Ch4Wing&Airplane

8/13/2019 Ch4Wing&Airplane

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INTRODUCTION TO AERONAUTICS: A DESIGN PERSPECTIVE

CHAPTER 4: WINGS AND AIRPLANES

After running the engine and propellers a few minutes to get them in working order, I got on themachine at 10:35 for the first trial. The wind, according to our anemometers at this time was lowing alittle o!er "0 miles# "$ miles according to the go!ernment anemometer at %itt& 'awk. (n slipping therope the machine started off increasing in speed to proal& $ or ) miles. The machine lifted from thetruck *ust as it was entering the fourth rail.+

rom the -iar& of (r!ille right for -ecemer 1$, 1/03

4.1 DESIGN MOTIVATION

The Lift and Da! "f Win!#The study of airfoils in Chapter 3 gave insight into how wings generate lift, but it did not tell the

whole story. The flow over a wing near the wingtips is very different from the two-dimensional flow

around an airfoil. The differences have profound effects on the lift and drag generated by a wing.Understanding these effects is crucial to the aircraft designer who must shape an aircrafts wing tooptimize its performance. ection !." discusses wing lift and drag theory and analysis methods.

Wh"$e Ai%aft Lift C&'e

#ther components besides the wing contribute to an aircrafts lift. The lift contributions of theaircrafts fuselage, control surfaces, high-lift devices, stra$es, etc. must all be considered in order toaccurately predict an aircrafts lifting capability. The aircrafts ma%imum lift coefficient is one of thegoverning factors in an aircrafts instantaneous turn capability, landing speed and distance, and ta$eoffspeed and distance. ection !.3 describes a variety of devices for increasing an airplanes ma%imum liftcoefficent, while ection !.! presents methods for estimating the lift curve slope and ma%imum liftcoefficient of a complete airplane, including the effects of stra$es, high-lift devices, control surfaces, etc.

Wh"$e Ai%aft Da! P"$a

The drag of all aircraft components must also be included when estimating whole aircraft drag.The variation of an aircrafts drag coefficient with its lift coefficient is called the aircrafts da! ("$a.The drag polar is the $ey information about an aircraft needed to estimate most types of aircraft

performance. &ircraft ma%imum speed, rate and angle of climb, range, and endurance depend so heavilyon an aircrafts drag polar that a '( change in drag can ma$e a huge difference in a )et fighters combateffecitivenes or an airliners profit potential. ection !.* presents a simple method for predicting anairplanes drag polar at low speeds, while ection !.+ describes how high flight ach numbers change anairplanes aerodynamics. ection !.+ also presents methods for estimating a complete airplanes lift curveslope and drag polar at high flight ach numbers. ection !. is an e%ample of an aerodynamic analysisfor a supersonic )et fighter aircraft. The analysis predicts aircraft lift and drag characteristics for achnumbers ranging from to "..

4.) WINGS

The Lan!&a!e/igure !.' illustrates a view of a wing planform with some of the important dimensions, angles

and parameters used to describe the shape of an aircraft wing. The wing span , , is measured from*in!ti(to wing tip. The symbol cis used for the chord length of an airfoil at any point along the wing span.The subscript rindicates the chord length at the wing ""t or the aircraft centerline. The subscript tdenotes the wing tip chord. The overbar denotes an average value of chord length for the entire wing.The symbolAis used for a parameter called a#(e%t ati". &spect ratio indicates how short and stubby or

long and s$inny the wing is. The symbol is used for wing #*ee( an!$ewith the subscript2denoting

0'


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the wing leading edge. The subscript "5denotes the line connecting the "*( chord positions on each

airfoil of the wing. The symbol is used for the wing ta(e ati", or ratio of tip chord to root chord.

b

ct

cr

12

=

=

=

c

c

A0 3

3 c

t

r

"

."5 c

(4.1)

(4.2)

(4.3)

+i!&e 4.1 +inite Win! Ge",et- Definiti"n#

/igure !." shows a side view of the wing to illustrate the an!$e "f t*i#t. 1ings which aretwisted so that the wing tip airfoil is at a lower angle of attac$ than the wing root airfoil are said to have*a#h"&t. 1ing twist in the opposite sense from washout is *a#hin. 1ing twist of this sort is also called!e",eti% t*i#t. &n effective twist of the wing can also be achieved by changing the airfoil shape alongthe wing span. 2f the airfoil at the wingtip has less camber than the airfoil at the root, this has much thesame affect on the wing lift as if the airfoils were the same but the wingtip airfoil was at a lower angle ofattac$ than the root. Changing airfoils along the wing span in this way is called ae"d-na,i% t*i#t.

