Aircraft design project-1 of fighter by veerappan

Velocity Vs Thrust available
velocity (m/s)
Thrust available (KN)
VelocityVs (CD) max
VELOCITY m/s
(CD)max
VelocityVs (CL) max
VELOCITY m/s
(CL)max
Velocity Vs Thrust required
velocity (m/s)
Thrust required (KN)
Velocity Vs power available
velocity (m/s)
power avialable (MN)m/s
Velocity Vs power required
velocity (m/s)
power Required (MN)m/s
Velocity Vs power required
velocity (m/s)
power Required (MN)m/s
Velocity Vs (R/C)max
velocity (m/s)
R/C max (m/s)
Velocity Vs (L/D)max
velocity (m/s)
L/D max
(CL)Vs (CD) max
CLmax
(CD)max
SUPERSONIC FIGHTER AIRCRAFT(SWEPT BACK WING)
A Project report
Submitted by
VEERAPPAN R 411011101021
PRABHAKARAN P 411011101015
In the partial fulfillment for the award of the degree
Of
BACHELOR OF ENGINEERING
IN
AERONAUTICAL ENGINEERING

ANNA UNIVERSITY : CHENNAI 600 025




















COMPARATIVE DATA SHEETS:


















GENERAL CHARACTERSTICES;
s.no
Name of the aircraft
Crew
Length (m)
Wing span (m)
Wing area (m^2)
Empty weight (kg)
Loaded weight (kg)
Max takeoff weight (kg)
Aspect ratio
Power plant
Power plant
H
E
I
G
H
T
(m)










Dry thrust(KN)
With After burner thrust (KN)

1
Grumman f-14 tomcat
2
19.4
11.58
54.5
19838
27,700
33,720
2.5
61.4
123.7
4.88
2
General dynamic f-111f
2
22.4
9.75
48.77
21400
37600
45300
1.95
79.6
112
5.22
3
Panavia tornado
2
16.72
13.9
26.6
13890

28000
7.2
43.8
76.8
5.95
4
Sukhoi su-17
1
19.02
11.02
34.5
12160
18400

3.5
76.4
109.8
5.12
5
Mig-23 mcd flogger-k
1
16.7
13.97
34.16
9595
15700
18030
5.7
83.6
127
4.82
6
Dassault mirage f-1
1
15.30
8.40
25.00
7400
10900
16200
2.8
49.03
70.6
4.50
7
MC donnell douglas f4 phantom ii
2
19.2
11.7
49.2
13757
18825
28030
2.8
52.9
79.4
5.0
8
Sukhoi su-24
2
22.5
10.34
55.2
22300
38040
43755
1.9
75
109.8
6.19
9
Vought xf8u-3 crusader-iii
1
17.86
12.16
41.8
9915
14660
17590
3.5
73.4
131.2
4.98
10
English electric lightning
1
16.8
10.6
44.01
14092
18638
20752
2.5
55.74
71.17
5.97
11
Mikoyan-gurevich mig-17F
1
11.26
9.63
22.6
3919
5350
6069
4.1
22.5
33.8
3.80
12
Chengdu j-7MG
1
14.885
8.32
24.88
5292
7540
9100
2.8
44.16
64.7
4.11




PERFORMANCES;
s.no
Name of the aircraft
Cruise speed(km/hr)
Range(km)
Service ceiling(m)
Thrust/weight
Rate of climb(m/s)
Wing loading
(kg/m^2)
1
Grumman f-14 tomcat
2485
2960
15,200
.92
229
508.25
2
General dynamic f-111f
2655
6760
20100
0.61
131.5
771.96
3
Panavia tornado
2400
3890
15240
0.55
76.7
707.95
4
Sukhoi su-17
1860
2300
14200
0.68
230
533.33
5
Mig-23 mcd flogger-k
2445
2820
18500
0.88
240
434.18
6
Dassault mirage f-1
2338
3300
20000
0.67
243
436
7
MC donnell douglas f4 phantom ii
2370
2600
18300
0.86
210
416.48
8
Sukhoi su-24
1654
2775
11000
0.60
150
689.13
9
Vought xf8u-3 crusader-iii
925
3290
19800
0.74
165
351
10
English electric lightning
2100
2040
16000
0.78
100
423.49
11
Mikoyan-gurevich mig-17F
1145
2060
16600
0.63
65
236.72
12
Chengdu j-7MG
2200
3290
17500
0.84
195
303.05



















PRELIMINARY GRAPHS OF VARIOUS PARAMETERS WITH RESPECT TO VELOCITY








1.

2







3

4






5

6






7
8







9

10




11

12








RETRIVED DATA FROM GRAPH
1
LENGTH
17.67(m)
2
HEIGHT
5.045(m)
3
ASPECT RATIO
3.44
4
WING AREA
38.449(m2)
5
WING SPAN
10.95(m)
6
EMPTY WEIGHT
12796.5(kg)
7
LOADED WEIGHT
19349(kg)
8
RANGE
3173.75(km)
9
TAKEOFF WEIGHT
23966(kg)
10
SEVICE CEILING
16870(m)
11
T/W
0.73
12
WING LOADING
484.295(kg/m2)
13
CRUISE SPEED
2048.08
14
Rate of climb
169.6(m/s)
15
Dry thrust
59.79(kN)
16
After burner thrust
92.4975(kN)























PRELIMINARY WEIGHT ESTIMATION














Weight estimation:
The common choice to subdivide and categorize the weight components of an airplane is:
1. CREW WEIGHT W crew-it comprises the people necessary to operate the plane in flight. For our design the crew is 2
2. PAYLOAD WEIGHT WP-The payload is what the airplane intended to carry.in our design payload is missiles.
3. FUEL WEIGHT Wf-is the weight of the fuel in the fuel tanks which decreases with time during flight.
4.EMPTY WEIGHT We-is weight of everything else –the structure ,engines ,avionics ,landing gear ,seats and anything else that is not crew, payload or fuel.
The designs take-off weight WO is the weight of the airplane at the instant it begins its mission. Hence it can be shown that,
W0 = Wcrew + WP + Wf + We
The crew and payload weight are both known since they are given in design requirement.The only unknowns are the fuel weight and empty weight. However, they are both depend on the total aircraft weight.
To simplify the calculation, both fuel and empty weight can be expressed as fraction of the total take-off weight (i.e) (Wf/W0) and (We/ W0).
Thus above eqn becomes
W0 = Wcrew + WP + (Wf/W0) W0 + (We/ W0) W0.
This can be solved for W0 as follows:
W0- (Wf/W0) W0 - (We/ W0) W0= Wcrew + WP
W0 =Wcrew + WP1-WfW0- (We/ W0)


Now we can be determine if (Wf/W0) and (We/ W0).can be estimated .these are described below.




CREW WEGHT ESTIMATION:
In our design crew = 2
On an average, taking 200kg person,
Crew load = 2 x 90.72=182kg
PAYLOAD ESTIMATION:
In our design,
Pay load=4000 kg, and it's given by
Armaments detail:
Type
Weight(kg)
Mk 82
227
Mk 83
454
Mk 84
907
Mk 117
340
GBU 10
907
BLU 109
907
GBU-12
257


FUEL WEIGHT ESTIMATION:




Mission profile:
Mission profile is explaining the various stages and maneuver's during flight of the aircraft from start to shut down. The mission for our fighter aircraft is shown in below
Phase 1 : engine start and warm up
Phase 2 : taxi
Phase 3 : take-off
Phase 4 : climb
Phase 5 : cruise-out
Phase 6 : loiter
Phase 7 : descend
Phase 8 : dash-out
Phase 9 : drop bombs
Phase 10 : strafe
Phase 11 : dash in
Phase 12 : climb to cruise
Phase 13 : cruise in
Phase 14 : descend
Phase 15 : landing

Mission fuel fraction (Mff):
The fuel weight ratio can be obtained from product of mission segment weight at the end of the segment divided by the weight at the beginning of segment.
1. Engine start up : start weight is WTO and end weight is W1
W1/WTO=.990
2. Taxing : start weight is W1and end weight is W2
W2/W1=.990
3. Take-off : start weight is W2 and end weight is W3
W3/W2=.990
4. Climb : start weight is W3 and end weight is W4
W4/W3=.971

The phase covered during climb phase needs to be calculated. It can be assumed, that the climb is performed at an average speed of 500m/s and with an average climb rate of 100m/s.to 16870m this takes 2.8 min. The range covered is 2.8*500=1400km (For direct climb to 40000ft. at max.WTO In 8 min is desired. Climb rate on one engine, at max. WTO should exceed 500fpm on a 950f day)
5. Cruise out : start weight is W4 and end weight is W5
W5/W4=.954
The cruise phase is to be carried out at 16870 m and with a speed corresponding to M=1.67(with external load), this means Vcruise=568.91m/s. fuel used during this part of the mission can be estimated from Braguest range equation:
Rcr = (V/Cj)cr (L/D)cr ln (W4/W5)
The range is 3173.75-1400=1773.75km. Because this fighter carries its bomb load externally and because it cruise at a rather cruise speed, the L/D value during cruise out likely to be very high. A value of 7.0 seems reasonable. for Cj , 0.6 might be an optimistic choice with these phase follows from range eqn
W5/W4=.928
6. Loiter : start weight is W5 and end weight is W6
During loiter the lift-to-drag ratio will be significantly better than during high speed cruise-out. A value of 9.0 for (L/D)ltr will be used. for Cj, indicates that 0.6 is o.k loiter is specified at 30min. the fuel fraction for this phase follows from Brequest endurance equation
Eltr= (Vcr/Cj) (L/D) ln W5/W6
This yields W6/W5=0.967
7. Descend : start weight is W6 and end weight is W7
W7/W6 =.99
8. Dash out : start weight is W7 and end weight is W8
W8/W7=.951
9. Drop bombs : start weight is W8 and end weight is W9
W9/W8=1
10. Strafe : start weight is W9 and end weight is W10
W10/W9=0.986

11. Dash in : start weight is W10 and end weight is W11
W11/W10=.966
12. Climb to Cruise: start weight is W11 and end weight is W12
W12/W11=.969
13. Cruise in : start weight is W12 and end weight is W13
W13/W12=.956
14. Descend : start weight is W13 and end weight is W14
W14/W13=.99
15. Landing : start weight is W14 and end weight is W15
W15/W14=.995
Therefore the mission fuel fraction is given by
Mff = {( W15/W14)*( W14/W13)*( W13/W12)*( W12/W11)*( W11/W10)*( W10/W9)*( W9/W8)*( W8/W7)*( W7/W6)*( W6/W5)*( W5/W4)*( W4/W3)*( W3/W2)*( W2/W1)*( W1/WTO)}
Mff=0.693
The weight of the fuel required for the mission is calculated using the formula
WF/W0 = (1-0.693)
Therefore WF = 0.307*W0
Where, W0-average Take-off value taken from the graph
W0 = 23966kg
WF = 0.307*23966
WF = 7357.562kg


