Chapter 7. Drag Polar

CENTRO UNIVERSITARIO DE LA DEFENSA

ACADEMIA GENERAL DEL AIRE

CONCEPTUAL AIRCRAFT DESIGN

MILITARY TRAINING FIGHTER

Trabajo Fin de Grado

Autor: A.A.D. Francisco Medina Sarmiento (LXVI – CGEA-EOF) Director: Francisco Javier Sánchez-Velasco Co-director: José Serna Serrano

Grado en Ingeniería en Organización industrial Curso: 2014/2015 – convocatoria: Junio

Tribunal nombrado por la dirección del Centro Universitario de la Defensa de San Javier, el día ____ de ______de 20____.

Presidente: Dr. D. Manuel Caravaca Garratón

Secretario: Dr. D. Alejandro López Belchí

Vocal: Col. Dr. Andrés Dolón Payán

Realizado el acto de defensa del Trabajo Fin de Grado, el día____ de ______de 20____, en el Centro Universitario de la Defensa de San Javier.

Calificación: ______.

EL PRESIDENTE EL SECRETARIO EL VOCAL

CONCEPTUAL AIRCRAFT DESIGN MILITARY TRAINING FIGHTER

RESUMEN: El presente trabajo trata sobre el anteproyecto/diseño conceptual de una aeronave, concretamente de un entrenador militar avanzado de tipo caza. En el mismo se describen las características de la aeronave obtenidas mediante leyes de diseño sencillas basadas en un análisis de aeronaves similares existentes en el mercado.

ABSTRACT: The following work deals about the draft/conceptual design of an airplane, specifically, a lead-in fighter trainer. Within we will describe the general characteristics of the aircraft, obtained by simple design rules.

A mi hermano José Eugenio, incansable trabajador y constante ejemplo a seguir

Content

Chapter 1. Introduction ...... 1

1.1. Goal and definitions ...... 1

1.2. LIFT concept ...... 3

1.3. Training ...... 4

1.3.1. Screening ...... 5

1.3.2. Primary aircraft training ...... 5

1.3.3. Basic training ...... 5

1.3.4. Lead-In Fighter Training ...... 6

1.3.5. Operational transition ...... 8

Chapter 2. Similar aircraft ...... 11

2.1. T-38 Talon [14] ...... 11

2.2. MiG-21 [1] ...... 13

2.3. Hawker Siddeley HS-1182 Hawk [1] ...... 15

Chapter 3. Fuselage design...... 17

Chapter 4. Weight calculations ...... 21

4.1. Maximum payload (MPL): ...... 21

4.2. Operative Empty Weight (OEW): ...... 23

4.3. Fuel weight (FW): ...... 24

4.4. Maximum Take-off Weight (MTOW): ...... 27

Chapter 5. Wing loading and T/W ratio ...... 29

5.1. Stall ...... 30

5.2. Take-off distance ...... 30

5.3. Landing distance ...... 32

5.4. Instantaneous turn ...... 32

Chapter 6. Geometric definition ...... 35

6.1. Airfoil Geometry ...... 35

6.2. Wingtip ...... 36

6.3. Wing Sweep ...... 37

6.4. Tapper ratio ...... 37

6.5. Wing incidence ...... 38

6.6. Wing vertical location ...... 38

6.7. Tail arrangement ...... 38

Chapter 7. Drag Polar ...... 41

Chapter 8. Payload-Range Diagram ...... 45

Chapter 9. Conclusions and further studies ...... 47

9.1. Methodology ...... 47

9.2. Further research ...... 48

9.3. Technological improvements to implement ...... 49

Appendix A. Similar planes tables ...... 51

.1. T-38 Talon ...... 51

.2. MiG-21 Fishbed ...... 55

.3. Sidderley Hawk ...... 57

References ...... 61

Acronyms list

C.U.D. Centro Universitario de la Defensa

A.G.A. Academia General del Aire

T.F.G. Trabajo Fin de Grado

LIFT Lead-In Fighter Training

MFD Multifunction Display

NATO North Atlantic Treaty Organization

HOTAS Hands On Throttle And Stick

HUD Head Up Display

HMD Helmet Mounted Display

AP AutoPilot

AOA Angle of Attack

CAS Calibrated AirSpeed

IAI Israel Aircraft Industries

MPL Maximum PayLoad

TO Technical Order

OEW Operative Empty Weight

MTOW Maximum Take-Off Weight

FW Fuel Weight

NM Nautical Miles

TOD Take-off Distance

Chapter 1. Introduction

1.1. Goal and definitions

The goal of this work is to perform the evaluation of an advanced military training jet. With the appearance of 5th generation of fighter aircraft and the rapid advance in technology, the training platforms used by some Air Forces are beginning to be obsolete. In advance to the expected obsolescence, it is necessary to provide new systems to meet the demand.

We will start by explaining the concept of a military training jet, best known as “trainer”. When we talk about a military trainer we make reference to a jet that belongs to an air force and it is used mainly as a training platform for the future pilots. As we will see later, these jets also fulfill a secondary role, such as that of advanced trainers, prepared to carry weapons and perform low profile missions, such as counterinsurgency, when necessary.

As the technology advances, new generations of fighter aircraft appear, thus, it becomes necessary to upgrade the technology used for future pilots training. The first jet trainers were modifications of the original design of an aircraft, however, nowadays most Air Forces own trainers that correspond to an operative fighter or a group of them.

In Table 1 we can see how the concept has changed through the years.