Angle of Twist

Root

Tip

+i!&e 4.) Win! T*i#t

Win!ti( V"ti%e#The flow around a wing section which spans the test section of a wind tunnel appro%imates the

flow around a wing with an infinite span, no twist, and a constant chord length along its span . 2n Chapter3,this type of flow was labeled two-dimensional, because flow properties did not vary in the direction.The flowfield around a finite *in!, or wing with a finite span is not two-dimensional. The ma)ority ofdifferences between the flow around a finite wing and that around an infinite wing result from flow

phenomena which occur at the wingtips. /igure !.3 shows a front view of the flowfield around a finitewing. ote that the differences between the pressures above and below the wing which produce lift also

produce a strong flow around the wing tip. The arrows in /igure !.3 are intended to illustrate a front viewof flow streamlines in the plane of the *( chord point on the wing. The lengths of the tails of the arrowsdo not indicate the magnitude of the velocity vectors. #f course, the actual magnitudes of the velocityvectors must be such that there is no flow through the surface of the wing.

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TOP SURFACE

BOTTOM SURFACE

(relative low pressure

(relative !ig! pressure

"ownwas!

+i!&e 4. +"nt Vie* "f Win! *ith +$"* A"&nd the Win! Ti(#

&s shown in /igure !.!, these circular flow patterns around the wing tips become concentratedinto very strong tornado-li$e swirling flows $nown as *in!ti( '"ti%e#or tai$in! '"ti%e#. The trailingvortices generated by large aircraft persist for many miles behind them and can pose serious hazards tosmaller aircraft which encounter them. &ir traffic controllers must allow sufficient spacing betweenaircraft so that the action of air viscosity and turbulence can dissipate a preceeding planes trailingvortices before the arrival of the ne%t one. This spacing re4uirement to allow vorte% dissipation is thelimiting factor on traffic density at most commercial airports.

+i!&e 4.4 Tai$in! V"ti%e#

D"*n*a#h

&lso note in /igure !.3 that the circular flow pattern around the wingtips results in a downwardcomponent to the flow over the wing. This downward flow component is called d"*n*a#h. /igure !.*shows that downwash adds vectorially to the freestream velocity to change the direction of the flowvelocity. ote that the resulting total velocity vector still results in flow parallel to the wing surface, butthe orientation of the effective free stream velocity direction relative to the airfoil is altered.

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4

"ownwas!Effective free strea# $irection

in vicinit% of t!e wing

+i!&e 4./ D"*n*a#h

The change in flow direction due to downwash is called the d"*n*a#h an!$e, and is given the

symbol . The angle between the airfoil chord line and the local flow velocity vector is called the

effective angle of attac$, eff. 5ach individual wing sections lift, drag, and angle of attac$ vary with theairfoils orientation to this local flow direction, but the whole wings lift, drag and angle of attac$ muststill be defined relative to the free stream direction. /igure !.+ reveals that, as a conse4uence of thechange in effective flow direction caused by the downwash, the effective angle of attac$ of the airfoil isreduced, and the lift generated by each airfoil has a component in the wings drag direction. Thiscomponent of lift in the drag direction is called ind&%ed da!. The reduction in effective angle of attac$due to the downwash causes the wing to produce less lift than it would if there were no downwash.

C!or$ line

&ift

'n$uce$ "rag( " i

Parallel to

c!or$ line

&ocal flow

$irection

i

eff

4

+i!&e 4.0 D"*n*a#h An!$e and Ind&%ed Da!

/igure !. ilustrates lift coefficient curves for an airfoil and for a finite wing with the same airfoilsection shape. ote that cldenotes two-dimensional airfoil lift coefficient while6

7 6 7 8!.!9

is used for the three-dimensional finite wing lift coefficient. This same convention will be followed for cdand6

-7- 6 7 8!.*9

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&ift Per Unit Span

)b*+,b*+

+i!&e 4. E$$i(ti%a$ Lift Di#ti3&ti"n

+i!&e 4.5 The S&(e,aine S(itfie and Re(&3$i% P24 Th&nde3"$t +i!hte Ai%aft "f W"$dWa II 6"th Had E$$i(ti%a$ Win! P$anf",# 7Ph"t"# C"&te#- Nati"na$ Ai and S(a%e Me&,8

+inite Win! Ind&%ed Da!

/igure !.+ shows that induced drag is a component of the three-dimensional lift in the dragdirection6

- 1 5 5i - 1i

= =sin sin or 8!.9

2t can be shownthat the induced angle of attac$ everywhere along the span of wings withelliptical lift

distributions is given by6

= =

A0radians

A0degrees1 1

* 3.

/or small, sin 8in radians9 and 6

5 5 5 5

A0

5

A0- 1 1

1 1

i= = =

"

8!.09

S(an Effi%ien%- +a%t"

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54uation 8!.09 applies only to wings with elliptical lift distributions. ?owever, it is possible tomodify 8!.09 slightly to ma$e it apply to any wing by using a #(an effi%ien%- fa%t", e, such that6

5 5

e A0-

1

i=

"

8!.ressure @rag

2nduced @rag

Total @rag

+i!&e 4.19 +inite Win! T"ta$ Da!

