Eliptical
lift distribution
Weight-shift control
lift distribution
Figure 2-14. Elliptical lift distribution compared to lift distribution
of a WSC wing.
Figure 2-15. Front view with projected area shown that produces
drag.
Because lift is a function of dynamic pressure ( q), it is
proportional to the square of the airspeed; therefore, small
changes in airspeed create larger changes in lift. Likewise, if
other factors remain the same while the CL increases, lift also
increases. The CL goes up as the AOA is increased. As air
density increases, lift increases. However, a pilot is usually
more concerned with how lift is diminished by reductions in
air density on a hot day, or if operating at higher altitudes.
All wings produce lift in two ways:
1. Airfoil shape creates a higher velocity over the top of
the wing and a lower velocity over the bottom of the
wing with Bernoulli’s venturi effect.
2. Downward deflection of airflow because of the
curvature of the wing with the principle of Newton’s
Third Law of Motion: for every action, there is an
equal and opposite reaction.
Both principles determine the lifting force. Review the
Pilot’s Handbook of Aeronautical Knowledge to understand
Newton’s laws of motion and Bernoulli’s venturi effect.
Figure 2-14 (top) shows the amount of lift produced along
the wing for an airplane wing with an elliptical planform.
Notice how the amount of lift generated is smallest at the
tips and increases slightly towards the root of the wing. This
is known as the “elliptical lift distribution.”
The WSC wing lift distribution is different because the wing
twist at the root is at a higher AOA than the tips. Most of
the lift is produced at the center of the wing with less lift
produced at the tips. The WSC lift distribution is compared
to the lift distribution for an optimum design elliptical wing
in Figure 2-14.
Drag
Drag is the resistance to forward motion through the air and
is parallel to the relative wind. Aerodynamic drag comes in
two forms:
1. Induced drag—a result of the wing producing lift.
2. Parasite drag—resistance to the airfl ow from the
carriage, its occupants, wires, the wing, interference
drag from objects in the airstream, and skin friction
drag of the wing.
Induced drag is the result of lift, and its amount varies as
discussed above for lift. Induced drag creates organized
circular vortices off the wingtips that generally track down
and out from each wingtip. Refer to the Pilot’s Handbook of
Aeronautical Knowledge for additional discussion on wingtip
vortices formation.
These wingtip vortex formations are typical for all aircraft
that use wings including WSC, PPC, helicopters, sailplanes,
and all fi xed-wing airplanes. The bigger and heavier the
aircraft, the greater and more powerful the wingtip vortices
are. This organized swirling turbulence is an important
factor to understand and avoid for fl ight safety. Refer to
the Aeronautical Information Manual (AIM) or the Pilot’s
Handbook of Aeronautical Knowledge (FAA-H-8083-25)
for additional discussion.
Parasite drag is caused by the friction of air moving over
all the components of the aircraft. Just as with lift, parasite
drag increases as the surface area of the aircraft increases,
and dramatically increases as airspeed increases (the square
of the velocity). Therefore, doubling the airspeed quadruples
parasite drag. [Figure 2-15]
The WSC aircraft can be designed for the purpose of being
a slow fl ying aircraft with a large wing where drag is not a
major concern, or can be designed to be a fast fl ying aircraft
with a small wing where drag is more of a concern.
Figure 2-16. Air flow around objects.
Figure 2-17. Fast WSC aircraft with complete streamlining (top) and
slow WSC aircraft with minimum streamlining (bottom).
The aircraft has plenty of items (area) for the wind to
strike including wing, wires, struts, pilot, carriage, engine,
wheels, tubes, fuel tanks, etc. Parasitic drag can be reduced
by streamlining the items. Round tubes can be streamlined
reducing the drag to one-third, and cowlings can be used
to streamline the pilot and the carriage completely, but not
without the additional expense and additional weight of the
streamlining. Streamlining does make a noticeable difference
in the speed and gas mileage of the WSC, especially for the
faster aircraft. [Figure 2-16]
With the large speed range of WSC aircraft, weight,
complexity, amount and expense of streamlining, and
resultant drag reduction are determined by the specific
mission for the aircraft and the manufacturers’ make and
model. [Figure 2-17]
Total drag is the combination of parasite and induced drag.
Total drag = parasitic drag + induced drag
To help explain the force of drag, the mathematical equation
D = CD x q x S is used. The formula for drag is the same as
the formula for lift, except the CD is used instead of the CL.
