Book Reviews - If you want to know who really has the better performance F-4 or MiG-21, who is more maneuverable or faster, you can find it only in this book based on official aircraft manuals. Who is faster or more agile operationaly and who is on paper can be seen only in this book. 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 the market. What I read is very good, with precision, you have focused in a good point of view of analysis. I would like 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

2. Fig. 5.5 RANGE
constant Mach/altitude cruise, tanks dropped
180
Fuel carried %
of aircraft max
170
internal
160
150
140
130
120
110
100
90 MiG-21bis at 10-11 km
80 MiG-21bis at 5 km
MiG-21bis at 0.5 km
70
MiG-21bis at 5 km with
60 warload of 20% basic weight
MiG-21bis at 0.5 km with
warload 20 % basic weight
50
F-4E at 11-12 km
40
0 20 40 60 80 100 120 140 160 180 200 220 240
Range
% of MiG-21bis max range on internal fuel
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.
56

3. 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.
57

4. endurance
minutes
MiG-21 F
clean
true airspeed
km/h
endurance
minutes
MiG-21 F
with two AAMs
true airspeed
km/h
Fig. 5.7 MiG-21F endurance depending on cruising altitude
(H meters) and true airspeed (operator’s diagram)
58

5. range
km
MiG-21 F
with 490 litre
external fuel tank
true
airspeed
Fig. 5.8 MiG-21F range depending on cruising altitude km/h
(H meters) and true airspeed (operator’s diagram)
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.
59

6. Fig. 5.9 F-4E max range & endurance speed
combat weight 18450 kg
20000
altitude
meters
15000
10000
F-4E slatted
5000
F-4 w ithout
afterburner
m ax endurance
m ax range
0
0.2 0.7 1.2 1.7
Mach
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.
60

7. max range
constant Mach/altitude cruise, max endurance payload
standard reserve
with 3
with 3 external with full
on on external with full
tanks, internal
internal internal tanks, internal
tanks dropped fuel and 3
fuel fuel tanks fuel
when empty external tanks
dropped
MiG- 1450 kg 150 kg
1250 km 1900 km 1.5 2.25 (25% of (2% of
21bis M 0.84 Mach 0.83
/11 km /10 km
hours hours basic basic
weight) weight)
5500 kg 1100 kg
1600 km 2950 km 1.9 3.5 (38% of (8% of
F-4E Mach 0.87 Mach 0.86
/39 Kft /36 Kft
hours hours basic basic
weight) weight)
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.
61

8. 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.
bank angle
81,0°
º
aircr pla
aft g ne of sy
(nor mme
ma try
lift l load fac
6,5 * to
vertical weig r) 6 ,5
ht
component
of lift =
(-) weight
horizontal componenet of lift
= (-) centrifugal force of turn
plane of turn
radial g √ (n² -1) = 6,42
Fig. 6.1 Sample steady horizontal turn
62

9. 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 80º
requires 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.
63

10. Fig. 6.2 F-4E max available load factor at H = 3 km
combat weight 18450 kg
13
12
structural
11
load 10 lift
factor,
thrust &
"g" 9 drag
8
7
6
5
4
3
2
1
0 0,5 1 1,5
Mach
Structure strength limit defines maneuvering load factor that will not
damage primary structure or shorten aircraft’s service life. The utmost
importance 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.
64

11. 65

12. 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.
Ultimate Yield Modulus
Temperature
tensile tensile of Density Relative
Material limit ºC***
strength, strength Elasticity kg/dm³** cost
Hi alt Mach
bar* bar 10³ bar
Aluminum 125 ºC
5200 4400 730 2.80 1
alloy 7075 2.1 Mach
Steel 540 ºC
18200 15400 2100 7.75 1
5Cr-Mo-V 3.7 Mach
Titanium 410 ºC
11200 10150 1120 4.45 10
Ti-6Al-4V 3.3 Mach
Graphite 125 ºC
6200 6200 1170 2.60 15
Epoxy 2.1 Mach
* 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 is
called 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 hour
and 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.
66

13. 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 can
result. 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 7,8
8 fuselage AIM-7s has
(< M 0.8/0.72) a/c limit
80 % of g
rolling maneuver limit not recognized
without rolling
2 IC missile
8 6.5
carriage limit
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 resulting
load factor. Tail lift is negative.
67

14. 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.
68

15. where:
q – dynamic pressure = ρ*V²/2 CDo – zero lift drag coefficient
D – drag AR – wing aspect ratio
T – thrust ¶ = 3.1416…
W – weight = m*g e – Oswald span efficiency factor
ρ – air density V – true airspeed
S – wing area
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.
80

16. 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.
81

17. 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.
82

19. 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 a
comparison of the performance of the F4 Phantom II and the MIG 21. Early chapters are devoted to
descriptions 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 and
Tumansky engines are provided for reference throughout the volume. The sources of data are not
stated 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 and
performance during take-off, acceleration, climb, cruise, descent, landing and maneuvering. Each
element includes the statement, but generally not the derivation, of the basic well-established
performance 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 working
on competitor aircraft analysis for marketing purposes and tactical evaluations by air arms. It does not
cover the more difficult areas such as the determination of aerodynamic characteristics and
engine installation effects, for example, which are essential to accurate comparisons without access to
manufacturers’ configuration and performance data.
In comparing the two aircraft types, the authors present many flight performance charts and flight
envelopes and offer a number of reasons for the flight limitations included in them. For example, the
limitation of the maximum speed of the MiG-21 to Mach 2⋅05 above an altitude of 11,000m is
attributed to reduced directional stability rather than a lack of engine thrust.
Particular emphasis is given to instantaneous and sustained turning performance culminating
in the authors’ view as to how a MiG-21 could be observed to perform a split-S manoeuvre below
3,000ft 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 a
number of photographs that illustrate their general features.
The editorial style of the book could be improved for western readers. Commas are used instead of
decimal points, figures are not generally referenced in the text, there is no single list of symbols and
equations are presented in a format foreign to UK practice.
In conclusion, the book gives an interesting insight into the quantitative comparison of
fighter aircraft and the interpretation of the significance of the differences presented in
the performance curves and flight limitation boundaries. It makes informative and
entertaining reading for anyone interested in the assessment of the merits of
competing 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 the
market.
What I read is very good, with precision, you have focused in a good point of view of analysis. I would
like 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-13
and Capt. Boyd: Aerial Attack Study are sent as a gift.