[american institute of aeronautics and astronautics 42nd aiaa/asme/sae/asee joint propulsion...

American Institute of Aeronautics and Astronautics

1

Co-flow Fluidic Thrust Vectoring Requirements for

Longitudinal and Lateral Trim Purposes

Fariborz Saghafi*, Afshin Banazadeh

†

Sharif University of Technology, Tehran, Iran

The feasibility of using fluidic thrust-vectoring system, as a control technique for the

longitudinal and lateral trim purpose was investigated in this study. For this purpose,

integration of a Co-flow method into the propulsion unit of a conceptual aerial vehicle was

assumed. The focus of the research presented was to estimate the required thrust vector

angle in order to trim the aerial vehicle in different flight phases. Since the fluidic thrust

vectoring requires secondary air flow to deflect the engine exhaust gas, this research also

provides an analytical toolset for preliminary sizing of a suitable secondary air supply. It

was found that thrust vectoring could be an effective mean of providing trim authority for

such a vehicle in all phases of flight. The mathematical model, developed in this study, can be

used as a preliminary tool for overall performance evaluation of similar future conceptual

vehicles.

Nomenclature

cb, = span, mean aerodynamic chord

bwC = wind to body transformation matrix

YDL CCC ,, = lift, drag and side force coefficients

nml ccc ,, = rolling, pitching and yawing moment coefficients

zyx fff ,, = force components

yzxzxyzzyyxx IIIIII ,,,,, = moments of inertia

NML ,, = moment components

Ma = mach number m = aircraft mass

im = moment vector

pm& = engine primary mass flow rate

sm& = secondary mass flow rate

hPP EN ,, = navigation altitudes rqp ,, = roll, pitch and yaw rates

r = thrust position vector

S = reference area

T = engine thrust wvu ,, = velocity components

TV = true velocity vector

TTT ZYX ,, = components of thrust position vector

βα , = angel of attack

* Assistant Professor, Department of Aerospace Engineering, Sharif University of Technology, [email protected]

† AIAA Student member, PhD Student, Sharif University of Technology, [email protected]

Current address: School of Engineering, Cranfield University, [email protected]

42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit9 - 12 July 2006, Sacramento, California

AIAA 2006-4980

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

TT βα , = thrust vectoring angles γ = flight pass angle

δ = control surfaces deflection

ψθϕ ,, = Euler angles

ω = angular velocity vector ρ = air density

q = dynamic pressure

AOA = Angle Of Attack

CFD = Computational Fluid Dynamics

CG = Centre of Gravity

CTAT = Conceptual Thrust-vectored Aerial Tail-sitter

Datcom = Data Compendium

FTV = Fluidic Thrust Vectoring

NED = North Earth Down

RANS = Reynolds Averaged Navier-Stokes

RIAV = Runway Independent Aerial Vehicle

SSF = Steady State Flight VSTOL = Vertical or Short Take off and Landing

MCbeRLPa .,,,,,, = subscripts for: aerodynamic, propulsion, left, right, earth, body, centre of mass

TB, = superscripts for: body coordinate system, transpose

I. Introduction

uring the last decade, there have been many proposals aiming to solve the launch and recovery problems and

introduce the new generation of VSTOL aerial vehicles1-6

, which the authors would like to name them RIAVs.

Helicopter is known to be the most successful RIAV over these years. However, in the authors’ opinion it poses

several drawbacks. It is a complex and costly vehicle especially in the field of maintenance. Also, its efficiency with

respect to energy consumption, relative to the fixed wing aerial vehicles, is poor. Moreover, fatigue is particular

problem of its blades, which demands redundancy in structure that leads to over engineered structure.

The other successful RIAV concepts that combine vertical and horizontal flight are the tilt-rotor, tilt-body,

compound helicopter and tail-sitter. However, the first three ones feature significant extra mechanical complexity in

comparison to the tail-sitter7-9

vehicle, which has fixed wing, body and nacelles. On the other hand, they all utilize

rotor/propeller type propulsion system which is not suitable for high speed flight, where wave drag increases rapidly

in the tip of rotors/propellers.

