) V min (m/s)

0 0.819 0.191 278.706 64.997

3 0.82 0.2372 269.452 77.944

6 0.823 0.295 260.48 93.37

11 0.839 0.4304 247.673 127.05

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Thrust(N)

Mach

Preq0

Preq3

Preq6

Preq1

1

Pavb

0

Pavb

3

Pavb

6

Pavb

11


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.permy.permmin

aSC

G2V

.optay.optmin

SC

G2V

,or

()

A is the tangency point of vertical straight line and curve )V(Preq corresponds to theoretical value of

minimum speed of horizontal steady flight .theorminV .

Minimum speed .permminV (point A of a figure above)

Tangency point B in figure shows optimal speed. i.e, Vmin opt

The tangency point C corresponds to the cruising speed of steady horizontal flight .cruisV


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Therefore from the graph ofthrust and mach no. We get the values below;

H V perm (m/s) V opti (m/s) V cruising (m/s) V contr (m/s)

0

72.586 95.012 145.2 40

3

87.112 110.081 165 54

8

104.45 129.765 181.5 61

11

142.05 171.63 224.4 74


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Speed of level flight with altitude

Determination of service ceiling

pH = p11 qH =

Where pH = pressure at static ceiling

;p11=

Pressure at altitude

11km=22700Pa;

Pa11= available thrust ;

= active thrust;

= passive thrust

We must note that the sum of active and passive thrusts give the required thrust,

At M=0.6,

( )

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300

V cont

Vmin

Vmax

Vopt

Vmin.per


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Xao11 = Cxao. qh. s

= 0.02211 X X 43.802=

N

Xai11 = Preq11 - Xao11 = 10522.2828= 4800.1223 N

Now PH = 22700 PH = 11635.98 Pa

The nearest altitude corresponding to this pressure is H= 15.3

H=11 Km At M=0.5

() Xao11 = Cxao. qh. s

= 0.02242 X X 43.802=

Xai11 = Preq11 - Xao11 = 11092.5723902.36

= 7190.21244 N

Now PH = 22700 PH = 14137.39838 Pa

The nearest altitude corresponding to this pressure is H= 13.9 Km

At M=0.7

()


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Xao11 = Cxao. qh. s

= 0.02183 X X 43.802= 3957.793 N

Xai11 = Preq11 - Xao11 = 11101.553957.793

= 7143.762 N

Now PH = 22700 PH = 13729.9 Pa


At M=0.8

()

Xao11 = Cxao. qh. s

= 0.02158 X X 43.802=

Xai11 = Preq11 - Xao11 = 12403.13= 2787.39 N

Now PH = 22700 PH = 10002.05


So my Static Celling is 15.3 Km


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Calculation of Power Altitude:

At H=11

V= 240

M= 0.705

= 11 + 3.012

= 13.95 Km

At H=11.5

V= 235

M= 0.691 = 14.31 km

At H=12

V= 225

M= 0.661 = 14.58 km

At H=12.5

V= 215

M= 0.632 = 14.85 km

At H=13V= 205

M= 0.602 = 15.14 km

At H=13.5

V= 175

M= 0.602

= 15.06km

H PH

11 13.95

11.5 14.31

12 14.58

12.5 14.8513 15.14

13.5 15.06

So, we obtain power height =15.14 Km


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Rate of Climb Of the Aircraft

Pi=(Pav-Preq)

Vyi- vertical flight speed

Vi- horizontal flight speed =M*330m/s

H=0

M 0.3 0.4 0.5 0.6

Po, N43986.17 41036.531 36137.44 31050.44

VYI m/s28.79 35.812 39.42 40.65

13.8

14

14.2

14.4

14.6

14.8

15

15.2

200 205 210 215 220 225 230 235 240 245

PH

V

Determination of Power Altitude

Vyi

Pi Vi

mg

PiPi


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H=3

M 0.3 0.4 0.5 0.6

Po, N34464.5 33091.942 29941.4252 27959.523

VYI m/s21.782 27.89 31.539 35.34

H=6

M 0.3 0.4 0.5 0.6

Po, N 22214.21823768.868 22439.611 21627.52

VYI m/s 13.52319.307 22.77 26.331

H=11

M 0.3 0.4 0.5 0.6

Po, N 1375.56 8773.6111347.43 12657.72

VYI m/s 0.521 4.98148.5903 14.373


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Dependence of Vyi on Altitude

The maximum rate of climb Vymax is found from the graph ofDependence of Vyi on

altitude H and their values are written in the table below:

H 0 3 6 11 15.3

Vymax 41 37 28.02 16.45 0

0

5

10

15

20

25

30

35

40

45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Vy

Mach Nos

Vy0 at

H=0

Vy3 at

H=3


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Since it is imposible for the aircraft to operate at zero Rate, the practicle ceiling at zero

rate is taken to be Vy*=4 m/s . This corresponds to Altitude 14.21 km (from graph)

Rate of Climb with Altitude

Barograms of Climb

The minimum time of climb from altitude H1 up to altitude H2 shall be calculated

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30 35 40 45

Height

Vymax

H


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In order to realize this, we shall need to draw a graph of against Mach number M,

and thereafter calculate the area under the graph for each rise of altitude. This area is

equal to the time.

H 0 3 6 11 0.02439 0.027027 0.035689 0.0608t, sec 0 81.08 214.134 668.8

Altitude Vs 1/Vymax

0

2

4

6

8

10

12

14

16

18

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

H

1/Vymax


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Take-Off Characteristics of the Airplane

0

2

4

6

8

10

12

0 100 200 300 400 500 600 700 800

Altilude Vs Time

Barograms of Climb


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2.10 Take-off Characteristics of the airplane

Take-off distance shall be calculated as the sum of take-off run distance and climb

distance

Ldist = L t-off+ Lclimb

= V2

t-off

2J xaw

Vt-off = 1.1 x Vmin-theory

= 1.1 x 66.48

= 73.125 m/s

Horizontal Acceleration Jxaw = g * ()+Where,

f= 0.03 Pav=Pt/o= 54900 N v2

av=0.5X V2

t/o

= 9.8* ()+=3.07 m/s

2

L t-off= 871.44 m

Time taken for take off

T take-off = Vt-off

J xaw

=23.84 sec


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For the climb distance L climb = * +

Vclimb=1.3X Vt/o= 1.3X73.125=95.063 m/s

So , Lclimb = *()() +

= 622.32 m

L dist = 871.44 + 622.32

=1493.76 m

2.11 Landing Characteristics of Airplane

Total Landing Distance shall be calculated as the sum of gliding, holding off and

landing run distance.

The summation of the gliding, flattening out and pan distance L*

L* = Kav

L* = 13.672() ()

= 1499.202m

Calculation of time and length of landing run of the airplane

L l run =

Jav = 3.82 m

L l run =() =346.21 m


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t run = =

CONCLUSION

We successfully completed the Flight Dynamics characteristics of our flight. The values

obtained from these calculations, when compared with those of the prototype

airplanes, are in good accord. A more precise value can only be obtained when a model

of

the airplane is subjected to wind tunnel tests. However, we can use these obtained

valuesto continue preliminary design of the airplane units

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Flight Dynamics Prakul Complete.docx11111111111111111111111