alexa Calculation of the Flight Characteristics of the Aircraft, AN-225 | Open Access Journals
ISSN: 2168-9792
Journal of Aeronautics & Aerospace Engineering
Make the best use of Scientific Research and information from our 700+ peer reviewed, Open Access Journals that operates with the help of 50,000+ Editorial Board Members and esteemed reviewers and 1000+ Scientific associations in Medical, Clinical, Pharmaceutical, Engineering, Technology and Management Fields.
Meet Inspiring Speakers and Experts at our 3000+ Global Conferenceseries Events with over 600+ Conferences, 1200+ Symposiums and 1200+ Workshops on
Medical, Pharma, Engineering, Science, Technology and Business

Calculation of the Flight Characteristics of the Aircraft, AN-225

Ahmed Soliman M.Sherif*

Novosibirsk State Technical University, Russia

*Corresponding Author:
Ahmed Soliman M.Sherif
Researcher, Novosibirsk State Technical University
pr. Karla Marksa, 20, Novosibirsk, Novosibirskaya-oblast', Russia
Tel: +7(952)900-64-61
E-mail: engsherifsoliman78@gmail.com

Received Date: February 10, 2017; Accepted Date: March 06, 2017; Published Date: March 10, 2017

Citation: Ahmed Soliman M.Sherif (2017) Calculation of the Flight Characteristics of the Aircraft, AN-225. J Aeronaut Aerospace Eng 6:183. doi: 10.4172/2168- 9792.1000183

Copyright: © 2017 Ahmed Soliman M.Sherif. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Visit for more related articles at Journal of Aeronautics & Aerospace Engineering

Abstract

Flight dynamics - The science of the laws of motion of aircraft under the influence of wind, gravity, and reaction forces. It is a combination of mainly three classic disciplines: solid mechanics, fluid dynamics, and mathematics. Among the wide range of problems in the dynamics of flight of great practical importance are the problems connected with the study of the steady rectilinear motion of the aircraft. The solution allows them to determine the flight characteristics of the aircraft, characterized by the range of possible speeds and heights, rate of climb, range, flight time, and so on.

Keywords

Calculation aerodynamic characteristics of the aircraft, AN-225; Thrust required and thrust available; Practical ceiling of aircraft; Building a polar flight; Flight dynamics

Introduction

Building a polar flight, making level flight at various speeds (Mach number 0.4 to 0.9) and on the same altitude, the aircraft as it passes from one polar to another, it is the flight of the aircraft polar.

From the equilibrium conditions of the lift Ya gravity (weight) G (G = mg) in a horizontal flight:

aeronautics-aerospace-engineering

Where, aeronautics-aerospace-engineering on the height and a constant weight of the aircraft,the value is constant.

All calculations are carried out in SI.

From this formula, it follows that, in a steady horizontal flight, each Mach number M complies to

a specific lift coefficient CYa.

For the aircraft, AN-225 with turbojet engines must use the curves of required and available thrust. Calculation and construction of required thrust PReq by the formula:

aeronautics-aerospace-engineering the aerodynamic quality of the aircraft.

When determining the flight characteristics of the aircraft used by the equation of power in the projection on the axis of the trajectory of the coordinate system, considering at the same plane as the material point of variable mass. And when the aircraft stability and controllability of the calculations it is regarded as solid [1-4].

Initial data for the implementation of the research is of course work in aerodynamics,

"Calculation of aerodynamic characteristics of the aircraft AN-225", its geometrical parameters, the aerodynamic characteristics and polar cruising.

Research includes calculations, graphics and drawings, explanation and justification of the calculation of performance, the characteristics of longitudinal stability and controllability of the aircraft.

To calculate the flight characteristics of the aircraft AN-225, used the method of N.E. Zhukovsky,

A method based on the construction of curves thrust required and thrust available, which is determined by the parameters of steady flight modes.

