chapter 09 - forces acting on an aeroplane

8/13/2019 Chapter 09 - Forces Acting on an Aeroplane

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WILJAM FLIGHT TRAINING

Chapter 9.

Forces Acting On An Aeroplane

Forces in Steady Level Flight

An aircraft is said to be in steady straight and level flight when the forces acting on it are in anequilibrium, or trimmed condition, i.e. there is no resultant force to accelerate or decelerate theaircraft. The main forces acting on an aircraft are shown in Fig. 9.1.

THRUST DRAG

LIFT

WEIGHT

FIG. 9.1

Lift acts through the centre of pressure and Weight acts through the centre ofgravity.

Thrust and drag act in opposite senses, parallel to the direction of flight, throughpoints, which vary with aircraft attitude and design.

In steady level flight:

Lift = Weightand Thrust = Drag

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9-2

Lift/Weight and Thrust/Drag Couples

It would be convenient if all four forces acted through a single point, i.e. the centre of gravity(Fig. 9.2).

LIFT

WEIGHT

DRAGTHRUST

CENTRE OF GRAVITY

FIG. 9.2

Unfortunately during flight the forces alter their points of action, and are normally arranged sothat the lift/weight and thrust/drag forces are as follows:

Lift/Weight Couple. Lift acting behind weight causes a nose-down pitch moment andlift acting in front of weight causes a nose-up pitch moment (Fig. 9.3).

CoG

LIFT

WEIGHT

CoP

NOSEDOWN

CoG

LIFT

WEIGHT

CoP

NOSEUP

FIG. 9.3

Thrust/Drag Couple. Thrust acting below drag causes a nose-up pitch moment, andthrust acting above drag causes a nose-down pitch moment (Fig. 9.4).

THRUST

NOSE

DOWN DRAGTHRUST

DRAG

NOSEUP

FIG. 9.4


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To prevent the aircraft rotating the forces can be distributed as shown in Fig. 9.5.

LIFT

DRAGTHRUST

WEIGHT

LIFT

THRUST

DRAG

WEIGHT

(A) (B)

FIG. 9.5

Most aircrafthave the forces arranged, so that if the thrust is removed, i.e. in theevent of engine failure, the remaining lift/weight couple will pitch the aircraft nose-down (without any action by the pilot), so that it assumes a gliding attitude.Alternatively, when power is added, thrust will increase and the nose will tend topitch nose-uptowards a level flight attitude (Fig. 9.6)

LIFT

THRUST

DRAG

WEIGHT

(NOSE-UPMOMENT)

T.DCOUPLE

L.WCOUPLE

(NOSE-DOWNMOMENT)

NOSE-UPMOMENT)

D

L.WCOUPLE

(NOSE-DOWNMOMENT)

CoG

(REDUCED

FIG. 9.6

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The forces are, normally arrangedso that lift acts behind weight and thrust actsbelow drag. There is usually also a considerable difference in magnitude between thetwo pairs of forces, with lift and weight being greatest. In an effort to balance the

pitching moments the spacing between the thrust and drag forces is normally greaterthan the spacing between the lift and weight forces. Ideally, the pitching momentsshould cancel each other out, but in practice this is not always possible and asecondary method of balancing must be used. This is normally provided by thetailplane (Fig. 9.7).

THRUST

LIFT

WEIGHT

DRAG

LIFT

LIFTUPLOAD

DOWNLOAD

FIG. 9.7

On some aircraft Canards or Foreplanes provide the secondary balancing required.Canard type aircraft do not use a conventional tailplane, in this design the horizontaltailplane is replaced with horizontal surfaces mounted in front of the main wing. Therearward location of the main wing allows more of the fuselage to be used as cabinspace than where the wing is mounted at the mid fuselage position (Fig 9.8).

FIG. 9.8

Unlike the conventional tailplane both the canard surface and the wingof the aircraftcreate an upwards lifting forceunder all normal conditions of flight, thus the weight ofthe aircraft is shared over both surfaces allowing a lighter wing loading to be obtainedand therefore a lighter structure to be used.