In this equation, drag (D) is the product of the coeffi cient of
drag (CD), dynamic pressure (q) determined by the velocity
squared times the air density factor, and surface area (S) of
the carriage and wing. The overall drag coeffi cient is the ratio
of drag pressure to dynamic pressure.
Induced and parasitic drag have opposite effects as AOA
decreases and speed increases. Note the total drag in
Figure 2-18. It is high at the slowest air speeds at high angles
of attack near the stall, decreases to the lowest at the most
effi cient airspeed, and then progressively increases as the
speed increases. The WSC wing can fl y with a large range
of airspeeds.
Generally, the most effi cient speed is at the lowest total
drag providing the best rate of climb, glide ratio, and cruise
economy. However, slower speeds provide higher angles
of climb, and faster speeds provide quicker transportation.
[Figure 2-18]
Drag
High Angle of Attack–
Low Speed
Low Angle of Attack–
High Speed
Total Drag
Stall
Induced Drag
Parasite Drag
LD-MAX
Figure 2-18. Airspeed versus drag.
CG
51 Glideslope
Root Wing Chord
Relative Wind
Flightpath
Lift
Drag
WL
WD
Weight
Resultant force
of lift and drag
components
that support the
weight during
flight
Component
of weight
that
opposes
lift (WL)
Component of weight acting along flight path.
(some call this thrust component during gliding flight)(WD)
Resultant force
Angle of Attack
Figure 2-19. Typical forces in gliding flight with no engine thrust.
to produce level fl ight, the relative wind stream becomes
horizontal with the Earth and the AOA remains about the
same. As described for the airplane in the Pilot’s Handbook
of Aeronautical Knowledge, thrust equals total drag for level
fl ight. [Figure 2-20]
When in straight and level, unaccelerated fl ight:
Lift (L) = Weight (W)
Thrust = Total Drag (DT)
At a constant airspeed, when excess thrust is added to produce
climbing fl ight, the relative air stream becomes an inclined
plane leading upward while AOA remains about the same.
The excess thrust determines the climb rate and climb angle
of the fl ightpath. [Figure 2-21]
When in straight and climbing, unaccelerated fl ight:
Lift (L) = Component of weight that opposes lift
Weight (W) = Resultant force (FR) of lift (L) and excess
thrust to climb (TE)
Thrust = Total drag (DT) plus rearward component of
weight
Weight
Weight is a measure of the force of gravity acting upon the
mass of the WSC aircraft. Weight consists of everything
directly associated with the WSC aircraft in flight: the
combined load of the total WSC aircraft (wing, wires, engine,
carriage, fuel, oil, people, clothing, helmets, baggage, charts,
books, checklists, pencils, handheld global positioning
system (GPS), spare clothes, suitcase, etc.).
During gliding flight, weight is broken down into two
components. The component that opposes the lift, acting
perpendicular to fl ight/glide path, and the component that
opposes the drag and acts in the direction of the fl ight/glide
path. During gliding fl ight, this component of weight is the
weight component providing the forward force which some
call thrust for gliding fl ight.
During gliding, straight, and descending in unaccelerated
fl ight:
Lift (L) and Drag (D) components = Resultant force (RF)
= Weight (W)
Total Drag (DT) = Weight component (WD) in the direction
of fl ight
Lift (L) = Weight component (WL) that opposes lift
Similar to airplanes, gliders, and PPC during gliding fl ight,
less lift is required because the resultant force composed of
lift and drag provides the force to lift the weight. In other
words, in gliding fl ight, drag helps support the weight.
[Figure 2-19]
Thrust
At a constant air speed, the amount of thrust determines
whether an aircraft climbs, fl ies level, or descends. With the
engine idle or shut off, a pilot is descending or gliding down.
Maintaining a constant airspeed, when enough thrust is added
Total thrustto climb
Root Wing Chord
Relative Wind
Flightpath
Component of weight
to oppose lift
Lift Resultant force
required to lift weight
Thrust required
to overcome
component
of weight
Excess Thrust
(Total thrust
minus Drag)
used to climb
Angle of Attack
CGWeight
Figure 2-21. Typical forces in climbing flight.
Earth’s Horizontal Plane
CG
Root Wing Chord
Relative Wind
Flightpath
Lift
Drag
Weight
Thrust
Resultant force
Resultant force
Thrust
Angle of Attack
Figure 2-20. Typical forces in level fl ight.