Initial Data

Characteristics of the standard atmosphere are as follows:

Calculate thrust required and thrust available

Calculation of the algorithm:

Specifies flight height, Н, m.; H=0

Specifies the number of flight Mach; M=0.3

Determine the relative density of the air; Δ (Table 1); Δ=1

Height,
H, (km)
Relative density,
Relative speed of sound, Ka Density,
aeronautics-aerospace-engineering  
 aeronautics-aerospace-engineering
0 1 1 1.225 141.8*103
2 0.822 0.977 1.0067 111.3*103
4 0.699 0.954 0.8194 86.3*103
6 0.538 0.930 0.6602 66, 08*103
8 0.429 0.905 0.5259 50*103
10 0.337 0.880 0.4136 37.06*103
11 0.298 0.867 0.3648 31.75*103
12 0.2536 0.867 0.3156 27.48*103
14 0.185 0.867 0.2306 20.08*103
16 0.135 0.867 0.1654 14.4*103
18 0.0983 0.867 0.1207 10.51*103
20 0.0718 0.867 0.0889 7.74*103

Table 1: Characteristics of the standard atmosphere.

aeronautics-aerospace-engineering

Determine the ratio; Ka (Table 1); Ka = 1

Determine the speed of sound at a given height with a given number M, (m/s).

aeronautics-aerospace-engineering

Where, aН=0=340.28 м/s - the speed of sound at sea level H=0

Determine the flight speed (m/s); V= [M×aН=0] =0.3×340.28=102.08 m/s.

aeronautics-aerospace-engineering

Determine the average gross weight of the aircraft, (N).

aeronautics-aerospace-engineering

where,W0= 640 ton-takeoff weight of the aircraft;

Wf =128 ton-mass of the fuel

The coefficient of aerodynamic lift in a horizontal flight.

aeronautics-aerospace-engineering

where,

Cymax cruiser is the maximum lift coefficient of the wing when stowed mechanization (Tables 2-4).

Changing the ratio of
the polar blade,
Ka(M)
Mach number
(M)
Change parasitic drag coefficient,
KCX0(M)
Changing the maximum lift coefficient,
Kcymax(M)
1 0 1 1
1 0.2 1 1
1 0.4 1 1
1.09 0.6 1.03 0.94
1.16 0.7 1.2 0.89
1.27 0.8 1.5 0.81
1.4 0.9 1.9 0.73
1.6 1.0 2.0 0.65

Table 2: Odd changes in the number of M.

Take-off weight, m0 Fuel
weight, mf
Wing area, S, m2 Take-off thrust, P0, k N Parasitic drag coefficient, Cx0 Wingspan,
Lwing, m
Specific fuel consumption, aeronautics-aerospace-engineering
640 128 905 6*234 0.021 88.4 0.057

Table 3: Personal data on the aircraft AN-225.

Cymax
cruiser
Mmax Qmax, aeronautics-aerospace-engineering Cmax, T.off KT.off Cymax const Kconst
1.7 0.88 22 2.5 8.5 3.1 5.0

Table 4: Personal data on the aircraft AN-225.

Determine the effective extension of the wing:

aeronautics-aerospace-engineering

aeronautics-aerospace-engineering

Where, δ =0.02….0.04;

S=905 m2- wing area;

Lwing = 88.4 - wingspan

Determine the ratio of the blade of the polar;

aeronautics-aerospace-engineering

Determine the rate of change of blade polar depending on the number of M, KA (Table 2); KA=1

Determine the rate of change of parasitic drag coefficient as a function of the number of M, KCX0 (Table 2).

KCX0 =1

Determine the drag coefficient in horizontal flight;

aeronautics-aerospace-engineering

where,Cx0=0.021- parasitic drag coefficient (Table 3).

Define flight aerodynamic efficiency;

aeronautics-aerospace-engineering

Identify thrust required for level flight, N.

aeronautics-aerospace-engineering

Determine the ratio of thrust change the number of M.

aeronautics-aerospace-engineering

Determine the takeoff thrust engines (N) (Table 3).