EMPTY WEIGHT ESTIMATION (We):
The value of empty weight is calculated using the formula
WEtent=W0Etent-Wtfo-WCrew
Where, W0Etent=W0-Wf-WPayload ,
Wtfo=0.005*W0
WOEtent= 23966-7357.562-4000
WOEtent=12608.438kg
Therefore empty weight
WEtent=12608.438-(0.005*23966)-182
WEtent=12306.608kg
Where,
WOEtent -operating empty weight tentative(kg),
WTfo -Trapped fuel-0il weight(kg)
We/ W0=12306.608/23966
We/ W0 =0.513
W0 =Wcrew + Wp1-WfW0- (We/ W0)
W0 =182 +4000 1-0.307- 0.513
W0=23233.33kg
ITERATION PROCESS:
We/ W0=A(W0)CKVS
For fighter aircraft {A=2.34, C=-0.13, Kvs=1}
Iteration-1:
We/ W0 = 2.34*(23233.33)-0.13*1
= 0.633
Wo = 19441.71
Iteration-2:
We/ W0=2.34*(19441.71)-0.13*1
=0.648
Wo=18987.07
Iteration-3:
We/ W0=2.34*(18987.07)-0.13*1
=0.650
Wo=18929.75
Iteration-4:
We/ W0=2.34*(18929.75)-0.13*1
=0.650
Wo=18921.18
Iteration-5:
We/ W0=2.34*(18921.18)-0.13*1
=0.650
=18920.2
Iteration-6:
We/ W0=2.34*(18920.20)-0.13*1
=0.650
Wo=18920.07
OVERALL WEIGHT ESTIMATION:
Take off weight:
Wo =18920Kg


WEIGHT OF FUEL:
Wf = 0.307*18920
=5808.44Kg
Empty weight:
WEtent=W0Etent-Wtfo-WCrew
Where, W0Etent=W0-Wf-WPayload , Wtfo=0.005*W0
WOEtent =18920-5808.44-4000
WOEtent = 9111.56kg
Therefore empty weight
WEtent = 9111.56-(0.005*18920)-182
WEtent = 8834.96kg

RESULTS OFF THE WEIGHT ESTIMATION:
WEIGHTS
UNIT(kg)
UNIT (N)
Empty weight
8834.96
86670.95
Weight fuel
5808.44
56980.79
Overall weight (or)maximum take-off weight
18920
185605.2
Weight of crew
182
1785.42
Weight of pay load
4000
39240










ESTIMATION OF CRITICAL PERFORMANCE PARAMETER:
1. Airfoil selection
2. Wing selection
3. Power plant selection
4. Wing tail and
5. Control surfaces (flap).














AIRFOIL SELECTION:
Airfoil nomenclature:
Chord length (c) – length from the leading edge to the trailing edge of a wing cross section that is parallel to the vertical axis of symmetry.
Mean camber line – line halfway between the upper and lower surfaces.
Leading edge (LE) – is the front most point on the mean camber line. trailing edge (TE) – Is the most rearward point on mean camber line.
Camber – maximum distance between the mean camber line and chord line, measured perpendicular to the chord line
Un camber – the airfoil is symmetric above and below the chord line.
Thickness – distance between upper surface and lower surface measured perpendicular to the mean camber line




Family
Advantages
Disadvantages
Applications
4-Digit
1. Good stall characteristics

2. Small center of pressure movement across large speed range

3. Roughness has little effect
1. Low maximum lift coefficient

2. Relatively high drag

3. High pitching moment
1. General aviation
2. Horizontal tails

Symmetrical:

3. Supersonic jets
4. Helicopter blades
5. Shrouds
6. Missile/rocket fins
5-Digit
1. Higher maximum lift coefficient

2. Low pitching moment

3. Roughness has little effect
1. Poor stall behavior

2. Relatively high drag
1. General aviation
2. Piston-powered bombers, transports
3. Commuters
4. Business jets
16-Series
1. Avoids low pressure peaks

2. Low drag at high speed
1. Relatively low lift
1. Aircraft propellers
2. Ship propellers
6-Series
1. High maximum lift coefficient

2. Very low drag over a small range of operating conditions

3. Optimized for high speed
1. High drag outside of the optimum range of operating conditions

2. High pitching moment

3. Poor stall behavior

4. Very susceptible to roughness
1. Piston-powered fighters
2. Business jets
3. Jet trainers
4. Supersonic jets
7-Series
1. Very low drag over a small range of operating conditions

2. Low pitching moment
1. Reduced maximum lift coefficient

2. High drag outside of the optimum range of operating conditions

3. Poor stall behavior

4. Very susceptible to roughness
Seldom used
8-Series
Unknown
Unknown
Very seldom used

SELECTION PARAMETER:
Normally to select an efficient aerofoil to produce maximum lift initially we consider about some parameters like,
1. Co-efficient of lift
2. Stalling velocity
3. Reynolds number
4. t/c ratio
STALLING VELOCITY:
Stalling speed of fighter aircraft is given by
VA=1.2Vstall
Where, velocity approach for fighter aircraft is given by
VA=150 kts
Vstall = 150/1.2
Vstall=64.43m/s
COFFICIEND OF LIFTS:
L=(1/2)*(Vstall)2 * *S*CLmax

Considering steady state level flight , L=W
1. calculation of aircraft maximum coefficient of lift(CLmax)
CLmax =2WVstall2 * *S
Where, W0=18920Kg
W0=185605.2N
S=38.449m2
=1.225 Kg/m3 at sea level
Vstall=64.43m/s


Therefore,
CLmax =2WVstall2 * *S
CLmax =2*185605.264.432 *1.225*38.449
CLmax =1.9
2.calculation of wing maximum lift coefficiend
Clmax(w) = CLmax0.95
=1.9/0.95
=2
3.calculation of wing airfoil gros maximum lift coefficient
Clmax(gross) = Clmax(w) 0.9
=2.2 (FLAP DOWN)
Where the wing airfoil gross maximum coefficient in which the effect of high lift devices is include eg, flap
3.calculation of wing airfoil net maximum lift coefficient
Cl max = Clmax(gross) - Cl(HLD)
HIGH LIFT DEVICE SELECTION (FLAP): Cl(HLD)

For an double sloteted flap CL is given by
Cf/C=0.3
Therefore CL= 0.3*1.6
=0.48
Therefore, The calculation of wing airfoil net maximum lift coefficient is given by
Cl max = Clmax(gross) - Cl(HLD)

HIGH LIFT DEVICE SELECTION:
The Functions of High Lift Device
One of the design goals in wing design is to maximize the capability of the wing in the generation of the lift. This design objective is technically shown as maximum lift coefficient (CLmax). In a trimmed cruising flight, the lift is equal to weight. When the aircraft generates its maximum lift coefficient, the airspeed is referred to as stall speed.

CLmax =2WVstall2 * *S

Two design objectives among the list of objectives are: 1. maximizing the payload weight, 2. minimizing the stall speed (Vs). As the equation 5.36 indicates, increasing the CLmax tends to increase the payload weight (W) and decrease the stall speed. The lower stall speed is desirable since a safe take-off and landing requires a lower stall speed. On the other hand, the higher payload weight will increase the efficiency of the aircraft and reduce the cost of flight. A higher CLmax allows the aircraft to have a smaller wing area that results in a lighter wing. Hence, in a wing design, the designer must find way to maximize the CLmax. In order to increase the lift coefficient, the only in-flight method is to temporarily vary (increase) the wing camber. This will happen only when the high lift device is deflected downward. In 1970's the maximum lift coefficient at take-off was 2.8; while the record currently belongs to Airbus A-320 with a magnitude of 3.2.

The primary applications of high lift devices are during take-off and landing operations. Since the airspeed is very low compared with the cruising speed, the wing must produce a bigger lift coefficient. The aircraft speed during take-off and landing is slightly greater than the stall speed. Airworthiness standards specify the relationship between take-off speed and landing speed with stall speed. As a general rule, we have,
VTO=K.VS
where k is about 1.1 for fighter aircraft, and about 1.2 for jet transports and GA aircraft.

The application of the high lift device tends to change the airfoil section's and wing's camber (in fact the camber will be positively increased). This in turn will change the pressure distribution along the wing chord as sketched in figure 5.52. In this figure, CP denotes the pressure coefficient.

In contrast, the leading edge high lift device tends to improve the boundary layer energy of the wing. Some type of high lift device has been used on almost every aircraft designed since the early 1930s. High lift devices are the means to obtain the sufficient increase in CLmax.

At the airfoil level, a high lift device deflection tends to cause the following six changes in the airfoil features:

1. Lift coefficient (Cl) is increased,
2. Maximum lift coefficient (Clmax) is increased,
3. Zero-lift angle of attack ( o) in changed,

4. Stall angle ( s) is changed,
5. Pitching moment coefficient is changed.
6. Drag coefficient is increased.
7. Lift curve slope is increased.


Pressure distribution of the wing when HLD deflected



CP




Pressure distribution of original wing








f x/C


Figure 5.52. Example of pressure distribution with the application of a high lift device

These effects are illustrated in figure 5.53. Along with three desirable advantages (first two items) to the application of high lift devices; there are a few negative side-effects (the last five items) as well. A plain flap tends to decrease stall angle, while a slotted flap and leading edge slat tend to increase the stall angle. In addition, among all types of flaps, the Fowler flap and leading edge slat tend to increase the lift curve slope (CL ). On the other hand, leading edge flap tend to increase (shift to the right) the zero-lift angle of attack ( o).

A reduction in stall angle is undesirable, since the wing may stall at a lower angle of attack. During the take-off and landing operation, a high angle of attack is required to successfully take-off and land. The high angle of attack will also tend to reduce the take-off run and landing run that is desirable in the airport at which have a limited runway length. An increase in pitching moment coefficient requires higher horizontal tail area to balance the aircraft. An increase in drag coefficient decreases the acceleration during take-off and landing. Although the application of high lift device generates three undesirable side effects, but the advantages outweigh the disadvantages.

If the natural value of CLmax for an aircraft is not high enough for safe take-off and landing, it can be temporarily increased by mechanical high lift devices. Thus, employing the same airfoil section; one is able to increase CLmax temporarily as needed without actually pitching the aircraft. Two flight operations at which the CLmax needs to be increased are take-off and landing. Table
5.14 shows the maximum lift coefficient for several aircraft at take-off and landing
configurations.



Cl


Cm Cd
Clmax








S


Cdmin





Cli Cl



without flap deflection with flap deflection

Figure 5.53. Typical effects of high lift device on wing airfoil section features

In a cruising flight, there is no need to utilize the maximum lift coefficient since the speed is high. These mechanical devices are referred to as High Lift Devices (HLD). High Lift Devices are parts of wings to increase the lift when deflected down. They are located at inboard section of the wing and usually employed during take-off and landing.

CLmax
Cessna
172
Piper
Cherokee
Short
Skyvan 3
Gulfstream
II
DC-9
Boeing
727
Airbus
300
Learjet
25
Take-Off
1.5
1.3
2.07
1.4
1.9
2.35
2.7
1.37
Landing
2.1
1.74
2.71
1.8
2.4
2.75
3
1.37
Table 5.14. Maximum lift coefficient for several aircraft

5.12.2. High Lift Device Classification
Two main groups of high lift devices are:

1. leading edge high lift device (LEHLD), and
2. trailing edge high lift devices (TEHLD or flap).