Win!$et# and Ti( P$ate#

& variety of devices have been used on aircraft to reduce induced drag. /igure !.''8a9 showsthree such devices. #f the three, the winglet is the most effective and most widely used. 2n addition, )et

fighter aircraft which carry fuel tan$s or air-to-air missiles on their wingtips e%perience a small reductionin induced drag when such wingtip stores are in place. &ll of these devices inhibit the formation of thewingtip vortices and therefore reduce downwash and induced drag. /igure !.''8b9 shows a winglet onthe wingtip of a c@onnell-@ouglas C-'.

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TipPlate

Front -iew Front -iew Front -iew

"roope$Tip .ing

let

7a8 Thee Ind&%ed2Da!2Red&%in! Win!ti( De'i%e#

738 Win!$et# "n a C21 7USA+ Ph"t"8

+i!&e 4.11 Win!ti( De'i%e# f" Red&%in! Ind&%ed Da!

#f course, )ust e%tending the wing to increase its span and aspect ratio will have a similar effect.?owever, the increased lift far out at the end of the wing will increase the bending moment at the wingroot and create greater loads on the wing root structure. The winglet increases wing span only slightly. 2tis preferred because it achieves an effective increase in aspect ratio without significantly increasing wingroot structural loads.

+inite Win! Liftince the the induced angle of attac$ for a wing with an elliptical lift distribution is constant

everywhere along the span, it is relatively easy to determine the lift of such a wing. 2f the wing has anelliptical planform and no geometric or aerodynamic twist, it will have an elliptical lift distribution for awide range of angles of attac$. & twisted rectangular or tapered wing will normally achieve a true

elliptical lift distribution at only one angle of attac$. The elliptical planform wings zero-lift angle ofattac$ will be the same as for its airfoil section. &t an arbitrary positive angle of attac$ below stall, anelliptical wings effective angle of attac$ will be given by6

eff1

A0= =

* 3. 8!.''9

&s shown in /igure !., the airfoil and finite wing lift curve slopes may be represented as6

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c c

5 5

l

l

l

1

1

1

=

== =8 9 8 9

8!.'"9

where is any arbitrary angle of attac$ in the linear range of the lift curves. and clare the lift

coefficients at that arbitrary value of . /rom /igure !. we recognize that6

c c

A01 1 1 l eff 1 l

11= = = = = =

8 9 8 9 8.

9 * 3

8!.'39

Combining 8!.'"9 and 8!.'39, the e%pression for 51becomes6

c

c

A0

1

l

l

=+'

* 3.

/ollowing the same convention as in 8!.9 for non-elliptical wings, the e%pression can be written6

c

c

e A0

1

l

l

=+'

* 3. 8!.'!9

ote that in general for a given wing, the value of ere4uired for 8!.'!9 is not the same as that re4uired for8!.9. The two values are typically 4uite close to each other, however.

Ea,($e 4.1& wing with a rectangular planform, a &C& "!'" airfoil, a span of * m and a chord of " m is

operating in standard sea level conditions at a free stream velocity of !" m;s and an angle of attac$ of 0degrees. 2f the wings span efficiency factor is .


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cl

=

=

'.*

0;

o o

o

8 9.

"'*

&lso from /igure 3."0, forcl7 '.* ande7 *. million6

cd7 .


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7 7 8 .*+ 8',0 ;m"9 8' m "9 7 +, '" !

-7 -7 8 .** 8',0 ;m "9 8' m "9 7 *<

2t is in teres t ing to compare these result s with the forces genera ted by an a ir foil in a

wind t unne l with t he same geomet ry and free s tr eam condi ti ons , but purely two-

dimensional flow around it, as ca lcula ted in 5%ample 3 .< . The decrease in lift andincrease in drag caused by the three- dimensional flow around the fini te wings tips

is significant.4. HIGH2LI+T DEVICES

=elatively thin airfoils with low camber generally give low drag at high speeds. Unfortunately,these airfoils also typically have relatively low values of ma%imum lift coefficient. ost aircraft aree4uipped with devices which can be used to increase lift when needed, at the e%pense of additional drag.These devices are of several types.

Tai$in!2Ed!e +$a(#

oveable surfaces on the rear portion of the wing which can be deflected downward to increasethe wings camber are called tai$in!2ed!e f$a(#or simply flaps. /igure !.'" shows four different typesof flaps. The plain flap changes camber to increase lift, but its effect is limited by additional flow

separation which occurs when it is deflected. The additional separation occurs because the upper surfaceof the deflected flap e%periences a stronger adverse pressure gradient . The split flap deflects only theunderside of the trailing edge so that, while it creates a great deal of pressure drag, it avoids the strongadverse pressure gradient on its upper surface and therefore $eeps the flow attached slightly longer. Thisgives the split flap slightly greater lift.