P0 =6*234000=1404000N

Identify the thrust available in horizontal flight.

When,

aeronautics-aerospace-engineering

aeronautics-aerospace-engineering

By algorithm, using a program in Excel.

The calculation results are shown in Tables 5 - 13 and in Figures 1 - 13.

Flight altitude, км 0
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 1 1 1 1 1 1 1 1 1 1
The air density, rH, kg/m3 1.225 1.225 1.225 1.225 1.225 1.225 1.225 1.225 1.225 1.225
Coefficient Ka 1 1 1 1 1 1 1 1 1 1
The speed of sound a, m/S 340.28 340.28 340.28 340.28 340.28 340.28 340.28 340.28 340.28 340.28
Flight speed , V, m/s 34.03 68.06 102.08 136.11 204.17 238.20 272.22 289.24 306.25 323.27
Dynamic pressure, N/m2 709 2837 6383 11347 25532 34752 45390 51241 57447 64007
The average gross weight of the aircraft, Gav. N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamiclift in horizontal flight, Cyh.f. 8.80 2.20 0.98 0.55 0.24 0.18 0.14 0.12 0.11 0.10
Effective of wing extension , λ 8, 38 8.38 8, 38 8, 38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1, 03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa h.f. 2.9664 0.2051 0.0574 0.0325 0.0241 0.0266 0.0324 0.0365 0.0405 0.0415
Flight aerodynamic quality, K 2.97 10.73 17.05 16.93 10.14 6.75 4.24 3.34 2.68 2.35
Thrust required
Prequired, N
1903984 526541 331364 333815 557029 837300 1331466 1690318 2107042 2403497
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0, 935 0, 950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N, 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available, Pavail, N 1364674 1336496 1319381 1313245 1333575 1359872 1396812 1419246 1444309 1471990
Vertical speed, Vy, m/S -3.25 9.76 17.85 23.59 28.06 22.03 3.15 -13.88 -35.92 -53.29

Table 5: The calculation of thrust required and thrust available, H = 0 km.

Flight altitude, км 2
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.822 0.822 0.822 0.822 0, 822 0.822 0.822 0.822 0.822 0.822
The air density, aeronautics-aerospace-engineering 1.0067 1.0067 1.0067 1.0067 1.0067 1.0067 1.0067 1.0067 1.0067 1.0067
Coefficient Ka 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977
The speed of sound a, m/S 332.454 332.454 332.454 332.454 332.454 332.454 332.454 332.454 332.454 332.454
Flight speed , V, m/s 33.25 66.49 99.74 132.98 199.47 232.72 265.96 282.59 299.21 315.83
Dynamic pressure, N/m2 556 2225 5007 8901 20028 27260 35605 40195 45063 50209
The average gross weight of the aircraft, GAv, N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
11.22 2.81 1.25 0.70 0.31 0.23 0.18 0.16 0.14 0.12
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0, 038 0.038 0.038 0, 038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1, 95
The coefficient of aerodynamic drag in horizontal flight, Cxa h.f. 4.8078 0.3202 0.0801 0, 0397 0.0257 0.0275 0.0330 0.0369 0.0409 0.0418
Flight aerodynamic quality, K 2.33 8.76 15.57 17.67 12.15 8.32 5.32 4.21 3.39 2.97
Thrust required Prequired, N 2420616 644803 362940 319796 465019 678749 1062836 1342999 1668846 1900779
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0, 940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available,
Pavail, N
1155234 1131380 1116892 1111698 1128908 1151169 1182439 1201430 1222647 1246080
Vertical speed, Vy, m/S -7.44 5.73 13.31 18.64 23.44 19.46 5.63 -7.08 -23.63 -36.59

Table 6: The calculation of thrust required and thrust available, H = 2 km.

