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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
The nearest altitude corresponding to this pressure is H= 14.5 Km
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
The nearest altitude corresponding to this pressure is H= 15.5 Km
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