+i!&e 4.1) Tai$in!2Ed!e +$a(# 7Ada(ted f", Refeen%e 18

S$"tted f$a(#have a gap or #$"tin them to allow faster-moving air from the lower surface to flowover the upper surface. The higher-energy air from the slot gives the boundary layer more energy to fight

the adverse pressure gradient and delay separation. & single-slotted flap creates the slot by moving awayfrom the wing slightly when it is deflected. @ouble- and triple-slotted flaps are also used. 5ach slotadmits more high-energy air onto the upper surface to further delay separation and increase lift. The+"*$e f$a( movesaft to increase the wing area before deflecting downward to increase camber. /owlerflaps usually have one or more slots to increase their effectiveness.

/igure !.'3 shows airfoil lift and drag coefficient curves for a typical trailing-edge flap. otethat in general the effect of flaps is to increase camber, moving the lift curve up and to the left. /or flapsother than /owler flaps the lift curve slope is unchanged. The angle of attac$ for zero lift is made morenegative. 1ith the flap e%tended, the wing generates more lift at all angles of attac$ below stall. The


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ma%imum lift coefficient is greater, but it occurs at a lower angle of attac$. The amount of this shift in

l80and increase in ma9is different for each type of flap. lots in flaps help delay the stall to higherangles of attac$ and higher values of ma9. The lift curve slope increases when /owler flaps are used.This is because /owler flaps increase the actual lifting area of the wing when they are e%tended, but thelift coefficient is defined using the same reference planform area as when the flaps are retracted.

Basic Wing Section

Wing with Flap

CL

Basic Wing Section

Wing with Flap

CL

CD

+i!&e 4.1 Lift and Da! C"effi%ient C&'e# f" Win!# *ith +$a(#

Sta;e# and Leadin!2Ed!e Etenti"n#/igure !.'! shows a #ta;e on an /-'+. & similar device on the /-'0 is referred to as a$eadin!

ed!e eten#i"n 7LE


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+i!&e 4.10 Leadin!2Ed!e +$a(# and 6"&nda- La-e C"nt"$ De'i%e# 7Ada(ted f", Refeen%e 18

6"&nda- La-e C"nt"$ince flow separation and stall are caused by depletion of flow velocity in the boundary layer,

several methods may be used to remove or re-energize this low-energy air and delay separation. #nemethod is to drill thousands of tiny holes in the wing surface and use #&%ti"nto pull the low-energy airinside the wing. &nother method is to use 3$"*in! of high-velocity air tangent to the wing surface to re-

energize the boundary layer and delay separation. &ir for tangential blowing is normally obtained as3$eed aifrom a )et engines compressor. :oth of these boundary layer control devices delay separationand stall to higher angles of attac$. Their lift curves loo$ similar to those for leading-edge devices shownin /igure !.'. 5%amples of boundary layer suction and blowing are illustrated in /igure !.'+.

Basic Wing Section

Wing with Leading-Edge Flap or Slat

or Boundary Layer Control

CL

+i!&e 4.1 Effe%t "f Leadin!2Ed!e +$a(# and 6"&nda- La-e C"nt"$ "n Lift C"effi%ient C&'e#

P"*eed Lift and Ve%t"ed Tht

&n intena$$- 3$"*n f$a(or>et f$a( has bleed air directed onto its leading edge and uppersurface from the rear of the wing. The high-velocity air delays separation and increases lift. /igure!.'08a9 shows a typical internally blown flap configuration. 5ngine e%haust may also be used to increaseor assist lift. /igure !.'0 shows three ways this may be done. The e%haust may be directed at the leading

edge of a flap as on the c@onnell-@ouglas C-', or at the wing and flaps upper surface, as on the:oeing BC-'!. 2n either case, the vastly increased airflow over the flap increases lift. The engine nozzlemay also be moveable to redirect or 'e%t"the engine e%haust downward. This re-orients the enginethrust vector so that it has a component in the lift direction to assist the lift generated by the wing. &lsonote in /igure !.'0 the multiple slots in each /owler flap. everal high-lift devices are often usedtogether on an aircraft. 5ach device adds to the total ma9. 2n some cases the devices complement eachother so that the total increase in ma9for several devices used together is greater than the sum of the ma9increments for each device used alone.


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7a8Intena$$- 6$"*n +$a(

738Etena$$- 6$"*n +$a(

7%8U((e2S&fa%e 6$"*in!

7d8Ve%t"ed Tht

+i!&e 4.1 +"& P"*eed Lift C"nfi!&ati"n# 7Ada(ted f", Refeen%e 18

4.4 WHOLE AIRCRA+T LI+T

& complete aircraft will fre4uently generate significantly more lift than its wing alone. &nestimate of a whole aircrafts lift can be made by summing the lift contributions of its various components.The following is a simple method for ma$ing an initial estimate of an aircrafts lift. The method issuitable for use in the early conceptual phase of design.Win! C"nti3&ti"n

/or most aircraft, the ma)ority of the lift is generated by the wing. The finite wing lift predictionmethods discussed in section !." give good initial estimates of wing lift curve slope, provided an


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appropriate value of ecan be estimated. The results of e%tensive wind tunnel testing"of a vast variety ofwing shapes suggest the following empirical e%pression for e6

eA0 A0 t

= + + +

"

" ! '" "8 tan 9ma%

8!.'*9

where tma9 is the sweep angle of the line connecting the point of ma%imum thic$ness on each airfoil ofthe wing.