One promising simple solution to have a RIAV with minimum mechanical complexity and maximum flight speed

is a jet-propelled tail-sitter. However, the negative side effect of the elimination of propellers should be somehow

compensated. This side effect is the propeller slipstream over the control surfaces which is a vital key of tail-sitter

stabilization in hover, early vertical to horizontal and late horizontal to vertical transition modes10

. The

compensation can be carried out by using a jet thrust vectoring system, either mechanically or fluidic. Mechanical

thrust vectoring designs have proven to be heavy, complex, expensive, and counter-productive to stealth. Fluidics,

on the other hand, offer reduced weight, higher reliability, and in the case engine airframe integration they may also

be more easily integrated with airframe structures to share loads and eliminate redundant structures11-13

. Figure 1

shows an overall view of different fluidic thrust vectoring methods.

It should be pointed out that even for conventional aircrafts, thrust vectoring can significantly improve the aircraft

design characteristics and performance even in a small part of the flight envelope. Actually, it works as a manoeuvre

effecter for next generation of aerial vehicles14

.

Overall, The study is based on the physical aspects of a conceptual scaled model of an aerial vehicle, potentially

able to take-off and land vertically, in three common phases of flight, named as transition (flying from zero to cruise

speed and vice versa), cruise and pull-up debut (beginning of pull-up manoeuvre) for definite range of airspeeds.

Also, it covers a simple constant altitude bank to turn manoeuvre. The vehicle is equipped with two micro-jet

engines, utilizing Co-flow fluidic thrust vectoring system that uses a source of secondary air and Coanda15

surface to

deflect the engine thrust.

D


3

The vehicle dynamic equations were

developed and implemented in trim

algorithm as well as in a non-real time

simulation program. The purpose of

trim investigation was to find out a

range of thrust vectoring angles, to

attain a feasible steady state flight for

the aircraft in different flight modes.

From flight dynamics point of view, this

is the first step for any further stability

and control analysis16

. The aircraft

dynamics is evaluated by simulating the

vehicle trajectory and attitude, using Matlab/Simulink simulation environment. Moreover a relationship is presented

between the thrust-vectoring angle and the required secondary mass flow rate throughout several computational

simulations.

II. Physical Representation of CTAT

CTAT is based on a carefully planed proposal for prove-of-the-concept demonstration. The CTAT

configuration characteristics are chosen based on the considerations such as; simplicity and data availability,

especially in dynamic analysis, microjet engine integration contrivance, foresight strategies in the next generation

of aerial vehicles, manufacturing feasibility and simplicity. Detailed configuration design process and related

decision makings, regarding the engine airframe integration, is beyond the scope of this paper. Therefore, only the

key characteristics are summarized in table 1 for the engine and table 2 for the whole aircraft. Also, the CTAT final

configuration is schematically shown in Fig 2.

In trim study, it was assumed that FTV is achievable by

using any source of the secondary air supply such as:

compressed air tank, engine compressor bleeding, power

extraction17, 18

or additional electrically driven compressor,

without a significant change in aircraft characteristics or

engine performance.

The performance, stability and control characteristics of

an aircraft highly depend on the aerodynamic forces and

moments acting on it, which means it relies on the vehicle

aerodynamic derivatives. These derivatives themselves are

functions of the shape, velocity, altitude and attitude of the

vehicle. The CTAT aerodynamic derivatives were derived in

three flight speed regimes: 3.0185.0,185.0 ≤≤< MaMa and

Ma<3.0 by use of the DatCom19

methods.

Since it was assumed that CTAT is a low subsonic

vehicle, there was no need to calculate derivatives in speed

regimes beyond 7.0=Ma . It is also assumed that the flight

altitude was less than 1500 m. Therefore, only three sets of

derivatives were sufficient to cover the whole predefined

Thrust

Vectoring

Mechanical Fluidic

Annular Impingement Co-flow Counter flow Synthetic

Jet Actuator

Shock Vector

Control

Sonic Throat

Skewing

Figure 1 Thrust Vectoring Systems

Table 2. CTAT Physical Characteristics

Reference Area 2 m2

Take off mass 46 kg

Mean Aerodynamic Chord 1.02 m

Wing Span 2.2 m

XC.G. from Trailing Edge 0.78 m

XT.V. from C.G. 0.91 m

YT.V. from C.G. 0.25 m

Table 1. CTAT Engine Characteristics

Maximum RPM 108,000

Compressor Pressure Ratio 4

Thrust @ Max. RPM 190 N

Fuel Consumption @ Max. RPM 640 gr/min

Max. Exhaust Temp. 973 K

YT.V

XT.V

X

Z Y

Fig Figure 2. Schematic Configuration of CTAT


4

flight envelope. It is worthwhile to point out that,

representation of the low-speed aerodynamic

characteristics20, 21

and calculation methods are beyond the

scope of research presented here but is strongly advised

for realistic studies. Consequently, concerning the

DatCom method, the most important derivatives are

highlighted in table 3 and other derivatives were believed

to be negligible regarding the flight condition and

configuration.