One of the effects of mounting a small wing forward of the main wing is that the lift from

the canard counters the negative pitching moment of the wing.

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Canards are mounted with a slightly larger angle of incidence than that of the mainwing; with the result that canards have a greater angle of attackthan the main wings(Fig. 9.8). Creation of a positive pitching moment by the wing will lift the nose of theaircraft further increasing the angle of attack of the canard, if the pitching continues thecanard will stall before the wing stalls.

The Contribution of the Tailplane

The tailplane is able to supply the force necessary to balance any residual pitching momentsbecause it is positioned some distance from the aircraft's centre of gravity and has a largemoment arm (Fig. 9.9).

MOMENT ARM

DOWNLOAD

CENTRE OF PRESSURE

WEIGHT

CENTRE OF GRAVITY

FIG. 9.9

For this reason the area of the tailplane and subsequent lift force required need only be small,compared to the lift force produced by the main-plane. If the overall pitching moment isnormally nose-down, it will provide a downward aerodynamic force (down-load) and viceversa.

During some phases of flight, the correcting moment provided by the tailplane may beinsufficient to counteract the out of balance moments, which exist. In this case the liftingcapability of the tailplane needs to be increased and this is achieved by altering the position of

the elevator to provide an upward or downward force. On other aircraft, the actualtailplane position is adjustable to maintain level flight. In producing this force at any givenairspeed an aircraft will experience an increase in drag, known as Trim Drag(Fig. 9.10).

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LIFT

WEIGHTFORWARD

CoG

DOWNLOAD

TRIM

DRAG

FIG. 9.10

Straight Steady Climb

An aircraft possesses a steady climb capability by converting propulsive energy in excess ofthat required to maintain steady level flight into potential energy. An aircraft can either beclimbed steeply at a low airspeed, or be climbed at a higher airspeed at a shallower angle(Fig. 9.11).

MAX ANGLEOF CLIMB VX

MAX RATEOF CLIMB VY

ALTITUDE GAINED INA GIVEN TIME

0 DISTANCE TRAVELLED IN A GIVEN TIME

BEST VERTICAL SPEED

BEST

GRADIENT

STARTOF

CLIMB

FIG. 9.11

If the airspeed is too low or too high, all of the power or thrust available will be needed toovercome the drag, thus reducing an aircraft's climb capability to zero. In a steady climb at aconstant airspeed in a given period of time an aircraft can be climbed at: -

The maximum angle of climb (Vx). This is achieved when an aircraft gains the mostaltitude in the shortest horizontal distance covered, i.e. best gradient. This occurswhen it is flown at a relatively low airspeed, and gives good ground obstacle clearance.

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The maximum rate of climb (Vy). This is achieved when an aircraft gains the mostaltitude in the shortest time. This occurs when it is flown at a small angle of climband a high airspeed.

Forces in a Straight Steady Climb

When an aircraft climbs at a constant airspeed the forces acting on it are in equilibrium, and actas shown in Fig. 9.12.

COMPONENT OF WEIGHT

ALONG FLIGHT PATH

FLIGHTPATH

ANGLE OF CLIMBCOMPONENT OFWEIGHT AT 90TO FLIGHT PATH

DRAG (D)

LIFT (L)

THRUST (T)

TAS (V)

WEIGHT (W)

FIG. 9.12

The angle between the flight path and the horizontal is known as the angle of climb(). Theweight is resolved into two components; one opposing the lift and the other acting in the samedirection as drag.

The following relationships therefore exist:

Thrust = Drag + component of weight opposing flight or T = D + W sin

Lift = component of weight acting perpendicular to the flight path, or

L = W cos .

With increasing angles of climb the amount of lift required steadily decreases, whilst the thrustrequirement increases (Fig. 9.13).

In a steady climb thrust is always greater than drag, andlift is always less than weight.