#ne effect of airfoil camber and wing twist on lift is to shift the zero-lift angle-of-attac$. & wayto avoid the need for predicting zero-lift angle-of-attac$ early in the design process is to wor$ in terms ofa3#"$&te an!$e2"f2atta%;6

a7 - 7 8!.'+9

:ecause of the way ais defined, it always e4uals zero when lift is zero. Using absolute angle of attac$ isusually ade4uate for early conceptual design.

5stimating wing ma%imum lift coefficient is difficult without more advanced analysis methods.?owever, a practical constraint of ta$eoffs and landings leads to a simple way to estimate the ma%imumusable lift coefficient for those two phases of flight. /igure !.'< shows an aircraft with a ti%-%$e$andin! !eaon a runway. 1hen the aircraft accelerates to ta$eoff speed, it must "tateto the ta$eoffangle of attac$ in order to generate enough lift to become airborne. The aircraft normally tips bac$ on its,ain $andin! !eaas it rotates. The amount which the aircraft can rotate is limited by the tail stri$ingthe ground. This limitation also applies to landing, since the aircraft will be at its landing angle of attac$when it touches down. /or many aircraft this angle is well below the wings stall angle. Therefore, the

ma%imum usable lift coefficient for ta$eoff or landing may be estimated as the wing lift curve slope, ,

multipled by the ma%imum usable absolute angle of attac$, ama9 7 '*o- 7, in the case of /igure !.'


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the increment can be appro%imated by another rule of thumb. &ircraft often use partial e%tension of flaps

for ta$eoff and full flaps for landing. &s a first appro%imation, a '-degree increment in a for ta$eoffflap settings and '* degrees for landing flaps is acceptable.

/or flaps which do not span the entire wing 8a much more common situation9, the increment in

a is scaled by the ratio of f$a((ed aea, f, to reference planform area, . f is the area of that part of

the wing which has the flaps attached to it. /igure !." depicts f 8shaded gray9 for a typical wing.

Flap FlapFl

appe$

Area F

lappe$Area

!0l0

+i!&e 4.)9 +$a((ed Aea and +$a( Hin!e Line S*ee( An!$e

#nce fis determined, the change in ma%imum usable absolute angle of attac$, a, is given by6

a af

h l-

3

3=

"cos . . 8!.'09

where h l. . is the sweep angle of the flap hinge line, as shown in /igure !.". 1ith aestimated, thema%imum usable lift coefficient with flaps is appro%imated as6

51ma% 1 no flapma% 8 9+ 1 a 8!.'


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Basic Wing Section

Wing with Flap

CL

$a% &sa'le Angle of Attack

+i!&e 4.)1 Effe%t "f +$a(# and Mai,&, U#a3$e An!$e "f Atta%; "n Ca1

+e$a!e and Sta;e#&n aircraft fuselageisusually relatively long and slender and therefore does not produce much

lift. 2n the region of horizontal lifting surfaces, however, the lift being generated by those surfaces carriesover onto the fuselage. This effect is modeled by treating the wing as if it e%tends all the way through thefuselage without any change in airfoil, sweep, or taper. 2n fact, the fuselage shape is significantlydifferent from the wings airfoil shape and may be less effective at producing lift. ?owever, since thefuselage lifting area is generally larger than the portion of the wing in the fuselage, the two effects may betreated as canceling each other out, at least for early conceptual design.

/or fuselages with stra$es or leading edge e%tensions, the effect should be included, even for afirst estimate. /or angles of attac$ below '* degrees, the stra$e vorte% is not very strong, and e%tensivewind tunnel testing3has shown that the lift curve slope of the wing with stra$e may be modeled as6

3 3

31 1

strake

8 9 8 9with stra$e without stra$e=

+ 8!."9

wherestrakeincludes only the e%posed surface area of the stra$e, not any portion inside the fuselage.

ince 7 '* degrees is usually the ma%imum usable , 8!."9 is ade4uate for the usable range.

H"i?"nta$ Sta3i$i?e# and Canad#

The purposes of additional horizontal lifting and stabilizing surfaces on an aircraft will bediscussed in Chapter +. /or a first estimate of the lift contributions of these surfaces, it is sufficient totreat them as additional wings. ?owever, the downwash created by the main wing will change theeffective angle of attac$ of smaller horizontal surfaces in the wings. /igure !."" illustrates this effect.The figure also shows an&(*a#h field which increases the effective angle of attac$ of horizontal surfacesahead of the wing. #f course, these smaller surfaces also create their own upwash and downwash. Theseupwash and downwash fields due to smaller surfaces will be ignored, because they are generally muchwea$er than those of the main wing.

