Effects of Leader’s Position and Shape on                               
Aerodynamic Performances of V Flight Formation 
H.P.Thien, M.A.Moelyadi, and H. Muhammad 
 
Aeronautics and Astronautics Department  
Bandung Institute of Technology 
Ganesha 10, 40132, Bandung, Indonesia 
e-mail: moelyadi@ae.itb.ac.id 
Phone:+62 – 22 - 2504529 
 
 
Abstract 
The influences of the leader in a group of V – flight 
formation are dealt with. The investigation is focused on the 
effect of its position and shape on aerodynamics 
performances of a given V – flight formation. Vortices 
generated the wing tip of the leader moves downstream 
forming a pair of opposite rotating line vortices. These 
vortices are generally undesirable because they create a 
downwash that increases the induced drag on leader’s wing. 
However, this downwash is also accompanied by an 
upwash that can beneficial to the follower’s wing flying 
behind the leader’s one, namely a favorable lift for the 
follower’s wing. How much contributions of the leader’s 
wing to the follower’s wing in the V – formation flight is 
determined by the strength of tip vortices generated by the 
leader’s wing which is influenced by its position and shape 
including incidence angle, dihedral angle, aspect ratio and 
taper ratio.  
The prediction of aerodynamic performances of the V – 
flight 
formation 
including 
lift, 
drag 
and 
moment 
coefficients is numerically performed by solving Navier – 
Stokes equations with k - ε turbulence model. The 
computational domain is defined with multiblock topology 
to capture the complex geometry arrangement of the V – 
flight formation. 
Nomenclature 
L , L′  
lift and the rotation of original lift 
D , D′  
drag and the rotational of original drag 
P  
power 
L
C ,
D
C  coefficient of lift and drag 
α  
angle of attack 
b 
wing span 
Δ  
change in parameter 
WTS  
wing tip spacing 
Subscript 
FF  
formation flight  
BL  
baseline 
1 
Introduction 
Formation flight can result in large induced drag reductions. 
By doing the V – shape formation consisting of 25 
members, each bird can achieve a reduction in induced drag 
as large as 65% that could result in a range increase about 
70% [1]. The full advantage of bird formation flying can be 
obtained by combining the variability of bird’s wings and 
their highly controllable flight, which allow them to change 
their wing geometry as well as fly very close together.  
The leader of an acute V formation saves less energy than 
the trailing participants do. The disadvantage of leading is 
reduced in more obtuse formations, and when the 
longitudinal distance between neighbor is small [2]. 
This paper presents an analysis of the effect of the leader to 
the aerodynamics performance of V – flight formation 
consisting of three members using the numerical simulation 
method, computed on simple wing model. The first section 
of the paper will focus on review of previous works on 
formation flight research as well as on the basic theory of 
this favor aerodynamic interference phenomena.  
The computational aerodynamics of wings in formation 
flight will be dealt with in the second section of this paper 
including discretized the computational domain and solve 
the governing flow equation. Then, result analyses together 
aerodynamics characteristics are described.  
2 
Background  
2.1 State of art  
Formation flight has been studied frequency in the past 
several decades. There have a numbers of researchers 
interested in the bird as well as airplane formation flight, 
and they have had various degree of success.  
In the early of 1970s, Schollenberger and Lissaman 
investigated the formation flight of bird; their analysis 
showed that induced drag reduction of each bird in an arrow 
formation could reach the number of 45%, compared with 
another one in solo flight [1]. Hummel [3] derived a theory 
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of optimal wing tip spacing to obtain the maximum 
reduction in induced power required, the optimum wing tip 
spacing that maximizes induced power saving will be a 
negative value, which can only be achieve in the V 
formation. Beukenberg and Hummel [4] gave flight test 
data for three aircraft flying in an arrow formation, and 
compared it to the theoretical aerodynamic results obtained 
with various vortex models. 
Recently, formation flying has again become of interest.  At 
Virginia Polytechnic Institute and State University, Iglesias, 
S. carried out the study on investigating the effect of 
relative distance in the three dimensions to the induced drag 
reduction and found out the corresponding spanloads for a 
group of aircraft in an arrow formation [5].  
Formation flight theory has been validated by analytical 
studies and recent autonomous formation flight. For 
example, Fowler, J.M. and Andrea, R.D. [6] conducted an 
experiment on large formation of 31 wings, the result 
showed that induced drag reduction was as much as 41%. 
NASA Dryden Research Center did the formation flight test 
on two F/A – 18 aircrafts which have the same 
configuration. Significant performance benefit have been 
obtained from the flight test phase, such as drag reduction 
of more than 20% and fuel flow reduction of more than 
18% has been measured at flight condition of Mach 0.56 
and altitude of 25000ft [7]. 
2.2 Basic theory  
The dominant aerodynamic forces that affect flight are lift 
and drag. The difference in the pressure of air above and 
below a wing produces lift. When a wing is hold at a sight 
angle to an air current, air flows faster over the upper 
surface than it does over the lower surface, thus creating 
less pressure above the wing than below it and causing lift. 
At the same time, drag, or resistance to the moving air, 
drags the wing backward. The combined effect of these two 
forces lifts the wing and drags it backward.  
The pressure difference between the upper and lower 
surface also causes a spanwise flow of air outward toward 
the tips on the lower surface, around the tips and inward 
toward the center of the wing, this motion creates what is 
called a wingtip vortex. Combined with the free stream 
velocity, this spanwise flow produces a swirling motion of 
the air trailing downstream of the wing. This motion is 
referred to as the wing’s trailing vortex system.  
Immediately behind the wing, the vortex system is shed in 
the form of a vortex sheet, which rolls up rapidly within a 
few chord lengths to form a pair of oppositely rotating line 
vortices. Looking in the direction of flight, the vortex from 
the left wing tip rotates in a clockwise direction; the right 
tip vortex rotates in the opposite direction. 
Figure 1 shows the vortices system in a finite wing. The 
principle effect of the trailing vortex system is that it 
reduces the angle of attack of each section by a small 
decrement known as the induced angle of attack 
i
α . The 
lift vector for a wing section is seen to be titled rearward 
through the induced angle of attack. This component, 
integrated over the wingspan, results in the induced drag.  
 
