AIAA Student Paper submission from Senior Design for our Biologically Inspired Aircraft

1. Unconventional and Morphable Biologically-Inspired
Aircraft Control Elements
Alan Brown, Aaron Bowe, Jamar Dawson, Seung Eun, Alex Gura,
Keena Holley, George Locklear, Jeremy Loman, Jason Morgan, and David Vickery1
Department of Mechanical and Aerospace Engineering
North Carolina State University
Raleigh, NC 27695
Research and experimentation suggest that the modification of conventional aircraft
design features by incorporating biologically inspired technologies can result in performance
enhancements. Several biologically inspired features were implemented in an effort to improve the
performance of a pre-existing aircraft. A Hobbico Nexstar EP trainer aircraft was used as a base
model on which to employ unconventional bio-inspired wing and tail designs. The wing design
incorporates morphing/variable geometry technologies and was directly inspired by basic anatomy
and characteristics of bird wings. Flexible skins with shape memory alloy actuators were used to
provide roll control and lift augmentation through continuous deformation of the primary lifting
surface airfoil. A sweep-adjustable outer wing consisting of thin overlapping feather surfaces was
used to provide yaw control and flight adaptability, though the former was found to be less
productive than desired.
Inspired by the efficiency and apparent simplicity of bird tails, a gimbaled tail was
developed without the use of a vertical stabilizer. A combination of pitch and rotation applied to a
simple NACA0012 tail geometry allows for complex, multiple degree of freedom motion in an
attempt to mimic bird tail movements and compensate for the vertical stabilizer omission. Loss of
flight stability is determined to be excessive compared to the relative improvements in
maneuverability. Much additional research is required for the successful integration of both system
designs, performance optimization, and quantitative analysis of performance improvements.
Additional design features are considered for future applications that may enhance and/or
supplement the current design.
NOMENCLATURE:
α = Angle of attack
Cl = Life coefficient
Cl,α = Lift coefficient per angle of attack
Cm = Pitching moment coefficient
Cm,α = Pitching moment per angle of attack
Cm,δ = Change in pitching moment per elevator deflection
Cmo = Pitching moment when the plane is at an angle of attack of zero
δ = Elevator deflection angle
h = Center of gravity as percent chord
hn = Neutral point as percent chord
I = Electric current
q = Dynamic Pressure
R = Resistance
V = Voltage
1
North Carolina State University, Mechanical and Aerospace Engineering, Box 7910, Raleigh, NC 27695

2. I. Introduction
Throughout history man has maintained a unique fascination with the natural aviators of our skies, creatures that
have evolved over time to become practically perfected flying machines. Humanity’s earliest attempts at flight were
often limited to pure imitation, with little to no understanding of the physical principles that make it possible. As we
progressed our fundamental understanding of the science involved, the reality of manned flight was realized.
Dominated by rigid, mechanical systems, the evolution of manmade aircraft seems to have little in common with the
natural flyers that provided the initial spark of inspiration (due largely to technological limitations of the structures
and materials available, etc.)
However, recent years have seen major advancements in areas such as material science and microelectronics and
allow for a much broader range of design possibilities. Strong, flexible and lightweight materials show an incredible
potential for aerospace applications and allow for nature to once again be used as a feasible source of inspiration in
designing new technologies. This is especially evident in a growing area of interest in the aerospace industry –
morphing. Morphing involves a seamless shape change, unlike the discrete, mechanical morphing typically seen
through the use of flaps and ailerons. Many researchers (see Namgoong, et. al. 1, Kornbluh, et. al.2) have begun
looking into various morphing technologies such as foldable, warpable, or twistable wings, continuous camber
change, etc.
This study aims to assess the characteristics and feasibility of several biologically-inspired control surface
modifications/additions to a standard RC trainer aircraft (Hobbico Nexstar EP). Primary design criteria involved
including unconventional technologies (morphing, etc.) inspired by basic principles of bird flight and anatomy,
while also striving to improve the overall performance and efficiency of the aircraft.
Entirely new wing and tail systems were developed through the application of the established design criteria just
mentioned. The wing design, directly based off basic bird anatomy, incorporates a rigid inner section to serve as the
primary lifting surface and an independent, variable-geometry outer wing section for auxiliary control. Avian
anatomy also influenced the decision to eliminate a vertical stabilizer, a major design challenge that required
innovative solutions and lead to the unique design of a multi-degree of freedom tail surface.