1 Chapter 1. Introduction

Year Operative fighter Jet trainer Country

1940 Great Britain

Gloster Meteor [1] Gloster Meteor two-seat[1]

1959 USA

F5 Freedom Fighter[1] T-38 Talon[1]

1996 Russia

Yakovlev Yak-130[1] Sukhoi PAK FA[1]

Table 1. Operative fighters and their jet trainers

One of the common characteristics of these jets is the existence of dual controls to allow the instructor and the student to fly the airplane, giving the instructor the capacity to control the airplane to facilitate the student’s learning and to ensure it is being flown safely. For the achievement of this goal, there are two main arrangements of instructor-student, side-by-side cabin or in tandem (one in front the other). It depends on the type of training mission, but normally when flying in tandem the student is placed in the front position while the instructor is in the rear one.

2 Chapter 1. Introduction

1.2. LIFT concept

Our goal is to evaluate the design of a LIFT type jet. The acronym stands for Lead-In Fighter Training, and it is necessary to define this concept correctly.

LIFT is defined as a jet that emulates advanced fighters to train the student to operate this weapons system. LIFT jets are usually propelled by a turbofan or turbojet engine. This type of jet also has advanced avionics systems to habituate the user to work in an advanced environment and in different scenarios that could be found in a modern conflict. To achieve this goal, the jet is able to receive information from an instrument similar to a memory stick, and show the information in a Multifunction Display (MFD), or, in the best case, it receives the information using real-time software and tactical data exchange networks such as the Link 16 used by the North Atlantic Treaty Organization (NATO).

In order to manage all this information, and the typical in-flight workload (such as pure flying tasks or communications) the pilot rely on MFD’s, HOTAS (Hands on Throttle and Stick) and HUD (Head-Up Display) (Figures 1, 2 and 3) that make the information clearer and manageable. In some cases even an autopilot system (AP) is available to relieve the pilot’s workload. In a critical situation, such as an emergency, the pilot can couple the AP and focus on solving the problem.

Since new generation aircraft start to show all the information on HMD (Helmet Mounted Display), some LIFT jets have begun to incorporate this type of technology.

The training received in this kind of platform is divided in: contact, instruments, formation, air-to-air tactics and air-to-ground tactics.

One of the examples of these jets is the T-38 Talon (Figure 3) used by the United States in the advanced flight training program.

3 Chapter 1. Introduction

Figure 1. MFD[2] Figure 2. HOTAS F/A 18[3]

Figure 3. HUD and American T-38 Talon[9]

1.3. Training

A short summary of the different phases of the training, focusing on the LIFT and transitional operation phases follows.

This classification is based on the American specialized undergraduate pilot training [4].

4 Chapter 1. Introduction

1.3.1. Screening

Many Air Forces use light aircraft, sometimes similar to those used in the civil industries to evaluate the skills and capabilities of the candidates. Since the first moment the predisposition can be intuited in relation to what kind of plane each candidate will pilot in the future.

1.3.2. Primary aircraft training

During this phase, propeller driven aerobatic aircraft are normally used, so that the student can learn the behavior of the aircraft during aerobatic maneuvers.

Figure 4. ENAER Pillán T-35[10]

1.3.3. Basic training

This phase is carried out inside an aircraft with greater capabilities (more thrust, higher service ceiling and in general more advanced flight features). The aircraft used are normally aerobatic jet aircraft. For example, the Spanish Air Force use the CASA C-101 (Figure 5) for this purpose. Approximately one hundred hours of flight training are completed in it.

5 Chapter 1. Introduction

Figure 5. CASA C-101 Aviojet[11]

1.3.4. Lead-In Fighter Training

The aircraft used for this task are low profile airplanes, light fighters, normally propelled by one or two turbojets. These aircraft normally fly in the high-subsonic range, even having the possibility of reaching the sound speed.

Inasmuch as they are generally light fighters, they are highly maneuverable, allowing the plane to perform tight turns.

A great difference in comparison with the other aircraft used in previous training phases, the aircraft used in this phase have the ability of carrying armament. However, for the training missions the used weapons are simulated or unloaded.

During this phase, the student begins to use radar technology, simulated in some cases, like in the Spanish F-5. This type of aircraft is equipped with a very advanced avionics system, with MFD,s and HUD,s, these last show the pilot the information on the windshield, so that he does not have to look inside the cabin and lose the enemy during a dogfight.

These aircraft are used by some countries to carry out low profile missions in spite of not being prepared to operate in a real-life scenario, unless they do it with the support of more advanced fighters.

The case of the Spanish F-5 it is because it was designed by the Northrop Corporation as a light attack aircraft. It has been used in some real-life scenarios; it was used during

6 Chapter 1. Introduction

the Vietnam War, serving the South side against the North. Between October 1965 and April 1967 the Skoshi Tigers flew a total amount of 9985 missions in Vietnam in which they lost nine aircraft.

Figure 6. Skoshi Tiger dropping napalm in a misión at Bien Hoa in 1967 [12]

The Spanish Air Force uses a version of the Northrop F-5 with an avionics upgrade carried out by Israel Aerospace Industries.

The fighter pilot training course in the Spanish Air Force comprises five phases: transition, instruments, formation, air-to-air an air-to-ground. Each of these phases will be explained below:

-Transition: it comprises fifteen missions in which the student learns how to handle the aircraft, performing aerobatic maneuvers, coordination maneuvers, traffic patterns, and “confidence maneuvers” to reach a high level of familiarization with the airplane. An example of the “confidence maneuvers” is the zero-velocity maneuver, in which the aircraft is flown at an extreme angle of attack (AOA) and loses almost all the translational velocity before being recovered. During this period, different emergency situations are also practiced. A “solo flight” is included in the program so that the self- confidence of the student increases.

-Instruments: like in the basic phase, the student is instructed in the handling of the aircraft having only the flying instruments as a reference. During this phase, flights to other fields and night flights are included along with a solo flight. This phase comprises 16 missions.

