1. Aero Engineering 315 Lesson 21 GR#2 Review

2. GR Breakdown  150 points total  25 multiple choice/matching Mostly conceptual 3 short work outs  2 long work outs worth 46 pts total Hand graded with partial credit available

3. General strategy  Prior to class Work your GR review handout Review reading for lessons 12 – 20 Work all problems through #25 Review slides and handouts  Lift and drag summary  NACA Airfoils  Mach effects Know your memory equations—including GR#1 equations (especially dynamic pressure, q) Be familiar with applicable supplemental data info  In class Bring calculator, straight edge, pencils

4. 2-D Airfoils  An airfoil is a __________________ cross-section of a wing. It may be thought of as a _____ object, an _____________ long object, or an object that completely _______ the width of the test section of a wind tunnel, such that no _________ effects influence the flowfield  The forward-most point on an airfoil is called the ______________, and the rear-most point is called the _________________  A straight line that connects the leading edge and the trailing edge is called the ___________; the length of this line is _______ (or _______________), abbreviated ___  A curved line drawn from the leading edge to the trailing edge so as to be midway between the airfoil’s upper and lower surfaces is called the ____________________  The maximum distance between the mean camber line and the chord line is called the airfoil’s _________________ (or just __________) two-dimensional infinitely 2-D spans wingtip leading edge trailing edge chord chord line mean camber line c max camber camber chord length

5. 2-D Airfoils  A symmetrical airfoil has _______ camber  For NACA 4-digit series airfoils, the first digit represents _______________ in _________ of chord, the second digit represents ___________________________ in _________ of chord, and the third and fourth digits together represent __________________ of the airfoil, in __________ of chord. By definition, the first two digits for a symmetric airfoil are _____.  The length (tip-to-tip) of an airfoil model tested in a wind tunnel is its ______, abbreviated ___  __________area (___) is the area of a projection of the airfoil’s shape onto a horizontal surface beneath it; S = _______  The direction of the freestream velocity is the ___________________; the angle between the relative wind and the chord line is __________________ (___), with leading edge ____ being the positive direction zero max camberpercent location of max camber tenths max thicknesspercent 00 span b  b c relative wind angle of attack up S Planform

6. 2-D Airfoils  The AOA at which an airfoil produces no lift is the ________________________________ (______);  l=0 = ___ for symmetric airfoils  The aerodynamic force acting on a wing is created by the ___________ and _______________ distributions over the wing surface  The aerodynamic force can be resolved into _____, the component perpendicular to ________________, and _____, the component parallel to _______________  Summing upper and lower surface forces, we find the existence of a pitching moment; this moment is positive in the L.E.- ____ direction  The ____________________ is the location on an airfoil at which the pitching moment is zero; this location can change with _________  The ____________________ is the location on an airfoil at which the pitching moment is constant (i.e. doesn’t change with _________); for subsonic flight, the aerodynamic center is located at approximately the ________________ point (x = ____) zero-lift angle of attack  l=0 0 pressure center of pressure lift relative wind drag up AOA aerodynamic center quarter-chord c/4 shear stress AOA

7. 2-D Airfoils  At the aerodynamic center, the moment is __________ for positively cambered airfoils and is _____ for symmetric airfoils  We define lift coefficient C l = _______, drag coefficient C d = _______, moment coefficient C m = _________; these coefficients are _______________ and can vary with ____, ____, and ____  The NACA airfoil data is for ____, ________________ flow  The slope of the linear part of the lift curve is the lift curve slope, _____; C l ≈ _____/deg for thin airfoils  The top of the lift curve rolls off due to _________________; the AOA where the curve peaks is _______, and lift coefficient is _______  To determine drag coefficient (C d ) at a given , we must first determine ___  Know how Reynolds number, camber, flaps, and boundary layer control affect the lift and drag curves!  Know how to find lift coefficient, drag coefficient, quarter-chord moment coefficient, and moment coefficient at the aerodynamic center from the NACA airfoil data charts! zero negative L/(q S) D/(q S)M/(q S c) nondimensional  Re M 2-D incompressible ClCl 0.11 airfoil stall  stall C lmax ClCl