II. Continuous Deflection with SMA Actuation
Traditional remote controlled aircraft utilize hinged flaps on the wings actuated by servos to provide lift
augmentation and roll control. Deflecting the flap effectively changes the airfoil camber, thereby increasing lift
production. However, this discrete mechanical change is not typically found in nature. Rather, birds use passive
shape modifications through the muscles and feathers in and along the wing to provide control while gliding. The
design goal was to replace the servo-hinge system and attempt to mimic the capabilities of avian wings in order to
increase aerodynamic efficiency and performance of roll control.
A. Continuous Deflection
The aerodynamics with which the design is concerned is
that influenced by low Reynolds numbers. It has been shown
that, except for very thin airfoils, the range of angle of attack
within which the aerodynamics is satisfactory decreases with
decreasing Reynolds number, but that a modest camber can
allow for significant aerodynamic improvements when
compared relative to similar airfoils with no camber (higher lift
curve slope, greater maximum lift and maximum lift to drag
ratio)3. The inner-wing incorporates the highly cambered S1210
high-lift, low Reynolds number airfoil which is necessary in
providing sufficient lift with the relatively small planform area.
Using the original Nexstar model wing as a comparison, two
distinct advantages of our wing design are realized. First, XFoil
analysis for the rigid wing suggests significant and necessary
improvements in the lift curve slope (slightly more inclined),
maximum lift coefficient and lift coefficient at zero angle of
attack. Theoretical lift calculations are promising in that the lift Figure 1. Continuous Surface during
provided by the inner-wing exceeds or matches that provided (a) rest; (b) deflection

3. by the entire Nexstar wing up to the S1210 stall angle. Second, the drag polar displays a favorable box shape
indicating a minimal drag penalty for increasing lift up to a precipitous increase in drag in the post-stall region.
In order to promote drag reduction, the inner-wing control surface camber is adjusted through a continuous
surface deflection/morphing rather than using discrete flap actuation. Eliminating any span-wise breaks in surface
continuity serves to maintain a smoother flow over the wing, thereby increasing overall lifting efficiency. Although
unable to deform the entire inner-wing span, the majority of the surface is variable with a large flap-to-chord ratio
(~0.7) covering 85% span. The large flap-to-chord ratio is beneficial in that it provides a greater moment arm for
the SMA actuators, reducing the necessary power required, as well as improving the chord-wise uniformity of
deformation. Additionally, the relative lack of internal structure afforded by the nature of the design greatly reduces
the overall system weight. XFoil analysis also suggests that a larger flap-to-chord ratio requires less
deformation/actuation to provide similar performance relative to those of more modest control surfaces.
B. SMA Characteristics
Shape memory alloys (SMAs) are alloys that remember their original shape and, after deformation through heat
application, return to that shape upon cooling. SMA wires contract by several percent of their length when heated
and can be easily stretched when cooled back to room temperature. Upon contraction, unlike ordinary thermal
expansion, they exert tremendous amount of force for its small size (at least around 25,000 psi). This makes SMA
actuators ideal for use in applications that require large movement. SMA actuators have an excellent power to mass
ratio and are quite reliable in general, producing enough deformation to cause significant improvement in the static
and dynamic characteristics of the inner wing design.
Three five-inch long SMA wires (Nickel-Titanium alloy) with 0.005-inch diameter are evenly mounted across
each flap. The inner wing is covered with a series of span-wise panels, and the SMA wires are attached to the rear,
upper panel, which has its front end pinned at 70% chord. The method of pinning the rear, upper panel to the airfoil
underneath the panel upstream of it applies a reaction moment that makes the rear panel act as though it is
effectively cantilevered, and by pulling on the cantilevered fiberglass panel from an acute angle, the component of
the bias force due to the fiberglass deformation is made to decrease as the contraction of the wire adjusts the
curvature of the final panel. Upon applying electric current which leads to heat conduction in the SMAs, the trailing
edge of the rear, top panel drops slightly, and in doing so it pushes the back of the rear, lower panel down as well,
resulting in a maximum trailing edge deflection of approximately 13˚.