There are many types of wing trailing edge flaps that the most common of them are split flap, plain flap, single-slotted flap, double-slotted flap, triple-slotted flap, and fowler flap as illustrated in figure 5.54a. They are all deflected downward to increase the camber of the wing, so CLmax will be increased. The most common of leading edge devices are leading edge flap, leading edge slat, and Kruger flap as shown by in figure 5.54b.

A common problem with the application of high lift devices is how to deal with the gap between high lift device and the main wing. This gap can be either sealed or left untouched. In both cases, there are undesirable side effects. If the gap left open, the airflow from downside escapes to the upper surface which in turn degrades the pressure distribution. On the other hand, if the gap is sealed by a means such diaphragm, it may be blocked by ice during flight into colder humid air. In both cases, it needs special attention as an operational problem. In the following, the technical features of various high lift devices are discussed.




a. Plain flap b. Split flap c. Single slotted flap







d. Double slotted flap






e. Triple slotted flap f. Fowler flap




a. Trailing edge high lift device
















g. Leading edge flap h. Leading edge slat i. Kruger flap





b. Leading edge high lift device





Figure 5.54. Various types of high lift devices

1. The plain flap (figure 5.54-a) is the simplest and earliest type of high lift device. It is an airfoil shape that is hinged at the wing trailing edge such that it can be rotated downward and upward. However, the downward deflection is considered only. A plain flap increases the lift simply by mechanically increasing the effective camber of the wing section. In terms of cost, a plain flap is the cheapest high lift device. In terms of manufacturing, the plain flap is the easiest one to build. Most home build aircraft and many General Aviation aircraft are employing the plain flap. The increment in lift coefficient for a plain flap at 60 degrees of deflection (full extension) is about 0.9. If it is deflected at a lower rate, the CL increment will be lower. Some old GA aircraft such as Piper 23 Aztec D has a plain flap. It is interesting to know that the modern fighters such aircraft F-15E Eagle (Figures 4.21 and 9.14) and MIG-29 (Figure 5.61) also employ plain flaps.

2. In the split flap (figure 5.54-b), only the bottom surface of the flap is hinged so that it can be rotated downward. The split flap performs almost the same function as a plain flap. However, the split flap produces more drag and less change in the pitching moment compared to a plain flap. The split flap was invented by Orville Wright in 1920, and it was employed, because of its simplicity, on many of the 1930s and 1950s aircraft. However, because of the higher drag associated with split flap, they are rarely used on modern aircraft.

3. The single slotted flap (figure 5.54-c) is very similar to a plain flap, except it has two modifications. First, the leading edges of these two trailing edge flaps are different as shown in figure 5.51. The leading edge of a single slotted flap is carefully designed such that it modifies and stabilizes the boundary layer over the top surface of the wing. A low pressure is created on the leading edge that allows a new boundary layer to form over the flap which in turn causes the flow to remain attached to very high flap deflection. The second modification is to allow the flap move rearward during the deflection (i.e. the slot). The aft movement of single slotted flap actually increases the effective chord of the wing which in turn increases the effective wing planform area. The larger wing planform area naturally generated more lift.

Thus a single slotted flap generates considerably higher lift than a plain and split flap. The main disadvantage is the higher cost and the higher degree of complexity in the manufacturing process associated with the single slotted flap. Single slotted flap are in common use on modern light, general aviation aircraft. In general, the stall angle is increased by the application of the slotted flap. Several modern GA light aircraft such as Beech Bonanza F33A and several turboprop transport aircraft such as Beech 1900D and Saab 2000 has deployed single slotted flap.

4. The double slotted flap is similar to a single slotted flap, except it has two slots; i.e., the flap is divided into two segments, each with a slot as sketched in figure 5.54-d. A flap with two slots almost doubles the advantages of a single slotted flap. This benefit is achieved at the cost of increased mechanical complexity and higher cost. Most modern turboprop transport aircraft such as ATR-42 (Figure 3.8); and several jet aircraft such as and jet trainer Kawasaki T-4 employ the double slotted flap. The jet transport aircraft Boeing 767 (Figure 5.4) has single slotted outboard flap and double slotted inboard flap. It is a common practice to deflect the first segment (slot) of the flap during a take-off operation, but employs full deflection (both segments) during landing. The reason is that more lift coefficient is needed during a landing that a take-off.

5. A triple slotted flap (figure 5.54-e) is an extension to a double slotted flap; i.e. has three slots.
This flap is mechanically the most complex; and costly most expensive flap in design and operation. However, a triple slotted flap produces the highest increment in lift coefficient. It is mainly used in heavy weight transport aircraft which have high wing loading. The jet transport aircraft Boeing 747 (Figures 3.7, 3.12, 9.4) has employed the triple slotted flap.

6. A Fowler flap (figure 5.54-f) has a special mechanism such that when deployed, not only deflects downward, but also translates or tracks to the trailing edge of the wing. The second feature increases the exposed wing area; which means a further increase in lift. Because of this benefit, the concept of the Fowler flap may be combined with the double slotted and triple slotted flaps. For instance jet transport aircraft Boeing B-747 (Figures 3.7, 3.12, 9.4) has utilized triple slotted Fowler flap. In general, the wing lift curve slope is slightly increased by the application of the Fowler flap. Maritime patrol aircraft Lockheed Orion P-3 with 4 turboprop engines has a Fowler engine.

7. A leading edge flap (or droop) is illustrated in figure 5.54-g. This flap is similar to trailing edge plain flap, except it is installed at the leading edge of the wing. Hence, the leading edge pivots downward, increasing the effective camber. A feature of the leading edge flap is that the gap between the flap and main wing body is sealed with no slot. In general, the wing zero-lift angle of attack is shifted to the right by the application of leading edge flap. Since the leading edge flap has a lower chord compared with the trailing edge flaps, it generates a lower increment in lift coefficient ( CL is about 0.3).

8. The leading edge slat (see figure 5.54-h) is a small, highly cambered section, located slightly forward of the leading edge the wing body. When deflected, a slat is basically a flap at the leading edge, but with an unsealed gap between the flap and the leading edge. In addition to the primary airflow over the wing, there is a secondary flow that takes place through the gap

between the slat and the wing leading edge. The function of a leading edge slat is primarily to modify the pressure distribution over the top surface of the wing. The slat itself, being highly cambered, experiences a much lower pressure over its top surface; but the flow interaction results in a higher pressure over the top surface of the main wing body. Thus it delays flow separation over the wing and mitigates to some extent the otherwise strong adverse pressure gradient that would exist over the main wing section.

By such process, the lift coefficient is increased with no significant increase in drag. Since the leading edge slat has a lower chord compared with the trailing edge flaps, it generates a lower increment in lift coefficient ( CL is about 0.2). Several modern jet aircraft such as two seat fighter aircraft Dassault Rafale (Figure 6.8), Eurofighter 2000 (Figure 3.7), Bombardier BD 701 Global Express, McDonnell Douglas MD-88 (Figure 9.4), and Airbus A-330 (Figures 5.51 and 9.14) have leading edge slat. In general, the wing lift curve slope is slightly increased by the application of leading edge slat.

No
High lift device
CL
1
Plain flap
0.7-0.9
2
Split flap
0.7-0.9
3
Fowler flap
1-1.3
4
Slotted flap
1.3 Cf/C
5
Double slotted flap
1.6 Cf/C
6
Triple slotted flap
1.9 Cf/C
7
Leading edge flap
0.2-0.3
8
Leading edge slat
0.3-0.4
9
Kruger flap
0.3-0.4
Table 5.15. Lift coefficient increment by various types of high lift devices (when deflected 60
degrees)

9. A Kruger flap is demonstrated in figure 5.54-i. This leading edge high lift device is essentially a leading edge slat which is thinner, and which lies flush with the bottom surface of the wing when not deflected. Therefore, it is suitable for use with thinner wing sections. The most effective method used on all large transport aircraft is the leading edge slat. A variant on the leading edge slat is a variable camber slotted Kruger flap used on the Boeing
747 (Figures 3.7, 3.12, and 9.4). Aerodynamically, this is a slat, but mechanically it is a
Kruger flap.

As a general comparison, table 5.15 shows the typical values of maximum wing lift coefficient for various types of high lift devices. In this table, the symbol Cf/C denotes the ratio between the chord of high lift device to the chord of the main wing body as shown in figure 5.55. Table 5.16 demonstrates various features for high lift devices of several aircraft.

5.12.3. Design Technique
In designing the high lift device for a wing, the following items must be determined:

1. High lift device location along the span
2. The type of high lift device (among the list in figure 5.54)
3. High lift device chord (Cf)

4. High lift device span (bf)
5. High lift device maximum deflection (down) ( fmax)

The last three parameters are sketched in figure 5.55. The first and second item must be selected through an evaluation and analysis technique considering all advantages and disadvantages of each option regarding design requirements. However, the last three parameters must be determined through a series of calculations. In the following, the design technique for high lift device to determine the above five items will be presented.



Cfbf/2b/2Cfbf/2b/2Fuselage




Cf

bf/2


b/2





Cf

bf/2


b/2

Center
Line
C









a. Top-view of the right wing



Leading edge





Chord line

Trailing edge


fmax
Cf

C

b. The side-view of the inboard wing (flap deflected)

Figure 5.55. High lift device parameters

a. HLD Location

The best location for high lift device is the inboard portion of both left and right of the wing sections. When high lift device is applied symmetrically on the left and right wing sections, it will prevent any rolling moment; hence the aircraft will remain laterally trimmed. The deflection of high lift device will increase the lift on both inboard sections, but since they are generated symmetrically, both lift increments will cancel each other's rolling moments.

There are two reasons for the selection of inboard section. First of all, it produces a lower bending moment on the wing root. This makes the wing structure lighter and causes less fatigue on the wing in the long run. The second reason is that it allows the aileron to have a large arm, which is employed on the outboard wing trailing edge. The larger arm for the aileron, when

installed on the outboard panels, means the higher lateral control and a faster roll. The design of the aileron will be discussed in chapter 12.

b. Type of High Lift Device

The options for the high lift device are introduced in Section 5.11.2. Several design requirements will affect the decision on the type of high lift device. They include, but not limited to: 1. Performance requirements (i.e. the required lift coefficient ( CL) increment during take-off and landing); 2. Cost considerations; 3. Manufacturing limitations; 4. Operational requirements;
5. Safety considerations; and 6. Control requirements. The following guideline will help the designer to make the right decision.

The final decision is the outcome of a compromise among all options using a table including the weighted design requirements. For a homebuilt aircraft designer, the low cost is the number one priority, while for a fighter aircraft designer the performance is the first priority. A large transport passenger aircraft designer, believe that the airworthiness must be on the top of the list of priorities.

The following are several guidelines that relate the high lift device options to the design requirements:

1. A more powerful high lift device (higher CL) is usually more expensive. For instance, a double slotted flap is more expensive than a split flap.
2. A more powerful high lift device (higher CL) is usually more complex to build. For example, a triple slotted flap is more complex in manufacturing than a single slotted flap.
3. A more powerful high lift device (higher CL) is usually heavier. For instance, a double slotted flap is heavier than a single slotted flap.
4. The more powerful high lift device (higher CL), results in a smaller wing area.
5. The more powerful high lift device (higher CL), results in a slower stall speed, which consequently means a safer flight.
6. A heavier aircraft requires a more powerful high lift device (higher CL).
7. A more powerful high lift device results in a shorter runway length during take-off
and landing.
8. A more powerful high lift device (higher CL) allows a more powerful aileron.
9. A simple high lift device requires a simpler mechanism to operate (deflect or retract)
compared with a more complex high lift device such as a triple slotted flap.

