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Groundschool Theory of Flight
Aerofoils andwings
Revision 58a page content
was last changed 18 August
2012
The lift force is generated by a small pressure differential
between the upper and lower surfaces of the wing, caused by the
aerodynamic reaction to the wing motion through the
atmosphere. The magnitude of the pressure differential, and the
consequent momentum applied to the airflow, is generally
dependent on the speed of the aircraft, the angle of attack andthe physical characteristics of the wing. The wing centre of
pressure moves fore and aft in response to changes in the
aerodynamic reaction, thereby introducing pitching moments
that affect the aircraft's trim. Drag induced by the generation of lift
is modified by the plan form, the twist and the aspect ratio of the
wing. Ailerons, flaps, and otherlift and drag changing devices are
fitted to the wing for control and performance purposes.
Content
4.1 Lift generationAerofoils and the aerodynamic forcePressure differentialLift coefficient
4.2 Aerofoil simulation
4.3 Boundary layer air flowLaminar and turbulent flow
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Flow separation
4.4 Aspect ratio
4.5 Spanwise pressure gradient
4.6 Induced dragElliptical lift force distributionWing twist or washout
Effect of wing span/aspect ratio on induced dragJabiru induced drag calculation
4.7 Parasite drag
4.8 Aircraft lift/drag ratioGlide ratio
4.9 Pitching momentAerodynamic centreNeutral point
4.10 AileronsAileron drag
4.11 FlapsFlap systemsSummary flap effect on coefficient of lift
Advantages of using flapsFlaperonsReflex flaps
4.12 High-lift devices
4.13 Lift spoilers and airbrakes
Things that are handy to know and some notes for homebuilders
4.1 Lift generation
In the 'Basic forces' module it was stated that when an aircraft is movingthrough the air, the consequent pressure changes oraerodynamic
reactions to its motion will be acting at every location on its surface.
We had a look at the formula for calculation of lift from the wings:
(Equation #1.1) Lift [ newtons] = CL rV S
It is usual to substitute the symbol 'Q' to represent dynamic pressure
[rV] so the expression above may be more simply presented as:
(Equation #4.1) Lift [newtons] = CL Q S
where Q S is a force.
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It is appropriate to state here that the formula is an approximation of the
average lift from the wings. At any one time, the aerodynamic reactions
will vary over the span of the wing and with the position at which the wing
control surfaces are set.
Aerofoils and the aerodynamic force
An aerofoil (airfoil, parafoil, wing section orwing profile) is an
object with the shape of the cross-section of the wing having the
function of producing a controllable net aerodynamic force by its motion
through the air. To be useful this aerodynamic force must have a lifting
component that is much greater than the resistance or drag component.
In a powered aircraft, motion through the air is provided by the thrust; so
in effect, the aerofoil is a device that converts thrust into lift; in a glider
the aerofoil converts much of the gravitational force (the potential energy
of height) into lift.
The aerodynamic force has two sources: the frictional shear stress, or
skin friction, that acts tangential to the surface at every point around the
lifting body; and the pressure exerted perpendicular to the surface at
every point. (At speeds over about 250 knots, flow compressibility
introduces other factors.) The resultant net aerodynamic force is the sum
of all those forces as distributed around the body. For wings, it is
conventional to show the resultant force as acting from an aerodynamic
centre and resolved into two components: that acting perpendicular to
the flight path is the lift, and that acting parallel to the flight path is the
drag. Forpropeller blades, the aerodynamic reaction is resolved into
the thrust component and the propeller torque component. For rotor
blades, a more complex resolution is necessary.
Note: normally the aerofoil is incorporated into a wing with upper and
lower surfaces enclosing the load bearing structure. However, when
designing a low speed minimum aircraft such as the Wheeler Scout
there are advantages in using a 'single surface' cambered aerofoil
wing, very similar to a hang glider wing. Such wings incorporate a
rounded leading edge (formed by the aluminium tubing leading edgemain spar) that directs the airflow into the upper and lower streams at
all angles of attack. The slight camber is formed by battens sewn into
sleeves in the 'sails'. Such wings are somewhere between a thin
curved plate and a full aerofoil, and are similar in cross-section to a
bird's wing. A parachute wing uses the ram air principle to form the
aerofoil shape see 'The ram-air parachute wing'.
Now we need to establish
how that airflow actually
produces the lifting force.
John S Denker has
published a web book
'See How it Flies' that has
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a particularly good section on lift generation with excellent illustrations.You should carefully read through section 3 'Airfoils and airflow' and
particularly acquaint yourself with the Eulerian approach of
'streamlines' to visualise airflow. In the illustrative diagram at left,
narrowing (A) of streamlines indicates accelerating local speed and
decreasing local pressure a favourable pressure gradient. Opening
up (D) of streamlines indicates flow deceleration and increasing
pressure an adverse pressure gradient. The term 'free stream' isusually substituted for 'flight path' when discussing aerofoil
characteristics because the aerofoil is presumed stationary, as in a
wind-tunnel, and the airstream flows around it.
The following summarises the content of section 3 of 'See How it Flies':
A flat plate, held at a small aoa, will generate an aerodynamic force
lift and drag and indeed, some low momentum aircraft do use
basically flat plates as their tailplane surfaces. As mentioned above, the
shape of sail-type wings is somewhere between a plate and the moreusual wing. However, for aircraft that cruise in the 50150 knot range, a
wing with a rounded leading edge, a sharp or square-cut trailing edge, a
cambered upper surface and a flat or slightly cambered bottom surface
i.e. a full aerofoil section will be far more efficient
aerodynamically and structurally and more effective in performance.
(The faster the aircraft, the more the aerofoil section tends to flatten
out. So, for supersonic aircraft we are nearly back to the sharp-edged
flat plate.)
Aerofoil characteristics
The straight line joining the leading edge (left) and trailing edge (right) is the chord
line. The curved mean camber line is drawn equidistant between the top and bottom
surfaces, and the light coloured gap between the chord and mean camber lines
represents the camber which, in this particular aerofoil [a NACA 4415], equates
to 4% of the length of the chord at its maximum point which occurs at 40% of chord
length from the leading edge. Aerofoil thickness is the distance between upper and
lower surfaces. The maximum thickness of this aerofoil equals 15% of the chord;
that is called the 'thickness ratio'. At the trailing edge the included angle between
the upper and lower surfaces is significant in wake generation a lower angle is
better, and if the trailing edge is square-cut the thickness there should not exceed
0.5% of the chord. In flight, the angle the wing chord line subtends with the flight
path is the geometric angle of attack.
A cambered wing will still produce lift at zero, and slightly negative,
geometric angles of attack, as shown in the lift coefficient diagram. The
aoa where no lift only drag is produced is called the zero-lift aoa
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which, in the diagram, is nearly 2. From that diagram you can infer that
camber contributes a lift coefficient of about 0.2 and anything greater
must be provided by aoa. Of course, this will vary with the amount of
camber in a particular aerofoil. If the aoa was reduced below the zero-lift
value, for example 4, then the direction of lift would be reversed. The
only time you would need such a negative aoa is when you are flying
inverted, or performing aerobatics, neither of which are currently
allowable in aircraft registered with the RA-Aus.
At the zero-lift aoa, all the aerodynamic force is acting parallel to the free
stream and is mostlyskin friction drag, with a less significant amount
of pressure drag but the latter will increase as the aoa is increased.
Pressure drag is explained in section 4.7 'Parasite drag'.
Cambered wings perform quite well in inverted flight, but are not as
efficient as in normal flight because a higher aoa is needed to make
up for the lower wing surface having the maximum camber when
inverted. For this reason, aerobatic aircraft tend to use symmetricallyshaped aerofoils i.e. the 'camber' of the bottom surface balances
the 'camber' of the top surface and aerodynamically the result is zero
camber thus such wings rely purely on the geometric aoa to
produce lift.