1. Sample Bend Tests
The continuous flap is constructed from molded fiberglass panels. In order to determine the most effective skin
thickness a series of 4”x4” material coupons were fabricated from 2oz fiberglass and evaluated in a simple bench-
top force test. Samples were mounted horizontally along one edge. A force gauge was mounted to the free side
perpendicular to the sample. Force was applied until the sample deflected 20 degrees (1.25”). At this point the
force required was recorded and converted into an equivalent force exerted by the SMA. Table 1 shows the sample
data and force results. The five layer sample was selected for additional testing due to its compromise between
material weight and deflection force required.
Test Sample Force Equivalent 5" Total Force
Deflection
Length Weight Reading SMA Force for 18” Flap
(deg)
(in) (oz) (lbs) (lbs) (lbs)
2 oz X 3 3.375 0.168 20 0.063 0.258 1.302
2 oz X 5 3.375 0.319 20 0.125 0.515 2.319
2 oz X 7 3.375 0.503 20 0.563 2.319 10.276
Table 1. Flap skin sample testing characteristics. Increasing number of fiberglass layers increases
pull force required. There is a significant weight increase between 5 and 7 layers.
2. Deflection Testing (Static and Dynamic)
To evaluate the mechanism effectiveness using SMAs a test rig was constructed. The test rig had an S1210
airfoil with 10” chord, 24” span, and an 8”x18” aileron. Three SMAs were mounted to the upper surface skin and
connected in parallel to an adjustable power source. A static bench-top test was performed first to establish the
general effectiveness. The flap deflection values from this test are recorded in figure 2.

4. q Velocity Velocity Deflection
(psf) (fps) (MPH) Rating
0.00 0.00 0.00 Substantial
0.50 20.51 13.98 Substantial
1.00 29.01 19.78 Substantial
1.50 35.53 24.22 Substantial
2.00 41.02 27.97 Substantial
2.50 45.86 31.27 Substantial
3.00 50.24 34.25 Moderate
3.50 54.27 37.00 Low
4.00 58.01 39.55 Low
4.50 61.53 41.95 Concerning
Figure 2. Inner wing camber deflection at various Table 2. Inner wing camber deflection at various
voltage inputs. Flap deflection angle increases linearly voltage inputs. Flap deflection angle increases
with the amount of current input to the SMAs. linearly with the amount of current input to the SMAs.
The deflection performance of the SMAs and flap design was then tested in the North Carolina State Subsonic
Wind Tunnel in a range of dynamic pressures from 0.0 to 4.5 pounds per square foot (psf). Run dynamic pressure,
wind speed, and flap deflection at maximum amperage were collected to establish the flight performance envelope
and can be found in table 2. Flap deflection performed excellently in the 0-2.5 psf dynamic pressure range, while
dropping performance in speeds higher than 3 psf. The team is continuing examination of the flight performance
envelope to ensure consistent control throughout flight.
3. Load Cell Testing
In order to have a better understanding of the actuation, a test for characterization of SMA is done. The
experimental set up will be composed of a SMA wire, load cell, linear variable differential transformer (LVDT), and
a thermocouple. They will be used so that a stress-strain relationship of the SMA wires mounted on the wing can be
determined. The wire is heated using electrical resistive heating and the temperature is monitored using a
thermocouple (K-Type) attached directly to the SMA wire. The load is measured using a load cell (10lb capacity)
while the contraction due to the heating of the wire is measured using the LVDT. The core of the LVDT is mounted
on the SMA wire, and the body of the LVDT is fixed at the base of the set-up. The set-up does not have to be
enclosed by a thermal chamber to prevent the surrounding conditions from influencing the temperature of the SMA
wire, because the wire mounted inside the wing would be performed independent of the surrounding temperature.
C. Design Evaluation
1. Power Usage
Because the SMAs require a different power source than the servos, it is necessary to measure how much power
SMAs would draw for a desirable flight time. The SMAs used in this project have electrical resistance of 1.8 ohms
per inch. The approximate current draw at room temperature is 0.25 amps. This is approximate since room
temperatures, air currents, and heat sinking of the test area varies. The voltage draw is found using Ohm's law,
V = IR (1)
Since six of the SMAs are used, the total current draw would be six times of the current draw of each single
wire, which would be 1500mA. Also, under assumption that the all of the SMAs are fully actuated during flight
time of 30 minutes, the ampere-hour would be,
(2)
It can be concluded that, given the basic characteristics of the SMAs, the battery necessary for proper flight
should have minimal voltages of 2.25 and that batteries with higher mAh will provide extra margin for longer flight
time.

