Tutorial_ Aerofoils and Wings_25.8.13

7/30/2019 Tutorial_ Aerofoils and Wings_25.8.13

1/35

25/08/13 Tutorial: aerofoils and wings

flysafe.raa.asn.au/groundschool/umodule4.html 1/35

Tutorial Search

| Tutorials home | Decreasing risk exposure | Safety tour| Emergencies | Meteorology|

Navigation| Communications | Builders guide |

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
http://flysafe.raa.asn.au/index.htmlhttp://flysafe.raa.asn.au/index.htmlhttp://flysafe.raa.asn.au/index.htmlhttp://flysafe.raa.asn.au/scratchbuilder/contents.htmlhttp://flysafe.raa.asn.au/comms/index.htmlhttp://flysafe.raa.asn.au/navigation/index.htmlhttp://flysafe.raa.asn.au/meteorology/index.htmlhttp://flysafe.raa.asn.au/emergencies/index.htmlhttp://flysafe.raa.asn.au/safety/safety_index.htmlhttp://flysafe.raa.asn.au/safety/intro2.htmlhttp://flysafe.raa.asn.au/index.html


2/35



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.
http://flysafe.raa.asn.au/groundschool/index.html#eq1_1http://flysafe.raa.asn.au/groundschool/index.html


3/35



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
http://www.av8n.com/how/#contentshttp://flysafe.raa.asn.au/groundschool/umodule10.html#parawinghttp://flysafe.raa.asn.au/scratchbuilder/fabrics.html#sailclothhttp://flysafe.raa.asn.au/regulations/benchmarks.html#minimum_aircrafthttp://flysafe.raa.asn.au/groundschool/propeller.html#prop_theoryhttp://flysafe.raa.asn.au/groundschool/flutter.html#machhttp://flysafe.raa.asn.au/groundschool/umodule2.html#pressurehttp://flysafe.raa.asn.au/scratchbuilder/metals.html#shearing_force


4/35



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
http://flysafe.raa.asn.au/groundschool/index.html#aoahttp://www.av8n.com/how/htm/airfoils.html


5/35



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
http://flysafe.raa.asn.au/groundschool/umodule2.html#bernoullihttp://flysafe.raa.asn.au/groundschool/umodule2.html#bernoulli


6/35



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.
http://flysafe.raa.asn.au/groundschool/propeller.html#variable_pitchhttp://flysafe.raa.asn.au/groundschool/index.htmlhttp://flysafe.raa.asn.au/groundschool/index.html


7/35



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
http://flysafe.raa.asn.au/groundschool/index.html#liftcalc


8/35



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:


9/35



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
http://flysafe.raa.asn.au/FoilSim/FoilSim.htmlhttp://flysafe.raa.asn.au/FoilSim/FoilSim.html


10/35



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
http://flysafe.raa.asn.au/FoilSim/FoilSim.html


11/35



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
http://flysafe.raa.asn.au/groundschool/umodule21.html#layer


12/35



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
http://flysafe.raa.asn.au/scratchbuilder/composites.html


13/35



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,


14/35



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


15/35



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
http://flysafe.raa.asn.au/safety/NZ_CAA_wake_turbulence.pdfhttp://flysafe.raa.asn.au/groundschool/umodule21.html#tornado


16/35



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
http://flysafe.raa.asn.au/groundschool/umodule7.html#incidence


17/35



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
http://flysafe.raa.asn.au/groundschool/flutter.html#washouthttp://flysafe.raa.asn.au/groundschool/umodule10.html#weight_shift


18/35



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:
http://flysafe.raa.asn.au/magazine/seafires1.html


19/35



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
http://flysafe.raa.asn.au/groundschool/index.html#draghttp://flysafe.raa.asn.au/groundschool/index.html#lift


20/35



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
http://flysafe.raa.asn.au/groundschool/index.html#draghttp://-/?-http://flysafe.raa.asn.au/scratchbuilder/composites.html


21/35



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
http://flysafe.raa.asn.au/groundschool/propeller.html#windmillinghttp://flysafe.raa.asn.au/navigation/wind.html#1in60


22/35



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
http://flysafe.raa.asn.au/groundschool/umodule6.html#handyhttp://flysafe.raa.asn.au/FoilSim/FoilSim.htmlhttp://flysafe.raa.asn.au/groundschool/umodule2.html#vbrhttp://flysafe.raa.asn.au/groundschool/umodule2.html#vbg


23/35



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;
http://flysafe.raa.asn.au/groundschool/flutter.html#flutterhttp://flysafe.raa.asn.au/groundschool/umodule8.htmlhttp://flysafe.raa.asn.au/groundschool/umodule7.html


24/35



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)
http://flysafe.raa.asn.au/FoilSim/FoilSim.htmlhttp://flysafe.raa.asn.au/groundschool/index.html#lifthttp://flysafe.raa.asn.au/groundschool/umodule6.htmlhttp://flysafe.raa.asn.au/groundschool/umodule9.html#mac_graphic


25/35



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.
http://flysafe.raa.asn.au/groundschool/umodule8.html#turnshttp://flysafe.raa.asn.au/groundschool/umodule6.html#handyhttp://flysafe.raa.asn.au/groundschool/umodule8.html#turns


26/35



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.)
http://flysafe.raa.asn.au/FoilSim/FoilSim.html


27/35



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.
http://flysafe.raa.asn.au/groundschool/umodule12.html#go_around


28/35



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


29/35



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


30/35



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
http://flysafe.raa.asn.au/groundschool/propeller.htmlhttp://www.zenithair.com/stolch801/design/design.htmlhttp://flysafe.raa.asn.au/cagit_trophy/bell_vanzella.htmlhttp://flysafe.raa.asn.au/groundschool/umodule1b.html#power_curve


31/35



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:
http://flysafe.raa.asn.au/students/joining_sra.html#aircraft


32/35



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

Tutorial_ Aerofoils and Wings_25.8.13

Documents

Transcript of Tutorial_ Aerofoils and Wings_25.8.13