Lecture_3 - Drag

8/15/2019 Lecture_3 - Drag

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MAE 154S Fall 2015

D.Toohey - University of California, Los Angeles

Lecture 3 - Drag

•

Aircraft Drag

74

Photo Courtesy USAF


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Two types of drag

• All types of drag can be included in these two groups:

– Skin friction drag• Results from the viscous shearing forces tangential to body’s surface

• Influenced by Reynold’s number and surface roughness

–

Laminar flow leads to lower skin friction coefficients than turbulent flow

– Pressure Drag• Results from pressure distribution normal to body’s surface

•

Dependent on Reynold’s number, projected frontal area. – Laminar flow can lead to an adverse pressure gradient that increases drag

• In general, both skin friction and form drag are difficult to

predict.

• Usually experimental wind tunnel tests are required to obtainaccurate predictions

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• Induced angle of attack due to downwash tilts liftvector backward.

• With respect to free stream AoA, a component of thelift vector is in the drag direction.

Reduce Induced Drag by: – Increasing Aspect ratio

– Optimizing spanwise lift distribution

– Disrupting tip vortices at wingtips

Induced Drag

!!"

#$$%

&=

Ae

C C

L

Di

'

2

76

!!"#$$

%&+= Ae

C C C L

D D

'

2

min

!i

!i

Di

L


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D =1

2" V

2SC D p +

1

2" V

2SC Di

Drag Equations

77

DSC V D

2

2

1 ! =

C D =C DP +C L

2

" Ae

If flying straight, then liftequals weight (L = W).

W = L =1

2

" V 2SC

L

C L=

2W

" V 2S

Parasite Drag Induced Drag


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Interference Drag

79

High Wing

Mid Wing

Low Wing

• Interference Drag: –

When two objects are placed in close proximity, theirboundary layers and pressure distributions interactwith each other.

–

The net drag is higher than the sum of eachcomponents’ drag by itself.

• Placement of wing on fuselage affects

interference drag. – In general, high wing configuration is better than low

wing.

– Low wing interference caused by airflow on top ofthe wing, which is usually has a more turbulent and

thicker boundary layer. –

However, low wings are better suited for retractablelanding gear.

• Also, to minimize interference drag, smooth

out sharp angles whenever possible


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Trim Drag

•

Drag due to horizontal tail loadsneeded to balance aircraft about pitchaxis.

•

Drag changes mainly a result ofchanges in induced drag on tail.

•

CG locations strongly influenced trimdrag. CG too far forward may result in

increases in trim drag.

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Designing for Drag Reduction

• Reducing Skin Friction – Laminar airfoils can be used, but not always very realistic depending

on the materials and construction tolerances being used.

– Wetted area should be minimized, usually by having the fuselage taperin the back. However, useful volume of fuselage is sacrificed.

– Can consider optimum fineness ratio for fuselage. However, thisusually isn’t very realistic either. Most aircraft fuselages are longer toprovide sufficient moment arms for tail control surfaces.

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Lancair 360

Photo by Omoo


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Designing for Drag Reduction

•

Reducing form drag – Make as streamlined as possible

– Retractable landing gear (added

complexity)

– Shorter wings lower cross-section and

reduce parasite drag (leads to increased

induced drag)

–

Avoid flow separation

82

F-104 Starfighter (1958)

Photo Courtesy USAF

•

Wingspan: 21 ft 9 in (6.36 m)

• Wing area: 196.1 sq ft (18.22 m")

• Loaded weight: 20,640 lb (9,365 kg)

• Aspect ratio: 2.45

•

Maximum speed: 1,328 mph• Rate of climb: 48,000 ft/min

• Wing loading: 105 lb/sq ft (514 kg/m")

•

Thrust/weight: 0.54 with max. takeoffweight (0.76 loaded)

• Lift-to-drag ratio: 9.2


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Laminar Airfoils

• Laminar airfoils are shaped to prevent or delay the onset of turbulentflow in order to reduce skin friction

• Laminar airflow is difficult to produce.

– Airfoil must be very smooth to promote laminar flow

•

For laminar airfoils, favorable pressure conditions only exist for anarrow CL and AoA range, leading to a “drag bucket” on the dragpolar.

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Richard Whitcomb (1921-2009)

• Richard Whitcomb was an American

aeronautical engineer that worked for Langley

Research Center. He made 3 very significantcontributions to aircraft aerodynamics:

– Transonic Area Rule

– Supercritical Airfoils

– Winglets

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Winglets

• Winglets alter the structure ofthe trailing vortex system.