Thrust Required for Increases in Speed
Above the lowest total drag airspeed [Figure 2-18], faster
speeds (lower angles of attack) for level and climbing fl ight
requires greater thrust because of the increased drag created
from the faster speeds.
AOA is the primary control of increasing and decreasing
speeds, and increasing thrust generally does not produce
higher speeds, but additional thrust is required to maintain
level fl ight at higher speeds.
Ground Effect
Ground effect is when the wing is fl ying close to the ground
and there is interference of the ground with the airfl ow
patterns created by the wing. At the same angle of attack,
lift increases slightly and the drag decreases signifi cantly.
The most apparent indication from ground effect is the
unexpected lift given to an aircraft as it fl ies close to the
ground—normally during takeoffs and landings. More details
for ground effect aerodynamics are found in the Pilot’s
Handbook of Aeronautical Knowledge. Flight characteristics
for ground effect are covered in the takeoff and landing
chapters.
Center of Gravity (CG)
The CG is the theoretical point of concentrated weight of
the aircraft. It is the point within the WSC aircraft about
which all the moments trying to rotate it during fl ight are
balanced. The most obvious difference in the CG for a WSC
aircraft is the vertical position compared to an airplane, as
it is always lower than the wing. The Pilot’s Handbook of
Aeronautical Knowledge accurately states the CG is generally
in the vertical center of the fuselage. The same is true for the
WSC aircraft. However, the WSC wing is higher above the
fuselage/carriage and, since most of the weight is centered
in the carriage, the CG is well below the wing.
In a two-seat WSC aircraft, the second seat is typically behind
the pilot’s seat and the CG is usually located close to the rear
passenger seat. Therefore, the CG location does not change
signifi cantly with a passenger. Fuel tanks are typically located
near the vertical CG so any difference in fuel quantity does
not signifi cantly change the CG fore and aft with different
fuel quantities.
For level fl ight, the CG is directly below the wing/carriage
attachment point known as the hang point, and the propeller
thrust line is typically designed to be near the vertical position
of the CG. [Figure 2-22]
CG
Aircraft center of gravity
Center of gravity is under wing hang point for
level flight.
Center of lift is directly above center of gravity,
above the wing hang point for level flight.
Thrust line is typically
designed to be at vertical
center of gravity
Fuel tank
Figure 2-22. CG location with passenger shown for level flight.
YawingRollingPitching
Lateral Axis Longitudinal Axis Vertical Axis
Figure 2-23. Axes of rotation.
Axes of Rotation
The three axes of rotation intersect at the CG.
[Figure 2-23]
Lateral Axis— Pitch
Motion about the lateral axis, or pitch, is controlled by AOA/
speed and the throttle. Lowering the AOA (increasing speed)
rotates the nose down while increasing the AOA (decreasing
speed) rotates the nose up.
Increasing the thrust of the propeller rotates the WSC aircraft
pitch up (nose up) to climb and pitch down (nose down) at
reduced throttle.
eight shifted to right
Aircraft rolls to right
Creates less twist on L.H.
side with tip increased AOA
Normal lift distribution
Less lift
More lift
Creates more twist on R.H.
side with tip reduced AOA
Lift distribution with wing warped
Figure 2-24. Shifting weight to one side warps the wing by
increasing the twist on the loaded side and decreasing the twist on
the unloaded side.
Longitudinal Axis— Roll
Turning is initiated by rolling about the longitudinal axis, into
a bank similar to an airplane using aileron and rudder control.
To turn, shift the weight to the side in the direction of the turn,
increasing the weight on that side. This increases the twist on
that side while decreasing the twist on the other side, similar
to actuating the ailerons on an airplane. The increased twist
on the side with the increased weight reduces the AOA on the
tip, reducing the lift on that side and dropping the wing into a
bank. The other wing, away from which the weight has been
shifted, decreases twist. The AOA increases, increasing the
lift on that wing and thereby raising it.
Thus, shifting the weight to one side warps the wing (changes
the twist) to drop one wing and raise the other, rolling the
WSC aircraft about the longitudinal axis. [Figure 2-24] More
details on the controls that assist wing warping are covered
in chapter 3, which should be considered with use of the
controls in the takeoff, landing, and fl ight maneuvers sections
of this handbook.