At positive angles of attack there is a stagnation point, or line, just
under the leading edge of the aerofoil where some of the airflow has
been brought to a standstill. The air molecules reaching that line, in the
incoming stream, are equally likely to go under or over the wing.Stagnation pressure, the highest in the system, exists along the
stagnation line. The location moves down and under the leading edge
as aoa increases, up to the stalling aoa. Another more confined
stagnation point exists at the trailing edge. If an imaginary line is drawn
between the two stagnation points, the cross-sectional view of the
division of the aerofoil into upper and lower flow areas becomes
apparent.
The behaviour of the airstream flowing around such a wing accords
with Bernoulli's principle. As the air accelerates away from thestagnation line, the local airflow over the upper surface gains a greater
speed than the lower. Consequently, to retain constancy, the static
pressure on the upper surface will decrease, and on the lower surface it
may decrease very slightly at low aoa but will increase as aoa
increases.
There is another concept for explaining the pressure differential
between upper and lower wing surfaces. Leonhard Euler was a
mathematician who was a contemporary of, and collaborator with,
Daniel Bernoulli. The Euler Equations (a special case of Newton's ThirdLaw of Motion) express the relationship between flow velocity and the
pressure fields in frictionless flow. Because the air particles follow the
curved streamlines above the upper surface, there must be a centripetal
force across the streamlines that accelerates the flow towards the
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centre of curvature. That force must be associated with a pressure
gradient across the streamlines; i.e. ambient atmospheric pressure at
some distance from the surface, grading to a lower pressure on the
upper wing surface. For more information enter the terms 'Euler
curvature airfoil OR aerofoil' into a search engine.
The usual way of looking at the lift force is that the wing produces an
upflow in the air in front of it and a downwash behind it. That downwashcontinuously imparts momentum with a downward velocity
component to the air affected by the passage of the aircraft. As you
will recall from the 'Basic forces' module the action of adding downward
momentum will have an equal and opposite reaction, which in this case
is an upward force applied to the wing. And, of course, the energy
provided to impart momentum to the air comes from engine power; in a
glider it would come from the gravitational potential energy of height.
There is a distinction between the 'downflow' produced by the aerofoil
and the additional 'downwash' produced by wing vortices (see below),
the deflection of which increases with angle of attack. However, for ourpurposes we can treat all the momentum imparted to the airstream as
'downwash'.
You will also recall, from the 'Basic forces' module, that thrust is the
reaction from the momentum imparted to a tube of air with the diameter
of the propeller. The associated slipstream or 'prop wash' is the added
momentum quite apparent if you stand behind a stationary aircraft
when 'running-up' the engine. Helicopter rotor blades are long, slender
rotating wings somewhere between variable pitch propellerblades
and normal wings and the momentum applied to the air the 'rotorwash' can be seen clearly by its effect on dust, vegetation and other
objects (like parked ultralights) beneath a hovering helicopter. Similarly,
a wing producing lift continuously accelerates a flattened tube of air with
diameter approximating the wing span; the longitudinal downward
inclination to the flight path of that flat tube increases as aoa increases.
Some liken that concept to the wing acting as an airscoop.
Another concept associated with the aerodynamic force
circulation theory is a mathematical description of a 'bound vortex',
which also fits in with the generation of the physical wing-tip vortices.
Vorticity is rotary motion in a fluid, and you could regard 'circulation' as
referring to the apparent flow rotation upwash then downwash
around the upper/lower surfaces.
Note: there is a long-held and still-continuing argument, particularly in
newsgroups and other internet venues, about the pros and cons of the
various lift generation theories. None of the arguments put forward
(often ill-informed) affect in any way how a light aircraft flies, how it
should be safely and economically operated, or how it should be built;so it is best to ignore them unless you are particularly interested in the
science of aerodynamics and skilled in mathematics.
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Pressure differential
At any aoa between the zero lift and stalling angles, the total pressure
pushing down on the wing upper surface will always be less than the
total pressure pushing up on the lower surface. The absolute pressure
difference between the upper and lower surfaces will increase as aoa
increases up to the stalling aoa.
Although it is still small in comparison with the ambient
atmospheric pressure, it is this pressure differential resulting
from the wing deflecting the air that initiates the lifting force; and
this is true however lift theory may be expounded. Much work
has been done in designing aerofoils that will maintain the
required pressure difference in the targeted flight conditions.
We can calculate the net pressure difference for the Jabiru using the
scenario in the 'Basic forces' module section 1.4; i.e. cruising at 6500feet, airspeed 97 knots or 50 m/s, air density 1.0 kg/m. The ISA
atmospheric pressure at 6500 feet is about 800 hPa:
static pressure = 800 hPa
dynamic pressure = Q = rV = 1.0 50 50 = 1250 N/m
= 12.5 hPa
Multiplying the dynamic pressure of 1250 N/m by the lift coefficient of
0.4 gives the pressure differential of 500 N/m. That pressure differential
of 500 N/m (5 hPa) is less than 1% of the ambient static pressure, butapplying that over the 8 m of wing area gives the lift force of 4000
newtons that we calculated in section 1.4.
Lift coefficient
The lift coefficient CL is a dimensionless (or nondimensional) quantity (it
has no units of measure) relating mostly to aoa. It increases as the aoa
increases from the normal aoa used in cruise flight, and also to the form
of the wing and the aerofoil section. CL represents the proportion of total
dynamic pressure converted to lift force.
When the aircraft designer calculates the CL curve for an aircraft it must
be related to a particular wing reference area. This may be the visible
plan area of the wings but it could also include that area of the wings
conceptually enclosed within the fuselage.
Note that the CL for an aerofoil will have a value perhaps 1020% higher
than the CL for any wing incorporating that aerofoil; this is discussed inthe spanwise pressure gradient section. (The convention is to use a
lower case 'L' [thus Cl] when referring to the lift coefficient for an
aerofoil to distinguish it from the lift coefficient for a wing, but I have
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retained CL for both.)
In level, non-manoeuvring flight, lift equals weight, so equation 4.1 canbe restated as:
(Equation #4.2) CL = W / (Q S)
The usable value ofCL in a very light aircraft with low-aspect ratio wingswithout lift-enhancing devices might range between 0.1 and 1.6. (Unless
it is a symmetrical aerofoil same camber top and bottom the lift
coefficient range will be different for the same wing when in inverted
flight.)
However, a very low CL value can be obtained momentarily if the wings
are 'unloaded' in flight. This can be achieved by applying sufficient
continuous forward pressure on the control column to attain a near-zero
aoa such that the net pressure differential between the upper and lower
wing surfaces is very low. This would imply low lift generation and
reduced drag, so the thrust will accelerate the aircraft a little faster thannormal.
Furthermore, a negative CL can be obtained by maintaining so much
forward pressure on the control column that the aerodynamic force is
reversed. If initially flying straight and level, the aircraft will 'bunt'; i.e.
enter the first few degrees of an outside loop with the centripetal force
for the turn being supplied by the reversed lift. (This reverses the
direction of the wing loading and should never be attempted in weight-shift aircraft nor three-axis aircraft unless the three-axis manufacturer's
flight manual allows such a manoeuvre.) And, of course a suitably
equipped aircraft can be flown in inverted level flight in which casethe under-wing surface becomes the upper and a completely different CLrange applies, because the cambered surface is now underneath and a
higher aoa is necessary to maintain the lift required for level flight.
Incidentally many pilots utilise the lowCL technique when landing a
taildragger. The application of forward pressure on the control columnafter touchdown 'pegs' the aircraft down by reducing the aoa and thus
generated lift, and thereby puts increased pressure on the tyres, and
amplifies friction and any braking force applied. The same technique
was used to bring military DC3 aircraft to a quick stop.
4.2 Aerofoil simulation
Whichever way lift theory is expounded, this simple equation is
applicable:
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Lift = CL Q S
I suggest you try out what you have learned so far in an aerofoil flight test
simulation program. You need a Java-enabled browser. Read the
instructions carefully and reset the measurement units from pounds to
newtons. In this case, airspeed will be shown in km/h but just mentally
divide by two (and add 10%) to get knots halve it again if you want
m/s.
