Falcon 12a Specifications
- Wings: Seven-pinion
design with progressive washout
- Wingspan: 47.75 feet
- Wing area: 150 square
feet (13.93 square meters)
- Weight, total: 288 lb
(131 Kg) ----- Pilot: 175 lb (79.5 Kg); Aircraft: 113 lb (51.4 Kg)
- Glide ratio: 20:1
- Power: 7 HP Halbach
Array electric motor, 1.4 lb (0.64 Kg) driven by
two 5.4 lb (2.45 Kg) Li-poly battery packs (0.9 KWH total)
- Controls: Each wing is
independently controlled through right and left haptic interfaces
- Flapping limits: plus
or minus 15 degrees (restricted to the power-stroke plane)
- Pitch/roll: rotation
of the entire wing about the pitch-control axis
- Wing folding: pilot
- Joint flexion: To
allow the wings to fold up, the forearms rotate in the horizontal plane
about the elbow joints. The wrist joints flex vertically downward
during the back-swing and rotate in unison with motions about the elbow
joints as the wings fold up and stretch out.
The version 12a incorporates the use of artificial
feathers to achieve a relative high glide ratio of around 20:1. A high
glide ratio generally requires high aspect ratio wings and the wing's pinion
feathers serve that purpose. In addition,
feathers maintain their aerodynamic shapes regardless of how much the
wings fold up during flight. Another advantage of
feathers is that they can be easily approximated by simple swept-back
trapezoidal shaped wings which allows the use of an airfoil
simulator to predict the wing's lift production.
Here is a link to the wing drawing used for the lift simulation.
The Falcon's hydraulic system pump is powered by a Halbach Array electric motor and
energized by two Lithium-polymer battery packs. These new technologies appear to provide an ideal
combination of power and light weight.
Given the above developments, it was decided
that a rigorous evaluation of the whole idea was called for. To
this end, a highly detailed, numerical feasibility study (linked to above) was undertaken
to see if the approach might prove to be possible.
Flapping Flight Made Simple
Edward Tufte's video, taken at 300
frames-per-second, of geese taking flight reveals that the flapping
flight of birds is less complicated than previously thought. Birds
employ a relatively simple scheme to accomplish what appears to be a
complex set of motions..
The power-stroke of the flapping cycle is
simple and straight forward; the wings sweep downward and forward while
stretched out flat with the joints locked.
During the backstroke, a bird simply relaxes
its wrist joints and allow its hands to fall limp while simultaneously
folding its wings inward. The relaxed hand-sections, caught up in the
wind stream, are quickly lifted and thrown backward requiring little or
no effort on the part of the bird.
Further simplifying the process, as the wing
folds, a parallelogram arrangement of the arm bones keeps the hand and
humerus sections aligned.
As shown below, the Falcon wing forearm
includes such a parallelogram structure. The illustration shows the
wing in three stages of extension. Note that the hand section stays
parallel to the humerus section in all three positions.
Unlike in a bird, the humerus section in the Falcon wing is also a
parallelogram mechanism. Its purpose is to prevent any forward or
backward sweep of the wing during the folding process. As will be
explained below, this makes the power-stroke function much simpler and
provides for a clean separation between the three control functions.
Flapping motions of the wing (the
power-stroke and backstroke) are confined to a single plane called the power-stroke
plane (illustrated below), determined by the tilt of the
shoulder joint axis. The power-stroke plane is both down and forward
(as it is with birds).
This arrangement allows for a mechanically simple power-stroke in which
the stroke angle can be adjusted for optimal efficiency and the entire
flapping function is cleanly separated from the wing-folding and
pitch-control functions. More importantly, it allows the entire
flapping sequence to be powered by only one hydraulic piston per wing.
A bird's hand section is equivalent to the
business end of a boat's oar, driving the bird forward as well as
upward. The Falcon's hand section, as in a bird wing, will be designed
to twist during a power-stroke to tilt the lift vector more forward
than it is for the inner two wing sections. In the bird wing and the
Falcon's wing, the inner two sections maintain a relatively fixed angle
of attack to the wind and so provide varying amounts of lift during all
phases of the flapping cycle.