Vertical Axis— Yaw
The WSC wing is designed to fl y directly into the relative
wind because it does not provide for direct control of rotation
about the vertical axis.
Stability and Moments
A body that rotates freely turns about its CG. In aerodynamic
terms for a WSC aircraft, the mathematical value of a moment
is the product of the force times the distance from the CG
(moment arm) at which the force is applied.
Typical airplane wings generally pitch nose down or roll
forward and follow the curvature of the upper airfoil camber
creating a negative pitching moment. One of the reasons
airplanes have tails is to create a downward force at the
rear of the aircraft to maintain stabilized fl ight, as explained
in greater detail in the Pilot’s Handbook of Aeronautical
Knowledge.
The WSC wing is completely different and does not need a
tail because of two specifi c design differences—a completely
different airfoil design creating a more stable airfoil and
lifting surfaces fore and aft of the CG, similar to the airplane
canard design.
WSC Unique Airfoil and Wing Design
As shown in Figure 2-2, the WSC airfoil has the high point
signifi cantly farther forward than does the typical airplane
airfoil. This makes the center of lift for the airfoil farther
forward and creates a neutral or positive pitching moment
for the airfoil. Most WSC airfoils have this unique design to
minimize negative moments or pitch down during fl ight.
Additionally, the design of the complete wing is a unique
feature that provides stability without a tail. To understand the
WSC aircraft pitch stability and moments, examine the wing
as two separate components—root chord and tip chord.
Trim—Normal Stabilized Flight
In Figure 2-25A, during normal unaccelerated fl ight at trim
speed, the lift at the root (LR) times the arm to the root (AR)
equals the lift of the tip (LT) times the arm to the tip (AT).
(LR x AR) + (LT x AT) = 0
LR + LT = Total Lift of the Wing (LW)
Adding all the lift from the wing puts the center of lift of
the wing (CLW) directly over the CG for stabilized fl ight.
[Figure 2-25A] If the pilot wishes to increase the trim speed,
the CG is moved forward. This is done by moving the hang
point forward on the wing. Similarly, to reduce the trim speed,
the hang point/CG is moved rearward on the wing.
High Angles of Attack
In Figure 2-25B, if the wing AOA is raised to the point of
minimum controlled airspeed at which the wing begins to
stall towards the center of the wing (root area), the lift in this
area decreases dramatically. The CLW moves back a distance
“b” creating a moment to lower the nose. Therefore, the
center of lift moves behind the CG at higher angles of attack,
creating a nose-down stabilizing moment. The average lift
coeffi cient verses AOA is shown for this minimum controlled
airspeed in Figure 2-26. The root area is partially stalled and
Normal Flight at Trim Speed
High Angle of Attack at
Minimum Controlled AirspeedLow Angle of Attack at High Airspeed
Top View Side View
CLW
CLW
cCLW
AT AR
LT
LR
Center of lift at
same longitudinal
position as center
of gravity.
Center of lift behind center of gravity
creating nose-down moment
Center of lift ahead of center of
gravity creating nose-up moment
Stalled area not producing lift.
Center of lift of wing (CLW)
behind center of gravity.
Tip area at low angle of attack not producing lift.
Center of lift of wing (CLW) ahead of center of gravity.
CG
CG
CG
CG
CG
CLW
CLW
CLW
LW
LW
LR
LT
LR
LW
Nose
Nose
Nose
CG
Trim
Minimum
Controlled
Airspeed
High Speed
High AOA
Low AOA
Figure 2-25. Trim, minimum controlled airspeed, and high speed pitching moments.
the tips are still fl ying. The specifi c stall characteristics of
each wing are different and this stall pattern shown here is
used for example.
Low Angles of Attack
At very low AOA, the tip chords are near zero AOA or below,
not producing any lift, as shown in Figure 2-25C. At this
point, the nose area is producing all of the lift for the wing.
The CLW moves forward a distance “c,” creating a positive
stabilizing moment to raise the nose.
Pitch Pressures
As the pilot pushes out on the control bar, this creates a pilot
input force that has a moment arm from the control bar up to
the wing hang point. [Figure 2-27]
From this pilot-induced pitch moment, the control bar is
pushed out, the nose raised, and the AOA increases an equal
amount for both the root and the tip chords. However, as
shown in Figures 2-26 and 2-28, the average CL change is
greater at the low AOA at the tip chords, while the amount