•

Sidewash velocity produces anangle of attack acting on the

winglet.

– Outward flow from beneath the

wing, inward flow on top.

– Lift force acting on winglet has a

forward component, resulting in

the generation of “negative drag.”

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Airbus A319 wingtip fence

Photo Courtesy NASA

Photo by D. Nehrener


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Compressibility

• Critical Mach Number:

– Mach number of the

aircraft at which the local

Mach number at some

point of the wing becomes

1.0

–

Mach numbers above the

critical mach number result

in shock waves forming on

the wing

• Divergence Mach No.

– Mach number at which the

aerodynamic drag of awing increases rapidly as

the Mach No. continues to

increase

–

Usually close to but

always greater than the

critical mach number

88

Image Courtesy of FAA


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Drag Divergence

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Transonic Area Rule

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Early version of the F-102 Delta Dagger withits straight fuselage design. Aircraft

performance was disappointing – designed

to fly Mach 1.2 but could not exceed Mach 1.

Later variants of the Delta Dagger followedthe transonic area rule.


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Transonic Area Rule

•

Not all aircraft follow the Area rule by narrowing the fuselage

at the wing location. This would not make much sense for

passenger aircraft that desire large fuselage volume.

• Instead, anti-shock bodies can be added to the aircraft to help

keep the changes in cross-sectional area smooth.

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Supercritical Airfoil

• At transonic speeds, drag for agiven lift coefficient can bereduced if using a supercriticalairfoil.

•

Airfoil shape results in a morerearward location and decrease inthe strength of the shock wave

• Onset of boundary layerseparation is also delayed to ahigher Mach number

• Lift is lost due to reducing theupper surface curvature, but thisis made up for by the supersonicflow on the upper surface, and bythe large camber on the rearportion of the airfoil

93

Image Courtesy of NASA


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Swept Wings and Supersonic Aircraft

95

• Airflow behind the shock isreduced such that thecomponent of the flow normal tothe shock is subsonic.

• As long as the aircraft lies within

the cone-shaped shock, it willsee subsonic flow.

• As Mach No. increases,the shock angle increases.

•

• At Mach 2, aircraftsweep angle wouldneed to be 60°

sinµ =1

M


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Swept Wings and Supersonic Aircraft

• Aircraft with high wing sweep suffer in performance at lowspeeds. – Loss in maneuverability

– High stalling angle

• Some aircraft like the F-14 employ variable sweep wings for

different flight conditions.

96

Photo Courtesy US Navy


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Ground effect

•

Ground proximity prevents trailingvortices from fully forming leading

to a reduction in induced drag

• With the downwash reduced, the

‘Wing in Ground’ effect increases

the effective angle of attack, makingthe wing more effective at

producing lift.

97

Image Courtesy of Flarecraft

Russion A-90 Orlyonok Image from of Wikimedia Commons Mike79Russia


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Drag Estimation

P L Misc

ii

P D D

comp

i ref

wet f ii

D C C S

S C Q K C

&

#

1

++= !=

98

Component build-up method

– Estimate parasite drag on various aircraft components

exposed to flow.

–

Add them up to estimate parasite drag for entire aircraft.

Sref : reference area (wing area)

Cf : skin friction coefficientK: form factor

Q: interference factor

CD,misc: additional miscellaneous drag terms

CD,L&P: Leakage and protuberance


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Drag Estimation

• There are various empirical equations that can be used to estimate the variousdrag terms…

–

Skin friction can be estimated withRaymer eq. 12.27

– Raymer eq. 12.30 estimates theform factor for wings, tails,canards, etc.

– Raymer eq. 12.12 can be usedto estimate form factor for smooth

surfaces like fuselages

–

Interference Factors are harder to estimate, but values range from 1 to 1.25 dependingon the surface.. Usually wings have a negligible interference so we can assume avalue of 1. Tail surfaces are vary from 1.03 to 1.08

99

C f =0.455

log10Re( )2.58

1+ 0.144 M 2( )0.65

K = 1+0.6

x /c( )m

t

c

"

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& ' +100

t

c

"

# $

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& ' 4(

) *

+

, - 1.34 M 0.18 cos .

m( )0.28[ ]

!!"

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&++=

400

601

3

f

f K

d

l f =


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References

1. McCormick, B.W., Aerodynamics, Aeronautics and Flight Mechanics,2nd edition, Wiley & Sons, 1995

2. E. Field, MAE 154S, Mechanical and Aerospace Engineering

Department, UCLA, 2001

3. Raymer, D.P., Aircraft Design: A Conceptual Approach, AIAA

Education Series

101

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