SELECTED HIGH LIFT DEVICE : IS DOUBBLE SLOTTED
For double slotted CL = 1.6(cf/c)
Where cf/c=0.3, CL = 0.48
Therefore, Cl max = 2.2 – 0.48
Cl max=1.72
(FLAP UP)
the corresponding airfoils are given by
The NACA airfoil series
The early NACA airfoil series, the 4-digit, 5-digit, and modified 4-/5-digit, were generated using analytical equations that describe the camber (curvature) of the mean-line (geometric centerline) of the airfoil section as well as the section's thickness distribution along the length of the airfoil. Later families, including the 6-Series, are more complicated shapes derived using theoretical rather than geometrical methods. Before the National Advisory Committee for Aeronautics (NACA) developed these series, airfoil design was rather arbitrary with nothing to guide the designer except past experience with known shapes and experimentation with modifications to those shapes.

This methodology began to change in the early 1930s with the publishing of a NACA report entitled The Characteristics of 78 Related Airfoil Sections from Tests in the Variable Density Wind Tunnel. In this landmark report, the authors noted that there were many similarities between the airfoils that were most successful, and the two primary variables that affect those shapes are the slope of the airfoil mean camber line and the thickness distribution above and below this line. They then
presented a series of equations incorporating these two variables that could be used to generate an entire family of related airfoil shapes. As airfoil design became more sophisticated, this basic approach was modified to include additional variables, but these two basic geometrical values remained at the heart of all NACA airfoil series, as illustrated below.

















WING SELECTION:
INTRODUCTION
After the final weight estimation of the aircraft, the primary component of the aircraft to be designed is the wing. The wing weight and its lifting capability are in general, a function of the aerofoil section that is used in the wing structure. The first setup towards designed the wing is the thickness estimation. The thickness of the wing, in turn depends on the critical Mach number of the aerofoil or rather, the drag divergence Mach number corresponding to the wing section.
The critical Mach number can well be delayed by the use of an appropriate sweep-back angle to the wing structure. The nature choice of the standard series is the 65 series which is designed specifically for use in high-speed.


WING GEOMETRY DESIGN
The geometry of the wing is a function for four parameter, namely the Wing loading (w/s), Aspect ratio (b2/s), Taper ratio (ʎ) and the sweepback angle at quarter chord (Ʌqc)
The take-off weight that was estimated in the previous analysis is used to find the wing area S (from W/S). The value of S also enables to calculate the wingspan b (using the Aspect ratio). The root chord can now be found using the equation.

POSITION OF WING
The location of the wing in the fuselage (along the vertical axis) is very important. Each configuration (Low, High and mid) has its own advantages but in this design, the mid wing
Mid Wing
In general, features of the mid-wing configuration (Figure 5.3-b, and Figure 5.4-4) stand
somewhat between features of high-wing configuration and features of low-wing configuration. The major difference lies in the necessity to cut the wing spar in two half in order to save the space inside the fuselage. However, another alternative is not to cut the wing spar and letting it to pass through the fuselage; which leads to an occupied space of the fuselage. Both alternatives carry a few disadvantages. Other than those features that can be easily derived from two previous sections, some new features of a mid-wing configuration are as follows:

1. The aircraft structure is heavier, due to the necessity of reinforcing wing root at the intersection with the fuselage.
2. The mid wing is more expensive compared with high and low-wing configurations.
3. The mid wing is more attractive compared with two other configurations.
4. The mid wing is aerodynamically streamliner compared with two other configurations.
5. The strut is usually not used to reinforce the wing structure.
6. The pilot can get into the cockpit using the wing as a step in a small GA aircraft.
7. The mid-wing has less interference drag than low-wing and high-wing.



. The Significance of Lift and Load Distributions
The distribution of wing non-dimensional lift (i.e. lift coefficient; CL) per unit span along the
wing is referred to as lift distribution. Each unit area of the wing along the span is producing a specific amount of lift. The total lift is equal to the summation of these individual lifts. The lift distribution goes to zero at the tips, because there is a pressure equalization from the bottom to the top of the wing precisely at y = -b/2 and +b/2. Hence no lift is generated at these two points. In addition, the variation of "lift coefficient times sectional chord (C.CL)" along span is referred to as the "load distribution". Both lift distribution and load distribution are of great importance in the wing design process. The major application of lift distribution is in aerodynamic
calculation, while the primary application of the load distribution is in wing structural design as well as controllability analysis.

In the past (1930s), it was thought that for an elliptic lift distribution, the chord must vary elliptically along the span. The direct result of such logic was that the wing planform must be elliptical. For this reason, several aircraft wing planforms such as Supermarine Spitfire (Figure
8.3), a famous British World War II fighter were made elliptic. But, today, we know that there are various parameters that make the lift distribution elliptic, thus, there is no need for the wing planform to be planform.

The type of both lift distribution and load distribution are very important in wing design; and will influence the aircraft performance, airworthiness, stability, control, and cost. Ideally both lift distribution and load distribution are preferred to be elliptical. For the above mentioned reasons, the elliptical lift distribution and the elliptical load distribution are ideal and are the design objectives in the wing design process. An elliptical lift distribution is sketched in figure
5.32, where a front view of the wing is illustrated. The horizontal axis in figure 5.32 is y/s where y is the location is y-axis, and s denotes the semispan (s = b/2). In this figure, no high lift device

(e.g. flap) is deflected and the effect of the fuselage is ignored. The elliptical lift distribution and elliptical load distribution have the following desirable properties:

1. If the wing tends to stall (CLmax), the wing root is stalled before the wing tip (CLroot = CLmax while CLtip < CLmax). In a conventional aircraft, the flaps are located inboard, while the ailerons are installed outboard of the wing. In such a situation, ailerons are active, since the flow over the wing outboard section is healthy. This is of greater importance for spin recovery (which often happens after stall); since the aileron (in addition to rudder) application are very critical to stop the autorotation. Thus, the elliptical lift distribution provision guarantees the flight safety in the event of stall (see figure 5.33).


2. The bending moment at the wing root is a function of load distribution. If the load distribution is concentrated near to the root, the bending moment is considerably less that when it is concentrated near the tip. The center of an elliptical load distribution is closer to the wing root, thus it leads to a lower bending moment, which results in a less bending stress and a less stress concentration at wing root (see figure 5.34). This means a lighter wing spar and lighter wing structure that is always one of the design requirements. The load distribution is a function of the lift distribution.





CL












Front view

y/s


-b/2 +b/2

Figure 5.32. Elliptical lift distribution over the wing


3. The center of gravity of each wing section (left or right) for an elliptical load distribution is closer to the fuselage center line. This means a lower wing mass moment of inertia about x- axis which is an advantage in the lateral control. Basically, an aircraft rolls faster when the aircraft mass moment of inertia is smaller.
4. The downwash is constant over the span for an elliptical lift distribution [4]. This will influence the horizontal tail effective angle of attack.
5. For an elliptical lift distribution, the induced angle of attack is also constant along the span.

6. The variation of lift over the span for an elliptical lift distribution is steady (gradually increasing from tip (zero) to the root (maximum)). This will simplify the wing spar(s) design.




CL

CLmax


CL

CLmax










0 root tip

0 root tip


a. Non-elliptical (tip stalls before the root) b. Elliptical (root stalls before the tip)

Figure 5.33. Lift distribution over the half wing






C.CL

Total lift generated by a half wing



C.CL

Total lift generated by a half wing





Bending moment arm





0 0
root tip root


Bending moment arm


tip


a. Non-elliptical (load is farther from root) b. Elliptical (load is closer to root) Figure 5.34. Load distribution over the half wing
The reader may have noticed that if the contribution of the fuselage is added to the wing lift distribution, the distribution may not be elliptical; due to negligible fuselage lift contribution. This is true, and more realistic, since in a conventional aircraft, the wing is attached to the fuselage. What we examined here in this section is an ideal case, and the reader may modify the lift distribution by considering the fuselage contribution. Figure 5.35 depicts the fuselage contribution to a low wing configuration. Similar case may be made for the effect of flap of lift distribution when deflected. Figure 5.36 illustrates the flap contribution to the wing lift distribution. In principle, the goal in the wing design is to obtain an elliptical wing distribution without considering the contributions of fuselage, flap, or other components.









Lift








Fuselage



Low wing

Figure 5.35. The fuselage contribution to the lift distribution of a low wing configuration










Lift












Wing




Flap

Flap


Figure 5.36. The flap contribution to the lift distribution

In Section 5.15, a mathematical technique will be introduced to determine the lift and load distribution along the wing.


SELECTED WING:
SWEEP-BACK WING:
SweepAngle
Consider the top view of an aircraft. The angle between a constant percentage chord line along
the semispan of the wing and the lateral axis perpendicular to the fuselage centerline (y-axis) is called leading edge sweep ( LE). The angle between the wing leading edge and the y-axis of the aircraft is called leading edge sweep ( LE). Similarly, the angle between the wing trailing edge and the longitudinal axis (y-axis) of the aircraft is called trailing edge sweep ( TE). In the same fashion, the angle between the wing quarter chord line and the y-axis of the aircraft is called quarter chord sweep ( C/4). And finally, the angle between the wing 50 percent chord line and
the y-axis of the aircraft is 50 percent chord sweep ( C/2).




If the angle is greater than zero (i.e. wing is inclined toward tail), it is called aft sweep or simply sweep; otherwise it is referred to as forward sweep. Figure 5.37 shows five wings with various sweep angles. Figure 5.37a illustrates a wing without sweep, while figures 5.37b through
5.37d show four swept wing. The leading edge sweep is depicted in the wing of figure 5.37b, while trailing edge sweep is shown in the wing of figure 5.37e. In addition, the quarter chord sweep is illustrated in the wing of figure 5.37d, and the 50 percent chord sweep is illustrated in the wing of figure 5.37c. Most high-speed airplanes designed since the middle 1940s – such as North American F-86 Saber - have swept wings. On sweptback tapered wing, typical of almost all high speed aircraft, the leading edge has more sweep than the trailing edge.

With reference to the definition of sweep angle, a particular wing may have aft leading edge sweep, while it has forward trailing edge sweep. Among four types of sweep angles, the quarter chord sweep and leading edge sweep are the most important ones. The subsonic lift due angle of attack normally acts at the quarter chord. In addition, the crest is usually close to the quarter chord. The discussion in this section regarding the characteristics (advantages and disadvantages) of sweep angle is mostly about leading edge sweep angle, unless otherwise stated. Basically, a wing is being swept for the following five design goals:

1. Improving the wing aerodynamic features (lift, drag, pitching moment) at transonic, supersonic and hypersonic speeds by delaying the compressibility effects.
2. Adjusting the aircraft center of gravity.
3. Improving static lateral stability.
4. Impacting longitudinal and directional stability.
5. Increasing pilot view (especially for fighter pilots).