You can try this simple model out with a popular aerofoil, the NACA
2412, which is one of a series dimensioned by the U.S. National
Advisory Committee for Aeronautics (the forerunner of NASA) in the
1920s and 1930s. The 2-4-12 (twenty-four twelve) has a camber of 2%
[2] of chord with maximum camber occurring at 40% [4] of chord from
the leading edge and a thickness/chord ratio of 12% [12].
Note that all dimensions are proportional to the chord so the same
aerofoil section shape is retained throughout a wing even if it istapered in plan form. The wing is thickest at the root and thinnest at the
tip; i.e. it must also be tapered in thickness. Most aerofoils suitable for
light aircraft have a camber of 24%, thickness ratio of 1215% and
the maximum thickness (not camber) occurring at around 30% of
chord.
Now type the following data into the FoilSim boxes using the 'enter' key
or use the sliders:
Size: chord 1 m, span 8 m (area 8 m)Shape: angle (of attack) 2, camber 2%, thickness 12%
Flight test: speed 166 km/h (90 knots), altitude 1947 m (6400 feet)
Check the results displayed in the black boxes and in the plots. The
static air pressure should be 80.0 kPa (800 hPa) and the lift is 4233 N. If
you select 'surface pressure' from the output plots, you will see a plot of
the pressure distribution across the chord for the upper (white line) and
lower (yellow line) surfaces. Anything appearing above the green line
(the atmospheric static pressure) can be regarded as a positive
pressure pushing that surface at that point. Anything below the greenline is a negative pressure pulling that surface at that point. The area
between the two curves represents the magnitude of the differential
pressure distribution. The horizontal axis indicates the percentage
distance from the mid-chord position.
The pressure gradient plot for the upper surface shows a maximum
decrease of around 1.5 kPa (15 hPa) close to the leading edge but
changing to a slight positive increase in pressure at the trailing edge.
The pressure gradient plot for the lower surface shows an increase in
pressure under the leading edge, quickly changing to a decreasedpressure of a few hPa then back to a positive pressure from mid-chord
back. If you press the 'Save Geom' button, a data table will be displayed
showing the pressure and local velocity readings at 19 X-Y coordinate
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positions on both the upper and lower surfaces.
If you now select 'surface velocity' for the output plot, you will see a plot
of the local velocity distribution across the chord for the upper (white
line) and lower (yellow line) surfaces. You can see that the local velocity
increases to about 40% above the free stream velocity a very short
distance downstream from the leading edge, then it gradually slows until
local velocity is less than free stream velocity at the trailing edge.
Now change the airspeed to 110 km/h (60 knots) and the aoa to 12,
and look at the surface pressure and surface velocity plots again. Note
the big increase in local velocity that is now some 2.5 times the free
stream velocity a very short distance downstream from the leading
edge. Also note the big increase in the pressure differential and that
most (about 70%) is occurring within the first 25% of the chord.
You should do a little exploration starting with the aerofoil design,
changing just one value at a time and noting the changes in the upperand lower pressure gradients. For instance change the camber from 2
to 4% (i.e. the NACA 4412 aerofoil) and see the lift generated increaseto 6369 N with a CL now 0.74. You can do the same with the flight
performance items under pilot control aoa, altitude and airspeed. Of
course, FoilSim doesn't provide any information concerning draggeneration or pitching moment.
4.3 Boundary layer airflow
In the following section I
use the concept of the
airstream flowing over a
stationary wing (as in a
wind tunnel experiment)
rather than the reality of
the aircraft moving through
stationary air, for easier
explanation.
The innermost molecules of the moving air come into contact with the
solid surface of the wing (and other parts of the aircraft) and are
entrapped by the surface structure of the airframe materials. This is
called the 'no-slip condition' and is common to all fluid flows. The
interaction between those air molecules and the molecules of the solid
surface transfers energy and momentum from the air molecules to thesolid surface molecules producing skin friction drag and shear
stress that act tangentially to the surface. Those surface-interacting air
molecules retreating from the surface consequently carry less
momentum than they did on approach. In the very thin viscous sublayer
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adjacent to the solid surface, these molecules with reduced momentum
move randomly into the fluid a small distance from the surface. The
streamwise momentum per unit volume of the molecules that have
interacted with the surface is less than the momentum a small distance
from the surface. The random mixing of the two groups of molecules
reduces the streamwise momentum of the molecules that have not
directly interacted with the surface. This exchange of momentum
between slower and faster molecules is the physical origin of airviscosity (the resistance to flow when a fluid is subject to shear stress)
and of that viscous sublayer orboundary layercomprising the region
between the wing surface and the unrestrained orinviscidouter stream.
The diagram shows the velocity gradient within the boundary layer; the
more turbulent the flow, the steeper the gradient and the greater the
shear stress and friction.
The atmospheric boundary layeris similar but, of course, on a grander
scale.
Laminar and turbulent flow
The thickness of the
boundary layer starts at
zero at the wing leading
edge stagnation point, but
will increase (as an
increasing number of
molecules lose momentum)
until a maximum thickness
is reached near the trailing
edge. The friction between air layers moving at different velocities within
the boundary layer is generally weak, so the flow from the stagnation
point is initially made up of smooth-flowing stream lines orlaminae
laminar boundary layer flow. But on both the wing upper and lower
surfaces not far downstream from the leading edge, the laminar flow,
less than 1 mm in thickness, usually transitions to a flow with small
irregular fluctuations turbulent boundary layer flow andcontinues to increase in thickness by around 1% of the distance
travelled to a maximum near the trailing edge of perhaps 1015 mm for
a 1200 mm wing chord. Drag increases as the boundary layer thickens.
The extent of laminar flow and thus the location of the transition zone
where boundary flow is a mix of laminar and turbulent depends on
the designed aerofoil shape in profile, the angle of attack, contour
variations (ripples, waviness) formed during construction and service,
the flexibility of the wing's skin, surface roughness/cleanliness, porosity,
and the pressure gradient along the wing chord. In the area where thepressure gradient is favourable (i.e. decreasing, thus the flow is
accelerating), laminar flow will tend to continue, though becoming
thicker, unless something trips it into the more irregular turbulent
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boundary layer flow even paint stripes can trip laminar flow.
The laminae nearest the skin move slowly and cohesively, thus
minimising skin friction drag. In the turbulent flow boundary layer, the air
nearer the wing is moving faster and somewhat chaotically, thus greatly
increasing skin friction drag. The transition zone tends to occur a
particular distance downstream (for a combination of the preceding
factors) rather than a percentage of chord even though the aerofoil mightbe designed for laminar flow for a particular percentage of chord.
The aerofoils used for light aircraft wings have very little laminar flow. But
specialised high-speed aerofoils are designed to promote laminar flow
over perhaps the first 3040% of the wing chord by providing a
favourable pressure gradient for at least that distance (i.e. maximum
thickness at 4050% of chord) and a properly contoured, very smooth,
clean, non-flexing, seamless skin. The latter conditions are also
important for minimising the thickness of the turbulent boundary layer
flow with consequent reduction in skin friction drag and are achievablein composite construction.
Flow separation
Generally at lower angles of attack, the boundary layer and the outer
stream will separate (break away or detach) from the wing upper
surface at the trailing edge or perhaps slightly upstream from the trailing
edge, causing a thin trailing wake to form between the outer streams.
As aoa increases past perhaps 12, the boundary layer separation onthe wing upper surface might tend to move upstream a little. But at the
stalling aoa, separation will suddenly move much further upstream, and
a thick turbulent wake will form between the two remnant boundary or
shear layers and will be dragged along by the aircraft. The reaction to
the wing accelerating and energising that previously stationary air is a
sudden deceleration of the aircraft, accompanied by a sudden increase
in the magnitude of the nose-down pitching moment. Downwash
disappears and the rate of loss of lift will increase rapidly as the aircraft
slows.