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FLIGHT

PATH

LIFT

DRAG

THRUST

WEIGHT

FIG. 9.13

FLIGHT PATH

THRUSTLIFT

DRAG

WEIGHT

Straight Steady Descent (Dive)

If the aircraft is placed in a nose-down pitch attitude, and the thrust remains constant, the forcesacting on the aircraft will change. This new attitude will cause a corresponding decrease in theangle of attack, and lift will momentarily become less than weight, causing the aircraft to beginthe descent. A component of weight will act forward along the flight path, and together with thecomponent of thrust, will cause the aircraft to accelerate. The engine is now doing less workcompared with climbing and level flight, and to maintain a constant airspeed the thrust will needto be reduced, until the two components acting along the flight path oppose the drag (Fig. 9.14).

DRAG

THRUST

LIFT

WEIGHT ANGLE OF GLIDE

COMPONENT OF WEIGHTACTING ALONG

FLIGHT PATH

FIG. 9.14

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The forces can be resolved as follows:

Thrust = Drag component of weight acting along flight path, or

T = D W sin

Lift = component of weight acting perpendicular to the flight path, or

L = W cos

This shows that in a straight steady descent lift is less than weight and thrust is lessthan drag.

Steady Straight GlideIf the amount of power available is reduced to zero, i.e. on engine failure, the component ofthrust will reduce to zero, and the drag force will act to decelerate the aircraft. This will lead toan overall reduction in lift, thus unbalancing the lift/weight couple and placing the aircraft in anose-down pitch attitude, i.e. a glide. A component of weight will act forward along the flightpath, and will oppose the drag (Fig. 9.15).

LIFT

DRAG

WEIGHT

THRUST

LIFT

DRAG

WEIGHT

NO THRUST

DRAG

WEIGHT

LIFTCOMPONENT

OF WEIGHTOPPOSING

DRAG

FIG. 9.15

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Forces in a Steady Straight Glide

In a steady straight glide the aircraft will be moving at a constant indicated airspeed, with theengine producing no thrust, and the remaining aerodynamic forces, i.e. lift, drag and weight,being in equilibrium(Fig. 9.16).

DRAG

TOTAL REACTION

LIFT

WEIGHT ANGLE OF GLIDE

NO THRUSTCOMPONENT OF WEIGHTACTING ALONG FLIGHT

PATH BALANCES DRAG

FIG. 9.16

The angle between the flight path and the horizontal is known as the aircraft's angle of glide(). The aircraft's weight is balanced by the total reaction (resultant of lift and drag), and isresolved into two components. One component acts perpendicular to the flight path, andbalances the lift, whilst the other acts along the flight path, and balances the drag.

The forward component also determines the aircraft's forward airspeed. For an aircraft of givenweight, any reduction in the angle of glide will result in a smaller component of weight actingforward along the flight path (Fig. 9.17).

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9-11

DRAG

TOTAL REACTION

LIFT

WEIGHT

LOW LIFT/DRAGRATIO

DRAG

LIFT

TOTAL REACTION

HIGH LIFT/DRAGRATIO

FIG. 9.17

WEIGHT

This will reduce the amount of drag required to maintain a steady glide, and the lift/drag ratio willincrease. The shallowest glide is obtained when the drag is least for the required lift, i.e. best

lift/drag ratio. The lift/drag ratio is therefore a measure of the aircraft's gliding efficiency orperformance. The aircraft will glide furthest through the air, i.e. best glide performance, whenit is flown at an angle of attack and airspeed that gives the best lift/drag ratio (V IMD) asillustrated in the polar diagram (Fig. 9.18).

FIG. 9.18

The Effect of the Lift/Drag Ratio on Glide Performance

Most aircraft are not fitted with an angle of attack indicator, so the airspeed is normally adjustedto correspond to that relating to the best lift/drag ratio, i.e. minimum drag speed (VIMD). This ispossible because in a glide a similar, although not exactly the same, relationship exists betweenindicated airspeed and the angle of attack as that in level flight. This speed is found in theflight-operating manual and is based on an aircraft's all up weight (AUW).


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9-12

Furthermore since the minimum drag speed produces the best glide performance, flight atany other speed will reduce the lift/drag ratio, and consequently increase the angle of glide.This will reduce the aircraft's glide performance, and reduce the overall glide distance

(Fig. 9.19).