These items will be described in more details in this section. For more information, the reader needs to refer to technical textbooks that are listed at the end of this chapter. The practical influence of the sweep angle on various flight features are as follows:

1. The sweep angle, in practice, tends to increase the distance between leading edge and trailing edge. Accordingly, the pressure distribution will vary.
2. The effective chord length of a swept wing is longer (see Figure 5.38) by a factor of 1/cos ( ). This makes the effective thickness-to-chord ratio thinner, since the thickness remains constant.
3. Item 2 can be also translated into the reduction of Mach number (Mn) normal to the wing leading edge to M cos ( ). Hence, by sweeping the wing, the flow behaves as if the airfoil section is thinner, with a consequent increase in the critical Mach number of the wing. For this reason, a classic design feature used to increase Mcr is to sweep the wing [6].
4. The effect of the swept wing is to curve the streamline flow over the wing as shown in figure 5.38. The curvature is due to the deceleration and acceleration of flow in the plane perpendicular to the quarter chord line. Near the wing tip the flow around the tip from the lower surface to the upper surface obviously alters the effect of sweep. The effect is to unsweep the spanwise constant-pressure lines; isobar. To compensate, the wing tip may be given additional structural sweep.
5. The wing aerodynamic center (ac) is moved aft by the wing aft sweep at about few percent. The aft movement of the ac with increase in sweptback angle occurs because the effect of the downwash pattern associated with a swept wing is to raise the lift coefficient on the outer wing panel relative to the inboard lift coefficient. Since sweep movers the outer panel aft relative to the inner portion of the wing, the effect on the center of lift is an aft ward movement. The effect of wing sweep on ac position is shown in figure 5.39 for aspect ratios of 7 and 10 and for taper ratios of 0.25 and 0.5.




6. The effective dynamic pressure is reduced, although not by as much as in cruise.
7. The sweep angle tends to change the lift distribution as sketched in figure 5.40. The reason becomes clear by looking at the explanations in item 5. As the sweep angle is increased, the Oswald efficiency factor (e) will decrease (Equation 5.25).


The Oswald span efficiency for a straight wing and swept wing are given respectively by equation 5.27a and 5.27b [12].

e 1.78 1 0.045AR0.68 0.64

LELEe 4.61 1 0.045AR0.68 cos
LE
LE




0.15 3.1

(5.27a)

(5.27b)


Equation 5.27a is for a straight wing and Equation 5.27b is for a swept wing where sweep angle is more than 30 degrees. When the Oswald span efficiency is equal to 1, it indicates that the lift distribution is elliptical, otherwise it is non-elliptic. Equation 5.27 is not valid for low aspect ratio wings (AR less than 6).

8. The wing maximum lift coefficient can actually increase with increasing sweep angle.
However, the maximum useful lift coefficient actually decreases with increasing sweep angle, due to loss of control in pitch up situation. Whether or not pitch up occurs depends not only on the combination of sweep angle and aspect ratio, but also an airfoil type, twist angle, and taper ratio. Thus, the sweep angle tends to increase stall speed (Vs). The maximum lift coefficient of the basic wing without high lift device is governed by
the following semi-empirical relationship [13]
Clmax( not eql zero) Cl max 0.86 0.002( )
where sweep angle ( ) is in degrees and Clmax denotes the maximum lift coefficient for the outer panel airfoil section.
9. Wing sweep tends to reduce the wing lift curve slope (CL ). A modified equation based on Prandtl-Glauert approximation is introduced by [13] as follows:



CL
2

2 AR
AR 2 1 tan 2 M 2 4


(5.29)


10. The aircraft pitching moment will be increased, provided the aircraft cg is forward of aircraft ac. The reason is that wing aerodynamic center is moving aft with increase in sweep angle.
11. An aft swept wing tends to have tip stall because of the tendency toward outboard, spanwise flow. This causes the boundary layer to thicken as it approaches the tips. For the similar reason, a swept forward wing would tend toward root stall. This tends to have an influence opposite to that of wing twist.
12. On most aft swept wing aircraft, the wing tips are located behind the aircraft center of gravity. Therefore, any loss of lift at the wing tips causes the wing center of pressure to move forward. This in turn will cause the aircraft nose to pitch up. This pitch up tendency can cause the aircraft angle of attack to increase even further. This may result in a loss of aircraft longitudinal control. For the similar reason, a forward swept wing aircraft would exhibit a pitch down tendency in a similar situation.
13. Tip stall on a swept wing is very serious. If the outboard section of a swept wing stalls, the lift loss is behind the wing aerodynamic center. The inboard portion of the wing ahead of the aerodynamic center maintains its lift and produces a strong pitch-up moment, tending to throw the aircraft deeper into the stall. Combined with the effect of tip stall on the pitching moment produced by the tail, this effect is very dangerous and must be avoided by options such as wing twist.
14. A swept wing produce a negative rolling moment because of a difference in velocity components normal to the leading edge between the left and right wing sections [14]. The rolling moment due to aft sweep is proportional to the sine of twice the leading edge sweep angle.


Clβ sin(2 LE )
This makes the dihedral effect(Clβ) more negative and it means that a swept wing has an


inherent dihedral effect. Hence, a swept wing may not need a dihedral or anhedral to satisfy lateral-directional stability requirements. Thus, the sweep angle tends to reinforce
the dihedral effect. It is interesting to note that making the dihedral effect (Clβ) more


negative will make an aircraft more spirally stable. At the same time, the dutch-roll damping ratio tends to decrease. This presents a design conflict [14] which must be resolved through some compromise.


15. In supersonic flight, the sweep angle tends to reduce the shock wave drag. The drag generated by the oblique shock wave is referred to as wave drag, which is inherently related to the loss of total pressure and increase of entropy across the oblique shock waves created by the wing. For this purpose, the sweep angle must be greater (see figure
5.41) than Mach angle,

sin- (1M)
1.2 90
where M is the aircraft cruising Mach number. A 20 percent higher sweep angle will guarantee the low wave drag at supersonic speeds.

16. A wing with high wing loading (W/S) and high quarter-chord sweep ( c/4) exhibits a good ride in turbulence.

At hypersonic speeds (e.g. Space Shuttle), if the oblique shock wave is very close to the wing leading edge; due to a low sweep angle; it generates very high temperature due to aerodynamic heating (about 3000 oF) such that the wing leading edge surface may be melted. Thus, the sweep angle must be such that wing leading edge surface survive very high temperature. This ensures that the wing is located inside Mach cone

17. With the application of the sweep angle, the wing effective span (beff) with be shorter than original theoretical span. This results in a lower wing mass moment of inertia about x-axis, which increases the lateral controllability of the aircraft. Hence, the higher the sweep angle, allows for better maneuverability.
SWEPT BACK WING PARAMETERS:
1.In supersonic flight, the sweep angle tends to reduce the shock wave drag. The drag generated by the oblique shock wave is referred to as wave drag, which is inherently related to the loss of total pressure and increase of entropy across the oblique shock waves created by the wing. For this purpose, the sweep angle must be greater (see figure
5.41) than Mach angle,

sin-1 (1M)
1.2 90
Where, M=1.67
Mach angle( ),
sin-1 (1/1.67)

sweep angle( )=1.2 90
from above eqn swept back wing angle is ( )=63.850
2.effective chord length of swept wing (Ceff)= 1/ cos(
Ceff = 2.26
3.leading edge sweptback( LE)= tan-1[tan( AR)*((1- ʎ)/(1+ʎ))]
Where, AR=3.44
ʎ=0.3
substitute all the values in above eqn.
LE= tan-1(2.19)

LE=65.480
4.sweep angle at a reference or half of the chord
c/4 = tan-1[tan( AR)*((1- ʎ)/(1+ʎ))]
c/4= tan-1(1.72)
c/4=59.860

5.The rolling moment due to aft sweep is proportional to the sine of twice the leading edge sweepangle
Clβ sin(2 LE )
Clβ


EFFECTIVE SPAN (beff)



WING PLANFORM


To determine the wing parameters
1. Wing span
2. Root chord
3. Tip chord
4. Equivalent aspect ratio
5. Mean aerodynamic chord
6. Taper ratio
7.wing loading(w/s)

WING LOADING:(W/S)
W/S=0.5*(Vstall)2*(Clmax)*
Where, Vstall=64.43m/s
Clmax=1.7
=1.225Kg/m3
W/S=4322.46N/m3
W/S=440.61Kg/ m3 (at max lift condition)
Wing loading at take off (W/S)TO:
(W/S)TO =0.5*(VTO)2*(Clmax (gross))*
Where, VTO=1.2Vstall
VTO=77.31m/s
=1.225Kg/m3
Clmax (gross)=2.2 (Flap down)
(W/S)TO=8053.78kg/m3
Wing loading at landing (W/S)L:
(W/S)L =0.85 (W/S)TO From, for fighter aircraft WL=0.85WTO
Where,
(W/S)TO=8053.78kg/m3
(W/S)L=6845.71 kg/m3
WING AREA (S):
S=W0/(W/S)
S=18920/(440.61)
S=42.93m2

WING SPAN(b):
b=(AR*S)0.5
Where aspect ratio is AR=3.44 (from retrived data)
b=12.15m


ROOT CHORD:
Croot = 2S b(1+ʎ )
where taper ratio(ʎ) is 0.3 in the order of aspect ratio 3.44

Croot = 2*42.93 12.15(1+0.3)
= 5.43m
TIP CHORD:
The tip chord is given by,
Ctip = ʎ × Croot
where taper ratio is 0.3 in the order of aspect ratio 3.34
Ctip = 0.3× 5.43
=1.63m
EQUIVALEND ASPECT RATIO:
AReq = A(Mmax)C
Where, A=2.34 , C=-0.13 (for fighter aircraft)
The mach no. =1.67
AReq=2.18

WING AERODYNAMIC CHORD(C):
C=(2/3)*Croot*(1+ʎ*ʎ+ʎ 1+ʎ)
(or)
C=b/AR
C=3.87
VOLUME OF FUEL IN THE WING:
= fuel weight(Kg) specific gravity of fuel used
= 5808.44 0.72*1000
=8.06m3
THICKNESS RATIO (t/c):
volume of fuel in the wing = (t/c)*c*0.5*c*0.5b*0.75*2
(t/c)root = 0.118
(t/c)tip = 0.66

THE THICKNESS DISTRIBUTION:
Y=(b/c)*[(1+2 ʎ)*(1+ ʎ)]
=6.53m
X=b/c
=3.14m
Wing Incidence
The wing incidence (iw) is the angle between fuselage center line and the wing chord line at root
(see figure 5.25). It is sometimes referred to as the wing setting angle ( set). The fuselage center line lies in the plane of symmetry and is usually defined parallel to the cabin floor. This angle

could be selected to be variable during a flight operation, or be constant throughout all flight operations. If it is selected to vary during flight, there is no need to determine wing setting angle for the purpose of the aircraft manufacture. However, in this case, the mechanism to vary the wing incidence during flight phases must be designed. Thus the required wing incidence for every flight phase must be calculated. The variable wing incidence is not recommended, since there is a huge safety and operational concerns. To allow for the wing to have a variable setting angle, there must be a single shaft around which the wing is rotated by pilot control. Such a mechanism is not 100% reliable for aviation purposes, due to fatigue, weight, and stress concentration concerns. In the history of aviation, there is only one aircraft (Vought f 8 u Crusader) whose wing had variable incidence. A flying wing; such as Northrop Grumman B-2
Spirit (Figure 6.8) has no wing incidence, since there is no fuselage, however the wing angle of
attack must be determined for operational purposes.