7 Chapter 1. Introduction

-Formation: It includes basic formation of 2 or 3 planes and tactical formation of 2 or 4 planes. A total amount of 19 missions are completed during this phase

-Air-to-ground: It includes the sub-phases of: low level, aerial interdiction, close air support (CAS) and air-to-ground dropping; the last one completed at Bardenas (Zaragoza). A total amount of 19 missions are flown.

-Air-to-air: this one is the most extensive phase, consisting on 26 missions of: aerial interdiction, basic combat maneuvers, dogfights and night interceptions.

As it can be observed, it is a really extensive and demanding course having the goal of forming the fighter pilots of the Spanish Air Force to fly the most advanced fighter planes, after passing through the operational transition of which we will talk about below.

1.3.5. Operational transition

Once the pilot has completed the training and is able to fly fighter planes and perform basic maneuvers, he has to learn how to handle the aircraft he will pilot from now on, the plane that he will pilot at his unit.

For this task, modified operative aircraft are used, with two-seat configuration with minimized modifications, so that the transition to the combat-ready aircraft is simpler. However, despite the modifications, these aircraft could be used in a real combat situation.

An example of this kind of plane in Spain is the F-18 used in Zaragoza.

8 Chapter 1. Introduction

Figure 7. Spanish McDonnell Douglas F/A 18 Hornet in Zaragoza [13]

All this training is accompanied, in most cases, by missions in the simulator, in which the pilot is able to practice situations that due to the risk, should not be practiced in flight. One of the main roles of the simulator is the presentation of simulated emergency situations that allow the pilot to learn the inputs needed in anomalous flight situations.

In this work we aim to design a LIFT aircraft, similar to the Spanish version of the F-5 Freedom Fighter. To do so, we will start studying a series of similar planes.

We will calculate the main characteristics we want our aircraft to have, from simple design rules. And finally we will make an invitation to a further study.

9 Chapter 1. Introduction

10

Chapter 2. Similar aircraft

The following chapter collects all the information regarding the similar planes that we are going to study. The T-38 Talon, the MiG21 and the British Hawk. In the Appendix A we will find the tables that represent the characteristics of the aircraft.

2.1. T-38 Talon [14]

11 Chapter 2. Similar aircraft

First of all, we will make an introduction to the main characteristics of the airplane. This introduction will be based on the official World Wide Web site of the United States Air Force Factsheet. [5]. The T-38 Talon is a supersonic jet trainer used by the USAF future fighter pilots, to prepare them to pilot jets such as the F-15 Strike Eagle, the F-16 Fighting Falcon, or the B1-B Lancer. This aircraft is also used by the NASA to train their pilots. Its characteristics allow this aircraft to be used in a great variety of roles, although its main use is the Air Education and Training Command. It is easy accessibility to critical parts of the airplane make it very easy to maintain. Depending on the version, it incorporates a gun sight, a practice bomb dispenser, and a “no drop” bomb scoring system, facilitating the Air-to-Ground and Air-to-Air training for the pilots. A great variety of test pilots use this platform to put into test new technologies. New modifications of the airplane will extend the service life to 2020 at least.

12 Chapter 2. Similar aircraft

2.2. MiG-21 [1]

As we did with the F-5 Freedom Fighter, we will make an introduction to the main characteristics of the airplane. This introduction will be based on [6]. The MiG-21 is a soviet aircraft of the 50’s decade. It is a supersonic aircraft, with retractable landing gear.

Along history, this airplane has suffered over 30 modifications, to turn it into a 4th generation aircraft. During this time, it has served around 50 countries, and has been present in several wars, such as Vietnam, Yom Kipur, Libia, or Ogaden.

The MiG-21 can reach Mach 2, with its single engine. The first design presented problems with its low autonomy.

Its wing configuration allows the aircraft to perform very sharp turns, which represent an advantage in a dogfight.

13 Chapter 2. Similar aircraft

The training versions are the “U” and “UM”. The Soviet Union built over 1200 training versions. The final training version is the MiG-21MF, built in 1971.

All these characteristics make the MiG-21 an airplane worthy of study.

14 Chapter 2. Similar aircraft

2.3. Hawker Siddeley HS-1182 Hawk [1]

All the information shown in the introduction is based on reference [7].

The Hawk is a low-wing, tandem seat, subsonic aircraft that allows the RAF pilots to carry out the advanced training. The Hawk is used to teach air combat, air-to-air firing, air-to-ground firing and low-flying techniques and operational procedures. This airplane is able to carry Sidewinder missiles.

This aircraft originated from a requirement of the British Royal Air Force (RAF) to obtain a new jet trainer in 1964.

15 Chapter 2. Similar aircraft

The British Royal Navy also operates this aircraft, for the training of ship gunners and radar operators. Another important operator is the British aerobatic team called “Red Arrows”.

The airplane suffered some modifications that aroused the export interest. Among its operators we can find Dubai, Kuwait, Finland, or South Korea.

16

Chapter 3. Fuselage design

To obtain an initial sizing of our aircraft’s fuselage, we will elaborate a list with the main components of it, and we will study the main characteristics and size of each component:

 RADAR  EQUIPMENT  CABIN  FUEL  ENGINES

RADAR

EQUIPMENT

CABIN

FUEL

ENGINES

17 Chapter 3. Fuselage Design

We proceed to obtain information of the dimensions of the different equipments.

Radar and equipment:

We can estimate this data observing the similar aircraft’s plans on Chapter 2. Simply measuring from the T38’s plan we obtain 136 centimeters, assuming the equipment we will need in our aircraft will be similar.

Cabin:

We will base our cabin dimensions according to an ergonomic study carried out by Tony Bingelis called “Basic Cockpit Accomodations”[8]. We can observe the dimensions expressed in inches. We remember 1 inch = 2’54 cm.