All of these factors add up to a simplified
flapping cycle for the Falcon that insures a clean separation between
the various power and control functions.
Birds fold and extend their wings during
flight for many reasons. They fold them to gain airspeed, to dump
excess forces, to maintain headway in a stiff wind and, as mentioned,
they fold them during the backstroke phase of the flapping cycle.
Since the lift and drag forces acting on the
wings are generally perpendicular to the force needed to fold them up,
our ornithopter wings are folded up using only the pilot's arm muscles.
The wings are tension loaded to maintain
full extension. The tension will be adjusted to allow the wing folding
process to be done by arm-power alone. You simply pull the hand grips
inward to fold the wings and relax your arms to let the wings spring
back to their extended positions
The wing sections are coupled to each other
by pulley-like devices called cable-gears that are
built into the ends of the long parallelogram links. The devices
function just like regular gears to keep the folding angles equal but
are lighter in weight. The left illustration below shows the cable-gear
arrangement of the right-wing elbow joint. The red cable wraps around
the gear on the forearm beam and crosses over to the trailing-link gear
of the humerus. The black cable similarly connects the other two gears.
The cables cross in a figure-eight fashion at the center of the joint.
In the wrist joint (right illustration below), in order to make space
for the flexion hinge, one cable joins beam to beam and the other
connects the two trailing-links.
Wrist joint hinges
The Falcon's wrist joints incorporate hinges
that allow the joints to flex downward even while the wings fold and
extend. The drawing below shows a top view and two posterior views of
the joint. The hinge incorporates two cable-guide assemblies with small
roller bearings mounted in spring steel brackets to guide the cables
over the bend as the joint flexes. In this way, the wrist flexion and
wing folding functions are independent and can be controlled
individually and simultaneously.
Here is a view of the whole wing structure
that shows more details of the joint parts.
At the start of a strong backstroke, the
wrist-joint hinge will unlock (the locking mechanism isn't shown yet)
and let the outer wing section drop, relieving the humerus of the task
of lifting the entire wing up as a stiff unit. This causes the rotation
of the humerus and forearm to accelerate. As the humerus and forearm
continue to rotate, the loose hand-section is dragged along by its
proximal end while being lifted and thrown backward by the air stream.
During this process, the pilot pulls on the hand grip to fold up the
wing, which further accelerates its angular rotation. At the apex of
the backstroke, the wing flattens out and the hinge locks up again.
This combination of wrist flexion and
wing-folding will enable the wing-flip (the backstroke) to happen very
quickly using little or no energy.
To allow for soft, slow back-swings and
prevent the wingtips from collapsing inadvertently, the wrist joint
hinges remain locked at all times except at the beginning of a strong
The wings will employ damping mechanisms (to
be designed) to soften the shock encountered as the wing sections snap
back into the locked, flat-wing configuration at the top of the
The Shoulder-Joint and actuator
The shoulder-joint accommodates three
independent functions: flapping, folding and pitch/roll-control.
The power-stroke and backstroke of the
flapping cycle are driven by a single hydraulic piston for each wing.
The pistons are double-acting, unbalanced actuators that are driven in
both directions. They produce more force in the pushing direction (for
the power-stroke) and less in the return direction (for the
backstroke). The pistons are 2 inches in diameter operating at 3400 PSI
and act through 3 inch connecting rods coupled to the shoulder-joint
hinge pins. The system can produce about 2670 foot-pounds of torque at
the shoulder joint. If the center of lift is located five feet out from
the shoulder joint and the total weight is 288 pounds (for both the
craft and its pilot), it would take 1425 foot-pounds of torque to hold
the wings flat while gliding. The excess torque (1245 foot-pounds) is
available for the power-stroke. The actuators are attached to the main
axle assembly as shown in the illustration below and coupled to the
hinge-pins through forward and aft connecting rods.
On each wing, a smaller pitch-control
actuator is attached between the top of the forward connecting rod and
the wing-root parallelogram link (shown in red).