Wing chord line at root
iw




Fuselage center line

Figure 5.25. Wing setting (incidence) angle

A second, very convenient option is to have a constant wing setting angle. The wing can be attached to the fuselage via welding, screw, or other manufacturing technique at the specified setting angle. This is much safer compared with variable setting angle. For this option, the designer must determine the angle at which the wing is attached to the fuselage. The wing incidence must satisfy the following design requirements:

1. The wing must be able to generate the desired lift coefficient during cruising flight.
2. The wing must produce minimum drag during cruising flight.
3. The wing setting angle must be such that the wing angle of attack could be safely varied
(in fact increased) during take-off operation.
4. The wing setting angle must be such that the fuselage generates minimum drag during cruising flight (i.e. the fuselage angle of attack must be zero in cruise).


These design requirements naturally match with the wing airfoil angle of attack corresponding to the airfoil ideal lift coefficient (see figure 5.26). Therefore, as soon as the wing ideal lift coefficient is determined, a reference to Cl- graph demonstrates the wing setting angle. Table 5.7 illustrates the wing incidence for several aircraft.


cl


llc
l
l
i










set
Figure 5.26. Wing setting angle corresponds with ideal lift coefficient

The typical number for wing incidence for majority of aircraft is between 0 to 4 degrees. As a general guidance, the wing setting angle in supersonic fighters, is between 0 to 1 degrees; in GA aircraft, between 2 to 4 degrees; and in jet transport aircraft is between 3 to 5 degrees. It is very hard to have the exact same incidence on both left and right wing sections. Due to this fact, when there is an inboard stall, the aircraft will roll. The wing outboard stall is unacceptable; if a transport aircraft is at approach, and an outboard stall occurs, it is a disaster. The reason is that the ailerons are not effective to apply roll control.

No
Aircraft
Type
Wing
incidence
Cruising speed
(knot)
1
Airbus 310
Jet transport
5o 30'
Mach 0.8
2
Fokker 50
Prop-driven transport
3o 30'
282
3
Sukhoi Su-27
Jet fighter
0o
Mach 2.35
4
Embraer FMB-120 Brasilia
Prop-driven transport
2 o
272
5
Embraer Tucano
Turbo-Prop Trainer
1o 25'
222
6
Antonov An-26
Turbo-prop Transport
3o
235
7
BAe Jetstream 31
Turbo-prop Business
3 o
282
8
BAe Harrier
V/STOL close support
1o 45'
570
9
Lockheed P-3C Orion
Prop-driven transport
3o
328
10
Rockwell/DASA X-31A
Jet combat research
0o
1485
11
Kawasaki
Prop-driven transport
0o
560
12
ATR 42
Prop-driven transport
2o
265
13
Beech Super King Air B200
Turbo-prop Transport
3o 48'
289
14
SAAB 340B
Turbo-prop Transport
2o
250
15
AVRO RJ
Jet Transport
3o 6'
412
16
McDonnell MD-11
Jet Transport
5o 51'
Mach 0.87
17
F-15J Eagle
Fighter
0
> Mach 2.2
Table 5.7. Wing setting angle for several aircraft [5]

The wing setting angle may be modified as the design process progresses. For instance, a fuselage with large unsweep over the rear portion to accept aft cargo doors may have their

minimum drag at a small positive angle of attack. In such cases, the wing incidence will be reduced accordingly. Another, les fundamental, consideration is that stopping performance during landing operation to get as much weight on the braked wheels as possible. Thus, there is a benefit to reduce the wing incidence slightly to the extent that the change is not felt significantly in the cabin. Reducing the nose gear length will do the same thing. This technique is limited in passenger aircraft because a level cabin floor is desirable on the ground. But, for fighter aircraft, the level floor is not a design consideration.

POWER PLANT SELECTION:
An aircraft engine is the component of the propulsion system for an aircraft that generates mechanical power. Aircraft engines are almost always either lightweight piston engines or gas turbines. This article is an overview of the basic types of aircraft engines and the design concepts employed in engine development for aircraft.
There are several types among this they are as follows:
Shaft Engine
- Incline Engine
- Rotary Engine
- V-type Engine
- Radial Engine
- Horizontally opposed engine
Jet Engine
- Turbojet
- Turbofan
- Turboprop
THRUST REQUIRED TO PROPEL THE ENGINE:
Thrust is one of the four aerodynamic forces acting on the aircraft in flight. it is the force that pushes an aircraft through the air. Thrust must be greater than drag to achieve the forward acceleration needed for take off and to increases an aircraft speed in level flight. an aircraft flying at constant speed will have thrust equal to drag.
the generalized thrust equation is given by,
T= (ma){(1+f)Ue-Ua}+ (Pe-Pa)Ae
The formula used for the thrust calculation is given by
T = Take off weight * Thrust loading
T = W0 *(T/W0)
Where, W0 = 18920 Kg
T/W = 0.73
T = 18920 * 0.73
T = 13811.6 Kg
T = 135.49kN
For TWIN ENGINE fighter aircraft (2) = 135.49KN
That means one engine producing the thrust of 67.45KN (with after burner)
The corresponding rang engine selected is given by (power plant)
S.
NO
Engine name
Dry thrust
(KN)
Wet thrust(after burner)
(KN)
1
General electric F414
55.6
75
2
Kaveri engine(k-9)
45
75
3
M52-P2
64
95
4
M88-2
50
75

SELECTED ENGINE: KAVERI (K-9)
History:
program:
In 1896 the Indian defence ministry's defence research and developed organization(DRDO) was authorized to launch a programmed to develop an indigenous power plant for the light combat aircraft. It had already been decided early in the LCA programmed to equip the prototype aircraft with the general electric F404-GE-F2J3 afterburning turbofan engine , but if this parallel program was successful, it was intended to equip the production aircraft with this indigenous engine.
the DRDO assigned the lead development responsibility to its gas turbine research establishment (GTRE), which had some experience in develop in jet engines. It had developed the GTX37-14U afterburning turbojet, which first jet engine to be designed entirely in India.
A turbofan derivative, the GT37-14UB, followed. the GTRE Returned to turbojet technology with the greatly redesigned, but unsatisfactory, GTX-35.
For the LCA programmed the GTRE would again take up a turbofan design which it designated the GTX-35VS "KAVERI" (Named after the kaveri river). Full scale development was authorized in April 1989 in what was then expected to be a 93 month programmed projected to cost 3.82 billion (taller ). A new engine typically cost up to 2(taller)billion to develop, according to engine industry executives.
DEVELOPMENT:
The original plans called for 17 prototype test engines to be built. The first test engine consisted of only the core module (named "Kabini"), while the third engine was the first example fitted with variable inlet guide vanes (IGV) on the first three compressor stages. The Kabini core engine first ran in March 1995. Test runs of the first complete prototype Kaveri began in 1996 and all five ground-test examples were in testing by 1998; the initial flight tests were planned for the end of 1999, with its first test flight in an LCA prototype to follow the next year. However, progress in the Kaveri development programme was slowed by both political and technical difficulties.
In 2002, little information had been publicly released concerning the nature of the Kaveri's technical challenges, but it was known that the Kaveri had a tendency to "throw" turbine blades, which required securing blades from SNECMA (as well as digital engine control systems).
Continuing development snags with the Kaveri resulted in the 2003 decision to procure the uprated F404-GE-IN20 engine for the eight pre-production Limited Series Production (LSP) aircraft and two naval prototypes. The ADA awarded General Electric a US$105 million contract in February 2004 for development engineering and production of 17 F404-IN20 engines, delivery of which is to begin in 2006.which is to begin in 2006.
In mid-2004, the Kaveri failed its high-altitude tests in Russia, ending the last hopes of introducing it with the first production Tejas aircraft.[7] This unfortunate development led the Indian Ministry of Defence (MoD) to order 40 more IN20 engines in 2005 for the first 20 production aircraft, and to openly appeal for international participation in completing development of the Kaveri. In February 2006, the ADA awarded a contract to SNECMA for technical assistance in working out the Kaveri's problems.
In Dec. 2004, it was revealed that the GTRE had spent over 13 billion (US$211.9 million) on developing the Kaveri. Furthermore, the Cabinet Committee on Security judged that the Kaveri would not be installed on the LCA before 2012, and revised its estimate for the projected total development cost to 28.39 billion (US$463 million).
In April 2005, "There is good progress" on the development of the Kaveri engine, M. Natarajan, Scientific Adviser to the Defence Minister told The Hindu. "We are planning to integrate a prototype Kaveri engine into one of the LCA prototypes sometime in 2007 to understand the nuances of such a complex powerpack," he further told The Hindu.[10]In Feb. 2006, the US experts told pti that "Kaveri is truly a world-class engine." "We are ready to join in partnership with the Defence Research and Development Organisation to make Kaveri work," General William J Begert of Pratt and Whitney, told PTI. But DRDO secretary Natrajan told PTI that "But Kaveri is and would remain an Indian project."
On 5 February 2007, Scientific Advisor to Defence Minister M Natarajan said nearly 90 to 93 per cent of the expected performance had been realised and the government had recently floated an expression of interest to seek partners to move the programme further.Till 11 February 2008, Kaveri had undergone 1,700 hours of tests and has been sent twice to Russia to undergo high-altitude tests for which India has no facility. The engine is also being tested to power the next generation of Unmanned Aerial Vehicles.
In July 2007, GTRE divided Kaveri program into two separate programs. They are K9+ Program and K 10 Program. K9+ Program is a program to prove concept of complete design and gain hand-on experience of aircraft engine integration and flight trials to cover a defined truncated flight envelope prior to the launch of production version of K10 Standard engine. While K 10 Program is a Joint Venture (JV) partnership with a foreign engine manufacturer. K 10 program engine will be final production standard Kaveri engine and shall have less weight and more reheat thrust along with certain other changes to meet the original design intent.
In September 2008, it was announced that the Kaveri would not be ready in time for the Tejas, and that an in-production powerplant would have to selected. Development of the Kaveri by the GTRE would continue for other future applications. It was announced in November 2008 that the Kaveri engine will be installed on LCA by December 2009,apparently for tests only.[citation needed]
In February 2009, it was published in flightglobal that the GTRE had spent 20 billion (US$326.0 million) in developing the Kaveri engine since 1989, but the powerplant is still overweight and does not have the 21,000-22,500 lb of thrust (93-100 kN) that its customer requires. Natarajan told Flightglobal that the programme will not be scrapped. "A team of air force engineers is working with GTRE and ADA in addressing the issues. As an ongoing project, the air force will be involved at the point of integrating the upgraded version of the engine with the aircraft," he told Flightglobal. "Discussions with Snecma have been going on for two years," he further adds. "Development and flight-testing of the new engine will take at least five to six years."
In December 2009, Kaveri-Snecma JV was trying Back-door Entry In LCA. The People's Post reported that GTRE has agreed to de-link Kaveri from LCA, but has put in a proposal that when the first 40 GE 404 engines in the initial two squadrons of the LCA for the IAF, get phased out should be replaced by the Kaveri-Snecma engine, in future.
On 3 May 2010, about 1880 hrs of engine test had been completed on various prototypes of Kaveri Engine. A total of eight Kaveri Engines and four core engines have been manufactured, assembled and tested. High Altitude testing on core engine has been completed successfully.
In June 2010, the Kaveri engine based on Snecma's new core, an uprated derivative of the M88-2 engine that powers the French Rafale fighter, providing 83-85 Kilonewtons (KN) of maximum thrust is being considered an option by DRDO.In July 2010, according to Vinayak shetty, Tejas aircraft will be Integrated with Kaveri engine and will be flying on board a Tejas Air frame by early 2011 or some time later in the year.
A press release in August 2010, stated that GTRE with the help of Central Institute of Aviation Motors (CIAM) of Russia is trying to match objective of fine tuning of Kaveri engine performance. Until August 2010, one major milestone which is altitude testing, simulating Kaveri engine performance at different altitude and achieving speed of Mach 1 had been completed successfully. One of Kaveri prototype (K9) was successfully flight tested at Gromov Flight Research Institute in Moscow, on 4 November 2010.
The test was conducted at the Flying Test Bed at Gromov, with the engine running right from the take-off to landing, flying for a period of over one hour up to an altitude of 6,000 metres. The engine helped the IL-76 aircraft test bed fly at speeds of 0.6 mach in its maiden flight, according to the Defence Research and Development Organisation (DRDO).
"The engine control, performance and health during the flight were found to be excellent. With this test, Kaveri engine has completed a major milestone of development programme," it added. After completing these milestone Kaveri engine is flight-worthy.[21][22] The Kaveri engine was tested for the first time on a flying testbed and the trials were a success.
Till April 2011, the first phase of Kaveri engine FTB trials have been completed successfully and further tests will continue from May 2011 onwards. The flight tests successfully carried out so far are up to 12 km maximum altitude and a maximum forward speed of 0.7 Mach No
In its annual report for 2010-11, The Comptroller and Auditor General of India noted that 18.92 billion (US$308.4 million) had been spent on development, with only two out of the six milestones prescribed having been met. Among its deficiencies, CAG says the engine weight was higher than the design specifications (1235 kg against 1100 kg) and there was no progress on developing the compressor, turbine and engine control systems.
On 21 December 2011, "9 prototypes of Kaveri engines and 4 prototypes of Kabini (Core) engines have been developed" told Defence Minister Shri AK Antony in Rajya Sabha. Further on, 2050 hours of test flight of engines has been taken place so far. 27 flights for 55 hours duration have been completed on testbed IL-76 aircraft as well as 12 km maximum forward altitude and a maximum forward speed of 0.7 Mach No had been recorded
CURRENT STATUS:
The DRDO currently hopes to have the Kaveri engine ready for use on the Tejas in the latter half of the 2010s decade and according to latest news still research on it is going on and date to complete its research has been extended to 2011-2012.