Figure 8. Basic cabin dimensions[8]

18 Chapter 3. Fuselage Design

We can estimate then:

60 inches * 2 cabins + 6 inches between cabins: 126’’ * 2,54cm = 320 cm

Engines dimension:

We want our aircraft to obtain a nominal thrust in the range of 8000 to 10000 pounds, since it is the nominal thrust of similar aircraft.

A good solution to our requirements could be to install two engines AI-222-25F with vector thrust.

Figure 9. Engine AI-222-25F[16]

The maximum thrust of the engine is approximately 5000 pounds, so it meets our demand.

According to [16], the length of the engine is 1’96 meters. And the diameter is 64 cm.

Fuel:

Taking into account the mission profile, and the consumption of the engines, we can estimate that 3000 pounds of fuel will be necessary to carry out the mission. So a good solution could be to introduce a 3000 pounds tank behind the pilot.

Since our widest part will be defined by the engines, we will approximate our tank to a parallelepiped like this:

19 Chapter 3. Fuselage Design

Figure10. Fuel tank approximation

Volume = 64 * 130 * x

Kerosene density ῤ = 800 Kg/m3 [17]

Volume = 3000 lbs * * = 1’7 m3

x = 204 cm

In [26] slenderness is defined as:

where lf is the length of the fuselage an af the width.

As 8 < < 12 an intermediate value an intermediate value of 10 is chosen to begin the calculations

; ; af = 102’2 cm

This solution is not possible, because does not meet the demand of the width of the two engines needed, therefore a different lambda value needs to be chosen:

; af = 130 cm

With this value he initial solution will be a cylinder with the following dimensions:

Figure 11. Initial sizing of the fuselage

Afterwards, this form will be streamlined to obtain a bluff shape.

20

Chapter 4. Weight calculations

The theoretical concepts used in this chapter are based on [26].

The Spanish Air Force Northrop F-5 Freedom Fighter aircraft has been used as a reference. Inasmuch as it has different configurations, the one used will be the most restrictive, and will be defined later.

The great importance of minimizing the plane’s weight is obvious, since the heavier the plane it is, the greater lift is needed to make it fly. Higher lift generates higher drag, thus a higher weight traduces into an increase of the need in thrust, and therefore in fuel consumption.

4.1. Maximum payload (MPL):

As dictated by [26], we will start calculating the MPL.

The first thing we have to do is to define the concept:

“The payload is the explosive power of a warhead, bomb, etc, carried by a missile or aircraft”.[18] In our case, the payload shall consist of the weaponry carried by the plane. All calculations needed about it will be included in Chapter 8.

The formula that will define our MPL shall be as follows:

MPL = number of people * [weight/pax + baggage/pax] + weapon’s weight (1)

21 Chapter 5. Wing Loading and T/W Ratio

The guidance document establishes that the baggage weight will be 16kg for short or medium range flights and 18kg for medium/long range flights. Considering all the equipment carried by a pilot in a real mission (helmet, anti-g suit, boots and even a knife and a shotgun in some cases) the estimated weight will be 18kg.

MPL = 2 * [78 + 18 (KG)] + weaponry’s weight

MPL = 2 * [209 (LBS)] + weaponry’s weight

The weaponry’s weight is estimated as follows:

The new aircraft aims to replace the existing one and the capacity for carrying weapons cannot be reduced. So it will be at least the greater F-5 configuration:

Figure 12. Aircraft configuration

Number Model Weight Picture

2 MK-82 500 LBS each

[21]

1 MK-83 104

LBS [25] each

22 Chapter 5. Wing Loading and T/W Ratio

1 M-39 223 + 450 LBS bullets

[22]

Chaff & 30 LBS flares dispenser

[23]

Table 2. Maximum Payload estimation

Adding all these weights:

MPL = 1976 LBS

4.2. Operative Empty Weight (OEW):

JAR OPS defines de OEW as:

The total weight of the aircraft for a specific type of operation, excluding all usable fuel and traffic loads. It includes such items as crew, crew baggage, catering equipment, removable passenger service equipment, and potable water and lavatory chemicals. The items to be included are decided by the Operator. The dry operating weight is sometimes referred to as the Aircraft Prepared for Service (APS) weight. The traffic load is the total weight of passengers, baggage and cargo including non-revenue load. [JAR-OPS 1.607 (a)].

There is a expression that stablishes a relationship between the OEW and the MTOW (Maximum Take-Off Weight).

23 Chapter 5. Wing Loading and T/W Ratio

OEW = α * MTOW (2)

The α term is defined though a state of the art observation as:

α =

OEW (lbs) MTOW (lbs) α ά

F5 9558 20000 0.4779 0.5232

Talon 7200 12474 0.5772

Hawk 8778 17061 0.5145

Table 3

So that the relationship remains as follows:

OEW = 0.5232 * MTOW

4.3. Fuel weight (FW):

The graphic below shows the typical profile of a flight.

Figure 13. Typical flight profile

The expression that defines the fuel weight is the following one:

FW = TF + RF

Where TF will be the mission fuel and RF the reserve fuel.

24 Chapter 5. Wing Loading and T/W Ratio

(3)

Many of the relationships shown in this expression could be estimated according to this table:

Table 4. Approximation of the weight relationships

= 1 – = 1 – 0.995 * 0.99 *

For the cruise parts a distance of 450 NM (Nautical Miles) will be considered, since it is approximately what a LIFT plane travels in an hour, and the time of a typical mission.

