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Fig. 5.5 RANGEconstant Mach/altitude cruise, tanks dropped

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

0 20 40 60 80 100 120 140 160 180 200 220 240

Range % of MiG-21bis max range on internal fuel

Fuel carried % of aircraft max

internal

MiG-21bis at 10-11 km

MiG-21bis at 5 km

MiG-21bis at 0.5 km

MiG-21bis at 5 km withwarload of 20% basic weight

MiG-21bis at 0.5 km withwarload 20 % basic weight

F-4E at 11-12 km

Endurance is the time an aircraft can remain in the air. It is not particularly altitude dependent because minimum drag is about the same at all altitudes, at the same indicated airspeed. Specific fuel consumption worsens with Mach and improves with altitude so product of (L/D)max and (1 / tsfc) is similar at all altitudes.

57

The F-4E achieves (L/D)max at Cl=0.36 (total wetted area 194 m², equivalent skin friction coefficient 0.00508).Maximum endurance of MiG-21bis at 500 m altitude is at lift coefficient of 0.3 / Mach 0.4 / CAS 480 km/h (L/D = 8, CdO = 0.019, Oswald span efficiency factor e = 0.7) and maximum range at Cl = 0.14 / Mach 0.58. As in theory, at higher altitudes endurance (where drag is lowest) is at similar CAS and at 11 km altitude it is equal to Mach 0.81.

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endurance minutes

MiG-21 Fclean

true airspeedkm/h

Fig. 5.7 MiG-21F endurance depending on cruising altitude (H meters) and true airspeed (operator’s diagram)

true airspeed km/h

endurance minutes

MiG-21 Fwith two AAMs

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Fig. 5.8 MiG-21F range depending on cruising altitude (H meters) and true airspeed (operator’s diagram)

rangekm

MiG-21 Fwith 490 litre

external fuel tank

true airspeed

km/h

Of course, best range Mach also increases with altitude, converges with endurance speed and it sooner bangs into the ‘sound barrier’ so best range Mach stays at Mach 0,84 at 11000 m where it almost coincides with best endurance speed. When aircraft is trimmed to best range cruise at optimum angle of attack or lift coefficient (Cl=0,3 at tropopause for MiG), as the fuel is being depleted aircraft will fly itself to new optimum higher altitude. Air traffic control does not permit commercial planes to fly that continuously variable cruise profile except in 2000 feet steps. Alternative for airliners is to cruise at a constant altitude that is optimum for some mid cruise weight.

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Fig. 5.9 F-4E max range & endurance speedcombat weight 18450 kg

0

5000

10000

15000

20000

0.2 0.7 1.2 1.7Mach

altitude meters

F-4E slatted

F-4 withoutafterburnermax endurance

max range

Heavily laden with warload after take off at max weight, the best cruising altitude is 5000-6000 m and in case of one engine operating (F-4), the best range is achieved at less than 1000 m altitude.

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Payload with full fuel is given as a percentage of an aircraft’s basic weight because a two times bigger aircraft carries two times the weight with about the same effort and range percentage.

max rangeconstant Mach/altitude cruise, standard reserve

max endurance payload

oninternal

fuel

with 3 external tanks,tanks dropped when empty

oninternal

fuel

with 3 external tanks, tanks dropped

with full internal

fuel

with full internal fuel and 3external tanks

MiG-21bis

1250 km M 0.84 /11 km

1900 kmMach 0.83

/10 km

1.5hours

2.25hours

1450 kg(25% of

basic weight)

150 kg(2% ofbasic

weight)

F-4E1600 kmMach 0.87 /39 Kft

2950 km Mach 0.86 /36 Kft

1.9hours

3.5hours

5500 kg (38% of basic weight)

1100 kg (8% of basic weight)

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6. Turn performance

As said, maneuverability is the ability to quickly change velocity vector, in other words, direction of flight and magnitude of aircraft speed.

Most missiles, having cruciform configuration (two pairs of wings and tails or without wings at all) can equally maneuver in any plane, without any bank angle. Since airplanes have wings in one plane, they can make significant turns only in one plane. Lateral turns with fuselage lift is possible but with not more than about 1.5 (g) load factor because of limited rudder (and aileron) control power and tail structural strength to trim that sideforce. Some of the most maneuverable missiles depend just on fuselage lift to turn at 30 g at high speed. At very high angle of attack body lift is significant as is vertical component of thrust which augments lift.

Fig. 6.1 Sample steady horizontal turn

vertical component

of lift = (-) weight

plane of turnradial g √ (n² -1) = 6,42

plane of symmetry

aircraft g (normal load factor) 6,5

81,0°

horizontal componenet of lift = (-) centrifugal force of turn

bank angleº

lift 6,5 * weight

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During a steady horizontal coordinated turn, the lift is inclined to produce a horizontal component of force to equal the centrifugal force of the turn. Vertical component of lift must equal the weight of the aircraft. Coordinated means without sideslip.

load factor (normal acceleration g) = lift / weight

load factor = 1 / cosine bank angle (

radial acceleration (g) = [√ (load factor² - 1)] * g

Steady, coordinated turn requires certain relationship between load factor and bank angle, as seen in the equation. For example, bank angle of 80ºrequires load factor of 5.76 for steady turn (bank angle of 89º requires 57.3 g). Of course, perfectly horizontal turn is irrelevant in combat. Only maximum and sustained load factors at any bank angle counts.