III. Aircraft Simulation

In order to construct the aircraft simulation code, the governing equations of motion were formulated to obtain

the mathematical model. The simulation method was based on Cartesian approach that formulates the equations in

Cartesian coordinates. Since the aerodynamic derivatives were in stability or wind axis system regarding the

negligible angle of sideslip, in consequence the forces and moments calculated in wind coordinate system had to be

transformed to the body coordinate system using the wind to body transformation matrix. The CTAT equations of

motion were assembled and listed as follow, according to the methods and notations in Refs. 22, 23.

A. Moment Equations

( )

( ) ( )( ) paXZXXYYXZZZ

paXZZZXXYY

paYYZZXZXZXX

NNqrIpqIIpIrI

MMrpIprIIqI

LLrqIIpqIrIpI

+=+−+−

+=−+−+

+=−+−−

&&

&

&&

22

(1)

where [ ]

+=

=

n

m

lB

p

zpa

ypa

xpa

Bpa

bC

Cc

bC

Sqm

N

M

L

m

,

,

,

, and

=

n

m

lT

BW

n

m

l

c

c

c

C

C

C

C

R

BpRL

BpLR

BpL

Bp

Bp frfrmmm ×+×=+=

(2)

where

−

=

−

−

=

T

T

T

R

T

T

T

L

Z

Y

X

r

Z

Y

X

r and 2222;)(

2

1wvuVVhq TT ++== ρ

and

−

−−=

αα

βαββα

βαββα

CosSin

SinSinCosSinCos

CosSinSinCosCos

CB

W

0

(3)

B. Force Equations

( )

( )

( )ZZ

YY

XX

pa

pa

pa

ffCosmgCosvpuqwm

ffSinmgCoswpurvm

ffmgSinwqvrum

++=+−

++=−+

++−=+−

φθ

φθ

θ

&

&

&

(4)

where [ ]

+=

=

Z

Y

XB

p

zpa

ypa

xpa

Bpa

C

C

C

Sqf

f

f

f

f

,

,

,

, and

−

−

=

L

DT

BW

Z

Y

X

C

Cy

C

C

C

C

C

R

BpL

Bp

Bp fff +=

Table 3. CTAT Major Derivatives

LC 0LC

αLC α&LC LqC uLC δLC

DC 0DC

αDC α&DC DqC DuC δDC

mC 0mC

αmC α&mC mqC muC δmC

lc 0

lc βlc β&l

c lpc lpc δlc

nc 0nc βnc β&n

c pnc

rnc δnc

cy 0yc βyc β&y

c pyc

ryc δyc


5

(5)

where

−

+

−R

R

L

L

TT

T

TT

TT

T

TT

SinCosT

SinT

CosCosT

SinCosT

SinT

CosCosT

αβ

β

αβ

αβ

β

αβ

and TTT RL ==

As it is shown in the equations, it was assumed that the pitching thrust deflection angle (Tα ) is different for left

and right engines but the yawing angle (Tβ ) is the same for two engines and the positive direction is according to

the right-hand-rule, respecting the Body-Axis. It is also notable that TTT ZYX ,, were absolute values, measured

from C.G.

C. Kinematics Equations

θφφψ

φφθ

θφθφϕ

sec)cossin(

sincos

tancostansin

rq

rq

rqp

+=

−=

++=

&

&

&

(6)

D. Navigation Equations

( )( )

( )( )

θφθφθ

ψθφψφ

ψθφψφψθ

ψθφψφ

ψθφψφψθ

CoswCosCosvSinuSinh

SinSinCosCosSinw

SinSinSinCosCosvSinuCosP

CosSinCosSinSinw

CosSinSinSinCosvCosuCosP

E

N

−−=

+−+

++=

++

+−+=

&

&

&

(7)

Additionally, in steady pull-up manoeuvre, equations were assumed to be derived for the beginning of pull-up

( 0=γ ) and with a reasonable constant pitch rate.