TOO SLOW

TOO FAST

70 KT

80 KT

55 KT

BEST L/D RATIOSPEED (VIMD) GIVES

BEST GLIDE DISTANCE

FIG. 9.19

The reduction in the lift/drag ratio at airspeeds above and below the minimum drag speed is dueto; high induced drag at slow airspeeds, and high profile drag at high airspeeds. If theaircraft is gliding at the recommended airspeed for maximum glide distance, and it looks like itwill not reach its designated landing point, the nose should not be raised, since the highernose attitude will decrease the glide distance.

The Effect of a Steady Wind on Glide Performance

A steady wind alters an aircraft's actual flight path and its effective gradient over the ground,thus altering its angle of glide (Fig. 9.20).

ALTITUDE

GROUND

FIG. 9.20

TAILWIND

NIL

WIND

HEADWIND


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A tailwind will increase an aircraft's gliding distanceover the ground, i.e. reduce the angleof glide, whilst a headwind will reduce the distance over the ground, and i.e. increase theangle of glide. The time taken to reach the ground from a given start altitude in either case willremain the same, i.e. glide endurance is unaffected by a steady wind.

The Effect of Weight on Glide Performance

Any change in aircraft weight will require a similar change in lift and drag to maintain the bestglide distance, i.e. range in a straight steady glide (Fig. 9.21).

RESULTANT

LIFT

DRAG

RL

D

W

WEIGHT

FIG. 9.21

The best lift/dragratio will therefore remain unchanged, as will the angle of glide, providedthat the airspeed is adjusted to maintain the optimum angle of attack. The glide distance istherefore unaffected by changes in aircraft weight, but the glide endurance will decreasewith increasing weight, due to the higher indicated airspeed, and vice versa.

Steady Co-ordinated Turn

To understand turning it is important to be familiar with Newton's three laws of motion. When anaircraft is in steady level flight it is in a state of equilibrium (Newton's First Law), but to turn, it isnecessary to apply an external force to change the direction and/or airspeed, i.e. it involves anacceleration (Newton's Second Law). In a steady co-ordinated turn at a constant altitude theaircraft will also be subject to Newton's Third Law of motion.

Forces Acting on an Aircraft During a Steady Co-ordinated Turn

During a steady co-ordinated turn, at a constant altitude, a force must continually acttowards the centre of the turn (centripetal force). If it is not present the aircraft will beunable to maintain a curved path, but instead will fly off at a tangent. When the aircraft isbanked the total lift force is tilted; the horizontal component of lift will provide the centripetal

force, and the vertical component of lift will support the weight of the aircraft (Fig. 9.22).

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9-14

TOTAL LIFTVERTICAL COMPONENT

(SUPPORTS WEIGHT)

HORIZONTAL COMPONENT(CENTRIPETAL FORCE)

LIFT

WEIGHT

ANGLEOF

BANK

OF

FIG. 9.22

Calculation of the Centripetal Force

Newton's second law states that when an external force acts a body it will accelerate in thedirection of the force. The centripetal force acting on an aircraft will give it acceleration towardsthe centre of the turn (radial acceleration). In a steady co-ordinated turn an aircraft of weight WNewton's, travelling at a velocity (TAS)of V metres per second, around the circumference

of a circle of radius r metres, will have an acceleration towards the centre of the circle ofV

2/r metres per second per second, so that: -

Centripetal Force = Mass x acceleration or F = mass xr

2V

=g

Wx

r

2V

where W = Aircraft Weight (kgf)

g = Acceleration due to Gravity (9.81 m/s2)

Turning an Aircraft

To perform a steady co-ordinated turn at a constant altitude the ailerons are used to maintain

the desired angle of bank, whilst the elevator is used to increase the wings angle of attack, andthe rudder is used to balance the turn. The airflowacting on the parts of the aircraft behindthe centre of gravitywill cause the aircraft to yaw towards the dropped wing, but the naturalinbuilt stability will try to resist the turn. The rudder is used to counter adverse yawdue tothe ailerons, and also balances the turn. If the total lift force remained the same as in steadystraight and level flight, the actual amount of lift supporting the weight of the aircraft willeffectively reduce (Fig. 9.23).