8. 3-D Wings  The length (tip-to-tip) of a wing is the ______ (___) and its projected area is the _______________ (___)  Aspect ratio (AR) = _______ and describes whether the wing is “_____________________” or “_______________________”  Taper ratio (__) is the ratio of _____________ to ______________, or c t /c r  Leading edge sweep angle (__) is the angle between the wing’s leading edge and a line _______________ to the root chord line  To delay stall near the wingtips, we can use ___________ twist (wingtip twisted ______) or ______________ twist (different airfoil)  Due to the top surface-to-bottom surface pressure imbalance on a wing, rotating ____________ form at the wingtips  Wingtip vortices form a downward velocity component, or _________, on the wing’s upper surface, deflecting the local flow velocity downward by the _________ angle (___) and reducing the effective angle of attack ( eff = _______), causing a _____________ in lift spanb planform areaS b 2 /S long and skinny short and stubby tip chord root chord  perpendicular geometric down aerodynamic vortices downwash   reduction

9. 3-D Wings  The 3-D lift curve slope is _______ than the 2-D lift curve slope, but the zero-lift AOA ( L=0 ) is ____________( L=0 ___  l=0 )  Wingtip vortices also cause a spanwise flow component: root-to- tip on the _______ surface, tip-to-root on the _______ surface  Wingtip vortices also tilt the net force vector back by the _________ angle, causing an increase in drag; this “drag due to lift” is called __________ drag. Physically, this drag results because the energetic vortices are “robbing” energy from the plane’s __________.  The span efficiency factor (___) is 1 for __________ wings, and ________ than 1 for all other types of wings  We can minimize induced drag by using ___________ wings, high-_____________ wings, _________ on the wingtips, ________ wingtips, or wingtip ________ (i.e. air-to-air missile) lower the same= lowerupper downwash induced engines e elliptical less elliptical aspect ratio winglets drooped stores

10. 3-D Wings  Total drag for a 3-D wing is the sum of _________ drag (composed of _____________drag and __________ drag) and __________ drag  Know how to calculate lift for straight-and-level flight (L = W), how to calculate 3-D lift coefficient (C L = L/qS), how to calculate induced drag coefficient (C Di = C L 2 /eAR), how to calculate total drag coefficient (C D = C d + C Di, where C d is found in the NACA airfoil charts), and how to calculate 3-D wing total drag (D = C D q S)  Or alternately, know how to calculate 3-D lift curve slope (C L = C l /[1+57.3° C l /eAR]) and then calculate 3-D lift coefficient (C L = C L (- L=0 ), where  L=0 =  l=0, found in the NACA airfoil charts) profile skin friction pressure induced

11. High-Lift Devices  For straight level unaccelerated flight (______), lift __ weight, and velocity required to maintain lift is V ∞ = ____________  The stall velocity, V stall, occurs at ______: V stall =___________; in equivalent airspeed, V e-stall = ____________  We must fly at relatively slow airspeeds during _________ and _________; takeoff speed is limited by ________ length and available engine ________, while landing speed is limited by _________ effectiveness, ______ specifications, and runway ____________  For a given aircraft weight, if you want to fly slower, you must increase ____, so we use __________ devices to improve C L  Trailing edge flaps increase wing ________, thereby increasing C L (the lift curve is shifted ___ and to the ______)  Flaps also increase ______ (the drag polar is shifted ___ and to the ______)  A plain flap’s effectiveness can be reduced because of flow ___________; split flaps and slotted flaps attempt to overcome this problem SLUF= C Lmax takeoff landing runway thrust braking tire condition CLCL high-lift camber upleft dragup right separation

12. High-Lift Devices  Similar to slotted flaps, _______ flaps help delay flow separation, but also increase wing _________________, further increasing lift  Like a trailing edge flap, a leading edge flap can increase C L by increasing wing ________  Boundary layer control devices, such as a fixed _____, a leading edge _____, upper surface ________, and upper surface _________ increase C Lmax by helping keep the boundary layer _________, delaying stall  Another approach to supplementing lift is _________ thrust, such as that used by the AV-8B Harrier and the Marine Corps JSF  Leading edge strakes produce strong _________ and direct them over the top of the wing; the very low _________ in the core of the vortices augments the _____ produced by the wing— especially at high _________________  Strakes cause the lift curve to rotate ___ and _______ Fowler surface area camber slot slatsuction blowing attached vectored vortices pressure lift angles of attack up extend