 
 
Figure 1: 
Regions of upwash and downwash created 
by trailing vortices 
Vortices are generally undesirable because they create a 
downwash that increases the induced drag on a wing in 
flight. However, this downwash is also accompanied by an 
upwash that can be beneficial to a second wing flying 
behind and slightly above the first.  
The common theory on formation flight states that drag 
reduction is actually attained because of the rotation of the 
lift vector that occurs while the rear wing is in the effect of 
the front airplane [7]. 
Figure 2: 
  Rotation of resultant force cause by 
upwash of the leading airplane 
Figure 2 show the rotation of resultant aerodynamic force 
caused by upwash of the leading wing. The rotation of lift 
and drag value are presented by 
'
L and 
'
D . Primary 
assumption in this derivation is that lift is much greater than 
drag and the increase of angle of attack 
α
Δ
is sufficiently 
small enough so that the approximations in trigonometry 
can be used with a great level of accuracy [7].  
Due to the traditional bookkeeping methodology, the actual 
lift and drag values are maintained relative to the vehicle’s 
global, rather than local flight path during formation flight. 
As a result, the resultant aerodynamic force remains 
constant because the upwash only rotates this force.  
 
2
2
2
2
L
D
L
D
′
′
+
=
+
 
(1) 
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The change in lift and drag due to the rotation of the lift 
force is  determined as 
 
(
)
sin
L
D
α
Δ
=
Δ
 
(2) 
 
(
)
sin
D
L
α
Δ
=
Δ
 
(3) 
The lift and drag in formation flight is obtained by 
 
(
)
cos
FF
D
D
D
α
′
=
Δ
+ Δ
 
(4) 
 
(
)
cos
FF
L
L
L
α
′
=
Δ
+ Δ
 
(5) 
Because lift tends to be an order of magnitude greater than 
drag L
D
≥
, so drag is influenced more by the rotation 
effect than lift  
 
(
)
(
)
sin
sin
L
D
α
α
Δ
≥
Δ
 
(6) 
Substituting eqs. (2) and (3) into (6), it becomes 
 
D
L
Δ
≥Δ
 
(7) 
A considerable reduction in drag can be obtained by a small 
upwash angle while an insignificant increase in lift 
simultaneously occurs.  
Percent drag reduction is determined as 
 