5. 2. Performance
Current flap deflection is limited to approximately 20 degrees (measured relative to trailing edge position) as
seen in the static and wind tunnel tests. While this exceeds typical deflection amounts, this does not match the flap
deflection possible using servo actuation. However, due to the increased size of the flap the effective influence is
still greater than a traditional hinge flap system.
Under no aerodynamic loads the SMAs require approximately one second to actuate full deflection and two
seconds to return to the non-deformed position. However, even with aerodynamic loading, this transition time is
remained constant for deflection and return. This is longer than the sub-second servo actuation time.
III. Morphing Planform through Outer Wing Sweep
A. Feather Design and Rationale
The general shape of the outer-wing incorporates three thin overlapping feathers with a sharp leading edge to aid
in the creation of leading edge vortices (LEVs). Relative to the rigid inner-wing, the feathered outer-wing will have
a slightly positive angle of attack (4-5 degrees) to provide a greater range of lift up to the generally shallow stall
angle of the inner-wing. The unswept outer-wing trailing edge contour from root to tip forms a favorable quarter-
elliptical curve designed to maximize area change between swept and unswept wing configurations (approximately
40% decrease in surface area). The decrease in area leads to a proportional decrease in lift, as well as a reduction in
the resultant moment arm of the lift force, increasing the effectiveness for roll control and stability. The LEVs serve
to augment the lift generation of the outer-wing. It has been shown that large angles of attack result in larger and
more unstable vortex flow, decreasing the benefits in performance. Additionally, the swept wing configuration will
result in generally higher quality vortex generation and sustainability than the unswept wing, therefore improving
lift generation. However, this is counterproductive in that a decrease in lift is desired through the reduction in
surface area and may lead to a decrease in the overall effectiveness of outer-wing roll control. The outer wing
sections were also designed to allow for independent, asymmetric sweep actuation in order to provide a means of
yaw control. The difference in drag produced for the swept and unswept configurations was intended to provide
enough moment for adequate yaw control, however, it was determined that this difference is not sufficient enough to
have a significant effect.
A major design feature of the morphing outer-wing is that it expands the aerodynamic performance envelope of
the aircraft. For example, a symmetrically un-swept configuration provides greater lift and is more suitable for slow
glides and turns. Alternatively, a symmetrically swept wing configuration provides a reduction in drag and is more
suitable for higher speed performances and sharper, more agile turns. In general, the variable wing-sweep design
allows for the potential of energy saving flight adaptation within the expanded range of flight performance. Also, it
is interesting to consider that the outer wing presence reduces the effects of wingtip vortices on the rigid inner-wing
section, allowing the inner-wing to be thought of as “quasi-two-dimensional” thus providing an extra advantage in
aerodynamic efficiency. It is unknown; however, if/how the transition between inner and outer-wing flow fields,
especially possible interactions concerning the outer-wing LEVs, will affect the overall aerodynamic performance of
the entire wing system.
Figure 3. Feather Mount Block and Mechanism Figure 4. Feather Mount Block and Mechanism

6. B. Linkage Design through Structural Analysis
A major design challenge for the outer wing was developing a sweeping mechanism that could be mounted
inside of the inner wing and not fail under aerodynamic loading. An aluminum mounting block serves as the
junction between the feathers and rigid wing (Figure 3). Through a series of mechanical linkages, the feathers are
actuated using a single degree of freedom. A servo is used to translate a linkage arm connecting all three feather
mounts, resulting in a graduated sweeping motion in all feathers. To withstand the high loads exerted on these
joints, the mounting block is constructed out of
machine aluminum. An ANSYS structural
analysis was used to determine stress peaks in
the mount material (Figure 4) and several
design modifications have since reduced the
weight of each aluminum block to .055 pounds.
Using the flight condition of a maximum 5g
force exerted on the feathers (0.99 lbs/in2), the
maximum stress was 8.69e5 psi with a factor of
safety of 6.74.
The design mimics the sweeping motion
exhibited by some birds during flight. The
sweeping mechanism transmits the movement Figure 5. (a) Swept; (b) Unswept Feather Position
from the servo to the swing arm which actuates
the feather via a cord link. The feathers can be swept back to a maximum of 50 degrees and are designed for
continuous collection and to minimize gaps in the swept and unswept positions, as shown in Figure 5.