Turn performance is defined by structural, control surface actuator power, lift (aerodynamic) and thrust limits.

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Fig. 6.2 F-4E max available load factor at H = 3 kmcombat weight 18450 kg

1

2

3

4

5

6

7

8

9

10

11

12

13

0 0,5 1 1,5Mach

load factor,

"g"

structural

lift

thrust &drag

Structure strength limit defines maneuvering load factor that will not damage primary structure or shorten aircraft’s service life. The utmostimportance in aircraft design is to keep structure weight to minimum, just to fulfill requirements. A short look at aircraft structure material characteristics should help understand structural limit of the aircraft.

65

66

Figure 6.3 shows the mechanical behavior of a material under a load and defines the strength. The stress is the ratio of the applied load divided by the cross sectional area of the material. The strain is the non dimensional elongation of the material to the applied tensile load. The portion of the stress-strain curve that is linear is known as the elastic range. The slope of the stress-strain curve in this elastic range is called the Modulus of Elasticity and denotes the stiffness of the material – ability to resist deformation within the elastic range.

Important material properties are strength (ultimate stress) and stiffness, both divided by material density or simply strength/weight and E/weight ratio, besides impact resistance (toughness) – the area under the stress-strain curve, property where graphite composites are weak.

Material

Ultimate tensile strength, bar*

Yield tensile strengthbar

Modulus of Elasticity 10³ bar

Densitykg/dm³**

Temperature limit ºC***Hi alt Mach

Relative cost

Aluminum alloy 7075

5200 4400 730 2.80125 ºC2.1 Mach

1

Steel5Cr-Mo-V

18200 15400 2100 7.75540 ºC 3.7 Mach

1

TitaniumTi-6Al-4V

11200 10150 1120 4.45410 ºC 3.3 Mach

10

Graphite Epoxy

6200 6200 1170 2.60125 ºC 2.1 Mach

15

* kilo psi (pressure) = 70 bar (bar ≈ atmospheric pressure = 10^5 Pa (N/m²))** lb/in³ (density) = 27.68 kg/dm³*** ºF (temperature) = ºC * 1.8 + 32

Materials should be safe if stressed below their yield strength and not subjected to impact loading, but the fact is that failure may still occur if the load is applied, removed and repeated many times. This type of failure iscalled fatigue. This cyclic loading is an every day occurrence for an aircraft as it is parked, takes off, maneuvers and then lands. Fatigue is one of the most important causes of material failure. If aircraft is designed for 3000 hours service life and limit load factor 8 with load factor spectrum 8 g once in hundred flight hours, 6 g on every flight hour and 4 g ten times per hourand if in actual conditions aircraft is subjected to an 8 g load on every flight hour, decreased service life or premature structural failure can be expected.

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Aircraft structure should experience no objectionable permanent deformation when subjected to limit load factor (say 8). Above limit load factor, the yield stress may be exceeded and permanent deformation canresult. Metals used in aircraft structures are ductile – they do not break immediately when deformations becomes plastic. Famous duraluminum alloy (2024) has ultimate tensile strength to yield strength ratio 1.5 (4410/2940 bar). It means that 50 % more load (say 12 g) is needed for failure in relation to one needed to start permanent deformation. Aircraft would be capable to withstand a load factor which is 1.5 times the design limit load. That became the usual safety factor. Now when many structural materials have ultimate to yield strength ratio ≤ 1.2 and when aircraft have electronic load factor limiters, safety factor might be less (e.g. limit load factor 9, ultimate 11), structure weight lighter or service life multiplied.

limit structural load factor “g” at combat weight *

MiG-21bis F-4E

combat weight 7550 kg 18450 kg

subsonic limit(< M 0.8/0.72)

8 7,8 fuselage AIM-7s has a/c limit

rolling maneuver limit not recognized80 % of g

without rolling

2 IC missilecarriage limit

8 6.5

limit at Mach 0.9 6.5 6.8

supersonic limit** 6.5 6

* Load factor at design weight (7100/17000 kg) is 8.5. Allowed load factor at other weights is in proportion to design weight.** Because of bigger static margin at supersonic speeds, both wing and tail must generate more lift (bigger bending moment) for the same resultingload factor. Tail lift is negative.

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In many aircraft, flight controls despite being hydraulically powered, at high dynamic pressures cannot move aerodynamic surfaces enough to turn the aircraft to structural or even thrust ‘g’ limit. If elevator hinge is far from elevator aerodynamic centre, hinge moment can be bigger than hydraulic actuator power and that could limit the available load factor.

Aerodynamic limit is defined by the ability of aircraft to generate lift (the product of wing area and maximum lift coefficient in respect to aircraft weight). Turns reaching the aerodynamic limit are called instantaneous. Dominator of aerodynamic turning performance is the wing level stall speed. When F-4E flies at stall α, at 265 km/h (143 kt) lift will be equal to weight of 18450 kg i.e. aircraft will fly at 1 g. Remember that:Lift = ½ (true airspeed)² * air density * wing area * lift coefficient CL

Basic wing area is used as reference area because it is most important lift generator and the easiest area to calculate, although most of aircraft planform surface produces lift.