Aerodynamicists devote much effort to controlling and energising the
boundary layer flow to delay separation and thus allow flight at lower
speeds; for example, see vortex generators. More lift and much less
pressure drag is generated in attached turbulent boundary layer flow
than in partially separated flow.
4.4 Aspect ratio
Aspect ratio is the wing span divided by the mean wing chord. An
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aircraft with a rectangular wing of area 12 m might have a wing span of
8 m and constant wing chord of 1.5 m. In this case the aspect ratio is
5.33. If the span was 12 m and the chord 1 m, then the aspect ratio
would be 12. However because wings have varied plan forms, it is usualto express aspect ratio as:
Aspect ratio = wing span / wing area
It is conventional to use the symbol 'b' to represent span, so the equationabove is written as:
(Equation #4.3) A = b / S
The Jabiru's aspect ratio (span 7.9 m, area 8.0 m) = 7.9 7.9 / 8 = 7.8,
whereas an aircraft like the Thruster would have an aspect ratio around
6. Consequently you would expect such an aircraft to induce much more
drag at high angles of attack, and thus slow much more rapidly than the
Jabiru.
And incidently, the mean chord (not the mean aerodynamic chord) of a
wing is span/aspect ratio. A high-performance sailplane wing designedfor minimum induced drag over the CL range might have a wingspan of
22 m and an aspect ratio of 30, thus a mean chord of 0.7 m. There are a
few ultralight aeroplanes, designed to have reasonable soaring
capability, that have aspect ratios around 1618, but most ultralights
would have an aspect ratio between 5.5 and 8, and averaging 6.5.
General aviation aircraft have an aspect ratio between 7 and 9,
probably averaging around 7.5. Note that the higher the aspect ratio in
powered aircraft, the more likely is wingtip damage on landing.
Note that 'wing area' includes the nominal extension of the wing shape
into and through the fuselage. This would appear quite apt for a
parasol wing or a high-wing aircraft, but will no doubt seem odd for a
mid or low wing. It is just a means for consistent
application/comparison between aircraft designs.
The span loading is the aircraft weight divided by the wingspan = W/b.The term sometimes refers to the loads applying at specified stationsalong the span.
4.5 Spanwise pressure gradient
There is a positive spanwise pressure gradient (the rate of pressurechange with distance) on the upper wing surface from the wing tip to the
wing root, imparting an inward acceleration to the airflow close to and
above the wing. Conversely, at other than a very small aoa, there is a
positive underwing pressure gradient from the wing root to the wingtip,
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and airflow under the wing acquires an outward acceleration. Thesespanwise (or more correctly semi-spanwise) pressure gradients on the
upper and lower surfaces are caused by the higher pressure air from the
undersurface revolving around the wingtip into the lower pressure upper
surface. This tip effect results in a near total loss of lift at the wingtip
because of the reduced pressure differential, with the loss of pressure
differential progressively decreasing with distance inboard.
Where these two
surface airflows
with different
spanwise
velocities
recombine past the trailing edge, they initiate a sheet of trailing vortices.
These are weakest near the fuselage and strongest at the wingtips, and
roll up into two large vortices, centred just inboard and aft of each
wingtip. The vortices increase in magnitude as aoa and lift increase,
and so increase the vertical component of, and the momentum impartedto, the downwash. As the centre of each vortex is a little inboard of the
wingtip, the vortices also have the effect of reducing the effective wing
span, the effective wing area and probably the effective aspect ratio.
The vortices also affect the air ahead of the aircraft by reducing the
magnitude of the upflow in front of the wing and thus modifying
(decreasing) the effective wing aoa, with the greatest effect near the
wing tip and little effect near the wing root. When a wing is at a low CLaoa the airstream affected by the wing has a slight downward flow.
When it is at maximum CL aoa, that airstream has a more substantial
downward flow contributed by the vortices.
Because of the
reduction in the
effective aoa, the
wing must fly at a
greater aoa to
achieve the same
lift coefficient that atwo-dimensional
aerofoil will achieve
in the laboratory.
Also, the wing tip
vortices have a
decreasing effect
with increasing aspect ratio. This is demonstrated in the diagram where
there are three (exaggerated) CL and aoa curves plotted. On the left is
the laboratory curve for an aerofoil, in the middle the curve for a high
aspect ratio wing utilising the same aerofoil and the curve on the right isfor a low aspect ratio version. The red horizontal line connects with a
particularCL value, say 1.2. The vertical red lines indicate a different aoa
for each curve at the same CL, thus the high aspect ratio wing must fly at
a higher aoa and the low aspect ratio wing must fly at a still higher aoa
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for either to achieve CL 1.2. Or to put it another way, at any aoa the
wings produce less lift than the laboratory aerofoil.
Also apparent from the diagram is that a higher aspect ratio has the
effect of a higher rate of lift increase, as aoa increases, than loweraspect ratio wings. A high aspect ratio wing will have a higherCLmaxbut
a lower stalling aoa than a low aspect ratio wing utilising the same
aerofoil. Induced drag has a direct relationship to aspect ratio; seesection 4.6.
Wing-tip vortices make up most of the wake turbulence created by an
aircraft in flight and are certainly the most hazardous to following
aircraft. They are usually referred to as wake vortices in the context of
air traffic and are the same as otheratmospheric vortices in that there
is a central low pressure core that is often visible as condensation
trails when an aircraft pulls higher g in a humid atmosphere. Read the
New Zealand Civil Aviation Authorities booklet 'Wake Turbulence'.
4.6 Induced drag
As explained in section 4.5 the effect of the vortices is to reduce the
effective aoa of the wing compared to that of the laboratory aerofoil,
which has the further effect of giving a more rearward inclination to the
resultant aerodynamic force for the wing, compared to the aerofoil, at aparticular geometric aoa. When that aerodynamic force is resolved into
lift and drag components, the additional inclination will produce a
reduced lift vector (apparent in the preceding CL/aoa diagram) and an
increased drag vector. That increase in the drag vector is the induced
drag.
Induced drag is least at minimum aoa and greatest at maximum aoa. It
is often said that the induced drag is the energy dissipated to induce lift;
i.e. ifCL is increased, induced drag increases, so thrust must beincreased to provide additional energy if the aircraft's flight path is to
continue as before. For example, if the pilot wants to increase aoa and
maintain the same airspeed (as in a constant rate level turn), then thrust
must be increased to counter the increase in induced drag.
There is a point in an aircraft's flight envelope where, because of the
increasing induced drag, the slower you want to fly the greater the power
you must apply known as 'flying the back of the power curve' which
is opposite to the norm of applying power to fly faster.
Elliptical lift force distribution
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As stated in section 4.5, with most wings particularly rectangular
wings the higher pressure air underneath the wing flows around the
wing tip into the lower pressure area above, thus reducing the pressure
differential and the lift; the effect of this decreases as span and/or
aspect ratio increase.
Induced drag is
minimised if the spanwisedistribution of the lift
forces can be made to
present an elliptically
shaped pattern, as shown
in the diagram, and that aerodynamic load is equally distributed over the
wing so that all areas of the wing contribute to load sharing. (This
idealised lift force distribution diagram presents a head-on view of the
whole wing without any representation of or distortion by the
fuselage.) .
Elliptical spanwise lift distribution will provide a desirable uniform
downwash along the span, and can be achieved by choice of wing plan
form and/or by twisting the wing to provide something near an elliptical
distribution in a speed band selected by the designer.
High aspect ratio elliptically shaped (in plan form) wings generally
achieve spanwise elliptical lift distribution; however, because of the
compound skin curvatures they are the most difficult and time-
consuming to construct. Low aspect ratio constant chord (i.e.
rectangular) wings without twist are the easiest to construct but generatethe most induced drag; however, the introduction of twist makes such a
wing much more efficient. Medium aspect ratio wings with a medium
taper ratio plus twist are probably the most used shape.
Taper ratio is the ratio of the tip chord to the wing root chord. 'Medium
taper' would indicate that the tip chord is greater than 50% of the root
chord.
