Aircraft Performance - Drag

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1 Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce this cefficient The drag cefficient (CD) is a nn-dimensinal parameter, but it takes int accunt every aerdynamic cnfiguratin aspect f the aircraft including large cmpnents as wing, tail, fuselage engine, and landing gear; and small elements such as rivets and antenna This cefficient has tw main parts lift-related drag cefficient r induced drag cefficient (CDi) zer-lift drag cefficient (CD). The calculatin f the first ne is nt very hard, but it takes a lng time and energy t determine the secnd part. In large transprt aircraft, this task is dne by a grup f engineers up t twenty engineers fr a time perid f up t six mnths. This calculatin is nt nly time cnsuming, but als is very sensitive, since it influences every aspect f 1 aircraft perfrmance.

2 Aircraft Perfrmance - Drag Classificatin f Drag A list f definitins f varius types f drag is presented, and then a classificatin f all f these drag frces is described Induced Drag: The drag that results frm the generatin f a trailing vrtex system dwnstream f a lifting surface with a finite aspect rati. In anther wrd, this type f drag is induced by the lift frce Parasite Drag: The ttal drag f an airplane minus the induced drag. Thus, it is the drag nt directly assciated with the prductin f lift. The parasite drag is cmpsed f drag f varius aerdynamic cmpnents

3 Aircraft Perfrmance - Drag Parasite Drag Skin Frictin Drag: The drag n a bdy resulting frm viscus shearing stresses (i.e., frictin) ver its cntact surface (i.e., skin) This drag is a functin f Reynlds number. There are mainly tw cases where the flw in the bundary layer is laminar r turbulent ver the plate A laminar bundary layer begins t develp at the leading edge and its thickness grws in dwnstream. At sme distance frm the leading edge the laminar bundary becmes unstable and is unable t suppress disturbances impsed n it by surface rughness r fluctuatins in the free stream In a distance the bundary layer usually underges a transitin t a turbulent bundary layer 3

4 Aircraft Perfrmance - Drag Parasite Drag Frm Drag (smetimes called Pressure Drag): The drag n a bdy resulting frm the integrated effect f the static pressure acting nrmal t its surface reslved in the drag directin. Unlike the skin frictin drag that results frm viscus shearing frces tangential t a bdy s surface, frm drag results frm the distributin f pressure nrmal t the bdy s surface Frm drag is based n the prjected frntal area 4

5 Aircraft Perfrmance - Drag Parasite Drag Interference Drag: The increment in drag resulting frm bringing tw bdies in prximity t each ther. Fr example, the ttal drag f a wing-fuselage cmbinatin will usually be greater than the sum f the wing drag and fuselage drag independent f each ther Trim Drag: The increment in drag resulting frm the (tail) aerdynamic frces required t trim the aircraft abut its center f gravity. Trim drag usually is a frm f induced and frm drag n the hrizntal tail Prfile Drag: Usually taken t mean the ttal f the skin frictin drag and frm drag fr a tw-dimensinal airfil sectin Cling Drag: The drag resulting frm the mmentum lst by the air that passes thrugh the pwer plant installatin fr the purpse f cling the engine Wave Drag: This drag; limited t supersnic flw; is a frm f induced drag resulting frm nn-canceling static pressure cmpnents t either side f a shck wave acting n the surface f the bdy frm which the wave is emanating 5

6 Aircraft Perfrmance - Drag Classificatin f Drag 6

7 Aircraft Perfrmance Drag Plar C D,0 is parasite drag cefficient at zer lift (a L =0) C D,i drag cefficient due t lift (induced drag) Oswald efficiency factr, e, includes all effects frm airplane C D,0 and e are knwn aerdynamics quantities f airplane C ear L C D CD, 0 CD,0 CD, i

8 Aircraft Perfrmance - Drag Classificatin f Drag Drag Plar 8

9 Aircraft Perfrmance - Drag Classificatin f Drag 9

10 Aircraft Perfrmance 4 Frces Acting n Airplane Mdel airplane as rigid bdy with fur natural frces acting n it Lift (L): Acts perpendicular t flight path (perpendicular t relative wind) Drag (D): Acts parallel t flight path directin (parallel t relative wind) Prpulsive Thrust (T): Fr mst airplanes prpulsive thrust acts in flight path directin Weight (W): Always acts vertically tward center f earth Apply Newtn s Secnd Law (F=ma) t curvilinear flight path Frce balance in directin parallel t flight path Frce balance in directin perpendicular t flight path 10

11 Aircraft Perfrmance Static vs Dynamic Analyses Static Perfrmance: Zer Acceleratins (dv/dt = 0) Maximum velcity Maximum rate f climb Maximum range Maximum endurance Dynamic Perfrmance: Accelerating Flight Take-ff and landing characteristics Turning flight Accelerated flight and rate f climb 11

12 Aircraft Perfrmance Level, Un-accelerated Flight Equatins f mtin reduce t very simple expressins Aerdynamic drag is balanced by thrust f engine Aerdynamic lift is balanced by weight f airplane T L D W 1

13 L D L D C C W T SC V W L SC V D T W L D T 1 1 D L W C C W T D L R T R is thrust required t fly at a given velcity in level, un-accelerated flight Ntice that minimum T R is when airplane is at maximum L/D Airplane s pwer plant must prduce a net thrust which is equal t drag Level, Un-accelerated Flight Aircraft Perfrmance

14 Aircraft Perfrmance Thrust Requirement TR fr airplane at given altitude varies with velcity Thrust required curve: TR vs V Select a flight speed V Calculate C L W 1 V C L S Calculate C D C D C D, 0 CL ear Calculate C L /C D Calculate T R This is hw much thrust engine must prduce t fly at V T R W CL C D 14

15 Aircraft Perfrmance Thrust Requirement Different pints n TR curve crrespnd t different angles f attack At b: Small q Large C L (C L ) and a (supprt W) D large 1 L W V D q SC D SC L q SC L At a: Large q Small C L and a D large 15

16 Aircraft Perfrmance Thrust Required vs Flight Velcity T T R R D q q SC D,0 SC D q q S C CL S ear D,0 C D, i Zer-Lift T R (Parasitic Drag) Lift-Induced T R (Induced Drag) Zer-Lift T R ~ V (Parasitic Drag) Lift-Induced T R ~ 1/V (Induced Drag) 16

17 Aircraft Perfrmance Thrust Required vs Flight Velcity Zer-Lift Drag = Induced Drag At minimum T R and maximum L/D 17

18 Aircraft Perfrmance Airplane Pwer Plants 18

19 Aircraft Perfrmance Thrust vs Pwer Jets Engines (turbjets, turbfans fr military and cmmercial applicatins) are usually rate in Thrust Thrust is a Frce with units (kg m/s ) Pistn-Driven Engines are usually rated in terms f Pwer Frce*velcity with units (kg m/s )*(m/s) = kg m /s 3 = Watts Usually rated in terms f hrsepwer (1 hp=550 ft lb/s = 746 W) Example: Airplane is level, un-accelerated flight at a given altitude with speed V Pwer Required, P R =T R *V 19

20 Aircraft Perfrmance Pwer Required P R vs. V qualitatively resembles T R vs. V 0

21 Aircraft Perfrmance Pwer Available 1

22 Aircraft Perfrmance Rate f Climb Prpeller Drive Engine Jet Engine Maximum R/C Occurs when Maximum Excess Pwer

23 Aircraft Perfrmance Pwer Required 3

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