Flight altitude, км 4
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.699 0.699 0.699 0.699 0.699 0.699 0.699 0.699 0.699 0.699
The air density, aeronautics-aerospace-engineering 0.8194 0.8194 0.8194 0.8194 0.8194 0.8194 0.8194 0.8194 0.8194 0.8194
Coefficient Ka 0.954 0.954 0.954 0.954 0.954 0.954 0.954 0.954 0.954 0.954
The speed of sound a, m/S 324.627 324.627 324.627 324.627 324.627 324.627 324.627 324.627 324.627 324.627
Flight speed , V, m/s 32.46 64.93 97.39 129.85 194.78 227.24 259.70 275.93 292.16 308.40
Dynamic pressure,
N/m2
432 1727 3886 6908 15543 21156 27632 31194 34972 38966
The average gross weight of the aircraft, GAv, N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
14.46 3.62 1.61 0.90 0.40 0.30 0.23 0.20 0.18 0.16
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa .h.f. 7.9686 0.5177 0.1191 0.0520 0.0283 0.0290 0.0340 0.0377 0.0416 0.0424
Flight aerodynamic quality, K 1.81 6.98 13.49 17.37 14.19 10.16 6.65 5.31 4.29 3.78
Thrust required Prequired, N 3113632 809179 418897 325377 398284 555998 849348 1065002 1316496 1495674
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available, Pavail, N 1006548 985764 973141 968616 983611 1003006 1030252 1046799 1065285 1085702
Vertical speed, Vy, m/S -12.11 2.03 9.55 14.78 20.18 17.98 8.31 -0.89 -12.99 -22.38

Table 7: The calculation of thrust required and thrust available, H = 4 km.

Flight altitude, км 6
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538
The air density, aeronautics-aerospace-engineering 0.6602 0.6602 0.6602 0.6602 0.6602 0.6602 0.6602 0.6602 0.6602 0.6602
Coefficient Ka 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93
The speed of sound a, m/S 316.46 316.46 316.46 316.46 316.46 316.46 316.46 316.46 316.46 316.46
Flight speed , V, m/s 31.65 63.29 94.94 126.58 189.88 221.52 253.17 268.99 284.81 300.64
Dynamic pressure,
N/m2
331 1322 2975 5289 11901 16199 21157 23885 26777 29835
The average gross weight of the aircraft, GAv, N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
18.89 4.72 2.10 1.18 0.52 0.39 0.30 0.26 0.23 0.21
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa .h.f. 13.5773 0.8683 0.1884 0.0740 0.0330 0.0317 0.0357 0.0392 0.0428 0.0434
Flight aerodynamic quality, K 1.39 5.44 11.14 15.96 15.88 12.14 8.27 6.68 5.45 4.82
Thrust required Prequired, N 4062046 1039072 507185 354010 355765 465442 683629 846343 1037020 1173100
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available, Pavail, N 805738 789101 778996 775373 787377 802903 824713 837959 852756 869100
Vertical speed, Vy, m/S -18.24 -2.80 4.57 9.44 14.50 13.23 6.32 -0.40 -9.29 -16.17

Table 8: The calculation of thrust required and thrust available, H = 6 km.

Flight altitude, км 8
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.429 0.429 0.429 0.429 0.429 0.429 0.429 0.429 0.429 0.429
The air density, aeronautics-aerospace-engineering 0.5259 0.5259 0.5259 0.5259 0.5259 0.5259 0.5259 0.5259 0.5259 0.5259
Coefficient Ka 0.905 0.905 0.905 0.905 0.905 0.905 0.905 0.905 0.905 0.905
The speed of sound a, m/S 307.953 307.953 307.953 307.953 307.953 307.953 307.953 307.953 307.953 307.953
Flight speed , V, m/s 30.80 61.59 92.39 123.18 184.77 215.57 246.36 261.76 277.16 292.56
Dynamic pressure,
N/m2
249 997 2244 3990 8977 12219 15960 18017 20199 22506
The average gross weight of the aircraft, GAv, N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
25.04 6.26 2.78 1.56 0.70 0.51 0.39 0.35 0, .1 0.28
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa .h.f. 23.8454 1.5100 0.3151 0.1141 0.0417 0.0367 0.0389 0.0418 0.0450 0.0453
Flight aerodynamic quality, K 1.05 4.15 8.83 13.72 16.69 13.92 10.06 8.30 6.87 6.12
Thrust required Prequired, N 5381413 1363125 640062 411870 338526 405953 561663 681076 822303 923415
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available, Pavail, N 664688 650963 642627 639639 649541 662349 680341 691268 703475 716958
Vertical speed, Vy, m/S -25.71 -7.76 0.04 4.97 10.17 9.78 5.17 0.47 -5.83 -10.69