R = k * ln

450 = k * ln where k =

25 Chapter 5. Wing Loading and T/W Ratio

From Table 5:

Cj = 1 ; v = 450 ; CL / CD = 6

Then k = 2700

0.17 450 = 2700 ln W3 / W4 ; 0.17 = ln W3 / W4 ; e = W3 / W4 ; W3 / W4 = 0.84

For the relationship W7 / W6 :

We consider 200 NM :

200 = k ln W7 / W6 ; 200 / 2700 = ln W7 / W6

W7 / W6 = 0.928

Table 5. Suggested values for L/D, Cj, Cp and np for several mission phases

Considering W9 / W8 as a minor contingency, such as going into a holding pattern in an alternative field, the same proportion that in taxi and take-off will be approximately maintained i.e. 0.99. 26 Chapter 5. Wing Loading and T/W Ratio

= 1 – 0.6657 considering W1 similar to MTOW :

= 0.3343

4.4. Maximum Take-off Weight (MTOW):

Once the other weights have been estimated, the expression that defines de MTOW is a function of these other parameters:

(3)

If we look at the similar aircraft’s MTOW, we can see that our initial result could be correct. Even though it is not an exact result, the minimum value of it represents a good approach.

27

Chapter 5. Wing loading and T/W ratio

All the calculations and theoretical concepts expressed in this Chapter are based on Daniel P. Raymer’s book: Aircraft’s design: a conceptual approach [26].

These two aspects are basic to describe the performances of the aircraft, so they will be fundamental when designing.

Due to the importance of these parameters, it is essential to perform a precise estimation, since the calculations carried out in this chapter will affect notoriously to the initial sizing of the plane.

Wing loading and T/W ratio are interconnected when we have to meet demand of a performance request.

For the same class, the T/W parameter shows a lower statistical variation, so it will be the first parameter to guess. According to the following table [26]:

Figure14. Typical T/W [26]

Once we have this parameter, it is easier to guess the wing loading. According to the literature, we will calculate the wing loading for different situations (stall situation, take-off distance, landing distance…), and having all this results, we will discard those

29 Chapter 5. Wing Loading and T/W Ratio

who are “outliers”, i.e. too high or too low. According to the rest of the results, we will choose the lowest, since it will be the most restrictive.

According to illustration 11, our wing loading should be around 70 lb/ft2

Now we will proceed to express several situations:

5.1. Stall

W = L

2 W = qS S CLmax = ½ ρ VS S CLmax (4)

According to [21], we will estimate the maximum lift coefficient (CLmax) to 1,6.

Then, we have to estimate de stall speed (Vs), to do so, we observe the similar aircraft:

Vs Hawk Talon F-5 Average Vs

Full Flap 102 kts 160 kts 130 kts 130 kts

Table 6. Average Vs

W/S = 0.5 * ρ* 1302 * 1.6

130 kts = 65 m/s

W/S = 80.444 lb/ft2

5.2. Take-off distance

W/S = (TOP) σ CLTO T/W (5)

The expression (5) represents the wing loading during the take-off. As we can see, it is related to the Thrust-to-Weight ratio.

TOP represents the take-off parameter.

σ , since we are at sea level, is 1.

30 Chapter 5. Wing Loading and T/W Ratio

There is a relationship between the lift coefficient at take-off and the maximum lift coefficient, we will use this relationship to introduce the CLTO in our expression:

CLTO = CLmax / 1.21 = 1.32

Now we will estimate the Take-Off Distance, observing the similar aircraft’s values, shown in this Table:

Hawk Talon F-5 Average TOD

TODistance 3500 ft 2700 ft 3000 ft 3000 ft

Table 7. Average TOD

Now that we know the Average TOD, the Take-Off Parameter can be obtained by this graphic:

[26]

Now we obtain the TOP, 200. The only thing we have to do now is to replace all the terms in expression (5).

W/S = 237 lb/ft2

31 Chapter 5. Wing Loading and T/W Ratio

As we said in the introduction, this value will be discarded since it represents a too high value.

5.3. Landing distance

Our reference document [26] shows an expression of the landing distance relating this one with the wing loading. We will use this expression to estimate the wing loading as we did before:

Sland = 80 (W/S) (1/CLmax σ) + Sa

There is another expression to represent de landing distance:

2 Sland = 0.3 * Vs = 5070

CLmax = 1.6

According to D. Raymer, Sa is 600 for general aviation planes and 450 for STOL [26], since our design does not correspond to neither of them, we will take an average number between them, 525.

Now that we know all the terms of the expression:

5070 = 80 (W/S) 0.625 + 525

W/S = 90 lb/ft2

5.4. Instantaneous turn

According to [26], the expression that represents the instantaneous turn situation is defined as:

W/S = q CLmax / n

The speed we have to introduce is the corner speed, since it optimizes the turn, for our situation, this value reaches 320 kts [26].

Our CLmax will be 0.7 [26]

32 Chapter 5. Wing Loading and T/W Ratio

We want at least that our g factor reaches a value of 8.

Introducing all these data in the formula:

W/S = 0.5*0.0238*1602*0.7 / 7 (6)

W/S = 30.464 lb/ft2

According to the methodology explained in the introduction, our final value will be the one obtained for the stall situation:

W/S = 80.444 lb/ft2

33

Chapter 6. Geometric definition

In this section we have used the results obtained in the previous chapters and the information in [26] to get a sketch of our plane.

It is important to say that this is not going to be the final design, it is just an approximation to the final one, that will be obtained through a further study referenced in Chapter 9.

6.1. Airfoil Geometry

As we are building a supersonic jet, a relatively sharp airfoil will be chosen. But it is not going to be a radical sharpened airfoil, since we want to reduce the drag.

As many of the similar aircraft, we will use a cambered airfoil that will increase the lift and will enable our airplane to fly at low speeds, this is achieved by avoiding the separation of the boundary layer as shown in Figure 13.

