Advanced Aerodynamics

�� Larry Bogan - Jan 2003 - Version 1.0

Aerodynamic DragDrag on a glider is divided into two distinct types:

1. Air friction over the glider surface produces drag.Parasitic Drag ~ air density * Contact Area * V2

Where V = air speed

2. Kinetic energy given to deflected air in theprocess of producing lift for the glider takes energyfrom the glider and appears as a drag force.Induced Drag ~ L2/[(density of air)*V2 * b2]Where b = aircraft wingspan and

L = Lift of the wingsNote tha parasitic drag increases with square of theair speed while induced drag decreases with thesquare of the velocity. Also induced drag increaseswith the square of the lift and decreases with thesquare of the wing span. (more on this later)

Sailplane performance dependence on airspeed isDrag force = D = A V2 + B/V2

Where A and B depend on the type of glider. Sincedrag causes the sailplane to lose energy and sink, therelationship for sink rate will be Vs ~ D*V and

Vs/Vso = ½ [ (V/Vo)3 + (Vo/V)]

Where Vs = sink rateVso and Vo are characteristic velocities.

Analysis of the shape of the curve can show that:Minimum sink rate occurs when V = 0.76 Vo.Minimum relative sink is a minimum when V = Vo

V/Vs minimum is the same as maximum L/D.So Vo = speed of maximum L/D and Vso = sink atmax L/D so Vo/Vso = (L/D)max

A more useful form is:Vs = ½ Vo/(L/D)max [(V/Vo)3 + (Vo/V)]

When V = Vo then Vs = Vso where Vo = speed ofmaximum

The drag force is related to the sink rate through therate of energy loss which = D*V = Vs * mg Where mg = weight of the glider

= mass * acceleration of gravitySo

D = ½ (L/D)max mg [(V/Vo)2 + (Vo/V)2]

Example: Schleicher model Ka6eEmpty Mass = 190 kg Max Mass = 300 kg(L/D)max = 33Speed of Max L/D = Vo = 43 ktsStall airspeed at 620 lbs = 33 ktsMin sink = 36 ktsPilot mass with parachute = 85 kgTotal mass = 190 + 85 = 275 kg (605 lbs)

Weight = 2695 Newtons

Using the (L/D)max and Vo

given here, the graph to theleft showing the drag forcesversus air speed wasgenerated. Note that theinduced drag equals theparasitic drag at Vo (43 kts)but is larger when V is lessthan Vo. At minimum sink (33kts) the parasitic drag is 1/3 ofthe induced drag.Since the lift, in straight, levelflight, is just equal to theweight of the glider, the glideratio is just mg/D. The graphon the next page shows theL/D for several of the private

Advanced Aerodynamics - Bluenose Soaring Club Ground School

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gliders in the BluenoseSoaring Club including aKa6E. The vertical scale on thegraph is in nautical mile(nm) per 1000 ft whichequals 6080 ft/1000 ft =L/D = 6.08. This is auseful number toremember. If the L/D is 30the the glide is 30/6 = 5nm/1000 ft

Increased Drag in a turnThe curves to the rightapply only to staight andlevel flight. Induced dragis proportional to loadsquared so when a gliderenters a well coordinatedturn, although the parasiticdrag remains unchanged, the induced drag increases.

The load factor is defined as the lift/weight. In a turnwith a bank angle of φ , the load factor is

1/cosine(φ). The sink rate is then expressed asfollows:

Vs = ½ Vo/(L/D)max [(V/Vo)3 +(Vo/V)/cos(φφφφ)2]

The steeper the turn,the larger the loadfactor which increasesthe sink rate of theglider. In a thermal, liftis better near the centerbut the glider sink rateincreases as it bankssteeper to turn in asmaller circle. Whenthermalling, a pilot hasto judge what bank isbest for each thermal.

The chart to the leftshows the performanceof the Ka6E. Sink ratesare plotted for 5different bank angles.The radius of the turnsare indicated for 45and 100 m. At 45


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knots, a typical flying speed, the radius of theturning circle is given for each bank angle.

Secondary Effect of Controls

Rudder:When the rudder is applied quickly, the yaw thatoccurs causes one wings airspeed to increase whilethe opposite to decrease. This results in a larger lift

on side with the higher airspeed. Thus the sailplanewill bank. The diagram below shows the effect ofright rudder.

Banking Turns:The ailerons will bank the sailplane and it will turn;when the ailerons are recentred it will stay in thebank. Because the glider is going in a circle with theinner wing travelling in a smaller circle than theouter wing, the outer wing will be travelling fasterthan the inner wing. Since the outerwing with the higher airspeed willnot only have more lift but also moredrag than the inner wing. Twosecondary effects result.

1. The differential drag willyaw the glider such that I will wantto turn away from the centre of thecircle. To counter ‘adverse yaw’,rudder must be maintained to yawthe glider toward the center of thecircle.