Table 9: The calculation of thrust required and thrust available, H = 8 km.

Flight altitude, км 10
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.337 0.337 0.337 0.337 0.337 0.337 0.337 0.337 0.337 0.337
The air density, aeronautics-aerospace-engineering 0.4136 0.4136 0, 4136 0.4136 0.4136 0.4136 0.4136 0.4136 0.4136 0.4136
Coefficient Ka 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88
The speed of sound a, m/S 299.446 299.446 299.446 299.446 299.446 299.446 299.446 299.446 299.446 299.446
Flight speed , V, m/s 29.94 59.89 89.83 119.78 179.67 209.61 239.56 254.53 269.50 284.47
Dynamic pressure,
N/m2
185 742 1669 2967 6676 9086 11868 13398 15020 16735
The average gross weight of the aircraft,
GAv, N
5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
33.67 8.42 3.74 2.10 0.94 0.69 0.53 0.47 0.42 0.37
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1, 09 1, 16 1, 27 1, 33 1, 4 1, 5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa h.f. 43.1065 2.7138 0.5529 0.1893 0.0579 0.0460 0.0449 0.0467 0.0491 0.0489
Flight aerodynamic quality, K 0.78 3.10 6.77 11.12 16.16 14.93 11.73 9.98 8.47 7.63
Thrust required Prequired, N 7234021 1821721 835106 508293 349600 378392 481800 565957 667341 740384
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available,
Pavail, N
541395 530216 523426 520992 529058 539490 554145 563045 572988 583970
Vertical speed, Vy, m/S -35.47 -13.69 -4.96 0.27 5.71 5.98 3.07 -0.13 -4.50 -7.87

Table 10: The calculation of thrust required and thrust available, H = 10 km.

Flight altitude, км 11
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298
The air density, aeronautics-aerospace-engineering 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648
Coefficient Ka 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867
The speed of sound a, m/S 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023
Flight speed , V, m/s 29.50 59.00 88.51 118.01 177.01 206.52 236.02 250.77 265.52 280.27
Dynamic pressure, N/m2 159 635 1429 2540 5715 7779 10161 11470 12859 14328
The average gross weight of the aircraft,
GAv, N
5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
39.33 9.83 4.37 2.46 1.09 0.80 0.61 0.54 0.49 0.44
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxah.f. 58.8019 3.6948 0.7467 0.2506 0.0711 0.0536 0.0497 0.0507 0.0524 0.0518
Flight aerodynamic quality, K 0.67 2.66 5.85 9.81 15.37 14.97 12.36 10.74 9.26 8.42
Thrust required Prequired, N 8448432 2123422 965534 576114 367586 377343 457240 526053 610317 671356
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available,
Pavail, N
487655 477586 471470 469277 476542 485939 499139 507156 516112 526004
Vertical speed, Vy, m/S -41.56 -17.19 -7.74 -2.23 3.41 3.97 1.75 -0.84 -4.43 -7.21

Table 11: The calculation of thrust required and thrust available, H = 11 km.