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9-15

LIFT

WEIGHT

REDUCEDLIFT

LIFT

45

WEIGHT

45

WEIGHT

LIFTTOTALLIFTLIFT DUE TO

INCREASING AoA

FIG. 9.23

Unless the lost lift is recovered, by primarily increasing the aircraft's angle of attack, it will leadto a loss of altitude. Thus to maintain a steady balanced turn at a constant altitude, the greaterthe angle of bank, the greater the centripetal force, and the greater the total liftrequirement (Fig. 9.24).

30

LIFT

WEIGHT

30 ANGLE OF BANK

60

LIFT

WEIGHT

TOTAL TOTAL

FIG. 9.24

Factors Affecting an Aircraft's Radius of Turn

In order to establish the factors, which affect an aircraft's radius of turn it is appropriate toconsider the forces acting on it (Fig. 9.25)


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9-16

WEIGHT

ANGLEOF

BANK

LIFT (L)

RADIUS OFTURN (R)

CENTRIPETALFORCE

g rW V2

FIG. 9.25

The resulting horizontal and vertical forces, which exist during a steady level turn, are:

L sin =g

Wx

r

2V

and L cos = W

So that: Tan =gr

2V

The aircraft's angle of bankis therefore totally independent of its weight, and depends onlyon its airspeed (TAS), and its radius of turn. By transposing the above formula it is possibleto establish the effect of airspeed and angle of bank, on the radius of turn:

r =Tanxg

2V

For a given angle of bankthe aircraft's radius of turn is solely determined by its airspeed,and for a given radius of turn, the steeper the angle of bank, the higher the airspeed.


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Other factors that determine an aircrafts radius of turn are:-

Wing Loading. This is a fixed valuefor a given aircraft type and weight, and doesnot vary during a turn, even though the wings are producing greater lift per unit area.For a given wing area, the greater the weight, the greater the wing loading. Toestablish the effect of wing loading on the radius of turn it is appropriate to consider twosimilar types of aircraft having the same wing areas, but differing gross weights, i.e.different wing loadings (Fig.9.26).

W1 L

F

W

W1 L

F

FOR A GIVEN LIFT (L)

THE LIGHTER AIRCRAFT HAS AGREATER INWARD COMPONENT (F)AND THUS A SMALLER TURNING RADIUS

FIG. 9.26

W

If both aircraft are turning with their wings at the highest usable angle of attack, anddeveloping the same total lift, the lighter aircraft will be able to achieve a lowerminimum radius of turn. This is because the lighter aircraft has a lower vertical liftrequirement than the heavier aircraft, thereby providing a greater centripetal force foracceleration purposes, thus the higher the wing loading, the greater the minimumradius of turn.

Flaps. The lowering of flaps to the take-off setting in flight is advantageous,particularly when manoeuvring an aircraft at low indicated airspeeds, or in poor visibility.This is because the subsequent rise in the coefficient of lift associated with flapdeflection increases an aircraft's overall lift capability at any given indicated airspeed. Itfollows that since the weight of the aircraft remains unchanged, then the additional liftproduced can provide a larger centripetal force, thus reducing an aircraft'sminimum radius of turn(Fig. 9.27).

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This can only be achieved if the flap limiting speed is not exceeded, and also ifsufficient thrust is available to overcome the additional dragassociated with flapdeflection.

CLEANWITH

IAS

FLAP

RADIUS OFTURN

FIG 9.27

Altitude. The effect of increasing altitudeis to increase an aircraft's minimumradius of turn. This is due to the IAS/TAS relationship, and the reduction in thrusthorsepower.

IAS/TAS Relationship. For a fixed indicated airspeed the true airspeed steadily

increases with altitude, so that for any given angle of bank the minimum radius ofturn must likewise increase.

Reduction of Thrust Horsepower. With increasing altitude the reduction in thrusthorsepower steadily increases, thereby limiting the maximum attainable indicatedairspeed, and reducing the margin above the stalling speed. It follows that insufficientthrust horsepower may be available at altitude to overcome the higher drag associatedwith the increase in angle of attack needed to provide enough lift to sustain a steadylevel turn. The minimum radius of turn therefore increases with increasingaltitude.