IV. Tail Design
The major design challenge for the tail section was how to successfully eliminate the vertical stabilizer while
also improving maneuverability and efficiency using unconventional means. The initial design allowed for a 3
degree of freedom system: pitch deflection, axial rotation, and surface area expansion/contraction. Unfortunately,
structural and mechanical issues involved in providing the area change were determined to be too complicated and
the idea was dismissed. The remaining degrees of freedom (pitch and rotation) are realized through the use of the
block mechanism, shown in Figure 6.
Figure 6. (a) Tail Maneuver Mechanism; (b) Universal Joint Movement
A. Tail Motion Mechanism
A micro servo connected to lever arms on either side of the block is used to provide the pitch actuation. The
servo moves the lever arms up and down which are connected to a carbon fiber shaft that provides the support
connection and means of rotation for the tail. Another micro servo is located at the end of the carbon fiber shaft and
is attached via washer and servo rods to produce an axial rotation about the shaft axis. A universal joint is used to
provide the necessary combination of pitch and rotation, the simultaneous implementation of which allows for
complex motions to be achieved.

7. The mounting block rests directly inside the fuselage and is constructed of balsa wood to minimize weight. A
small gap exists between the fuselage and the tail leading edge to provide the necessary clearance through a full
range of motion. Figure 7 shows the block inside the fuselage and the actuation mechanism performing a
combination pitch and roll displacement.
Figure 7. (a) Tail with Pitch and Roll; (b) Isometric view of Tail in Horizontal Position
B. Planform Area Expansion
The area expansion of the tail was desired for three reasons, the first being that an area increase would provide
more lift for the aircraft. This would help with the extra weight that was added to the plane from both the wing and
tail. Also the plane would be able to fly at a slower stall speed which is desirable particularly for experimental
aircraft. Secondly, an area decrease would be used during standard cruise to reduce drag, increasing the efficiency
and range of the aircraft. Finally, an area increase/decrease can be used to counteract adverse effects from tail pitch
and rotation.
Figure 8. (a) Swept; (b) Unswept Tail Configurations
Figure 8 above shows a model of the tail with an area decrease (a) and an area increase (b). This movement is
achieved by SMAs pulling on a torsional spring. As the SMA contracts it twists the connecting rod attached to a
feather, sweeping the feather outwards. Unfortunately, the manufacturing of this part proved to be more complicated
than anticipated leading to unacceptable weight gain. At this time only a bench top model was created and the tail on
the plane does not have the area increase/decrease capabilities.
C. Coupled Tail Control Analysis
The aircraft maneuverability was increased with the elimination of the vertical tail at the detriment of stability.
The aircraft stability was analyzed in AVL to obtain the forces and moments for all different deflections of the tail
and wing control elements. A table was then created for different flight profiles (Table 3) and then a configuration
for the control surfaces was chosen. For example, the case of climbing would require no sweep of the outer feathers,
full flap deflection and positive tail pitch. The forces and moments were then compared for these configurations to
set the control surfaces to the desired position. The control surfaces would be deflected until the forces or moments

8. were balanced. For the purposes of this report a list of all configurations would be impractical, however an extensive
example is given below.
For this example the Outer-Wing Aileron Tail
Tail Pitch
flight profile of cruise will Sweep Deflection Rotation
be analyzed. During cruise Steady Level
it was decided that the outer NONE NONE NONE NONE
Flight
feathers should be swept Banked Left
back and the ailerons and RIGHT RIGHT UP LEFT
Turn
tail are in their neutral
position. This is done to Banked
LEFT LEFT UP RIGHT
minimize the drag and wing Right Turn
tip vortices, which in return
Climbing NONE BOTH UP NONE
minimizes power
consumption and
maximizes endurance. Descending BOTH NONE DOWN NONE
Using the equations below5
the trim alpha was found to Table 3. Plane Flight Cases. Configuration of control surfaces to optimize
be 1.5 degrees. performance during specified maneuvers.
Cm  Cmo  Cl  (h  hn ) (3)
Where the pitching moment (Cm) was set to zero, Cmo was found by graphing the pitching moments from AVL,
Cl,α and the neutral point (hn) was found from AVL, and the range for h was given by the Nexstar flight manual.