(
)
/
1
/
BL
FF
BL
Percent drag reduction
D D
D
D
=Δ
= −
 (8) 
Equation for calculating the power reduction is expressed as 
 
(
)
/
1
/
BL
FF
BL
Percent power reduction
P P
D
D
=Δ
= −
 (9) 
The flowing paragraph focuses on analysis the effect of the 
distances between members in an arrow formation flight 
consists of three aircrafts,   including streamwise, spanwise, 
and vertical distance, on the induced drag reduction.  
According to Munk’s theory, the change in induced drag 
coefficient for each aircraft will be changed as the 
streanwise relative distance is changed but the total induced 
drag for the formation is not changed, namely the formation 
induced drag is independent of the streamswise location of 
the airplane. 
 
Considered for each aircraft, the induced drag coefficient 
are highly dependent on streamwise position as the aircrafts 
are close together. For a streamwise distance between two 
aircrafts greater than three spans, the induced drag in each 
aircraft reaches a steady value and no longer depends on 
streamwise separation.   
On the aspect of spanwise separation, the formation induced 
drag is highly dependents on this parameter. The maximum 
induced drag reduction occurs at a negative wing tip 
spacing value [8]. However, beyond a critical negative 
spacing, the following aircraft starts to fly in the central 
downwash and experiences a negative saving. Conversely, 
for a wing tip spacing of one span, the drag saving are very 
small and formation flight is no longer beneficial.  
The formation flight achieves the maximum drag reduction 
value when the aircrafts are on the same horizontal plane, 
namely no separation in vertical direction.                                           
In summary, the formation induced drag reduction is 
independent of the streamwise position of aircraft. The 
maximum reduction is obtained at negative wing tip spacing 
and zero vertical separation.  
According to Hummel [9] the optimum of wing tip spacing 
that maximizes the induce power saving will be a negative 
value, expressed as 
 
(
)
0.5
1 0.89
optimum
WTS
b
=
−
 
(10) 
3 
Numerical Simulation Method for Formation 
Flight Aerodynamics Analysis 
This section describes two main steps of the numerical 
simulation method that is used to find the solution for 
formation flight problems in this research; domain 
discretization  and flow field properties evaluation. The 
dicscretization of domain of interest is performed by 
generating mesh using the available grid generator. Then, 
flow field properties are obtained by solving the Navier – 
Stokes equations with k - ε turbulence model.  
3.1 Formation flight model definition  
The following paragraph depicts clearly the formation flight  
models that used in this research.  
Each bird in a V – shape formation flight consisting of three 
members will be treated as a simple wing. Different leading 
wing configuration is used while the two same trailing 
wings are kept intact. All of wings use the same airfoil. 
Table 1. The characteristics of the trailing wings  
Airfoil 
NACA9405 
Span  
1.6m 
Chord 
0.16m 
Aspect ratio 
10 
Taper ratio  
1 
Sweep angle  
0deg 
 
The same configuration will be used for the whole wings in 
the investigation of the effect of incidence and dihedral 
angle of the leader to the aerodynamics performance. Three 
cases of incidence angle; 0, 5, 10 will be dealt with for 
analyzing the effect of incidence angle. The effect of 
leader’s position in terms of dihedral angle is conducted by 
doing the computational simulation on formation model 
with different leading wing dihedral angle, which is 0deg, 
20deg and 45deg.  
An aspect ratio of 10 together with an aspect ratio of 6, 
which is obtained by varying only the span are used for 
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leading wing model in the study of leader’ shape effect in 
terms of aspect ratio.  
In the other case of leader’s shape effect, three values of 
taper ratio; 0, 0.3 and 0.5 are obtained by varying the chord 
along the span, that is the same with the trailing wing’s. 
One the wings configuration is established, it is necessary 
to consider the relative position between wings in formation 
group. This relative position is kept to be same for all of  
formation cases mentioned above. The arrangement of 
formation is symmetric, illustrated in figure 3. Distance 
between wings in three directions are showed in table 2, 
these distance includes: 
• 
Streamwise distance: distance between the trailing 
edge of the front wing to leading edge of the rear 
wing, measured in the streamwise direction. 
• 
The spanwise distance: the spacing between two 
wing tips, measured in the spanwise direction.  
• 
Vertical distance, preferred to the distance between 
sections at the middle of wings, measured in the 
vertical direction.  
 