Sailplane designers have demonstrated that the most effective highaspect ratio wing is one that has a straight (i.e. non-tapered) trailing
edge with a leading edge that is increasingly tapered in sections from
root to tip.
Wing twist or washout
The terms 'wing twist' and 'washout' refer to wings designed so that the
outboard sections have a lowerincidence, 34 or so, and thus lower
aoa than the inboard sections in all flight conditions. The main reasonfor wing twist is to reduce induced drag (see section 'Elliptical lift force
distribution') and particularly so at a cruising angle of attack or perhaps
the climb speed angle of attack. Another reason is to improve the stall
characteristics of the wing so that flow separation begins near the wing
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roots and moves out towards the wingtips.
With twist, the sections near the wing root reach the stalling aoa first,
thus allowing effective aileron control even as the stall progresses from
inboard to outboard. This is usually achieved by building geometric twist
into the structure by rotating the trailing edge, so providing a gradual
decrease in aoa from root to tip. Washout reduces the total lift capability
a little but this disadvantage is more than offset by the wing twistimproving elliptical lift distribution and thus decreasing induced drag.
Another form of washout aerodynamic twist might be attained by
using an aerofoil with a higher stalling aoa in the outboard wing
sections.
Aircraft incorporating washout tend to not drop a wing during an
unaccelerated stall. Instead, there is a tendency to just 'mush' down
sedately then drop the nose and regain flying speed. The turbulent wake
from airflow separation starting at the wing root buffets the tailplane, thusproviding some warning of the oncoming stall before it is fully
developed. Also, washout is usually applied, for aerodynamic balance,
to the swept wings utilised in weight-shift ultralights. However, geometric
washout can cause problems at excessive speed.
Effect of wing span/aspect ratio on induced drag
The equation for calculating induced drag for a wing is:
Induced drag = (k CL / A) Q S where A is the wing aspect
ratio [b/S] and k is related to a span effectiveness ratio.
So, induced drag is directly proportional to CL and inversely
proportional to dynamic pressure [Q], and might comprise 50% of total
drag at maximum angle of climb speeds. The lower the span loading
[W/b](i.e. the greater the physical span or the 'effective' span), the lesser
the induced drag at all angles of attack. This results in a decrease in the
thrust needed, particularly for climb or an increase in the potentialenergy of height for a sailplane. Various wingtip designs, such as
Hoerner wingtips, have the effect of moving the vortices slightly further
outboard, thereby increasing the effective span and thus reducing the
span loading and induced drag.
The information in the following box may only be of interest to aircraft
homebuilders, so skip it if you wish and go to the next part.
Aspect ratio equals b/S (equation #4.2), so the equation abovecan be rewritten as:
(Equation #4.4) Induced drag = (k CL S / b) Q S
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The factork equals
1/Pe where P [pi]equals 3.14 and e is
the span
effectiveness factor
that might varybetween 0.7 and 0.9
for the aircraft as a
whole. For an elliptic
plan form wing,
something like that of
the near-elliptical wing
of the Seafire 46 at
left, with (theoretically) no fuselage interference, then e=1.0 and k
=1/3.14 1.0 = 0.32. A non-twisted tapered wing will have a span
effectiveness factor of perhaps 0.9, so induced drag will be 10%greater and greater still (+20%?) for a non-twisted rectangular
wing. However, fuselage and fuselage junction interference will
reduce the span effectiveness of the wing.
Equation #4.2 states that CL = W / (Q S). Substituting that forCL
in Equation #4.4:
Induced drag = k [W/ (Q S)] (S / b) Q S
Some of the terms cancel out, leaving:
(Equation #4.5) Induced drag = k W / (b Q)
Equation #4.5 shows that induced drag is proportional to span
loading squared [W/b] and inversely proportional to dynamic
pressure [Q], so that two aircraft with quite different aspect ratios
but having an identical span effectiveness factor, wing span and
weight would produce the same induced drag at the same dynamic
pressure (e.g. same density and TAS or lower density and higherTAS, etc). Anything done that gives a small increase in effective
wing span will provide a proportionately higher reduction in induced
drag.
Jabiru induced drag calculation
If we guess that the Jabiru aircraft span effectiveness factor is about 0.8,
we have enough information to do a rough calculation of the induceddrag on our Jabiru cruising at 97 knots at 6500 feet (as in the pressure
differential calculation above). We will use a more practical form of
induced drag equation for those who skipped the preceding box:
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Induced drag = k CL / A rV S
For the Jabiru, k = 1/(3.14 0.8)= 0.4, aspect ratio [A] is 7.8 and the CLat that speed is 0.4.
= 0.4 (0.4 0.4 / 7.8) (0.5 1.0 50 50) 8.0
= 0.4 0.02 1250 8 = 80 newtons
If you repeat the CL calculation in section 1.4 using the Jabiru's stall
speed at 6500 feet, say a TAS of 25 m/s, you will find that CLmaxis 1.6.
Now if you repeat the induced drag calculations, you will find it has
increased fourfold:
Induced drag = 0.4 (1.6 1.6 / 7.8) (0.5 1.0 25 25) 8.0
= 0.4 0.33 312.5 8 = 330 newtons
4.7 Parasite drag
Parasite drag is all the air resistance to a light aircraft in flight that is not
considered as 'induced', and consists solely of pressure drag and skin
friction drag; the latter is due to viscous flow and has been covered in
the boundary layer air flow section above. The parasite drag constitutes
much of the total aircraft drag at minimum aoa (i.e. high speed) butcomparatively little at maximum aoa (minimum speed). Refer to the
diagram in section 1.6. When associated with airflow around an
aerofoil, the parasite drag is termed profile drag.
Pressure drag orform drag is the net pressure differential of those
points on the wing; for example, where a component of the pressure
acts in the fore and aft direction, and that pressure differential tends to
retard the aircraft. Pressure drag, like skin friction, applies to all parts of
the aircraft 'wetted' by the airflow. It is greatest for any part of the
airframe that presents a flat surface perpendicular to the flow and least
for a streamlined shape that has a fineness ratio (i.e. length to breadth)
between 3:1 and 4:1.
The illustration a cross-section of a 3:1 fineness ratio wing strut shows the flow
streamlines detaching from the surface close to the trailing edge, with the
characteristic wake associated with pressure drag. What is not apparent from the
illustration is that, in this instance, the skin friction drag would be significantly greater
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than the pressure drag
There are two specially named classes of parasite drag: interference
and cooling drag. Interference drag occurs at the junctions of airframe
structures; for example, the junction of the wings and fuselage or the
junction of the undercarriage legs and fuselage. The boundary and outer
streamflows interfere with each other at the intersections and causeconsiderable turbulent drag. Interference drag for a well-designed
composite aircraft might be 510% of total parasite drag but can be
very much higher. The cross-flow associated with unbalanced flight
(slip/skid) exacerbates interference drag.
If interference drag potential is ignored by the designer, vortex
development can occur at the wing/fuselage junctions, effectively
splitting the spanwise lift distribution into two separate elliptical patterns;
this is particularly so with low-wing configurations but not so much with
high wings. The problem is minimised, and total parasite dragconsiderably decreased, by careful design to reduce the number of
junctions, and to use fillets and fairing to direct a smooth airflow around
the remainder. Usually the most visible evidence of an interference drag
reduction program is the large wing root fillet used in low wing aircraft as
seen in theAR-5 photograph.
Engine cooling drag is normally associated with the cooling airflow for
engines enclosed in a drag reducing cowling. The cooling airflow is
designed to be efficiently directed from an air intake through a system of
baffles for optimum engine cooling, and perhaps to utilise the energy ofthe added heat to provide a little thrust at the cowling exit point. Where
the engine is not cowled, there is a great deal of parasite drag that
certainly cools the engine but would not be specially classed as cooling
drag.