&pwash Downwash

+i!&e 4.)) U(*a#h and D"*n*a#hTo determine a horizontal surfaces contribution to the whole aircrafts lift curve slope, it is first

necessary to determine the rate at which downwash 8or upwash as appropriate9, , changes with changingaircraft angle of attac$. 2n the e%treme case where the rate of change in the downwash angle e4uals the


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where uis the upwash angle and lc is the distance from the wings 4uarter chord to the canards 4uarterchord as shown in /igure !."3.

#nce

uis estimated, the canards contribution to the aircrafts is appro%imated as6

1 8 9due to canard = 51 c '+

u 3

3c 8!."!9

where the subscriptcidentifies 4uantities related to the canard. Contributions of canards to the totalaircraft lift curve slope are typically larger than those for horizontal tails. This is partly due to the canrd

being in an upwash field rather than the downwash field surrounding most horizontal tails. 8#nce thecontributions of canards and horizontal tails are estimated, the whole aircraft lift curve slope is given by6

5 5 5 5 1 whole aircraft 1 ing od& 1 due to hori:ontal tail 1 due to canard 8 9 8 9 8 9 8 9= + ++ +w stra$e 8!."*9

4./ WHOLE AIRCRA+T DRAG

The drag polar for the complete aircraft is written somewhat differently than that for a wingalone. /or the whole aircraft, drag is identified as either (aa#ite da!or da! d&e t" $ift. The parasitedrag is all drag on the aircraft when it is not generating lift. This includes both s$in friction and pressuredrag, as well as several additional types of zero-lift drag which are associated with the complete aircraftconfiguration. The drag due to lift includes all types of drag which depend on the amount of lift theaircraft is producing. These include induced drag due to downwash, the pressure drag which increaseswith lift due to forward movement of the separation point, induced and pressure drag from canards andhorizontal tails, and addition drag such as vorte% drag due to the leading-edge vortices on stra$es andhighly swept wings. &ll of these types of drag may be appro%imated by the following simple e%pressionfor drag coefficient6

5 5 k 5 k 5 - -o 1 1= + +'

"

" 8!."+9

where6k1 8 '6; eoA< 8!."9

and $"is chosen to allow modeling of wings with airfoils which generate minimum drag at some non-zerovalue of lift. -ois called the parasite drag coefficient. 2t represents all drag generated by the aircraftwhen it is not generating lift 8hence the Do subscript9. The variable eoin the e%pression for k'is calledthe O#*a$d@# effi%ien%- fa%t". 2t is not the same as the span efficiency factor, e, used in 54uations 8!.


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0

0.05

0.1

0.15

0.2

0.25

0.3

-1 -0.5 0 0.5 1 1.5

CD( )*)+ , )*.C

L+

CL

CD( )*)//. , )*. C

L+ - )*)0 C

L

CD

C&,inD

A 9.

+i!&e 4.)4 Ea,($e "f Da! P"$a *ith Mini,&, Da! C"effi%ient at N"n2Be" Lift C"effi%ient

Paa#ite Da!

Hust as lift predictions for the early stages of conceptual design rely heavily on the results of windtunnel testing of similar configurations, so drag predictions rely heavily on drag data for similar types ofaircraft. 2n later design stages, it is necessary to ma$e very precise predictions of the aircrafts drag, since

)ust a '( difference in the drag at cruise conditions, for instance, can ma$e the difference between successand failure of a design. The methods used in ma$ing these precise predictions go far beyond the scope ofthis te%tboo$ and re4uire details of the design which are generally not available early in the conceptualdesign phase. 2t is important, however, to understand in a 4ualitative sense where the drag on an aircraftcomes from.

$in friction drag on a complete aircraft configuration is generally much greater than that on the

wing alone, because the *etted aea= wet, is greater. 1etted area of an aircraft is all the surface areaover which air flows, and therefore to which the flowing air imparts shear stress. >ressure drag for thecomplete aircraft includes drag due to separation of the airflow around the aircraft fuselage, controlsurfaces, etc., in addition to the wing. Intefeen%e da! results from flow interactions between thevarious components of an aircraft which cause them to have more drag when assembled together than thesum of their drags when tested in a wind tunnel separately. iscellaneous drags include drag due tocooling air flowing through heat e%changers, air which lea$s through doors and fairings which dont fit

perfectly and around moveable surfaces, plus the profile drag of antenae, gun barrels, sensors, etc. whichprotrude from the aircraft. The total of all these drags is the profile drag of the complete aircraft. To thismust be added wave drag if the aircraft flies at or near the speed of sound. 1ave drag will be discussed ina later section.

& very good initial estimate of subsonic parasite drag may be made from drag data for similaraircraft using the concept of an e&i'a$ent #;in fi%ti"n da! %"effi%ient, fe, which is defined as

follows6

5 5 3

3f -

wete o

= 8!."09

Table !.' lists average fevalues for several classes of aircraft. These values are based on historical data!,*

for large numbers of each type of aircraft. feis a function of such diverse factors as aircraft s$inmaterials and shapeI paintI typical flight =eynolds numbersI number of additional air scoops forventilationI type, size, number, and location of engine air inletsI and attention to detail in sealing doors,control surface gaps, etc. aturally, these details vary significantly from aircraft to aircraft, but the data

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in =eference * suggest that there is enough similarity among aircraft of a given class that useful averagefevalues can be established. Table !.' lists the most commonly used values of fe!,*.