Flight altitude, км 12
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.2536 0.2536 0.2536 0.2536 0.2536 0.2536 0.2536 0.2536 0.2536 0.2536
The air density, aeronautics-aerospace-engineering 0.3156 0.3156 0.3156 0.3156 0.3156 0.3156 0.3156 0.3156 0.3156 0.3156
Coefficient Ka 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867
The speed of sound a, m/S 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023
Flight speed , V, m/s 29.50 59.00 88.51 118.01 177.01 206.52 236.02 250.77 265.52 280.27
Dynamic pressure,
N/m2
137 549 1236 2198 4944 6730 8790 9923 11125 12396
The average gross weight of the aircraft,
GAv, N
5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
45.46 11.36 5.05 2.84 1.26 0.93 0.71 0.63 0.56 0.50
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxa h.f. 78.5576 4.9295 0.9906 0.3278 0.0877 0.0631 0.0559 0.0557 0.0567 0.0554
Flight aerodynamic quality, K 0.58 2.31 5.10 8, 67 14.40 14.69 12.72 11.29 9.91 9.09
Thrust required Prequired, N 9764610 2450941 1108159 651889 392361 384584 444301 500309 570447 621625
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available,
Pavail, N
425163 416384 411052 409141 415475 423667 435176 442165 449973 458598
Vertical speed, Vy, m/S -48.76 -21.25 -10.92 -5.07 0.72 1.43 -0.38 -2.58 -5.66 -8.09

Table 12: The calculation of thrust required and thrust available, H = 12 km.

Flight altitude, км 12.4
The number of flight Mach 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.85 0.9 0.95
Relative density of the air, D 0.2399 0.2399 0.2399 0.2399 0.2399 0.2399 0.2399 0.2399 0.2399 0.2399
The air density, aeronautics-aerospace-engineering 0.2986 0.2986 0.2986 0.2986 0.2986 0.2986 0.2986 0.2986 0.2986 0.2986
Coefficient Ka 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867 0.867
The speed of sound a, m/S 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023 295.023
Flight speed , V, m/s 29.50 59.00 88.51 118.01 177.01 206.52 236.02 250.77 265.52 280.27
Dynamic pressure, N/m2 130 520 1170 2079 4678 6367 8317 9389 10526 11728
The average gross weight of the aircraft, GAv, N 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560 5650560
The coefficient of aerodynamic
lift in horizontal flight, Cyh.f.
48.05 12.01 5.34 3.00 1.33 0.98 0.75 0.67 0.59 0.53
Effective of wing extension , λ 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38 8.38
Factor Blade of the polar, A0 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038 0.038
Coefficient Ka 1 1 1 1 1.09 1.16 1.27 1.33 1.4 1.5
Coefficient KCX0 1 1 1 1 1.03 1.2 1.5 1.7 1.9 1.95
The coefficient of aerodynamic drag in horizontal flight, Cxah.f. 87.7547 5.5044 1.1041 0.3637 0.0954 0.0676 0.0587 0.0581 0.0586 0.0571
Flight aerodynamic quality, K 0.55 2.18 4.84 8.26 13.99 14.51 12.79 11.46 10.12 9.32
Thrust required Prequired, N 1E+07 2589322 1168646 684376 403975 389474 441832 493270 558414 606117
The Rate of changes in the thrust of the number of flight Mach , ξ 0.972 0.952 0.940 0.935 0.950 0.969 0.995 1.011 1.029 1.048
Take-off thrust engines, P0, N 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000 1404000
Thrust available,
Pavail, N
405560 397185 392099 390276 396318 404133 415110 421777 429226 437452
Vertical speed,
Vy, m/S
-51.77 -22.89 -12.16 -6.14 -0.24 0.54 -1.12 -3.17 -6.07 -8.37