4.8 Aircraft lift/drag ratioIn unaccelerated straight and level flight, lift equals weight, and thus will
be a constant value. If you look at the total drag diagram in section 1.6
you will see that the drag varies with the airspeed which means, of
course, that it varies with angle of attack. The diagram on the left is a
plot of the fixed lift value divided by the total drag value; i.e. the L/D ratio,
at varying aoa for a reasonably efficient aircraft. It can be seen that L/D
[L over D] improves rapidly between zero or negative aoa up to 45
then drops off until the stall angle, where the deterioration rate
accelerates. Note that a non-aerobatic light aircraft in normal flight wouldnot experience these low L/D values at aoa between 0 and 2.
The maximum L/D for light aeroplanes a measure of the
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aerodynamic efficiency of
the aircraft is possibly
between 8 and 12. Some
of the ultralights designed
with wide span, high
aspect ratio wings to
provide some soaring
capability have amaximum L/D around 30.
High-performance
sailplanes that are built
with very wide span,
slender, high aspect ratio
wings have the greatest
L/D, at 40 50, and thus the greatest efficiency. Powered parachutes
have a L/D ratio around 3.
There is a limit to the thrust that the engine/propeller can provide (i.e. thedrag that it can match) thus there is also a minimum L/D at which
maximum engine power is required to maintain constant altitude.
Consequently, there will be a minimum aoa (maximum airspeed) and a
maximum aoa (minimum airspeed) at which an aircraft can maintain
level flight. As there may not be much range between minimum and
maximum L/D, the minimum L/D can be quite significant for ultralight
aircraft, where a range of engines, some with rather low power, may be
utilised in the same model. An under-powered aircraft will perform very
badly at the back of the power curve.
Glide ratio
Maximum L/D usually occurs at an angle of attack between 4 and 5, or
where the CL is around 0.6. This L/D ratio is also termed the glide ratio
because it is just about the same ratio as distance covered/height lost in
an engine-off glide. For example, if maximum L/D =12 then the glide
ratio is 12:1, meaning the aircraft will glide a distance of 12 000 feet for
each 1000 feet of height lost, in still air.
We can use the '1-in-60' rule to calculate the angle of the glide path
relative to the ground; for example:
L/D = 12, then 60/12 = 5 glide path angle.
If the aircraft is maintained in a glide at a degraded L/D, then the glide
path will be steeper: L/D = 8, then 60/8 = 7.5 glide path angle. This is
one effect of using flaps (see section 4.11).
Be aware that quoted L/D ratios rarely take into account the
considerable drag generated by a windmilling propeller.
The aoa associated with maximum L/D decides the best engine-off
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glide speed [Vbg] for distance and the best speed for range [Vbr]according to the operating weight of the aircraft. But because of the flat
shape of the curve around maximum L/D, these speeds are more akin
to a small range of speeds rather than one particular speed.
4.9 Pitching moment
When using the
FoilSim aerofoil
flight test
simulation
program, the static
pressures around
the aerofoil are
given in the output
plot that shows the
pressure
distribution pattern
changing with the
aoa. It is
convenient to sum
that distribution and represent it as one lift force vector acting from the
centre of pressure [cp] of the aerofoil or wing for each aoa; much the
same way as we sum the distribution of aircraft mass and represent itas one force acting through the centre of gravity. The plot on the left is a
representation of the changing wing centre of pressure position with
aoa. The cp position is measured as the distance from the leading edge
expressed as a percentage of the chord. (Please note the diagram is
not a representation of the pitching moment.)
At small aoa (high cruise speed) the cp is located around 50% chord.
As aoa increases (speed decreases) cp moves forward reaching its
furthest forward position around 30% chord at 1012 aoa, which is
usually around the aoa for Vx, the best angle of climb speed. With furtheraoa increases, the cp now moves rearward; the rate of movement
accelerates as the stalling aoa, about 16, is passed. Most normal flight
operations are conducted at angles between 3 and 12, thus the cp is
normally positioned between 30% and 40% of chord.
The movement of the cp of the lift force changes the pitching moment
of the wing, a rotational force applied about some reference point the
leading or trailing edges for example which, in isolation, would result
in a rotation about the aircraft's lateral axis. The consequence of the
rotation is a further change in aoa and cp movement that, depending onthe cp starting position may increase or decrease the rotation. Thus a
wing by itself is inherently unstable and will change the aircraft's attitude
in pitch i.e. the aircraft's nose will rotate up or down about its lateral
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axis, which may be reinforced or countered by the action of thelift/weight couple so there must be a reacting moment/balancing
force built into the system provided by the horizontal stabiliser and its
adjustable control surfaces. This will be discussed further in the Stability
and Control modules.
Aerodynamic centre
There is a point on the
wing's mean
aerodynamic chord (see
below) called the
aerodynamic centre
[ac] where the pitching
moment coefficient [Cmac] about that point is small for the NACA 2412 aerofoil Cmac is
0.1. The negative value indicates the moment produces a nose-downtorque, which is the norm for cambered wings. Cmacremains more or
less constant with aoa changes but becomes more nose-down at the
stall. For the cambered aerofoils used in most light aircraft wings, that
aerodynamic centre will be located in a position between 23% and 27%
of the chord length aft of the leading edge, but for standardisation,
aerodynamicists generally establish the lift, drag and pitching moment
coefficients at the 25% (quarter) chord position. The notation for the
pitching moment at quarter chord is Mc/4.
The pitching moment is consistently nose-down, changing in magnitude
as airspeed changes. When plotted on an aerofoil wind tunnel data
graph, the moment coefficient Cmc/4 is a roughly horizontal line for most
of the angle of attack range, but the straight line may have a slight slope
if the actual aerodynamic centre varies a little from the 25% chord
location.
Pitching moment equation:
(Equation #4.6) Pitching moment [ Mc/4 ] = Cmc/4 rV S c
The pitching moment equation is much the same as the lift and drag
equations with the addition of the mean aerodynamic chord [c] for the
moment arm; using SI units the result is in Nm. As the coefficient is
always negative and nearly constant (up to the stall), then V is the
significant contributor to the nose-down pitching torque, which must be
offset by tailplane forces to keep the aircraft in balanced flight. However,
high torsion loads may still exist within the wing structure; see
aerodynamic effects of flight at excessive speed.
The concept of the aerodynamic centre is useful to designer/builders,because it means the centre of application of lift can be assumed fixed
at 25% chord and only the lift force changes. For non-rectangular wings,
a mean aerodynamic chord [MAC] for the wing has to be calculated;
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see ascertaining mean aerodynamic chord graphically in thatdiagram the aerodynamic centre position [ac] is shown on the root
chord line.
Neutral point
It is not just the wings that produce lift, the tailplane surfaces alsoproduce lift (which is discussed in module 6), and so do parts of a well-
designed fuselage. Consequently the aerodynamic centre for the aircraft
as a whole, known as the neutral point, will not be in the same location
as the wing aerodynamic centre but for a tailplane aircraft behind
it and on the fuselage centreline. This is the fixed point from which net
lift, drag and aircraft pitching moment are assumed to act.
4.10 Ailerons
We mentioned in section 1.4 that the pilot cannot change the shape of
the wing aerofoil. But this, like many statements made regarding
aeronautics, needs qualification. In fact, the pilot manoeuvres the aircraft
in the lateral plane by altering the effective camber of the outboard
sections of the wings. And remember in the last paragraphs of section
4.1 above, using FoilSim, we found that altering camber from 2% to 4%
produced a substantial increase in CL and lift.
If you examine the Seafire
photograph, in section 4.6,
you will see that each wing
has a separated section
at the outboard trailing
edge. These are ailerons,
hinged to the main wing
so that they can move
down or up and linked, viacontrol rods or cables, to
left/right movement of the
pilot's control column. The
control column is a simple
lever which amplifies
forces applied by the pilot. Thus the pilot can, in effect, increase or
decrease the camber of the outer portion of each wing; as shown by the
effective chord lines in figures A and B at left. The ailerons are
interconnected so that downward movement a camber increase in
one is combined with an upward movement a camber 'reflex' in
the other. The aileron movement then increases the lift generated by the
outer section of one wing whilst decreasing that from the other, thus the
changed lift forces (at a distance from the aircraft's longitudinal axis)
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impart a rolling moment in the lateral plane about that axis. This rolling
moment is primarily used to initiate a turn but other manoeuvres depend
on the amount and timing of aileron movement; more about this in the
'Control' module; see 'Control in a turn'.