Next, the forces were analyzed in AVL. For cruise, the lift generated should balance the weight of the plane, but at
this angle of attack and 45 degree sweep, the lift force is too low and thus it will be necessary to have the wings in
an un-swept configuration. This will allow for more lift to be produced, however, the trim angle of attack must be
raised and so the tail will be pitched up. This is found by setting the trim alpha such that the lift balances the weight
of the plane and solving for elevator deflection using the equation:
Cm  Cmo  Cm   Cm  (4)
Thus, all of the desired settings can be realized. This was done for all the different flight profiles. This is
important because now these configurations can be given to a team of electrical engineers that are designing the
radio controller. This radio controller will be programmed so that the pilot can fly the aircraft like any other aircraft,
even though the control surface deflections will be different.
V. Conclusions and Further Work
It has been determined that SMA actuated,
continuous deformation flaps are a viable means of
roll control under low to modest aerodynamic loading
based on the deflection performance observed in
testing. Potential benefits in power consumption and
performance were not found to be as dramatic as
originally hypothesized, though still remain
noteworthy. The SMA actuated wing is a successful
proof of concept prototype for biologically inspired
morphing flight systems. To further understand the
effectiveness of SMA actuated deflection, additional
study into various configurations and force testing
should be implemented. Also, it will be necessary to Figure 9. Implementation of described design elements.
continue gathering data on lift and moment forces of
the flap in wind tunnel and flight tests in an effort to quantify and increase performance margins. Potential future
design modifications may involve independently deflecting either the inner or outer (relative to wing root) portion of

9. the control surface, thus providing a twisting/warping of the surface rather than just a constant span-wise deflection.
This would improve the control resolution by allowing the flap to essentially be “partially deflected” while also
providing the option of morphing the surface in various distinct ways. In addition, the option to selectively recruit
individual SMAs instead of an all-or-none approach would greatly reduce energy consumption.
The sweeping outer-wing was mechanically successful. The design exceeded all structural expectations
although aerodynamic performance was not as strong as desired. It is believed that more sophisticated feather
designs which contain a slight degree of camber will contribute to increased aerodynamic performance and improve
the roll and yaw control exercised by the feathers. Additional research should be done to determine effective
methods for implementing camber and other forms of morphing into sweeping feather designs.
It was found that the elimination of the vertical stabilizer in the tail design provided more complications than
benefits. While the maneuverability of the plane was greatly increased, the loss of dynamic stability (lack of yaw
control) proved to be too great. The roll rates and rates of sideslip are likely too high for a pilot to overcome,
although this will not be known for certain until flight tests are done. A future design incorporating area expansion
may aid in eliminating some of the stability issues and may also benefit from a larger section of variable sweep on
the wing. Serious research should also be done concerning the benefits of incorporating biologically-inspired leading
edge tubercles on either/both wing and tails surfaces6. The greatest challenge seems to involve the successful
integration of both the wing and tail systems from a stability and control standpoint, and thus future work should
focus on extensive quantitative control analysis. Overall, the novelty and feasibility of these unconventional control
elements provide a promising first step toward realizing the benefits of biological design features and morphing
technologies.
VI. Acknowledgements
The North Carolina State University Bioflight design team would like to express gratitude for the North Carolina
Space Grant Consortium for their financial support.
VII. References
1. Namgoong, H., Crossley, W. A. , and Lyrintzis, A. S.: Aerodynamic Optimization of a Morphing Airfoil
Using Energy as an Objective, AIAA Paper 2006-1324, 2006.
2. Kornbluh, R., Pelrine, R., Eckerle, J., and Joseph, J., “Electrostrictive Polymer Artificial Muscle Actuators,”
Proceedings of the 1998 IEEE International Conference on Robotics & Automation, Leuven, Belgium,
1998, pp. 2147-2154.
3. Viieru, D., Tang, J., Lian, Y., Liu, H., and Shyy, W.: Flapping and Flexible Wing Aerodynamics of Low
Reynolds Number Flight Vehicles, AIAA Paper 2006-503, 2003.
4. Elsayed, M., Scarano, F., and Verhaagen, N. G.: Leading-Edge Shape Effect on the Flow over Non-Slender
Delta Wings, AIAA Paper 2008-344, 2008.
5. Etkin, B., and Reid, L. D., Dyanmics of Flight Stability and Control, 3rd ed., Wiley, New York, 1996.
6. Watts, P., and Fish, F.E.: The Influence of Passive, Leading Edge Tubercles on Wing Performance.