2. The differential lift willtend to increase the bank of theglider because the outer wing hasmore lift. To counter this effect, the

stick can not be held in neutral position but a slightbit of aileron must be maintained to counter the bankof the turn.

In turns that are slow or have a gentle bank, thesesecondary effects are small and additional rudderand aileron control is not needed.

Torques, Weight and Balance

When discussing the forces on a glider in stableconstant velocity flight, the Lift, Weight, andDrag are usually shown acting at the same point.There three forces must add to zero in this case.This must be true for translational acceleration tobe zero.

The glider must not only not be accelerating in theup-down or forward directions, it must not berotating. The forces that act to rotate a glider arecalled torques. Whereas a force will accelerate anobject with mass, a torque will cause angular

acceleration about a rotation axis. As is shown in thediagram below the forces on a glider do not all act atthe same point. Each one will act to rotate the gliderand if the sum of all their actions (torques) do notadd to zero then the glider will rotate.

A torque is defined as the force acting times thedistance to a parallel line through the rotation point. In the diagram, the reference line is the datum line.The torque due to the pilot’s weight is WP x d1.


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Torque is positive if it tends to cause rotationclockwise and negative if it causescounter-clockwise rotation.The sum of all the torques on the glider in this caseis given below and should add to zero for constantspeed flight.

Wp x d1 + L x d3 - W x d2 - LE x d4 = 0

L = aerodynamic lift of the gliderW = empty glider weight

The pilot of the glider can vary the elevator lift, LE,by pushing the stick forward or backward and by thismean counter the rotation caused by the other forces.Here we show the lift down but it can be up or downdepending on the elevator setting. In normal flightthe pilot adjusts the elevator lift with the trim so thatthe glider will fly with no hands on the stick. Thetrim is only able to apply a limited amount of forceso it is necessary that the glider be ‘balanced’properly for safe flight.

Center of Gravity (C of G)In order for a glider to be balanced properly itscenter of gravity must be located within certainspecified position limits. The C of G is determinedon the ground with no lift present. It is that point onthe glider at which it can be balanced and not rotatedue to the pull of gravity.

The method of determining the C of G is to weighthe glider and add in the weight of the pilot to

determine its location. The following example showshow a ‘Weight and Balance’ is done.

The Ka6E glider shown in the diagrams must haveits C of G 18 to 38 cm behind the datum line(defined as the leading edge of the wing at rib #3)when it is at flying weight. While empty, the glideris placed on two scales; one under a support on thefront and one under the tail skid. The glider isleveled during this procedure since it must be in itsflying attitude. The distances from the supports tothe datum line are measured (d1 and d2 in thediagram below) as well as the two weights (W1 andW2). The sum of the two weights is the weight ofthe empty glider, W.

Wempty = W1 + W2The torques produced by the two weights measuredmust be the same as the total weight acting at the Cof G. This can be written as

d x Wempty = W1 x d1 - W2 x d2 Where d = distance to the C of G (empty).Since we have values for everything except d, wecan solve for it.

Let’s do this quantitatively:Measured: W1 = 142 kg

W2 = 49 kgd1 = 72 cmd2 = 438 cm

Wempty = W1+W2 = 142 + 49 = 191 kg

d = [W1 x d1 - W2 x d2 ]/Wempty

d = [142kg x 72cm - 49kg x 428cm]/191 kgd = - 56 cm (negative

means same as d2)The Ka6e specificationsrequire that the CofG ( whenempty) be between 53 to 64cm behind the datum line.Find the glider C of G withpilot and parachute. Measure: Weight of pilot + parachute,Wp = 85 kgDistance of pilot CofG fromdatum line, d3 = 47 cm.


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Now sum all the torques due to the three forces, W1,W2 and Wp and equate them to the torque due to thetotal weight, W.NowW = W1 + W2 + Wp W = 191 kg + 85 kg = 276 kgThe distance to the C of G (full weight) is givenfrom the torque equation.d = [W1 x d1 + Wp x d3 - W2 x d2]/Wd = [142kg x 72cm + 85kg x 47cm - 49kg x 438cm]/276kgd = - 26 cmThis is between the required limits of 18 to 38 cmbehind the datum line for the Schleicher Ka6E. If apilot were too light then the C of G would be too farback. In this case the glider would tend to fly with anose up attitude, stall easily and possible be difficultto get out of a spin. A pilot that is to heavy wouldput the CofG too far forward and the glider would bedifficult to trim back to a speed for bestperformance. The glider would also not flareproperly on landing.