Ailerons span perhaps the outer 35% of each wing and occupy
perhaps the aft 20% of the wing chord at that location. High-speed
aircraft may have two sets: a normal outer wing set used only for low-speed flight (because of the moment of force they are capable of
applying at high speed) and a second, high-speed set ofspoiler-type
ailerons located at the inboard end of the wing.
Aileron drag
Increasing camber and thus CL also increases induced drag (in
proportion to CL) so that the wing that is producing greater lift will also
be producing greater induced drag, tending to rotate (yaw) the aircraft's
nose in the direction of the lowered aileron. Parasite drag will be
increased on the wing with the lowered aileron. This induced plus
parasite drag reaction is called aileron drag and particularly
complicates aileron effects at low speeds when CL is high, the
aerodynamic pressure on control surfaces is low, and it is easy to
impart an excessive control movement. Because the yaw is towards the
lowered aileron and thus opposite to the required direction of turn, the
effect is called adverse yaw and is particularly evident in aircraft that
have long-span wings where the ailerons have a much longermomentarm.
Aileron drag can have an opposite yaw effect. When an aircraft is
turning at low speed and the pilot applies aileron to roll upright, the
downwards movement of the aileron on the lower wing might take the
aoa, on that part of the wing, past the critical aoa. Thus that section of
wing rather than increasing lift and making the wing rise will stall
and lose lift. The aircraft, instead of straightening up, will roll into a
steeper bank. Although the wing section may be stalled, CL and thus
induced drag will still be fairly high, so there will be a substantial yaw
toward the lower wing which pulls the nose down and increases the rate
of descent. There is potential for other aileron-induced problems when
turning at low speeds; see 'Control in a turn'.
There are a number of configurations which, used singly or jointly,
reduce aileron drag. For example, differential ailerons, where the
down-going aileron moves through a smaller angle than the up-going
aileron orFrise ailerons, where the leading edge of the up-going
aileron protrudes below the wing undersurface, increasing parasite dragon the down-going wing.
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4.11 Flaps
The other camber increasing devices, forming part of the inboard wing
trailing edge in the Seafire photo, are the flaps. Plain flaps are also a
hinged section of the wing as in figures C and D in the aileron
diagram above but move only (and jointly) downward usually to fixed
predetermined positions, each position providing varying degrees of
increased lift coefficient and increased drag coefficient that thedesigner thought appropriate. For instance, for one particular aircraft, at
5 deflection there is a good increase in CL with only slight increase in
drag. At 15 the drag increase starts to equate with the increase in the
CL, whereas at 25 or 30 the increase in drag is much greater than the
increase in CL; at 45 the flap is starting to act as an airbrake.
The change in camber (over perhaps 5060% of the wing span and 20
25% of the wing chord) caused by lowering flaps in flight, without
changing other control positions, has effects which will vary according tothe amount of deflection employed:
The aircraft's nose will pitch down a few degrees about its
lateral axis (i.e. its attitude in pitch is altered) because of the
nose-down pitching moment associated with flaps.
The position of the aircraft's line of drag will change and this
also tends to change the aircraft's attitude in pitch.
Depending on the relative mounting of the aircraft's wings and
tailplane, the change of direction (and the increase) of
downwash may affect the trim of the aircraft nose up or down.The lift increases and the aircraft will initially tend to rise.
The drag increases and the aircraft slows below its trimmed
airspeed, lift reduces, and the aircraft sinks unless power is
increased.
The pilot has to take appropriate control action depending on
the reason for lowering flaps.
The effects of trim associated with lowering or raising flaps for a
particular aircraft type will be noted in the Pilot's Operating Handbook.
As we saw in FoilSim, the effect of increasing camber is an increase in
CL (the ratio of lift to dynamic pressure or airspeed) at all aoa. This is
shown in the plot at the left. At an aoa of 6 CL is about 1.0 with flaps
lowered about 50% greater than the CL of 0.65 with flaps raised.
What this means is that the minimum controllable flight speed is lower
with flaps deployed.
So, returning to the equation:
lift = CL rV S
thus for lift to remain constant ifCL
increases then V must decrease.
Consequently, the stall speed is also lower with flaps deployed.
(Incidently, this diagram shows that the zero lift aoa for this wing occurs
at 2.)
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Note that the flapped
section will stall at a lower
aoa than the unflapped
section. Generally the
flapped wing area, being
the inboard section of the
wing, represents a verylarge proportion of the total
wing area check the
Seafire photo. Also, even if
the flapped section has
passed its stalling angle, it
is still producing lots of lift.
Providing there is sufficient
thrust available to overcome the big increase in drag, the aircraft can
still maintain height and stability because the wing outboard section and
ailerons are not stalled.
Bear in mind that to maintain the same airspeed and altitude after
lowering flaps, that thrust, if available, must be increased to counter
the additional drag from the lowered flaps. Similarly, when flaps are
raised, the aircraft will initially sink due to the loss of lift unless the pilot
takes compensating control action; this is particularly important when
a landing approach is discontinued and a go-aroundinitiated.
Now what aoa are we measuring? If you look at figure C (in the drawing
in section 4.10) which represents the unflapped part of the wing, you can
see that it has an aoa of about 5 or so whereas, at the same time, the
flap extended section of wing (figure D) has a considerably greater aoa.
As the flapped section will still have a stalling aoa around 16 we can
surmise that this flapped wing section is going to stall when the
unflapped section is only at 13 or so. (The horizontal axis of the plot
shows only the aoa of the unflapped wing.) However, we also have to
take into account the increased downwash and thus the change in
effective aoa associated with it, so the effect of flaps is not as straight-
forward as implied in the preceding.
Flap systems
There are a many types of flap systems, but if flaps are used at all in
ultralights or other very light aircraft, then only the simpler devices shown
at left are needed.
The most common (because of its simplicity) is the plain flap, which
might provide a 0.5 increase in CLmaxwith a large increase in drag whenfully deflected. The split flap provides slightly more increase in lift but a
larger increase in drag, and is more difficult to construct and thus
probably not worth the effort.
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The slot incorporated into the
junction between the main wing
and the plain flap in the slotted
flap arrangement allows airflow
from under the wing to energise
(i.e. accelerate and smooth) the
turbulent boundary layer flow overthe upper surface of the lowered
flap. This provides better
downstream boundary layer
adherence, and thus allows a
larger angle of attack to be
achieved before stall, with higherCL and lower drag than the plain flap.
Ailerons may also be 'slotted' for improved performance.
The rearward extension of the Fowler flap as it is deflected increases
wing area as well as camber, so it provides the best increase in lift of allthe simpler systems although perhaps even a single-element Fowler
flap like that shown is not that simple to construct.
Summary flap effect on coefficient of lift
In the diagram above, it can be seen that the deflection of flaps provides
an increase in CL of about 0.4 at all angles of attack. This is probably
representative of plain flaps extending along 50% of the wing trailingedge with chord equivalent to about 20% of the wing chord, and
deflected 25. The attainable CL increase depends on flap span, chord
and degrees deflected, plus the complexity of the flap system CL
increase of 0.8 might be achieved with long-span Fowlerflaps deflected
to 35. Incorporating slots into plain or Fowler flaps increases CL.
Advantages of using flaps
If flaps are fitted, a small flap deflection say 10 might be used for
safer take-off, due to the lower lift-off speed available. But half to full flap
deflection is always used for landing to provide:
lower safe approach and touch-down speeds
a nose-down attitude for a better view of the landing area
a steeper approach path (because of the degraded L/D) for
better obstacle clearance, which can be controlled at will
a shorter 'float' after rounding out because of increased drag
a shorter ground roll, if flaps are left fully extended until the
aircraft has exited the runway.