The power source
Pressure for the hydraulic system will be
supplied by a high-pressure pump driven by a seven horsepower Halbach
Array electric motor currently under development
by LaunchPoint Technologies. The motor will be energized by a pair of
Lithium polymer battery packs with a total capacity of 0.9
kilowatt-hours. Control will be provided by a small, on-board computer
coupled to the pilot through haptic interfaces. Such systems are
presently under development or being manufactured by Berkeley Bionics
in Berkeley, CA. and are employed in their
Human Universal Load Carrier Exoskeleton. The
operator controls their exoskeleton by simply walking (or running) in a
normal fashion. No other conscious effort is needed. In the Falcon, you
will simply move your arms and hands in appropriate flapping motions to
control the system and, likewise, no other conscious effort will be
The Haptic Interface
A haptic interface is a sensing and feedback
mechanism that acts as the interpreter between a human and a robotic
device. The interface senses the human's actions and returns
information about the state of the device. The Falcon employs two such
interfaces, one for each wing. Each interface includes a hand grip, two
sensors and a small parallelogram.
Wing motions are initiated by either
lifting, rotating or pulling on the handgrips.
As shown below, the hand grip and sensors
are mounted on a small parallelogram attached to the larger
parallelogram of the wings' humerus section. The same cable-gear
devices as used in the wing joints are used in the interface joints to
force the interface and your arm to mimic the folding motions of the
wing. The hand section of the interface tracks both the horizontal
rotation (radial deviation) of the outermost wing section and imitates
its vertical flexion. Because the human wrist has a lesser range of
motion in the horizontal plane, the radial deviation of the interface's
hand-section is less than the rotation of its counterpart in the wing.
The only connection between you and the
aircraft (other than being strapped in) is through the two hand grips.
You simply grasp the hand grips and move your arms and hands in an
appropriate manner. The haptic interfaces detect your motions and
direct the hydraulic actuators to move the wings in a corresponding
manner. All the while, you receive constant feedback about the
configuration of and forces acting on the wings.
Feedback is achieved in two ways. First, the
centers of the joints of the small parallelograms are closely aligned
with those of your wrist and elbow joints. This insures that your arm
positions and motions coincide with those of the wings. The other means
of feedback has to do with how the hand grips pivot. When the wing
begins to swing upward, the outer section relaxes and bends downward.
When you lift up on a hand grip to initiate the back-swing, the fact
that it is hinged distally to your hand, causes your wrist to,
likewise, bend downward. The two motions coincide. In this manner, you
get feedback with no actual linkage between your hand and the wing's
Flapping Control: An
electronic sensor (shown in gray in the drawing above) mounted on the
flapping-control-axis of the hand grip detects vertical motions of your
arm and activates the large actuator to move the wing in the
Pitch and Roll Control:
Rotating the hand grips about their pitch-control axes cause the
aircraft to either pitch or roll. Sensors aligned along the
pitch-control axes of the interfaces detect those rotations and direct
the small actuators to rotate the wings about their long axes
accordingly. Turning one grip at a time causes the craft to roll.
Turning both grips in opposite directions results in a more extreme
roll. Rotating them in the same direction will result in pitching the
nose either up or down.
Yaw Control: Like with
birds, our ornithopter has no direct yaw control that is independent of
motion around the other two axes. Rotation of a hand grip on one wing
to initiate a roll, for example, will naturally include "adverse yaw"
as the pitched wing is dragged backward due to the added drag on that
side. If the right hand grip is rotated for a downward pitch, the
aircraft will roll to that side and the right wing will be dragged
backward, resulting in a properly banked turn.
The wings are built in three sections: the
humerus, the forearm and the hand. As shown below and in previous
illustrations, all three sections are parallelogram mechanisms
comprised of an expanded-foam beam forming the leading-edge and a
hollow trailing-rod positioned just aft of the beam. Short links at
each end complete the parallelograms, connecting the leading-edge beams
to their respective trailing-rods. For added strength, the leading-edge
beams include embedded hollow rods. The wings are made made
progressively thinner and more flexible approaching the tip.
As a wing folds and extends, the distance
between the leading-edge beam and its trailing-rod varies. A
hollowed-out slot in the beam accommodates these variations.