Figure 15. Effect of camber on separation [26]

35 Chapter 6. Geometric definition

The airfoil selected will be the 64 A010, a six-series airfoil from the NACA family.

Figure 16. Typical airfoils [26]

The 64 A010 is a typical airfoil for high-speed wing aircraft, designed for an increased laminar flow. This NACA airfoil will cause a gradual loss of lift in an stall situation, which will be much safer for the pilot, giving him time to react.

Figure 17. Types of stall [26]

6.2. Wingtip

At the wingtip, missile rails will be placed. This will have two intentions:

1. Ability to carry wingtip missiles.

2. Reduce the 3-D effects on drag, since the aspect ratio of our aircraft will be relatively low.

36 Chapter 6. Geometric definition

6.3. Wing Sweep

As we want our aircraft to be supersonic, we will need to reduce the effects of supersonic flow, just like aerodynamic center movement, or drag increasing due to shock formation.

Our leading edge sweep will be of approximately 40 degrees, according to wing sweep historical trend (Figure 16). This fact will allow our aircraft to fly at supersonic speeds.

Figure 18. Wing sweep historical trend [26]

6.4. Tapper ratio

“Tapper affects the distribution of lift along the span of the wing. As proven by the Prandtl wing theory early in this century, minimum drag due to lift, or “induced” drag, occurs when the lift is distributed in an elliptical fashion” [26].

As an elliptical wing is very difficult to be built, we will approximate our wing to an elliptical one by using the tapper ratio “λ”.

λ = Ct / Cr (7)

37 Chapter 6. Geometric definition

λ = 100 / 280 = 0,35

According to [26], most swept wings have a tapper ratio of about 0,2-0,3.

6.5. Wing incidence

This aspect use to be determined in wind tunnels, this corresponds to a further study of the conceptual design, so initially our wing incidence will be approximately zero, as it uses to be for military aircraft.

6.6. Wing vertical location

A mid-wing arrangement will be selected. This arrangement will allow the aircraft to carry bombs at a safe distance from the ground.

6.7. Tail arrangement

Twin tails have been proved to be more effective for the use of the rudder, since they avoid the fuselage shielding. For this reason, a twin tail will be selected for our aircraft.

Figure 19. Aft tail variations [26]

38 Chapter 6. Geometric definition

Figure 20. Initial solution 1

Figure 21. Initial solution 2

39 Chapter 6. Geometric definition

Figure 22. Initial solution 3

40

Chapter 7. Drag Polar

It is known that a direct relationship between drag and lift exist. The lift force affects to the drag one and this can be expressed through a diagram known as drag polar. A parabolic approach is used to express this relationship:

2 CD = CD0 + KCL (8)

We will calculate CD0, the parasite drag, according to (8). In accordance to the flat plate analogy:

Figure 23. Flat plate analogy

2 2 D0 = ½ ρ V CD0 Sw = ½ p V Cf Swet

CD0 = Cf Swet/Sw

CD0 = [CD0wings + CD0fuselage] Form factor * Interference factor (9)

CD0 = [Cf Swet/Sw + Cf Swet.fus/Sw] FF*IF Now we will have to calculate the three unknown parameters: Reynolds number,

Mach number and the wet surface (Swet). 41 Chapter 7. Drag Polar

To estimate the wet surface, we will approximate the aircraft to the initial solution obtained in Chapter 3, a cylinder. So the wet surface of the fuselage will be: S = 2 π r l = 41’74 m2, obviating the front and the rear parts, since in the further design, the fuselage will be more aerodynamic. For the wings: As we said in Chapter 5:

W/Sw = 80

MTOW/Sw = 80

12500/80 = Sw

2 Sw = 14’516 m * 2

2 Sw = 29’032 m For the rest of the parameters, we will consider an altitude of 20.000 ft and 260 KIAS, characteristics that will resemble a cruise.

According to the atmospheric calculator [27]: µ = 1’26 * 10^-5

ρ = 0’6527 kg/m3 Re/D = 5485432 being D the fuselage length = 10’22 m Re = 54854320 M = 0’423 Replacing all the terms in (9):

CD0 = 1’7 * 10^-3 Now we can estimate the “k” parameter: k = 1/πAφ (10)

Using the Anderson method: k = (1 + ζ) 1/ πA (11)

. ζ = [0’015 + 0’016 (λ – 0’4)2] (βA – 4’5)

Being λ = Ct/Cr = 0’35 . ζ = 4’62*10^-3

42 Chapter 7. Drag Polar

2 k = (1-4’62*10^-3) Sw/π b = 0’03193

2 CD = 0.0017 + 0.0319 CL

Representing this result in a graphic:

CL

CD Figure 24. Drag Polar

43

Chapter 8. Payload-Range Diagram

For this Chapter we will use some of the data calculated in the previous Chapters, such as the MTOW, OEW, or the specific fuel consumption. Using the calculations we will explain later, we achieve this diagram:

Figure 25. Payload-Range Diagram

The A point represents the Operative Empty Weight plus the Maximum Payload (both values calculated in Chapter 4. A = MPL + OEW = 1976 lbs + 7255.04 lbs = 9231.04 lbs

45 Chapter 8. Payload-Range Diagram

To obtain B we will calculate the range using the Breguet expression (12) and see where it crosses with the horizontal line drawn from A. The expression (12) maximizes the range of the aircraft:

(12)

CJ = 0.64 kg/kgf*hr [16] = 1.77 E -4 N/(N·S) Considering the same conditions as in Chapter 7: ρ = 0.6527 kg/m3 [27] S = 70.722 m2

The initial weight (W0) and at the final weight (We) will be:

W0 = MTOW = 6289.8157 kg (from Chapter 4) We = OEW + MPL = 4187.12931 kg (from Chapter 4)

We know CD0 and K from Chapter 7:

CD0 = 0.0017 K = 0.0319 Now that we have all the terms from expression (12):

RB = 7406.901 km Now, using the same procedure, we will calculate the range in C:

The only changing parameter will be We.