Balancing the Turn

If the turn is unbalanced an aircraft will eitherslipinto, or skidout of the turn, thereby reducingthe aerodynamic efficiency of the aircraft. To help correct for these unwanted conditions thebalance part of the turn and balance indicator is used (Fig. 9.28).

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2 MIN TURN

L RTURN INDICATOR

BALANCEINDICATOR

FIG.9.28

When the ball is in the centreit indicates that the turn is balanced, whilst any displacement ofthe ball indicates that the turn is unbalanced (Fig. 9.29).

BALANCED TURN UNBALANCED TURN

RIGHT RUDDERREQUIRED

FIG. 9.29

If the ball is only partially displaced from its centre position the turn may be balanced using onlythe rudder, i.e. ball to the right, apply right rudder. If the ball is at the extremities of the indicatorthe use of rudder alone will produce a highly inefficient turn, and therefore the ailerons are usedinitially to primarily balance the turn.

Slipping turn. A slipping turn will occur if the angle of bank is too large for a given

rate of turn, i.e. the aircraft is over-banked. This is indicated by the ball moving towardsthe lower side of the balance indicator, and you leaning in towards the centre of the turn(Fig. 9.30).

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9-20

L

R

SLIPPING TURN

FIG. 9.30

Skidding turn. A skidding turn will occur if the angle of bank is too smallfor the rateof turn, i.e. the aircraft is under-banked. This is indicated by the ball moving towardsthe upper side of the balance indicator, and you leaning towards the outside of the turn(Fig. 9.31).

L

R

SKIDDING TURN

FIG. 9.31

Balanced turn. During a balanced turn the ball remains in the centre of the balanceindicator, and you remain upright in your seat relative to the aircraft (Fig. 9.32).


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9-21

L

R

BALANCED TURN

FIG. 9.32

Any deviation from a balanced turn is corrected by applying rudder according to theposition of the ball in an attempt to maintain it in the centre, thereby maintaining abalanced turn.

Rate of Turn

This is measurement of how long it takes for an aircraft to turn, and is measured in degrees persecond. This is particularly important when instrument flying where rate-1 turns are usuallycarried out at a rate of 3 per second. This means that the aircraft will turn through 180 in 1minute, or 360 in 2 minutes. A steeper angle of bankwill be required to carry out a rate-1

turn at higher airspeeds.

Load Factor

The additional lift required to maintain a steady co-ordinated turn at a constant altitude will placean increased structural loading on the aircrafts wings. This is because the wings need toproduce lift in excess of the aircraft weight to provide the necessary centripetal force. A ratioexists between the total lift produced by the wings, and the weight of the aircraft. This gives ameasure of the structural loading which, will occur during a balanced turn. This ratio is termedthe load factor.

Load factor =AUW

LiftTotal

In straight and steady levelflight the load factor is one, but during a turn the increased liftrequirement will produce a value greater than one. A relationship exists between angle of bankand load factor, such that:

Load Factor =AUW

LiftTotal=

cos

1

The total amount of lift required in a turn can be directly measured in terms of weight. For

example in a 60 banked turn:


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Total Lift = AUW x

cos

1

06

= 2 x AUW

The wings will have to produce liftequivalent to twice the weight of the aircraft; i.e. the loadfactor is 2. This is more popularly referred to as the g loading, which is sensed as anapparent increase in weight, e.g. at an angle of bank of 60, 2g will be experienced. Thesteeper the angle of bank the greater the load factor, but this is limited by structuralconsiderations (Fig. 9.33).

FIG. 9.33

4

3

2

10 20 4010 30 50 60 70 80

L=2W

L=3W

L=W

LOADFACTOR

L/WOR

g-LOADING

ANGLE OF BANK

The Effect of Turning on Stalling Speed

For any given aerofoil section the indicated stalling speed is related to liftas follows:-

Lift is proportional to (IASSTALL)2

The additional lift required to carry out a steady co-ordinated turn at a constant altitude thus

results in an increase in the stalling speed. Since the angle of bank also determines the amountof extra lift required to support an aircraft in a turn, it is also related to the stalling speed (Fig.9.34).