IV. Co-flow Fluidic Thrust Vectoring

The concept of fluidic thrust vectoring is to deflect the thrust of a jet by using the influence of a second smaller

exhaust stream. This secondary flow would typically be injected into or near the primary jet stream and would

require few, if any, moving parts. Nozzle weight and complexity would therefore be reduced. The secondary flow

may also be helpful to provide cooling for nozzle surface. FTV control systems are lightweight, simple and

relatively inexpensive. They have also fixed geometry and affordable technology24

. However, the main challenge

with fluidic system is in creating an efficient system with acceptable control response characteristics.

Co-flow FTV system relies on a phenomenon known as the “Coanda effect”. The Coanda effect is the tendency

of a fluid, either gaseous or liquid, to follow the convex curvature of a solid boundary. It happens due to reduction of

surface pressure due to a vortex action as the liquid passes over the boundary25

. It is notable that, by this method the

flow can be even turned through 180o

curvature. This concept is schematically illustrated in Fig. 3. By positioning

Coanda surface to the rear of the micro-jet engine nozzle and introducing secondary stream of Co-flowing air,

parallel to the Coanda surface, thrust vectoring can be formed.

In the research presented, it was assumed that such a system was integrated with CTAT engine, adding no

excess weight and no changes in aircraft mass and inertia properties. Therefore, the analysis of required thrust

vectoring angle and mass flow rate was likely to be achieved in different flight phases by use of the aircraft

simulation model. Also, a relationship between required thrust-vectoring angle and secondary mass flow rate was

derived utilizing CFD methods, which is presented in section VI.


6

V. Analysis of Required Thrust-

Vectoring Angle

Analysis of required thrust vectoring angle is based on trim ability of CTAT in a predefined trajectory. This trajectory is so defined that CTAT first flies from a vertical to a horizontal position through a smooth un-stalled transition. Then, the mission phase is performed in horizontal or cruise mode. Finally, it flies from horizontal to vertical position through a pull-up maneuver to regain vertical attitude

26. In this

trajectory, the aircraft velocity changes from zero to cruise speed and vice versa. A typical

trajectory is shown in Fig. 4. The mathematical formulations, described in preceding section, were programmed, first into Matlab for trim analysis and later in Simulink for trajectory simulation. Derivatives were expressed in terms of polynomial functions of AOA and velocity, in order to be precisely calculated inside the trim algorithm for different flight conditions. In trimmed flight there is no rotation about CG and it means that the forces and moments balance. An aircraft must be trimmed to fly in a steady condition. So by means of trim algorithm, the control inputs that are thrust and its deflection angle were found in each flight condition. The trim algorithm was solved using Matlab fsolve function by minimizing the error term. The results are presented in table 5.

A. Take-off and Transition; Trim Simulation

In this phase, the input parameters were

velocity and flight pass angle. They were chosen

in order to fulfill the mission profile. As

mentioned before, the flight altitude has

negligible effect on the results. So it has been

disregarded as an input in all flight phases. AOA,

thrust and its vectoring angle were obtained by

solving trim equations and presented in table 5.

Meanwhile, the obtained range for angle of attack

was less than 16 degrees, which entirely satisfied

the aerodynamic derivatives enclosure band. The

minus sing in Tα shows that the control system

would try to pitch up the CTAT during the

transition and this potentially means that the

aircraft is statically stable.

In order to evaluate the accuracy of trim outputs, the results were fed into Simulink simulation environment.

This simulation was very useful for initial performance and trade studies. CTAT was flown in every flight condition

by implementing the trim results as an initial condition. Simulation was run for 8 seconds. It seemed that during this

time, CTAT was fairly stable and tends to gradually rotate downward. This arose mostly because of the numerical

error congregation and somehow due to the modeling of derivatives.

CTUT trajectory and attitude are shown in Fig 5 for the first trim condition

in table 5. The overall behavior confirmed the validity of the equations and

the feasibility of the transition flight, regarding the novel control scheme

for such a vehicle. In Fig. 5 the minus sing for the altitude is due to the

defined direction of coordinate system that is similar to NED system.