Table 13: The calculation of thrust required and thrust available, H = 12.4 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 1: Thrust required and thrust available at a height of H = 0 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 2: Thrust required and thrust available at a height of H = 2 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 3: Thrust required and thrust available at a height of H = 4 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 4: Thrust required and thrust available at a height of H = 6 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 5: Thrust required and thrust available at a height of H = 8 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 6: Thrust required and thrust available at a height of H = 10 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 7: Thrust required and thrust available at a height of H = 11 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 8: Thrust required and thrust available at a height of H = 12 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 9: Thrust required and thrust available at a height of H = 12.4 km.

aeronautics-aerospace-engineering-Thrust-required

Figure 10: Thrust required and thrust available at a height of H = 0…. 12.4 km.

aeronautics-aerospace-engineering-practical-ceiling

Figure 11: Finding a practical ceiling of the aircraft.

aeronautics-aerospace-engineering-Real-possible

Figure 12: Real possible area of the aircraft (maximum for traction).

aeronautics-aerospace-engineering-Real-possible

Figure 13: Real possible area of the aircraft (minimum for traction).

Area velocity values, at which horizontal flight is possible at a fixed weight of the aircraft and the altitude, it called horizontal flight speed range.

At this altitude:

aeronautics-aerospace-engineering

At this altitude, the curve of Thrust available (or power) not intersects the curve of thrust required, but only touches it.”

Determination of the Flight Range of the Aircraft H = f (v)

At the intersection point of the curve Thrust Required and Thrust Available, we define the boundaries of the possible limits of the aircraft (Table 14).

Height Flight, Н, km 0 2 4 6 8 10 11 12 12.4
Minimum speed, vmin, m/s (left) 46 55 60 70 94 118 140 170 200
Maximum(Full) speed, vmax, m/s (right) 277 275 275 267 264 255 248 230 200

Table 14: Calculation of a possible aircraft flight boundaries

Drawing a schedule of possible aircraft flight boundaries under the conditions of thrust required and thrust available (Figures 11-13).

On the left side, should be restrictions on the minimum flight speed of the conditions for safe values of the coefficient of lift of the aircraft.

aeronautics-aerospace-engineering

The significance of this factor determines the minimum speed of horizontal flight of the conditions of a possible lift of an aircraft wing.

The minimum flight speed by the formula:

aeronautics-aerospace-engineering

On the right side, should be limits on the N/m2 maximum velocity head from the condition of strength qmax,max = 22000 .

Defining this condition maximum speed flight according to the formula (Tables 15 and 16):

Height, Н, km 0 2 4 6 8 10 11 12 12.4
Density of air, ρH, kg/m3 1.225 1.0067 0.8194 0.6602 0.5259 0.4136 0.3648 0.3156 0.2986
Minimum speed, Vmin,m/s 81.6 90 99.8 111.2 124.6 140.5 149.6 160.8 165.3

Table 15: Calculation of the minimum flight speed.

Height, Н, km 0 2 4 6 8 10 11 12 12.4
Density of air, ρH, kg/m3 1.225 1.0067 0.8194 0.6602 0.5259 0.4136 0.3648 0.3156 0.2986
Minimum speed, Vmin,m/s 189.5 209.1 231.7 258.2 289.3 326.2 347.3 373.4 383.9

Table 16: The calculation of the maximum flight speed of conditions limitations on the maximun velocity head.

aeronautics-aerospace-engineering

Conclusion

1. By, considering level flight at various altitudes with the same weight of flight and angle of attack, when performing level flight at any altitude is necessary to ensure equality of lifting forces and gravity of the aircraft, as Ya =G. To fulfill this condition for constant weight and angle of attack at high altitudes where the air density is less true speed horizontal flight should be more, but the airspeed remains constant.

2. In carrying out flight on a modern passenger airplane Flight weight is significantly reduced due to fuel production. Such a change of flight mass causes a significant change in the aircraft flight characteristics. To perform horizontal flight of flight with less weight requires less lifting force, hence for the same attack and altitude angle requires less speed and less traction.

aeronautics-aerospace-engineering

3. As can be seen from the graphs of Thrust Required and Thrust Available (power), the speed range is reduced by raising at height, So all the speed characteristics increases by raising at height, with the exception of the Vmax, because its value is determined by the characteristics of the engine.