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9-23

FIG. 9.34

100

5041

1970

0 30 45 60ANGLE OF BANK

PERCENTAGEINCREASE

INSTALLING

SPEED

Fig. 9.34 shows the percentage increase in stalling speed compared to that in steady level flightwith increasing angles of bank. At angles of bank less than 30 the percentage increase installing speed is minimal, but at greater angles it becomes more marked. For example if anaircraft normally stalls at 50 Knots in steady level flight, in a 60 banked turn it will stall at:

141% of 50 Knots = 71 Knots

Like lift, the stalling speed is also related to the load factor, so that:

Stalling Speed in Turn = Normal Stalling Speed x FactorLoad

For example if an aircraft has a normal stalling speed of 60 knots, and a load factor of 2(60 angle of bank) the stalling speed in the turn will be:

60 x 2 = 85 Knots

In this example the stalling speed in the turn has increased by 25 knots, which effectivelyreduces the safety margin, i.e. the margin above the stalling speed (Fig. 9.35).


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9-24

40

60

80

100

120140

160180

200

220240AIRSPEED

KNOTS

STALL SPEEDINCREASESIN A TURN

REDUCED SAFETYMARGIN

AIRSPEEDDECREASES IN A TURN

FIG. 9.35

This margin is further reduced by the reduction in airspeed resulting from the increase ininduced drag, thus steep turns must be avoided when operating at low airspeeds.

Aircraft Response During a Level Banked Turn

Once an aircraft begins a level banked turn the outer wingwill start to travel faster than theinner wing, thus producing greater lift(Fig. 9.36).

L

L

FIG. 9.36


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The aircraft's angle of bank will steadily increase, or the aircraft will have a tendency tooverbank. It is therefore important to apply aileron as appropriate in order to counteract thiseffect and avoid any associated problems, i.e. increased load factor. The rudder is also applied

to maintain a curved flight path, since the faster moving outer wingalso develops increasedprofile drag, and will tend to yaw the aircraft.

Aircraft Response During Climbing and Descending Turns

Previously it was established that during a steady level banked turn an aircraft has a tendencyto overbank because the faster moving outer wing produces greater lift. In climbing anddescending turns this effect is however further complicated by the fact that an aircraft issubject to additional rolling momentsresulting from the variation in each wings angle ofattack. This is because although the whole aircraft covers the same altitude during a completeturn, the wings follow differing spiral paths due to the variation in turn radii.

Climbing Turns. During climbing turns an aircraft describes an upward spiral path.The airflow therefore comes downwards to meet the wings, thereby reducing theirangles of attack, and hence their coefficients of lift (Fig. 9.37).

L L

INNER WING

FLIGHT PATH OF

OUTER WING

LARGER AoA

GAIN INHEIGHT

FIG. 9.37

The faster moving outer wing however results in a smaller reduction in angle ofattack, so that the net coefficient of lift is higher than on the inner wing, therebyproducing greater lift. Its increased velocity further enhances the lifting capability of theouter wing. An aircraft in a climbing turn will therefore tend to overbankmore than in asteady level turn, and if necessary the desired angle of bank should be maintained

using the ailerons.

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Descending Turns. During descending turns an aircraft describes a downward spiralpath. The airflowcomes upwards to meet the wings, thus increasing their anglesof attack, and hence their coefficients of lift (Fig. 9.38).

LARGER AoA

INNER WING

FLIGHT PATH OF OUTER WING

HORIZONTAL DISTANCE TRAVELLED

LOSS INHEIGHT

LL

FIG. 9.38

The increase in angle of attackof the outer wingis however less than that of the

inner wing, as is its lifting capability. The faster outer wing may compensate for thevariation in lift due to the difference in angle of attack, although the aircraft may stilltend to underbank. If this occurs the desired angle of bank should again bemaintained by using the ailerons.

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chapter 09 - forces acting on an aeroplane

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