Ta3$e 4.1 C",,"n Cfe Va$&e#

T-(e Cfe

Het :omber and Civil Transport .3

ilitary Het Transport .3*

&ir /orce Het /ighter .3*

Carrier-:ased avy Het /ighter .!

upersonic Cruise &ircraft ."*

Fight ingle >ropeller &ircraft .**

Fight Twin >ropeller &ircraft .!*

>ropeller eaplane .+*

Het eaplane .!

Using fe to predict -o for an aircraft which generates minimum drag when it is generatingzero lift only re4uires selecting a fe for the appropriate category of aircraft and estimating the totalwetted area of the aircraft concept. The value of -o is then obtained by solving 8!."096

3

3- f

wet

o e= 8!."


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1 1 a 1 1

= =

= =

8 9 8 9 since a7 - 80and 7 8!.3"9

and6

5 51

min-1

1=

=

"8!.339

This value of min-is then used for the entire aircraft. This is done because it is assumed thatthe aircraft designer will design the fuselage, stra$es, etc. so that they also have their minimum drag atthe angle of attac$ that puts the wing at its min-. 1hen this is done, the minimum value of -, which isgiven the symbol-min, must not be any lower than the -opredicted by 8!."09. =ecall that -ois theaircrafts zero-lift drag coefficient. /or aircraft with minimum drag at non-zero lift this leads to thefollowing revised predictions6

3

3- f

wet

min e= 8!.3!9

k - - 1o min min-= + '"

8!.3*9

4.0 MACH NUM6ER E++ECTS

The lift curve and drag polar predictions of ection !.* above are valid for relatively low speeds.&s with airfoils 8discussed in ection 3.+9, pressure changes around an aircraft are magnified by densitychanges at higher ach numbers. &s ach number increases to near unity and above, additional changesoccur to the flow which have profound effects on the aircrafts lift and drag

Consider an infinitesimally small body moving in the atmosphere. The body is ma$ing smallpressure disturbances which are transmitted as sound waves. The bodys ach number indicates therelative speed between it and the sound waves it creates. 2f=7 , then the sound waves radiate outwardin concentric circles from the body li$e ripples from the point where a stone lands in a pond. /igure!."*8a9 illustrates this situation.

8a9 =7 8b9= ' 8c9 = 7 ' 8d9 = G '

+i!&e 4.)/ S"&nd Wa'e# Geneated 3- a M"'in! 6"d-2f the body is moving, then the sound waves upstream of it are closer together, because each

successive wave is generated from a point further upstream, and the speed relative to the body at whicheach wave moves upstream is a > 4, since the body is moving the same direction as the wave.@ownstream of the body )ust the reverse is true. The spacing between the waves is greater and the wavesare moving at a ? 4 relative to the body. The closer spacing of the waves upstream of the body causesthe sound to have a higher fre4uency or pitch, while the sound downstream has a lower pitch. This is whythe sound of an automobile horn or train whistle shifts to a lower fre4uency as the vehicle passes. Theeffect is called the D"(($e #hift. imilar shifts in the fre4uencies of reflected radio waves are the basisfor radar speed detectors. The situation is illustrated in /igure !."*8b9.

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The situation when= 8' is illustrated in /igure !."*8c9. ote that the body is moving at thesame speed as the sound waves it emits, so all of the sound emitted by the body reaches a point ahead of itat the same time it does. The sound waves collect into a single pressure wave $nown as a Ma%h *a'e=which is perpendicular to the direction of movement of the body..

1hen=G ', the ach wave trails bac$ from the body at an angle, as shown in /igure !.""8d9.

&n e%pression for, the angle of the ach wave 8also $nown as the Ma%h an!$e9, may be derived fromthe relationship between the velocity of the body and the velocity at which the sound waves move out fromtheir point of origin, as shown in /igure !."+.

-

a

+i!&e 4.)0 Ma%h Wa'e Ge",et-

#n the basis of the geometry of the /igure !."+, the e%pression for is6

= =

sin sin' ' 'a

4 =8!.3+9

Sh"%; Wa'e#

The pressure waves caused by a body moving through the air li$ewise influence the flowfieldahead of the body. Consider now a large body such as an aircraft or missile moving through the air. Theinfluence of the high pressure at a stagnation point on the front of the body is transmitted upstream at thespeed of sound, so that the flow slows down gradually rather than suddenly when encountering it.?owever, as the speed of the body through the air e%ceeds the speed of the sound waves, this process ofJwarningK the air ahead that the body is approaching becomes impossible. 2n such a situation, the

pressure change occurs suddenly in a short distance. This sudden pressure change is called a #h"%;*a'e. &ir flowing through a shoc$ wave undergoes a rapid rise in pressure, density, and temperature, arapid decrease in velocity, and a loss of total pressure. The angle of a shoc$ wave is usually different thanthe ach angle. 2t depends on the ach number and the angular change of the flow direction as it goesthrough the shoc$ wave. /igure !." shows shoc$ waves around a model of the pace shuttle in theU&/ &cademys tri-sonic 8high subsonic, transonic, and supersonic9 wind tunnel. The waves are madevisible by the bending of the light waves as they pass through the regions of rapidly changing air density.