B. Cruise; Trim Simulation

In this phase, the only input parameter was velocity. Here, CTAT was

flown in a horizontal plane and attitude angle was set to zero. AOA, thrust

and its vectoring angle were found by solving trim equations. The results,

which are presented in table 5, wholly show that increasing flight speed

decreases required thrust vectoring angle. This was predictable seeing as,

by pushing the aircraft in higher velocities the produced drag also

Fig

Main Nozzle

P rimary Jet

Secondary Jet

Vectored Thrust

Low Pressure Area Coanda P lane

Figure 3. Co-flow Fluidic Thrust Vectoring Concept

Cruise Vert ical to Horizontal

Transition

Horizontal to Vertical Transition

Hovering

Figure 4. CTAT Typical Flight Trajectory

0 5 10 15 20

-50

-40

-30

-20

-10

0

Xe (m)

Ye (m)

Heig

ht

(m)

Hei

ght

(m

)

Figure 5. Take off Simulation for

First Static Trim Condition


7

increases, demanding more required thrust. As a result, the moment produced by the thrust component will also get

greater and causes reduction in the required thrust vectoring angle to keep the vehicle in trim situation. Once more,

CTAT was flown from all trim conditions in cruise and simulation was performed for 15 seconds. The results

confirm fantastic stability in cruise. CTAT trajectory and attitude for the first trim condition in table 5 are shown in

Fig. 6.

C. Pull-up; Trim Simulation

To investigate the air vehicle ability

to carry out landing transition, the trim

was performed for the beginning of

pull-up, where CTAT is going to pitch-

up from horizontal into vertical position.

The inputs were velocity and required

thrust which were previously obtained

from cruise; trim simulation. Also the

pitch rate was set 2deg/sec, regarding the

vehicle physical size and characteristics.

Thrust vectoring angle, AOA and pull-

up radius were desired outputs, which

are presented in table 5. Simulation, which was performed for 15 seconds in every trim point, verified trim stability

in this phase and showed, thrust vectoring system as an adequate control authority for pull-up maneuver. Figure 7

illustrates CTAT trajectory for the forth

trim condition in table 5( hrkmu /432= ).

D. Turn; Trim Simulation

Banking turn was the only lateral-

directional flight phase that has been

investigated throughout this study.

Velocity and bank angle were lone

program input pair and AOA, thrust,

thrust deflection angle and turn radius

were achieved by solving the trim

algorithm. Referring table 5, the CTAT

trajectory and routing location are

shown in Fig. 8 for the first trim condition in turn manoeuvre. Additionally, the thrust deflection angles and turn

radius were investigated as a function of bank angle for the

fixed flight speed ( hrkmu /216= ) and presented in table 4.

The results confirm the validity of the equations and the

feasibility of turn manoeuvre.

0100

200300

400500

600700

800900

1000

-150-100-500

Xe (m)

Ye (m)He

igh

t (m

)H

eight

(m)

CTAT Flight Path

Figure 6. Cruise Simulation for the First Static Trim Condition

0200

400600

8001000

12001400

1600

-600

-400

-200

0

Xe (m)

Ye (m)

He

igh

t (m

)

CTAT Flight Path

Figure 7. Pull-up Simulation for the Forth Static Trim Condition

0

20

40

60

80

1000 2 4 6

-100

-50

0

50

Xe (m)

Ye (m)

Heig

ht

(m)

Figure 8. Turn Simulation for the First Static Trim

Condition

Table 4. Turn Radius and Required Thrust

Deflection Angle for Several Banking


8

VI. Analysis of the Required

Secondary Mass Flow Rate

In order to obtain the required

secondary mass flow rate so as to

deflect the main engine exhaust induced

to study the jet behavior after the

exhaust nozzle. As a consequence, a

volume ought to be modeled thanks to

the jet deviation evaluation.

Concerning the nozzle, the exhaust

was ended by means of a divergent

Coanda surface, which the secondary

jet follows in order to vector the

primary flow. It is notable that the FTV

analysis was performed in the x-z plane

in the direction of vectoring component.

Since, the classical and most

efficient well-known nozzles were

designed with a circular cross section, it

was also remarkable to analyze the

circular shape for exhaust nozzle. This

concept is schematically shown in Fig.

9. The nozzle has been modelled with

half of the geometry because of symmetry considerations in x-z plane. The secondary jet was allowed in upper

secondary duct around the nozzle casing in order to produce thrust vectoring in pitch-up direction.

The engine exhaust gases were modelled

as a mass flow inlet assuming that the engine

mass flow rate does not vary whatever the

nozzle shape is. The secondary jet was also

modelled as a mass flow inlet in order to run

simulations knowing the ratio between

primary and secondary mass flow rates.