WeC = OEW = 3290.83 kg All the rest of the terms will remain equal.

RC = 10621.4 km We have already taken all the Payload, without reaching the Maximum Fuel Weight (MFW), so points C and D will match.

46

Chapter 9. Conclusions and further studies

9.1. Methodology

First of all, we will start reviewing the way we proceeded to obtain all our results, and the expression of the main of them.

With the knowledge obtained and the documentation needed for the beginning of the project, added to Chapter 1. We obtained a cursory knowledge of the state of the art. According to the interests of this work, similar aircraft were selected as references for our design.

Though the research in the literature and the T.O,s (Technical Orders) we get most of the data needed for a further analysis and use.

Starting from the general knowledge of the aircraft’s content (two pilots, needed equipment, fuel…) we proceeded to the approximation of the dimensions of the airplane.

Later, we adjusted all these data to slenderness requirements according to our aircraft’s characteristics, obtaining:

Fuselage length 1022 cm

Fuselage width 130 cm

Table 8. Sizing results

For the main weights, the bibliographic query proposed a series of approximations for the calculations. Using these approximations and the data obtained from similar planes we get some estimative results:

47 Chapter 9. Conclusions and further studies

Maximum Payload 1976 lbs

Operative Empty Weight 0.5232 MTOW

Fuel Weight FW/W1=0.3343

Maximum Take-off Weight MTOW>=13866.67 lbs

Table 9. Weight results

For the wing loading and the thrust-to-weight ratio, we followed the approximations proposed by Daniel P. Raymer at his book “Aircraft design: a conceptual approach”, for different flight situations. Obtaining:

T/W 0.9

W/S 80.444

Table 10. T/W and W/S results

According to the results obtained in the previous paragraphs, as well as the study of the different aerodynamic shapes, we get the initial three view drawing.

Using the parabolic approximation formula:

2 CD=CD0 + KcL

And estimating the parameters “CD0” and “k”, we get the initial formula for the representation of the drag polar.

9.2. Further research

The obtained data is an initial approach to the aircraft design, we cannot forget the initial aim was to get a CONCEPTUAL design. To continue the development we should delve into the procedures followed, so that we can obtain a more accurate design. A deeper study should also include a selection of the materials that should be used to meet the demanded requirements that our results show (what type of flying profile is

48 Chapter 9. Conclusions and further studies

going to be used, what engines we are going to incorporate…). We should also perform an accurate design of the aircraft (the exact measures of each surface).

A scale model could be built, maintaining the main parameters as Thrust-to-weight ratio or the wing loading, to carry out a study in wind tunnels.

If we are going to design an aircraft, we should also consider the maintenance aspects, like how we are going to plan it.

To finish, it is necessary to calculate the initial budget of the project, and compare it to similar plane’s budget.

9.3. Technological improvements to implement

Since the design of similar planes to ours, some technological improvements have been carried out, that could make the difference with this similar planes if we implement them to our design:

-Thrust vectoring: this technology allows the nozzle to move changing the direction of the thrust vector. The use of thrust vectoring has proved to provide some advantages in combat, since it facilitates the aircraft to perform some maneuvers that conventional planes cannot do.

Figure 26. Thrust vectoring [24]

49 Chapter 9. Conclusions and further studies

-Helmet mounted display: most of the similar planes incorporate a HUD that allows the pilot to control the aircraft and all the basic parameters at the same time he is looking outside. But the problem comes when the pilot has to turn his head to look for the other plane in a dogfight for example. The helmet mounted display finds a solution to this problem, since it shows the information on a reticle incorporated to the helmet. Apart from this, another capabilities comes with this technology like optical or electromagnetic tracking.

Figure 27. Helmet Mounted Display [25]

-Better simulation systems implementable by data-link. In most cases, a real situation is very difficult to represent, or the big exercises carried out to represent them are expensive and dangerous, and require a big coordination. For this reason, it is necessary to do more emphasis in the development and implementation of simulation systems allowing the pilot to experience all kind of situations that he could find in a real mission.

50

Appendix A. Similar planes tables

.1. T-38 Talon

GENERAL DATA NAME T-38 TALON PRODUCER Northrop Corporation FIRST FLIGHT March the 10th,1959 hmáx 3,8 m lmáx 14 m WINGSPAN 7,6 m

THRUST NUMBER OF ENGINES 2 POSITION Rear part of the fuselage KIND OF ENGINE turbojet MODEL J85-GE-5 DEVELOPER General Electric

Weng 400 lbs Teng 2200 dry 3300 with afterburner Ce at idle 7300 lbs/h with afterburner 11400 lbs/h Pto 6600 lbs

WEIGHT EW 7200 lbs

51

EW/MTOW 1,666666667 Tto/MTOW 0,55

FUSELAGE AND CABIN FUSELAGE LENGTH lf 14 m RATIO lf/b 1,842105263 FUSELAGE WIDTH bf 1,834482759 FUSELAGE HEIGHT hf 1,440677966 dmin MINIMUM DISTANCE TO THE FLOOR 0,84 m CABIN LENGHT lc 3,09 m CABIN WIDTH bc 0,76m VOLUME AND POSITION OF THE CARGO CABIN none NUMBER OF SEATS AND POSITION 2 in tandem