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+i!&e 4.) Sh"%; Wa'e# A"&nd a M"de$ "f the S(a%e Sh&tt$e atM 1. and T*" DiffeentAn!$e# "f Atta%; in the USA+ A%ade,-@# Ti2S"ni% Wind T&nne$

Citi%a$ Ma%h N&,3ehoc$ waves also occur around a body even when it is flying at speeds below the speed of sound.

This happens because the air accelerates as it flows around the body. &n airfoil, for instance, may bemoving at= 7 .0 relative to the free stream, but it was shown in Chapter 3 that the shape of the airfoilcauses the flow to be moving much faster over its upper surface. The local flow velocity over the uppersurface of the airfoil may be greater than the speed of sound. This situation is described by saying the$"%a$ Ma%h n&,3eis greater than one 8= G '9, and the flow in this region is said to be #&(e#"ni%.The free stream ach number6

= 4

a= 83."09

at which the local ach number first e4uals unity is called theCiti%a$ Ma%h n&,3e,=crit. /igure!."08a9 illustrates this situation.

= @ '

= 8 '

= @ '= @ '= G '

= G '= G '

Bow S!oc/

Ter#inating

S!oc/

= G '

= G '

= G '

= 8 '

Obli2ue

S!oc/sObli2ue

S!oc/

Separate$

.a/e

8a9 = 7=crit 8b9=crit = ' 8c9 = G ', :lunt ose 8d9 = G ',harp ose

+i!&e 4.) +$"*fie$d# at Tan#"ni% and S&(e#"ni% S(eed#

&t = 7=crit no shoc$ wave forms, because the local ach number only e4uals '. at one

point. &s = increases above=crithowever, the region where=G ' grows. &s shown in /igure "08b9,pressure waves from decelerating flow downstream of the supersonic region cant move upstream into thatregion, so they Jpile upK into a shoc$ wave. This shoc$ wave at the downstream end of the supersonicregion is called a te,inatin! #h"%;because it terminates the supersonic region and slows the flowabruptly to below the speed of sound. The strong adverse pressure gradient in the shoc$ wave whichslows the supersonic flow also slows the flow in the boundary layer, and often causes it to separate. This

phenomenon is called #h"%;2ind&%ed #e(aati"n. 2t causes a significant increase in drag and decrease in

'*


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lift. The sudden rise in drag as = approaches ' was once thought to be an absolute barrier to higherspeeds. 2t was called the #"&nd 3aie. The ach number at which this rapid rise in drag occurs iscalled the da! di'e!en%e Ma%h n&,3e,=--.

&s = e%ceeds '., another shoc$ wave forms a short distance in front of bodies with blunt orrounded leading edges. &s shown in /igure "08c9, air flowing through this shoc$ wave, called the 3"*

#h"%;, is abruptly decelerated to = '. The subsonic flow downstream of the bow shoc$ may accelerateagain to be supersonic as it flows around the body, but it will e%ert a significantly lower pressure on therear part of the body since it has lost so much total pressure. This low pressure on the rear of the body

produces a great deal of pressure drag which is called *a'e da!. The bow wave is perpendicular ornormal 8it is also called a n",a$ #h"%;9 to the flow directly ahead of the body, but its angle to the flow

becomes the same as the ach angle off to the sides of the bodys path. The terminating shoc$ moves tothe trailing edge of the body, and no longer slows the flow to subsonic.

2f = is sufficiently greater than unity and the leading edge of the body is sharp, the bowshoc$ will touch the bodys point, as shown in /igure "08d9. The shoc$ is said to be atta%hed. 5%cept atthe point of attachment, the flow no longer decelerates below=7', but remains supersonic as it flows

past the body. The shoc$ wave at the leading edge and the one at the trailing edge trail off at an anglewhich initially depends on the shape of the body. /urther from the body the shoc$ angles become the

same as the ach angle. These shoc$ waves are referred to as"3$i&e #h"%;#, because they are notperpendicular to the flow. The loss of velocity and total pressure in obli4ue shoc$s is less than for normalshoc$s.

+$i!ht Re!i,e#The range of ach numbers at which aircraft fly is divided up into f$i!ht e!i,e#. The regimes

are chosen based on the aerodynamic phenomena which occur at ach numbers within each regime, andon the types of analysis which must be used to predict the conse4uences of those phenomena. /igure !."

Ch4Wing&Airplane

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