Safety FactorsAll commercial gliders have been designed andtested to fly within certain stress limits. These limitsare specified with maximum load factors andairspeeds. As am example, the limits for theSchleicher Ka6E are:

Maximum Allowed Load Factor (positive) = 4.0

Maximum Allowed Load Factor (negative) = -2.0Factor of Safety = 2.0Maximum airspeed, VNE =108 ktsMaximum airspeed in gusty air, VA= 75 ktsMaximum Aerotow Airspeed = 75 ktsMaximum Winch tow Airspeed = 54 ktsThese are different for each glider and should bememorized (along with the weight limits of theglider) by a pilot before flying that type of glider.The load factors relate to the stress that are put onthe glider during flight. As we saw a banking turn isone maneuver that increases the load factor on theglider. Stall Speed Versus Load FactorsThe load factor, n , is defined as the ratio of the liftand weight of the glider = L/W.As the load factor increases, the stall speed of theglider increases. This puts a limit on the minimumairspeed can maintain and still stay flying.

In straight and level flight the load factor is 1 and Lo = W = ½ ρρρρ CL(max)Vs0

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Where, Vs0 is the stall speed (33 kts for the Ka6E).At a higher loads the stall speed, Vs1 is determinedby this same relationship L1 = ½ ρρρρ CL(max)Vs1

2 From these two relationships the stall speed at loadfactor, n, can be written simply as

Vs1 = Vs0 (n)1/2

On the chart below this appears ascurved line indicating the upperlimit on load as a function ofairspeed. To the left and above theupper curved line, flight is notpossible because the glider will bein a stalled conditon. This samerelationship gives the stall speed forvarious bank angles shown in thelower figure on page 2.

The graph to the left shows, in lightgray, the region of airspeed and loadfactors that are safe for the Ka6Eglider. The darker gray region is theregion where flight is not possiblebecause the glider will be stalled.


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The unshaded region and the region to the right areareas of large load factors and airspeed which willdamage the glider. The safety factor for the glidergives the factor by which limits can be increasedbefore the the glider will break.

The glider can also have a negative load factorduring brisk negative g maneuvers or in gustyconditions. A negative lift would be downwardduring normal flight and since the airfoil is notdesigned for this type of lift, its stall speed is higher.The limits on negative load factors is a downwardcurve defining the maximum negative load beforestalling.

The safe flight region is cut off for load factorsbetween 1 and -1 at the stall speeds. It is possible tohave a glider with a load factor less than 1 but thiswould only be momentarily while the glider is in asemi-free fall situation and is not part of normalflight and hence the limit.

The high speed limit for a sailplane is the VNE or theairspeed never to exceed (108 knots for the Ka6E).This is the limit for flights in smooth air. Sometimesthere is a dive airspeed limit but the VNE is used inthis case.

Wind Gust Loads

Wind gusts create transient increased loads on theglider, especially the wings and elevator. The gustcan come from any direction. The most dramaticload increases usually comes from wind gusts up anddown. Gusts from the front will also increase lift(and load) while those from the rear decrease lift andcan lead to a stall when the airspeed is low enough.

It can be shown that upward gusts increase the loadproportional to the gust speed times the airspeed ofthe glider. These gusts increase the attach angle ofthe wing to the flow of air. This increases the lift ofthe wing. The increase load due to gusts is shown asa sloped line from the load factor of 1 a zeroairspeed to a limiting gust speed on the chart below.Smaller wind gusts have load lines of lesser slope.

An upward gust can also stall the glider byincreasing the angle of attack enough to put the wingin its stall region. A downward gust would reducethe lift and can create a negative load in very stronggusts, hence there are limits for such gusts

The glider is limited in airspeed in rough air becauseof the possibility of load damage at higher speeds.The Ka6E is limited below 75 knots in rough air.This is also the limit for aerotow since tubulencefrom prop wash, rotor, or thermal gusts are possiblypresent on launch.

Glider DesignHistory and Evolution (Outline)Construction:

- Wood and Fabric- Steel Frame and Fabric/Plastic- Plywood and fabric (laminar airfoil)- Fibreglas - Carbon Fibre and Fibreglas*(longer thinner wings - large aspect ratio)

Type- Primary- Single Seat Enclosed Cockpit- Two Seat (training method change)

Variations- V-tails (reduce drag)- All-flying tail- Water Ballast- Flying Wings- Motor Gliders

Refinements:- flaps (variable profile wing)- Winglets (reduce vorices - reduce drag)

*NOTE on drag and glider design: The total dragcoefficient is given byCD = CDo + (k CL

2/ππππA)Where Cdo is the coefficent for parasitic drag andCL is the lift coefficient, k is a geometry factor andA is the wing aspect ratio. To reduce CD, decreaseCL and increase A.

Resource:“The Complete Soaring Pilot’s Handbook” Revised Edition 1977 By Ann and Lorne Welch and Frank Irving


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David McKay Co., New York, New York

“Wings Like Eagles: The Story of Soaring in theUnited States”By Paul A. Schweizer1988 Smithsonian Institution Press


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Advanced Aerodynamics