"In recent times, the engine has been able to produce thrust of 82 Kilo Newton but what the IAF and other stake-holders desire is power between 90—95 KN", senior officials told The Hindu. "On using the Kaveri for the LCA, they said the engine would be fitted on the first 40 LCAs to be supplied to the IAF when they come for upgrades to the DRDO in the latter half of the decade." Article further adds that in 2011,50-60 test flights will be carried out to mature the engine in terms of reliability, safety and airworthiness.
India's Gas Turbine Research Establishment (GTRE) aims to integrate the Kaveri powerplant with the Hindustan Aeronautics Ltd (HAL) Tejas fighter within the next nine months. A test aircraft operated by India's Aeronautical Development Agency will be used for the integration, says an industry source familiar with the programme. If the integration is successful, the GTRE hopes to see a Tejas fly with a Kaveri powerplant by the end of 2013.
In Lok Sabha on 10 December. 2012 Defence Minister A K Antony gave an update on the progress made by the Kaveri Engine Development Project as follows:

So far, 9 prototypes of Kaveri Engine and 4 prototypes of Kabani (Core) Engine have been developed.
2200 hours of test (ground and altitude conditions) has been conducted.
The following two major milestones have been achieved:
Successful completion of Official Altitude Testing (OAT) ; and
Demonstration of First Block of flight of Kaveri Engine in Flying Test Bed (FTB).
Kaveri Engine was integrated with IL-76 Aircraft at Gromov Flight Research Institute (GFRI), Russia and flight test was successfully carried out up to 12 km maximum altitude and maximum forward speed of 0.7 Mach No. Twenty Seven flights for 57 hours duration have been completed.
DRDO demonstrated its technological capability in aero-engine technology. This has been a great achievement in the aerospace community of the country, when the first ever indigenously developed fighter aircraft engine was subjected to flight testing. Tacit knowledge acquired by the DRDO scientists during this project will also be applied for further aerospace technology. Kaveri spin-off engine can be used as propulsion system for Indian Unmanned Strike Air Vehicle (USAV).
In January 2013, the GTRE director said that they are abandoning the plan for co-development with Snecma, but they still need an overseas partner, which will be selected through competitive bidding.
APPLICATION:
Plans are also already under way for derivatives of the Kaveri, including a non-afterburning version for an advanced jet trainer and a high-bypass-ratio turbofan based on the Kaveri core, named as Kabini.[31]
GTX-35VS Kaveri:
HAL Tejas (planned for production models)
Kaveri Engine for LCA
Name of the Project / Programme -- Kaveri Engine for LCA[18]
Date of Sanction—30 Mar 1989[18]
Original Probable Date of Completion (PDC) -- 31 Dec 1996[18]
Revised PDC—31 Dec 2010[18]
Technologies / Products developed and status of Projects / Programmes on 3 May 2010—About 1880 hrs on engine test has been completed on various prototypes of Kaveri Engine. A total of eight Kaveri Engines and four core engines have been manufactured, assembled and tested. High Altitude testing on core engine has been completed successfully.
HAL Advanced Medium Combat Aircraft (conceptual)
Unmanned Aerial Vehicles
Derivatives:
The Indian government plans to adapt and further develop the Kaveri engine design and technology to create a gas-turbine powerplant for armoured fighting vehicles such as the Arjun tank.
Kaveri Marine Gas Turbine (KMGT), a recently developed derivative of the GTX-35VS Kaveri engine for ships.
Indian Railways has expressed interest in utilizing Kaveri to power locomotives.


Type : After burning Turbofan
Length : 3490 mm
Diameter : 910 mm
Dry weight : 45kN (of their 900Kg weight)
Afterburner(Wet thrust) : 70KN (of their 900Kg weight)
T/W Ratio : 7.25:1(wet thrust)
Blade : DS blades
Manufacturer: gas turbine research establishment
National origin: INDIA
First run: 1996
Major application: originally designed for HAL Tejas
Stage : 1. Six stage core high pressure compressor with variable inlet guide vanes
2. There stage low pressure compressor with transonic blading
Combustion chamber: annular combustion chamber
Fan pressure ratio: 4:1
Overall pressure ratio: 27:1


figure: T/W VsW/S
AERODYNAMIC ESTIMATION:
Lift estimation
drag estimation

LIFT ESTIMATION:
LIFT: lift is the one of the aerodynamic force.
Component of aerodynamic force generated on aircraft perpendicular to flight direction.

LIFT COEFFICIENT (CL):
Amount of lift generated depends on:
Platform area (S), air density (ρ), flight speed (V), lift coefficient (CL)
Lift = (1/2 ρV2)SCL = qSCL
CL is a measure of lifting effectiveness and mainly depends upon:
Section shape, platform geometry, angle of attack (α), compressibility effects (Mach number), viscous effects (Reynolds number).



Generation of Lift:
Aerodynamic force arise from two normal source:
Variable pressure distribution.
Shear stress distribution.
Shear stress primarily contributes to overall drag force on aircraft.
Lift mainly due to pressure distribution, especially on main lifting surface, i.e. wing.
Require (relatively) low pressure on upper surface and higher pressure on lower surface.
Any shape can be made to produce lift if either cambered or inclined to flow direction.





L F


V

Mo

ac D




The lift equation is given by,
L=0.5* *V2*S*Cl
LIFT AT CRUISE:
Where, at cruise speed
Density ( )=2.7975 slug/ft3=0.144 kg/m3
wing area S=42.93m2
velocity=568.91m/s
coefficiend of lift= 1.7
therefore, L=1.7 MN
LIFT AT TAKE-OFF:
Where, at take off
Density ( ) = 1.225kg/m3
wing area S=42.93m2
velocity (VTO) = 1.1*Vstall
Vstall = 70.87m/s
VTO=77.31
coefficient of lift at take off (Clmaxgross) = 2.2 (flap extended and kept at take off position of 20o)
Therefore L = 345.74 KN
With, gear down
flap take off
power is maximum
LIFT AT LANDING:
Where, at landing condition
wing area S= 42.93m2
Density( )=1.225kg/m3
coefficient of lift at landing: Clmax(L) = Clmax(TO)/(Velocity take off coefficient)2
Velocity take off coefficient = 1.2
Clmax(L)=1.52
Velocity at landing (VL)= {(W/S)L/(0.5* * Clmax(L))}0.5
Where (W/S)L= 6845.11 kg/m3
VL=85.75m/s

Therefore,
L=293.88KN
With, gear up
flap landing
power is minimum
DRAG ESTIMATION
DRAG:
Drag is the revolved component of the complete aerodynamic force which is parallel to the flight direction (or relative on coming airflow).
It always acts to oppose the direction of motion.
It is undesirable component of the aerodynamic force while lift is the desirable component.
Drag coefficient (CD):
Amount of drag generated depends on:
platform area (S), air density (ρ), flight speed (V), drag coefficient(CD)

CD is a measure of aerodynamic efficiency and mainly depends upon:
Section shape, platform geometry, angle of attack (α), compressibility effect (Mach number), viscous effects (Reynolds number).

Drag components:
Skin friction:
Due to shear stresses produced in boundary layer.
Significantly more for turbulent than laminar types of boundary layers.



Form(pressure) Drag:
Due to static pressure distribution around body – component resolving in direction of motion.
Sometimes considered separately as forebody and rear (base) drag components

Wave drag:
Due to the presence of shock wave at transonic and supersonic speeds.
Result of both direct shock losses and the influence waves on the boundary layer.
Often decomposed into portions related to:
Lift.
Thickness or Volume.

Typical streamlining effect:


Lift induced (or) trailing vortex drag:


The lift induced drag is the component which has the included to account for the 3-D nature of the flow (finite span) and generation of the wing lift.