4. With increasing altitude, the air density decreases, which leads to an increase in required speed and reduction of vertical speed(climb). Characteristics of climb is getting worse due to the fall of the engine thrust. At a certain height excess thrust is reduced to zero, so a further climb is not possible.

5. With increasing altitude, the excess thrust is reduced and at some certain height becomes zero. This means that the vertical velocity of the steady rise is also reduced to zero. At this altitude and above the aircraft is not able to make a steady recovery.

6. Flight altitude at which the vertical velocity of the steady rise equal zero is called a theoretical (or static), the ceiling of the aircraft.

7. There’s not an excess thrust On a theoretical ceiling therefore the only possible is horizontal flight, and only the most advantageous angle of attack (and only in the most advantageous rate) at which the lowest Required thrust power. Speed range at this moment equal zero.

8. With the steady rise of the plane, almost cannot reach the theoretical ceiling, because as you get closer to it excess thrust becomes so small, that in order to set the height of the rest needs to spend too much time and fuel. Due to the lack of excess flying thrust on a theoretical ceiling is almost impossible, because any violation of the flight mode cannot be eliminated without excessive traction. For example, when randomly formed even small roll plane loses a considerable height (falls). Therefore, in addition to theoretical concepts (static) Ceiling introduced the concept of practical ceiling.

References

Select your language of interest to view the total content in your interested language
Post your comment

Share This Article

Article Usage

  • Total views: 712
  • [From(publication date):
    March-2017 - Aug 17, 2017]
  • Breakdown by view type
  • HTML page views : 595
  • PDF downloads :117
 
 

Post your comment

captcha   Reload  Can't read the image? click here to refresh

Peer Reviewed Journals
 
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
 
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

Agri, Food, Aqua and Veterinary Science Journals

Dr. Krish

agrifoodaquavet@omicsonline.com

1-702-714-7001 Extn: 9040

Clinical and Biochemistry Journals

Datta A

clinical_biochem@omicsonline.com

1-702-714-7001Extn: 9037

Business & Management Journals

Ronald

business@omicsonline.com

1-702-714-7001Extn: 9042

Chemical Engineering and Chemistry Journals

Gabriel Shaw

chemicaleng_chemistry@omicsonline.com

1-702-714-7001 Extn: 9040

Earth & Environmental Sciences

Katie Wilson

environmentalsci@omicsonline.com

1-702-714-7001Extn: 9042

Engineering Journals

James Franklin

engineering@omicsonline.com

1-702-714-7001Extn: 9042

General Science and Health care Journals

Andrea Jason

generalsci_healthcare@omicsonline.com

1-702-714-7001Extn: 9043

Genetics and Molecular Biology Journals

Anna Melissa

genetics_molbio@omicsonline.com

1-702-714-7001 Extn: 9006

Immunology & Microbiology Journals

David Gorantl

immuno_microbio@omicsonline.com

1-702-714-7001Extn: 9014

Informatics Journals

Stephanie Skinner

omics@omicsonline.com

1-702-714-7001Extn: 9039

Material Sciences Journals

Rachle Green

materialsci@omicsonline.com

1-702-714-7001Extn: 9039

Mathematics and Physics Journals

Jim Willison

mathematics_physics@omicsonline.com

1-702-714-7001 Extn: 9042

Medical Journals

Nimmi Anna

medical@omicsonline.com

1-702-714-7001 Extn: 9038

Neuroscience & Psychology Journals

Nathan T

neuro_psychology@omicsonline.com

1-702-714-7001Extn: 9041

Pharmaceutical Sciences Journals

John Behannon

pharma@omicsonline.com

1-702-714-7001Extn: 9007

Social & Political Science Journals

Steve Harry

social_politicalsci@omicsonline.com

1-702-714-7001 Extn: 9042

 
© 2008-2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version