As described earlier, wing folding is
controlled by pulley-gear devices. At each elbow joint, one pulley-gear
is integral to a beam and the mating gear is integral to the
trailing-rod of the adjacent section. In the wrist joint, one cable
connects the two beams and the other cable connects the two
Unlike previous versions, the Falcon 12a
wings are covered with feathers. This change was made for several
reasons, the main one being that, with feathers, a higher glide ratio
is possible because each pinion feather is a high aspect ratio wing.
Another big reason is that, unlike with a membrane-covered wing,
feathers don't lose tension and change their airfoil shape as the wing
folds up. Each feather consists of a central quill sandwiched between
two thin aerodynamic surfaces. The quills are hinged to both the
leading edge beam and its trailing-rod and, therefore, their alignment
doesn't change during the wing-folding process.
The fuselage, illustrated below, includes a
cage that incloses the pilot's torso and supports the wings and
actuator units, a saddle platform, a thick, memory-foam saddle, a keel
and two bulkheads. The bulkheads enclose the electric motor with its
planetary-gear coupling (yellow) and hydraulic pump (red). The battery
packs are mounted to the sides of the pilot cage. Control modules for
the electronics and hydraulics are mounted to the bottom of the saddle
platform on either side of the keel. The forward section of the
fuselage includes a windshield and canopy.
Not that it would ever be needed, of course,
but a skid-plate is mounted to the bottoms of the bulkheads just in
case you stumble during a landing.
Head Support Gimbals
To save you from getting a tired neck, your
helmet is suspended from a spring mounted, gimbals-like device that
allows full freedom of head motion. Your chin rests on a foam pad built
into the helmet. The mounting structure behind the head doubles as a
neck protection aid in case of accidents.
The tail structure is fixed and
non-articulated. It provides pitch stability for the aircraft in its
default glide mode.
Using The Legs
How much one will use one's legs while
flying is an open question. Primarily, you will need them to be free
for a running takeoff and for landing. However, during flight, your
legs will provide significant weight-shifting to maintain a stable
attitude or to enhance maneuvers---especially at low speeds. During a
take-off, when flapping motions are most extreme, birds noticeably
shift their legs down and backwards during the backstroke and shift
them up and forward during the power-stroke. The reason for this is to
maintain level flight. Moving the wings forward shifts the center of
lift forward which would result in an upward pitch, so the bird
compensates by shifting its legs (and its center of gravity) forward to
match the changing center of lift. The backstroke moves the center of
lift aft-ward, causing the bird to dive, so, it shifts its legs to the
rear to compensate. The same conditions would prevail with our
ornithopter so, while flapping the wings, you would, likewise,
constantly shift your legs forward and backward to compensate for the
changing center of lift.
Window Shade Stirrups
If the legs are left to simply dangle, the
pressure on the groin area in contact with the saddle would quickly
become uncomfortable (the "dangling legs problem"). To alleviate the
condition, the Falcon includes "window shade" stirrups for you to stand
on to lift your body weight off the saddle---like standing on the
pedals of a bicycle.
The stirrups (shown in the illustration above ) are attached by cables
to spring-loaded drums. As with window shades, the drums allow the
stirrup cables to extend but automatically lock to prevent the cables
from winding up. If you give the stirrups a quick tug, the drums unlock
and the springs try to wind up the cables. If you do this and relax
your legs, the springs will draw your legs up into the folded position
shown below. This folded-leg position is the default glide-mode
position in which the craft is balanced for a stable glide.
You can extend your legs at any time. The more you straighten them, the
tighter the springs are wound. The stirrup cables become fully taught
just before your legs are completely straight. Fully extending your
legs, then, will lift you an inch or so off the saddle and free up your
legs for a running takeoff or a landing.
Taking off and landing:
Although it can't be ruled out, it's probably not possible with this
ornithopter to take off in still air on level ground. Most likely,
takeoffs will require a gentle headwind or a sloping surface. Simulator
studies indicate that, for an aircraft with this wing area, 288 lbs of
lift is obtained at 14 MPH. Since humans can easily run at well over
this speed, a running takeoff down a slope is well within the design
envelope. Landing would be a matter of gliding down at the slowest
possible airspeed and performing a stall maneuver at the last second,
just as your feet touch the ground.