 
Figure 3: 
Geometry arrangement in V formation  
 
Table 2. Wings relative position 
Stream wise 
Spanwise (wing tip spacing) 
Vertical 
0.16 m (1C) 
0 
0 
 
3.2 Topology definition 
The procedure of mesh definition in computational domain 
is initiated with the geometry definition. Then, a initial 
block is obtained based on a suitable topology. Multi-block 
technique together with modificative tool such as splitting 
block, merging the block , O – grid block are used to 
achieve a more precise block topology with the complex 
geometry arrangement of V formation flight. The topology 
and blocks of the basic case of V formation is presented in 
figure 4.  
Distribution of points along the edges of the block is carried 
out as the prepared step for mesh generation. A significant 
numbers of points are distributed in critical regions such as 
on leading edge, trailing edge, streamwise and spanwise 
section of the geometry. The point distribution is also 
different for these above mentioned sections, it becomes 
denser when the points approaching the body surface. The 
mesh generation for the wings in V – formation is exhibited 
in figure 5.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4: 
Topology of formation flight model 
 
 
 
 
 
 
 
Figure 5: 
Mesh generation for wings in V formation 
model  
3.3 Solver definition  
The solver based on solution of the Navier – Stokes 
equations with k - ε turbulence model is used to obtain the 
flow field properties.  
 
 
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4 
Results and Discussions 
Lift, drag and moment of each member in a group of three 
wings flying in an V – shape formation will be found, and  
these coefficients will be compared as a function of shape 
and position of the leading wing, including incidence angle,  
aspect ratio, dihedral and taper ratio.  
4.1 Incidence angle and Aspect ratio effect  
The incidence angle i , showed in figure 6 will be varied 
from 0 to 5 and 10deg, the variation in lift and drag saving 
will be studied as a functions of this angle.  
 
 
 
 
Figure 6: 
Incidence angle between two wings 
Figure 7, 8 and 9 shows the change in total lift, drag and 
pitching moment for each wing in formation as the relative 
incidence angle is changed. The results are shown as the 
ratio of these values in the formation to their corresponding 
values when flying a lone.  
  
 
 
 
 
 
 
 
 
 
Figure 7: 
Effect of leader’s incidence angle on lift 
 
 
 
 
 
 
 
 
 
 
Figure 8: 
Effect of leader’s incidence angle  on drag 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 9: 
Effect of leader’s incidence angle on 
pitching moment 
Wings in formation get the benefit of increase in lift due to 
the effect of the leader’s upwash. As a result, a wing flied in 
a formation group will able to get a higher lift compared 
with a same wing in alone flight. The lift increase in trailing 
wing is directly proportional to the incidence angle of the 
leader, while the increase lift in the leading wing tends to 
decrease with the increase of its incidence angle.  
Aspect ratio also influences the lift increase; a low aspect 
ratio leading wing leads to a high lift increase in trailing 
wings. The difference in lift increase can achieve up to 10% 
for a wing has aspect ratio of 10 compared with a wing with 
aspect ratio of 6 at the same angle of incidence.  
In terms of drag saving, the aspect ratio nearly has a weak 
influence. An inappreciable different between drag ratio on 
the rear wing with different front wing aspect ratio at the 
same incidence angle can be observed in the figure 8. 
Maximum value of this difference is about 0.5%. On the 
contrary, the incidence angle of the leading edge is highly 
effects on the saving of drag in the rear wing. The effect is 
taken place in the trend that reduces the drag ratio of the 
wing in formation and wing in alone flight as the incidence 
angle of the leader increases, it means that rear wing will 
get a higher drag saving as increase the leader’s incidence 
angle.  
The pitching moment on rear wing of formation, also 
caused by the lift and drag, tends to increase as the leading 
wing’s incidence angle increase because the prevailingness 
of lift increase over the drag reduction tends to increase.  
The effect of aspect ratio on change of rear wing pitching 
moment is significant, as the leader’s aspect ratio decreases 
the three-dimension effect on lift and drag increase.  
In summary, aspect ratio of the leader affect the change of 
lift and moment on rear wing of formation, its effect to the 
drag reduction is insignificant. Leading wing’s incidence 
angle has a highly influence on the change of lift, drag and 
pitching moment.  
 