DRAG POLAR ESTIMATION:
assuming a parabolic drag polar, the drag coefficiend of an airplane can be written as:
CD= CDo+CL2/πeAR
The zero lift coefficiend ,CDo can be expressed as:
CDo=f/S
where f- equivalend parasite area
S-Wing area
it is possible to related equivalend parasite area ,f to wetted area. and its shown in fig


The value of a &b depend on Cf value



where c and d value for fighter is given by
C=-o.1289, d=0.7506 W0=18920kg
There fore substitute all the values in above
Swet=1206.02
To find f:
from above eqn with table
a= -2.5229 , b= 1.0000
f=3.61
The zero lift drag eqn is given by
CDo =f/S
wing area=42.93m2

CDo =0.0842

CD= CDo+CL2/πeAR
Where , 1/ πeAR=K
K= 1/π*0.7*3.44 [assuming e=0.7]
K=0.132
The above eqn become

CD=0.0842+0.132CL2










CALCULATION:
The general drag equation is given by,
D=(1/2) *V*S*CD
CD=CD0+K(Cl)2
The drag polar is given by
CD=0.0842+0.132CL2
Therefore above equation become
D=((1/2)pV2S)( 0.0842+0.132CL2)
Drag at Crusie:
P=0.144kg/m3 (at cruising altitude of 16870m)
V=568.91m/s
S=42.93kg/m2
CL(Cruise)=1.7(from the wing and aerofoil estimation)
Substituting all the values in the general drag equation,
D=((1/2)0.144x568.912x42.93)( 0.0842+0.132(1.7)2)
Drag at Cruise D=465.87KN
Drag at Take-off:
Where, at take off
Density ( ) = 1.225kg/m3
wing area S=42.93m2
velocity (VTO) = 1.2*Vstall
Vstall = 64.43m/s
VTO=77.31
coefficient of lift at take off (Clmaxgross) = 2.2 (flap extended and kept at take off position of 20o)
Wher the ground effect is consider CD=CD0+ φ K(Cl)2
For calculating φ, we use the formula,
φ =(16 h/b)/(1+(16h/b)2)
Where h=height above ground=5.045m,
b=wing span=12.15m.
φ =(16x5.045/12.15)/(1+(16x5.045/12.15)2)=0.147

Substituting all the values in the general drag equation,
D = ((1/2)1.225x77.312x42.93)( 0.0842+0.01943(2.2)2)
Therefore, Drag at Take-off ,D = 28.00KN
With, gear down
flap take off
power is maximum

Drag at Landing:
Where,
wing area S= 42.93m2
Density( )=1.225kg/m3
coefficient of lift at landing: Clmax(L) = Clmax(TO)/(Velocity take off coefficient)2
Velocity take off coefficient = 1.2
Clmax(L)=1.52
Velocity at landing (VL)= {(W/S)L/(0.5* * Clmax(L))}0.5
Where (W/S)L= 6845.11 kg/m3
VL=85.75m/s
Therefore, Substituting all the values in the general drag equation,
D = ((1/2)1.225x85.752x42.93)( 0.0842+0.132(1.52)2)
Drag at Landing, D=75.24 KN With, gear up
flap landing
power is minimum
CRUISING FLIGHT PERFORMANCE:
CALCULATION OF VELOCITY AT MINIMUM THRUST REQUIRED:
VTR(min)= {(2/ )(k/ CD0)0.5(W/S)}0.5
Where = 0.144kg/m3
CD0=0.0842
W/S=4322.46N/m3
W/S=440.61Kg/ m3 (at max lift condition)
K=0.132
VTR(min) = {(2/ 0.144)(0.132/ 0.0842)0.5(440.16)}0.5
VTR(min)= (7654.38)0.5
VTR(min)=87.48m/s
CALCULATION OF MAX LIFT TO DRAG RATIO (L/D)max:
(L/D)max={1/(4* CD0*K)}0.5
(L/D)max={1/(4* 0.0842*0.132)}0.5
(L/D)max= 4.74
CALCULATION OF VELOCITY AT MAX LIFT TO DRAG RATIO V(L/D)max:
V(L/D)max= VTR(min)
Therefore
V(L/D)max=87.48m/s
THRUST REQUIRED MINIMUM(TR)min:
(TR)min =W0/(L/D)max
whrer, W0=18920kg
(TR)min= 39.15 KN
POWER REQUIRED MINIMUM(Pr):
for level unaccelerated flight
power = Energy/time =force*(distance/time)
=F*V
Pr=TRmin*V
Where V = 568.91m/s
TRmin= 39.15 KN
Pr=39.15*568.91
Pr= 22.27 MN m/s

THRUST AVILABLE:
TA=135.39KN (from engine selection)

POWER AVAILABLE PA:
PA = TA*V
Where TA=135.49KN , V=568.91
PA = 135.49*103*568.91
PA = 77.08MN m/s

MAX RATE OF CLIMB (R/C)max:

(R/C)max={(W/S)Z/3* *CD0}0.5{T/W}3/2{1-(Z/6)-(3/(2*(T/W)2(L/D)2Z))}
Where, z=1+{1+[3/(L/D)2max(T/W)2]}0.5
(L/D)max= 4.7
T/W = 0.73
=1.225Kg/m3
CD0=o.0842
(W/S)TO=8053.78kg/m3
Therefore,
z=1+{1+[3/(4.74)2max(0.73)2]}0.5
Z=2.11

(R/C)max={(8053)2.11/3*1.225*0.0842}0.5{0.73}3/2{1-(2.11/6)-(3/(2*(0.73)2(4.74)2*2.11))}

(R/C)max=103.26m/s
VELOCITY AT MAX RATE OF CLIMB:
V(R/C)max={[(T/W)(W/S)Z]/[3* * CD0]}0.5
Substituting all the values in above eqn

V(R/C)max={[(0.73)(8053.78)2.11]/[3*1.225* 0.0842]}0.5
V(R/C)max=200.22m/s
LEVEL TURN:
Level turn is one in which the curved flight path in horizontal plane parallel to the plane of around (i,e) in level turn altitude remain constant.
The performance characteristics of turning flight are
1.turn ratius(R)
2.turn rate (ώ)
Turn radius:
R=V2/(g(n2-1)0.5)
Where, n=L/W=9.16
V=568.91m/s
g=9.81 (acceleration due to gravity)
R= 3623.58m
Turn rate (ώ):
ώ = (g(n2-1)0.5)/V
ώ =0.15 rad
LANDING PERFORMANCE:
let examine the constraint imposed by the specified landing distance the landing distance is the sum of approach distance Sa, The flair distance Sf, and the ground roll Sg,following the discussion we have for the path radius during flare.
Flare velocity:
Vf=1.15*Vstall
Vf=1.15*64.43
Vf=74.09m/s
Flare height:
flare height hf is given by,
hf=R(1-cosϴa)
Where, R=3623.58m
ϴa=sin-1([1/(L/D)]-(T/W))
ϴa= -31.260
hf=3623.58*(1-cos(-31.26))
hf=526.06m
Approach distance:
The approach distance required to clear the50ft(15.24m) distance is,
Sa=(50- hf)/(tan ϴa )
sub all value in above eqn
Sa=841.48m
Flare distance(Sf):
Sf=R*sin ϴa
sub all value in above eqn
Sf=-1880.74m
Ground roll distance:
Sg= j*N{(2W/ SClmax}0.5+[(j2(W/S))/g Clmax VTD)
N=3s-time increment in ground roll
VTD=77.31m/s
W0=18920kg
CLmax=1.52
W/S=6845.71kg/m3

=1.225kg/m3
j=1.1
sub all the values in above eqn
Sg=307.08m


The total landing distance Ld=Sa+Sg+Sf
Ld = 307-1880+841.48
Ld=-732.18m [negative sign indicate the direction of landing(fighter-return)]
Ld=732.18m


PERFORMANCE CURVES:
1.Velocity Vs Thrust required
2.Velocity Vs power required
3.Velocity Vs rate of climb
4.Velocity Vs L/D ratio
5.Cl Vs Cd
6.Velocity Vs Thrust available
7.Velocity Vs power available
8.Velocity Vs Cl
9.Velocity Vs Cd

VELOCITY Vs THRUST AVIALABLE:
V = 568.91m/s Vs TA=135.49KN

VELOCITY
(m/s)
THRUST AVAILABLE (KN)
56.891
135.4
113.787
121.86
170.673
108.32
277.564
94.78
284.455
81.24
341.346
67.70
398.232
54.169
455.128
40.629
512.09
27.09
568.91
13.549






VELOCITY VS THRUST REQUIRED:

V = 568.91m/s Vs TR=39.15KN

VELOCITY
(m/s)
THRUST REQUIRED (KN)
56.891
3.915
113.787
7.83
170.673
11.745
277.564
15.66
284.455
19.575
341.346
23.49
398.232
27.405
455.128
31.32
512.09
35.23
568.91
39.15



VELOCITY Vs POWER AVIALABLE:
V = 568.91m/s Vs PA=77.08(MN)m/s

VELOCITY
(m/s)
POWER AVIALABLE (MN)m/s
56.891
77.08
113.787
69.372
170.673
61.664
277.564
53.956
284.455
46.248
341.346
38.54
398.232
30.832
455.128
23.124
512.09
15.416
568.91
7.708



VELOCITY Vs POWER REQUIRED
V = 568.91m/s Vs PR=22.27 (MN)m/s

VELOCITY
(m/s)
POWER REQUIRED (MN)m/s
56.891
2.227
113.787
4.454
170.673
6.681
277.564
8.908
284.455
11.135
341.346
13.362
398.232
15.589
455.128
17.816
512.09
20.043
568.91
22.27








VELOCITY Vs (R/C)max:

V = 568.91m/s Vs (R/C)max =103.26m/s

VELOCITY
(m/s)
(R/C)max m/s
56.891
10.326
113.787
20.652
170.673
30.984
277.564
41.310
284.455
51.63
341.346
61.96
398.232
72.28
455.128
82.61
512.09
92.94
568.91
103.26



VELOCITY Vs (L/D)max:

V = 568.91m/s Vs (L/D)max =4.7 NO UNIT


VELOCITY
(m/s)
(L/D)max
56.891
0.47
113.787
0.94
170.673
1.41
277.564
1.88
284.455
2.34
341.346
2.82
398.232
3.29
455.128
3.76
512.09
4.23
568.91
4.7



COEFFICIENT OF LIFT VS DRAG [CL Vs CD]max:

CL=1.7 Vs CD=0.46
CL
CD
0.34
0.093
0.88
0.18
1.02
0.27
1.36
0.37
1.7
0.46




VELOCITY Vs CLmax:


VELOCITY (m/s)
CL
117.382
0.34
234.764
0.88
352.146
1.02
469.528
1.36
586.91
1.7



VELOCITY Vs CDmax:


VELOCITY (m/s)
CD
117.382
0.093
234.764
0.18
352.146
0.27
469.528
0.37
586.91
0.46








CENTRA OF GRAVITY CALCULATION:
The c.g. calculation of an aircraft is very important. This c.g. must be properly located so that the airplane will be stable during its operation over different loading schedules. Initially for fully loaded condition, the c.g. of the individual component in the fuselage and the wing is found out. From that the c.g. of the fuselage and the wings are estimated. The c.g. of the aircraft is generally fixed at 0.3c by adjusting the location of the wing on the fuselage. After fixing the wing the c.g. is calculated for different configurations. The c.g. calculation is done to see how much the c.g. shifts either forward or backward. The allowable shifts are only ±5% over the basic value of 30% mach.
The length of fighter L=17.67m
S.No
Components
Weight (W)
Arm(X)
Moment(WX)
1

2

3

4
Crew

Fuel

Armmaments

Engine
1785.42

56980.79

39240

63000

1.7

8.23

11

8.23

3035.214

468951.90

431640

518490
161006.21

1422117.114

Using the above tabulation values, we obtain the location of the centre of gravity of the fuselage section from the nose of the airplane
WX/W=8.835m
Centre of Gravity is 8.835m