The volume in which the nozzle exhaust

gases were released had large dimensions

compared to the nozzle in order to obtain the

least volume boundaries influence on the jet

exhaust. Its boundaries were defined as

“Velocity Inlet”(in order to take into account

the aircraft velocity), “Pressure Outlet” and

“Symmetry”, as shown in Fig. 10. A cell centred

Table 5. CTUT Static trim results in longitudinal flight modes

Coanda Surface

Secondary Nozzle

Entrained Air

Figure 9. Half Geometry of the Circular Cross

Section Nozzle

Secondary Jet Inlet

(b) Close-up of nozzle simulation

Figure 10. FTV Nozzle Simulation for CDF Study

Half Nozzle Volume Exhaust

(a) Far-field of nozzle simulation


9

finite volume technique was used to solve the RANS equations. For these equations, the flow was assumed to be

turbulent in all flow-fields and the standard K- ε model was selected to study the effects of turbulence on flow27

.

Figure 11 shows the mass flow rate for variety of FTV angles. It can be deduced from the results that for high

secondary mass flows, fluidic thrust vectoring is more efficient whatever the secondary duct thickness is. At low

secondary mass flow rates, the secondary jet separates early from the Coanda surface. If the secondary duct is thick

enough reverse flow appears whereby primary jet is vectored in the opposite direction as the expected one.

Using the second order trend line, a

relationship was found between the thrust

vector angle and the secondary required

mass flow, to produce this vector angle.

This is shown as a data label in Fig. 11.

Also, by putting together the results

obtained in trim part and the results obtained

in this section, the quantity of required

secondary mass flow rate was easily

identified in each flight condition to trim the

aircraft in that point. This means that, as a

case study, if CTAT is cruising at the speed

of 288 km/h in steady state condition, the

required mass flow rate to keep the vehicle

trim would be 13.86 percent of primary

mass flow for each engine, which makes

13.81 degree thrust vectoring angle.

Figure 11 also shows that at very low

secondary jet blowing rates, i.e. ps mm && 12.1< , there will be a dead zone, where no thrust vectoring and control

power exists. Since, one of the most efficient ways to provide the secondary air was through the engine bleeding, the

effects into engine performance were also predicted using a gas turbine performance simulation program. This

program was run for different bleeding air percentages. It was assumed that the turbine entry temperature remained

constant. The result is presented as a graph in Fig. 12. In general, bleeding air results in a changeover of engine

performance.

VII. Concluding Remarks and Future

work

The purpose of the air vehicle dynamic

role is to ensure that the vehicle is

controllable and has a satisfactory flight

performance. As a prelude for such a great

trip, a longitudinal and lateral-directional

trim ability of a conceptual aerial vehicle,

named CTAT, using Co-flow fluidic thrust-

vectoring system was studied throughout

this paper. The results show that CTAT trim

is feasible in flight phases including take-off , cruise, pull-up and blunt banking turn, demanding thrust vector angles

up to 30 degree. Moreover, according to he results presented in take-off and pull-up sections, transition flight from

vertical mode to horizontal mode and vice versa seemed possible for the novel configuration presented in this study.

Furthermore, it was obtained that required secondary mass flow rate, for the studied nozzle, is a second order

polynomial of thrust-vectoring angle and the “dead zone” appears at low secondary mass flows. In addition,

bleeding this secondary air from the engine will lead to the less efficient engine and severely reduces the thrust.

It is worthwhile to point out that the Coanda surface radius, secondary jet blowing rate, secondary nozzle height

and the nozzle shape were the main elements determining the efficiency of Co-flow fluidic thrust vectoring. This

study investigated a very limited number of those parameters to verify the effectiveness of Co-flow technique and no

attempt was made to optimize the configuration as well as the dynamic performance. A related study is in process to

investigate the flight dynamic view of this concept and also the efficiency of such a system for different types of air

vehicles. Moreover, future studies are planed to obtain an optimal Coanda surface geometry and secondary slot size

to achieve the maximum thrust-vectoring angle.

Figure 11. Thrust Vectoring Efficiency Versus

Secondary Mass Flow (real result and the trend line)

Figure 12. Thrust Efficiency Versus Compressor Bleeding Air


10

Acknowledgments

A. B. Author would like to acknowledge the British Council and Shell Company for their kind financial support

as a partial scholarship, during the sabbatical year at Cranfield University.

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