Effect of Leader's Incidence Angle on Drag
0.8
0.85
0.9
0.95
1
0
2
4
6
8
10
Incidence Angle (deg)
CD(formation)/CD(single)
Front wing, AR = 10
Rear wing, AR front wing = 10
Front wing, AR = 6
Rear wing, AR front wing = 6
Effect of Leader's Incidence Angle on Lift 
1
1.05
1.1
1.15
1.2
0
2
4
6
8
10
Incidence Angle(deg)
CL(formation)/CL(single)
Front wing, AR = 10
Rear wing, AR front wing = 10
Front wing, AR = 6
Rear wing, AR front wing = 6
Effect of Leader's Incidence Angle on Pitching Moment
0.95
1
1.05
1.1
1.15
0
2
4
6
8
10
Incidence Angle(deg)
CM(fomation)/CM(single)
Front wing, AR = 10
Rear wing, AR front wing = 10
Front wing, AR = 6
Rear wing, AR front wing = 6
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4.2 Dihedral angle effect 
The dihedral angle of the leading wing is varied from 0 to 
20 and 45deg while the rear wings’ dihedral angle are kept 
to zero. Figure 10, 11 and 12 shows the effect of dihedral 
angle of the leading wing on the wings in formation in 
terms of lift, drag and pitching moment.  
 
 
 
 
 
 
 
 
 
Figure 10: 
Effect of leader’s dihedral angle on lift 
 
 
 
 
 
 
 
 
 
Figure 11: 
Effect of leader’s dihedral angle on drag 
 
 
 
 
 
 
 
 
 
Figure 12: 
Effect of leader’s dihedral angle on 
pitching moment 
Figure 10 shows the behavior of the lift ratio of rear wing in 
formation and in alone flight to the dihedral angle of the 
leader. This ratio increases considerably at low value of 
dihedral angle, and changes a little, as the angle is higher.  
 
In the respect of drag reduction, the leader’s dihedral angle 
acts an adverse effect on the amount of drag saving in the 
rear wing of formation. Rear wing drag reduction seems to 
linear decrease as the dihedral angle increase. At high value 
of dihedral angle, the effect of the leader on the rear wings 
in term of drag reduction no longer exists; the drag on both 
leading wing and rear wing is nearly same with their value 
as flying alone.  
Figure 12, presents the change in pitching moment ratio as 
the dihedral angle of the leader is varied. On rear wing, 
pitching moment ratio increases significant at low leader’s 
dihedral angle.  As the angle is higher, the rear wing nearly 
maintains its pitching moment ratio. 
4.3 Taper ratio effect 
Leading wing with different taper ratio, namely, 0, 0.3 and 
0.5 are used to survey the effect of leader shape on the 
aerodynamic forces and moment of wings in V – formation.  
The results of this survey are shown in figure 13, 14 and 15 
as the ratio between the lift, drag and pitching moment on 
leading wing and trailing wing in V – formation to the 
corresponding ones in alone flight. 
Figure 13 shows that at low taper ratio the ratio in lift of 
rear wing in formation and in alone flight increase as the 
taper ratio increase. For high taper ratio, the rear lift ratio 
tends to decrease. Lift ratio is smallest as the leader has the 
rectangular platform (taper ratio of 1). 
 
 
 
 
 
 
 
 
 
Figure 13: 
Effect of leader’s taper ratio on lift 
 
 
 
 
 
 
 
 
 