WING VERTICAL POSITION 1,27m HORIZONTAL POSITION 0,54 WING SURFACE Sw 16,69 m2 b ( 3,36 m Ct (cuerda que hay al final del ala) 0,86 m Cr 2,9 m LAMBDA 0,296551724

FLAPS TYPE Trailing edge flaps bf 1,54 m bf/b 0,458333333 Yf 0,77 m Yf/b 0,229166667

AILERONS AND SPOILERS ba 0,86 m ba/b 0,255952381 AILERON Ya 2,37 m SPOILER Ya over the wing

52

Ya/b 0

HORIZONTAL STABILIZER AND ELEVATOR POSITION rear part of the fuselage bh 1,54 m bh/b 0,458333333 Cth 0,57 m Crh 1,59 m LAMBDA 0,358490566

VERTICAL STABILIZER AND RUDDER bv 1,96 m bv/b 0,583333333 Ctv 0,76 m Crv 2,28 m

LANDING GEAR TYPE retractable T 10 fts B 19 fts T/B 0,526315789 B/lf 0,413043478 Np 2

PERFORMANCES Vmax MN 1,3 (858 kts) Vcr optimal FL 350 485 KTAS Vs 160 KTS V2 (FAR 25.107 y JAR 25.107) 165 KTS V3 185 kts Vasc 270 kts Hser 50000 ft TAKE-OFF DISTANCE (different conditions)

53

Sea Level 3000 ft 4000 ft 4000ft LANDING DISTANCE (different conditions)

Sea Level 6000 ft 2000 ft 7000 ft 4000 ft 7500 ft

54

.2. MiG-21 Fishbed

GENERAL DATA NAME MiG-21 PRODUCER MIKOYAN-GUREVICH FIRST FLIGHT 14-feb-55 hmáx 4,1 m lmáx 15,76 m WINGSPAN 7,154 m

THRUST NUMBER OF ENGINES 1 POSITION Rear part of the fuselage KIND OF ENGINE turbojet MODEL R-11F2S-300 PRODUCER Tumansky Weng 1,124 kg (2,477 lb) Teng 8708lb military power // 13635 with afterburner at idle 97 kg/(h·kN) (0.95 lb/(h·lbf)) at idle with afterburner 242 kg/(h·kN) (2.37 lb/(h·lbf))

WEIGHT MTOW 21607LBS 10050KG EW 4871KG Tto/MTOW 242 KG/H*KN / 10050KG

FUSELAGE AND CABIN lf 12.285m (40 ft 3½ in) RELACIÓN lf/b 12,285 / 1,24 ANCHURA DEL FUSELAJE bf 1.24 m ALTURA DEL FUSELAJE hf 2,24 m dmin 0,95 m lc 1,90 m bc 0,66 m NUMBER OF SEATS AND POSITION 2 seats in tandem

WING VERTICAL POSITION LOW Sw 23 M2 b 3,12 m Ct 0,52 m Cr 5,20 m

55

LAMBDA PARAMETER 0,1 DIHEDRAL MINUS 2º AERODYNAMIC PROFILE TSAGI S-12

FLAPS TYPE Floating with SPS bf 1,17 m bf/b 0,1635 Yf 0,585 Yf/b 0,0817

AILERONS AND SPOILERS ba 1,39 ba/b 0,194296897 Ya 2,79 Ya/b 0,389991613

HORIZONTAL STABILIZER AND ELEVATOR POSITION Rear part of the plane bh 1,64 bh/b 0,229242382 Cth 1,39 Crh 2,05 LAMBDA PARAMETER 0,67804878

VERTICAL STABILIZER AND RUDDER bv 1,85 bv/b 0,258596589 Ctv 1,14 Crv 3,611 NARROWING 0,315702022

LANDING GEAR TYPE retractable T 1,43 B 5,25 T/B 0,272380952 T/b 0,199888174 B/lf 0,333121827 Np 2

PERFORMANCES Vmax Mach 2,3 2230km/h a gran altura Hser 16100 m MiG-21F 1300 km

56

.3. Sidderley Hawk

GENERAL DATA NAME HAWK PRODUCER BRITISH AEROSPACE FIRST FLIGHT 21-8-1971 hmáx 3,99 m lmáx 11,17 m WINGSPAN 9,39 m

THRUST NUMBER OF ENGINES 1 POSITION Rear part of the fuselage TYPE OF ENGINE turbofan MODEL Turboméca Adour Mk151-01 PRODUCER Rolls-Royce Teng 2334 kg

WEIGHT MTOW 7755 kg EW 3990 kg MFW EW/MTOW 0,5145

FUSELAGE AND CABIN lf 11,17 m lf/b 1,189563365 bf 8,057 hf 1,76 dmin 0,88 lc 3,66 bc 0,85 NUMBER OF SEATS AND 2 in tandem POSITION

WING VERTICAL POSITION 1,11 m Sw 16,69 m2 b 4,39 Ct 0,95

57

Cr 2,44 LAMBDA PARAMETER 0,389344262

FLAPS TYPE Trailing edge flaps bf 2,44 bf/b 0,259850905 Yf 1,83

AILERONS AND SPOILERS ba 1,64 ba/b 0,174653887 Ya 3,13

HORIZONTAL STABILIZER AND ELEVATOR POSITION Rear part of the fuselage bh 1,95 bh/b 0,207667732 Cth 0,54 Crh 1,22 LAMBDA PARAMETER 0,442622951

VERTICAL STABILIZER AND RUDDER bv 1,87 bv/b 0,19914803 Ctv 0,91 Crv 2,3 NARROWING 0,395652174

LANDING GEAR TYPE retractable T 3,47 B 4,57 T/B 0,759299781 T/b 0,369542066 B/lf 0,409131603 Np 2

PERFORMANCES Hser 14000 m

58

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59

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