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where:q – dynamic pressure = ρ*V²/2D – dragT – thrustW – weight = m*gρ – air densityS – wing area

CDo – zero lift drag coefficientAR – wing aspect ratio¶ = 3.1416…e – Oswald span efficiency factor V – true airspeed

It is often said that MiG-21 loses energy in turn. MiG-21F has better sustained maneuverability than most fighters of its generation. If it turns to the stall speed of 220 km/h, of course that it will lose energy faster than F-4C at say 270 km/h, because load factor would be much higher. If MiG holds it’s allowed angle of attack (28 units), that will give similar instantaneous turns as F-4 but with only slight buffet as opposed to a heavy one in unslatted F-4. Lower aspect ratio of MiG wing does not give the whole picture of sustained turns.There are various official performance comparisons of F-4 and MiG-21, both western and eastern which all differ. US claims that MiG is better and east side draws graphs that F-4 is better. The reason behind most claims is myth or politics.

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With the advent of all-aspect missiles turns are usually maximum (instantaneous) with thrust and drag (SEP at high g) determining whether speed will be preserved. If one aircraft has better sustained turn capability that does not mean that it will dissipate less speed during maximum turns. A high thrust to weight fighter may, during e.g. 8 g turn lose energy much faster than jet trainer, although fighter may sustain e.g. 6 g and trainer 5 g.

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Diagrams which present longitudinal acceleration vs. load factor and speed help visualizing what happens with speed in turns. But when aircraft makes,for example 360º max turn neither instantaneous nor sustained turn plots tell end speed or total turn time. Computers must be used for a precise analysis.Without aerodynamic force, moment and stability derivatives, it is difficult to compare other fighter measures of merit such as control surfaces effectiveness at high angle of attack or departure resistance at aileron/rudder application.

Book Reviews - The Aeronautical Journal (May 2010) :

Naucna KMD, Belgrade, Serbia. 2009.(Contact/order e-mail: marina.biblija@gmail.com).103pp. Illustrated. €25 including postage/packing.ISBN 978-86-6021-017-5.

This book, written by two aeronautical engineers from the former Yugoslavia, sets out to provide acomparison of the performance of the F4 Phantom II and the MIG 21. Early chapters are devoted todescriptions of both aircraft together with relevant weights, dimensions and configurations.Data on the F-4C, F-4E, F-4J, MiG-21bis, MiG-21-MF and MiG-21-F-13 and their General Electric andTumansky engines are provided for reference throughout the volume. The sources of data are notstated but simply described as ‘official and already available to the public’.This is followed by chapters devoted to the comparison of the aircrafts’ flight envelopes andperformance during take-off, acceleration, climb, cruise, descent, landing and maneuvering. Eachelement includes the statement, but generally not the derivation, of the basic well-establishedperformance equations and many diagrams comparing the performances of the two aircraft types.In essence the book leads the reader through the processes normally carried out by engineers workingon competitor aircraft analysis for marketing purposes and tactical evaluations by air arms. It does notcover the more difficult areas such as the determination of aerodynamic characteristics andengine installation effects, for example, which are essential to accurate comparisons without access tomanufacturers’ configuration and performance data.

In comparing the two aircraft types, the authors present many flight performance charts and flightenvelopes and offer a number of reasons for the flight limitations included in them. For example, thelimitation of the maximum speed of the MiG-21 to Mach 2⋅05 above an altitude of 11,000m isattributed to reduced directional stability rather than a lack of engine thrust.Particular emphasis is given to instantaneous and sustained turning performance culminatingin the authors’ view as to how a MiG-21 could be observed to perform a split-S manoeuvre below3,000ft a.g.l during combat when published data stated that 6,750ft were required this.The final chapter records the authors’ conclusions as to how the two aircraft compare and provides anumber of photographs that illustrate their general features.The editorial style of the book could be improved for western readers. Commas are used instead ofdecimal points, figures are not generally referenced in the text, there is no single list of symbols andequations are presented in a format foreign to UK practice.

In conclusion, the book gives an interesting insight into the quantitative comparison offighter aircraft and the interpretation of the significance of the differences presented inthe performance curves and flight limitation boundaries. It makes informative andentertaining reading for anyone interested in the assessment of the merits ofcompeting fighter aircraft.

Dick Poole CEng, MRAeS

I'm working like performance test engineer for Airbus, after work for Lockheed Martin.I congratulate you for your book. It's good and specially there are not another book like this in themarket.What I read is very good, with precision, you have focused in a good point of view of analysis. I wouldlike to be so good as you to compare 2 aircraft !!! )It's really a good job.I hope 2012. will be the year when you will offer a new and excellent publication about aircraft !! )Whiskey Golf

E-books: Aircraft MiG-21 UM (US) Pilots Manual (in English),Manual on the Techniques of Piloting and Military Use of the MiG-21F-13and Capt. Boyd: Aerial Attack Study are sent as a gift.