Figure 14: 
Effect of leader’s taper ratio on drag 
Effect of Leader's Dihedral Angle on Lift
1
1.05
1.1
0
10
20
30
40
50
Dihedral Angle (deg)
CL(formation)/CL(single)
Front wing
Rear wing
Effect of Leader's Dihedral Angle on Pitching Moment
0.95
1
1.05
1.1
0
10
20
30
40
50
Dihedral anlge(deg)
CM(formation)/CM(single)
Front wing
Rear wing
Effect of Leader's Dihedral Angle on Drag
0.85
0.9
0.95
1
0
10
20
30
40
50
Dihedral Angle(deg)
CD(formation)/CD(single)
Front Wing
Rear wing
Effect of Leader's  Taper Ratio on Lift 
1
1.03
1.06
1.09
1.12
1.15
0.2
0.4
0.6
0.8
1
Taper ratio
CL(formation)/CL(single)
Front wing
Rear wing
Effect of Leader's Taper Ratio on Drag
0.85
0.88
0.91
0.94
0.97
1
0.2
0.4
0.6
0.8
1
Taper ratio
CD(formation)/CD(single)
Front wing
Rear wing
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The increase of leader taper ratio has positive effect to the 
drag saving of the rear wing in formation. As a result, 
rectangular platform of the leading wing will give the 
highest drag reduction in rear wing.  
 
 
 
 
 
 
 
 
 
Figure 15: 
Effect of leader’s taper ratio on pitching 
moment 
The behavior of the pitching moment on the rear wing in V 
formation is the same with the behavior of lift as the 
leader’s taper ratio is varied. Pitching moment ratio on rear 
wing reduces significant, as taper ratio is higher.    
5 
Conclusions 
Investigation on the effects of the leader’s shape and 
position on aerodynamics performance of V formation is 
conducted by using the numerical simulation method.  
Leader wing with variation in shape and position parameter 
including incidence angle, dihedral angle, aspect ratio and 
taper ratio is used to find out the behavior of lift, drag and 
moments on the same rear wing.  
Some conclusions can be listed as follows:  
• 
Incidence angle has a positive effect on increasing 
the lift, pitching moment, and reducing the drag and 
of the rear wing. 
• 
Aspect ratio has a significant effect on increasing 
the rear wing lift and pitching moment, but seems 
to be no effect to the drag reduction.  
• 
Dihedral angle has an adverse effect on drag saving 
in the rear wing. The change in lift of the rear wing 
is nearly constant at high value of dihedral angle. 
• 
Taper ratio is positive effect to the drag reduction, 
and its effect on the change of lift is also 
considerable.  
• 
The behavior of lift and pitching moment are nearly 
the same in all cases of this investigation.   
 
 
 
 
References 
[1] Lissaman, P.B.S. and Schollenberger, “Formation 
Flight of Bird”, Science, vol. 1968, pp. 1003 – 1005, 
May, 1970.  
[2] Malte, A. and Wallander, J., “Kin selection and 
reciprocity in flight formation”, Behavioral Ecology, 
vol. 15 No 1: 158 – 162, 2004 
[3] Hummel, D., “Die Leitungsersparnis in Flugformation 
von Volgeln mit Unterschieden in Grobe, Form and 
Gewich”, J. Orn., Lpz 119, 52 – 73  
[4] Beukenberg, M., Hummel, D., “Aerodynamics, 
performance and control of airplanes in formation 
flight,” 
Technische 
Universität 
Braunschweig, 
Brunswick, Federal Republic of Germany. ICAS-90-
5.9.3, Congress, 17th, Stockholm, Sweden, Sept 1990. 
[5] Iglesias, S. and Mason, W.H., “Optimal spanloads in 
formation flight” AIAA, 2002 
[6] Fowler, J. M.,  Andrea, R. D., “Distributed Control of 
closed Formation Flight” Conference of Decision & 
Control, Las Vegas, Nevada USA, December, 2002 
[7] Ray, R.J., Cobleigh, B. R., Vachon, M. J. and John, C. 
S., “Flight Test Techniques Used To Evaluate 
Performance Benefits During Formation Flight”, 
NASA Dryden Flight Research Center, California 
[8] Cutts, C.J. and Speakman J.R., “Energy Saving In 
Formation Flight  of Pink – Footed Geese”, J. Exp. 
Biol, 189, 251 – 261, 1994 
[9] Hummel, D, “Aerodynamics Aspects of Formation 
Flight in Birds”, J. Theor. Biol. 104, 321 - 347 
 
Effect of Leader's Taper Ratio on Pitching Moment
0.95
1
1.05
1.1
0.2
0.4
0.6
0.8
1
Taper ratio
CM(formation)/CM(single)
Front wing
Rear wing
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