And flaps enable the approach to be made with engine power well
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above idle, which is beneficial to the engine, allows power changes toeither increase or decrease the rate of sink and provides better engine
response in case of a go-around.
Flaperons
In some light aircraft designs, particularly those with short take-off andlanding [STOL] capability, it has been found expedient to incorporate
the aileron and a plain flap into one control surface that extends the full
length of the wing trailing edge. The different functional movements are
sorted out by a control mixer mechanism. Usually, the flaperon is not
integral with the wing but bracketed to the underwing to provide a slotted
flap acting like an external aerofoil flying in close formation with the
main wing. Although the CL increase attainable might be 1.0, there are
drawbacks to this arrangement, which particularly exacerbate low speed
aileron drag.
Reflex flaps
Some aircraft are fitted with flaps that also can be deflected upward 5
or 10 above the normal neutral or stowed position in addition to the
normal downward deflection positions described above. Upward
deflection of flaps is done at cruising speed, and increases the
maximum cruise speed perhaps 5% by reflexing camber and reducing
drag, and is often associated with aerofoils that have good laminar flow.
4.12 High-lift devices
Another short take-off and landing [STOL] device used in light aircraft is
an aerofoil section a slat fixed to the leading edge of the wing,
with a slot between the slat and the wing. The slat/slot works in much
the same way as the slotted flap except that leading edge slats induce a
nose-up pitching moment. At low aoa, the fixed slat has no value; it just
increases drag and thus degrades cruise performance. At high aoa, the
higher pressure on the underside of the slat is channelled through the
slot, gaining velocity and energising the boundary layer flow over the
upper surface of the wing thus delaying boundary layer separation,
adding perhaps a 0.6 CL increase and increasing the stalling aoa to
perhaps 20. The usual increase in CL and the stalling aoa is illustrated
with the green curves in the CL/aoa diagram above.
Some slat/slot systems also have the effect of increasing wing area thus
reducing W/S and stall speed.
Leading edge slots combined with long-span slotted flaps, as used in
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STOL aircraft, allow a critical aoa much greater than the usual 16. They
can perhaps double the maximum CL of the basic wing, which allows
much lower landing speeds but requires flight at the back of the power
curve. Fixed leading edge slots work particularly well with a tailwheel
configuration in a 'utility' aircraft such as the Slepcev Storch, but in a
touring aircraft they have no value unless the pilot intends operating into
very small, rough airstrips. There are simple automatic slat/slot systems
where the slat is stowed when flying at lower angles of attack but popsout to form the slot when a particular angle of attack is reached. There
are also retractable slat/slot systems that provide STOL capability when
required without sacrificing cruise performance, except for the weight
increase due to the more complex operating system.
I suggest now you have a look at the diagrams inAnatomy of a STOLaircraft.
4.13 Lift spoilers and airbrakes
The converse of the high-lift devices is the light aircraft spoiler, common
in gliders but occasionally seen in high L/D ratio ultralights. The usual
spoiler is a flush-mounted front-hinged spring-loaded flat plate
incorporated into the upper wing surface, which can be elevated by lever
operation to varying degrees of opening. When activated, it induces
separation over part of the wing, thereby acting as a lift-dumper. But it isnot speed limiting; the nose will pitch down and the pilot must use
elevator to maintain the required approach speed; thus the spoiler is
used to increase the sink rate on the approach path.
Airbrakes or speedbrakes have a similar but more effective function.
They are often vertically mounted plates, pairs of which are incorporated
into the wing structure and which protrude from the upper and lower wing
surfaces when activated. They create a lot of drag but little or no change
in pitch, so the pilot must lower the nose to maintain approach speed.
Airbrake or spoiler configurations are sometimes associated with flapsystems that are primarily directed to lift generation, rather than lift
generation plus drag creation. Such flap systems would have maximum
downward deflection of perhaps 20.
Military aircraft utilise very complex flaperon/spoileron systems.
The next module in this Flight Theory Guide discusses engine
and propeller performance.
Back to top
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Things that are handy to know
The aerofoil is often referred to as a 'two-dimensional'
object. This means that that the spanwise thus 'third-
dimensional' pressure gradient effects associated with a
normal wing, and varying significantly with the wing form rather
than the aerofoil shape, are ignored when considering aerofoil
characteristics.
Wing upflow: all the air disturbances caused by the passage of
an aircraft are propagated as pressure pulses moving outward
(from molecule to molecule) in all directions at the speed of
sound. Thus, in subsonic flight, the pressure variances
(compression then relaxation) contribute to the air upflow
occurring in front of the wings.
In sport and recreational aviation the term aircraft is a genericcovering all types of aerial (airborne) vehicles; it includes 'lighter-
than-air' (aerostats) and 'heavier-than-air' (aerodynes) but not
vehicles that derive their lift from air reaction with the surface,
e.g. hovercraft. The aerostats include hot-air balloons and
power-driven hot-air airships, both deriving lift from buoyancy.
The aerodynes derive their lift from the aerodynamic reactions
described above and are in two classes rotary-wing
(rotorcraft) and fixed-wing. Rotorcraft are represented by
helicopters, gyroplanes and the towed gyrogliders or rotor-kites.
The fixed-wing aerodynes may be power-driven or unpowered,
the latter represented by the various glider classes sailplanes,
hang gliders, paragliders and the towed parasails or para-kites.
The power-driven aerodynes are represented by three groups:
the weight-shift controlled trikes, powered parachutes,
powered hang gliders and powered paragliders.
the 3-axis controlled power-assisted sailplanes and
motor-gliders
and finally the ubiquitous 3-axis controlled aeroplanes.
For more information see sport and recreational aircraft
categories.
Notes for homebuilders
The parasite drag coefficient. The equation for calculation of the
total parasite drag for an aircraft is:
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Parasite drag [newtons] = CDp rV S
Unlike the lift coefficient, the parasite drag coefficient CDp is more or less
a constant the ratio of drag to dynamic pressure and thus provides
a means for comparing the relative aerodynamic 'cleanness' of two
aircraft. The coefficient is usually in the range 0.03 to 0.08 for fixed-
undercarriage aircraft.
There is another value, the 'equivalent flat plate area' [FPA] used
by aircraft, motor vehicle and structural engineers who are concerned
with the calculation of air resistance. FPA is often quoted in aviation
magazines when comparing the parasite drag efficiency of an aircraft
with other similar aircraft, and it is usually stated in terms of square feet.
FPA is calculated as CDp times the wing area divided by the CDp for a flat
plate. However, it is assumed that the CDp for a flat plate held at 90 to
the airstream = 1 (in fact it is about 20% greater, but that is of no real
consequence) so the flat plate CDp is omitted from the calculation, thus:
FPA = CDp S ft
For example, the FPA for the run-of-the-mill two or four-seater fixed-
undercarriage general aviation aircraft would be around 6 ft with CDp of
0.03 to 0.05, and the retractables around 45 ft with CDp of 0.02 to 0.03.
FPA of a very clean, high-performance general aviation aircraft like a
Mooney model, is around 3 ft with CDp about 0.015. Some very clean,
high-performance GA kit-built aircraft have FPA less than 2. Note thatFPA does not represent the frontal cross-section area of the aircraft.
One of the smallest known
FPA is not associated with a
general aviation aircraft but
with an owner-designed and
built ultralight! Californian Mike
Arnold's 65 hp two-stroke Rotax
582 powered AR-5 held the worldspeed record, in the under 300 kg
FAI efficiency Class C1-A/0 of 213 mph in August 1992. This handsome
little glass-epoxy aircraft has an FPA of 0.88 ft with CDp about 0.016. It
demonstrates the efficiency that can be achieved an unmatchable 3.3
mph per hp in an ultralight design when the home designer/builder
pays the utmost attention to detail. Note the drag reduction achieved by
the beautifully shaped engine cowling, the wing root fillet and the
minimisation of the junctions of undercarri