13. Whole Aircraft Lift and Drag  When determining whole aircraft lift, the lift of the wing is modified by the __________, ________ and other high-lift devices, and the ____________ tail and/or ________  The general form for the whole aircraft drag coefficient is C D = C Do + k 1 C L 2 + k 2 C L, but the _______ term is generally negligible and can be ignored; we use C D = _____________, an equation known as the whole aircraft ____________  k 1 (often referred to simply as k) = 1/e o AR, where e o is _________ efficiency factor, which will be ______ than span efficiency factor e  C Do, which represents _________ drag, is _________ and includes the following drag contributions: ______________ drag, _________ drag at zero lift, _____________ drag from wing/fuselage coupling, and ______ (supersonic) drag fuselagestrakes horizontalcanard linear C Do + kC L 2 drag polar Oswald’s lower parasiteconstant skin friction pressureinterference wave

14. Whole Aircraft Lift and Drag  kC L 2 represents drag due to _________ and includes the following drag contributions: wingtip _______-induced drag, __________ drag that varies with lift, and any other drag that varies with lift (due to leading edge _________, for example)  Similar to 3-D wing calculations, know how to calculate lift for straight-and-level flight (L = W), how to calculate whole aircraft lift coefficient (C L = L/qS), how to calculate whole aircraft drag coefficient (C D = C Do + kC L 2, where C Do will be given, k may be given or may be calculated by k = 1/e o AR), and how to calculate whole aircraft drag (D = C D q S) lift vortex pressure strakes

15. Supersonic Flow  Speed of sound (__) varies only with temperature: a = _________; the ratio of specific heats  = 1.4 for air  Mach number (__) is the ratio of freestream velocity and speed of sound: M = ______  The Mach angle (__) represents how steeply a Mach wave sweeps back, and sin  = _____  Critical Mach number (______) is the freestream Mach number at which the flow somewhere on the airplane first reaches M = __  As Mach number increases beyond M crit, ____________ form on aircraft surfaces, which can cause flow ____________, reducing _____ and increasing _____; the additional drag resulting from shock-induced separation is called ______ drag a M v/a  1/M M crit 1 shock waves separationlift drag wave

16. Supersonic Flow  The different flight regimes are __________ flight, at Mach numbers below ______, where the flow is everywhere __________ than the speed of sound; ___________ flight, at Mach numbers above M crit and below about ____, where regions of both ____________ and ___________ flow exist; ____________ flight, where the flow is everywhere ________ than the speed of sound; and ___________ flight, at Mach numbers above about __, where extreme high _____________ significantly change the chemical properties of air  As flow crosses a _______ shock (perpendicular to flow direction), ________________and __________ fall, while _________________, _____________, and _________ rise  When the freestream exceeds Mach 1, _____________shocks will form in front of bodies with blunt leading edges, while ____________ shocks will attach to bodies with sharp leading edges subsonic M crit slowertransonic 1.3 subsonicsupersonic faster hypersonic 5temperatures normal total pressure velocity static pressure temperaturedensity bow wave oblique

17. Supersonic Flow  In the airfoil lesson, we discussed the fact that lift and drag coefficients vary with a, Re, and __; to predict the variation (due to compressibility effects) of lift coefficient with Mach numbers between 0.3 and 0.7, we use the ______________________ correction  C l ______ with Mach number until ___________ causes a large drop in C l ; once the shock moves to the trailing edge, C l _________  C Do remains essentially constant below M crit, but begins to _________ rapidly above the __________________ Mach number, M DD  When M ∞ > 1, the wing’s aerodynamics center shifts back from the ________-chord point (c/4) to the _______-chord point (c/2)  If we want to fly at high subsonic speeds while avoiding wave drag, we want to increase ______; strategies for doing so include the use of _____ wings; less _________ wings; _________ wings; ______, ________ leading edges; and _______________ airfoils M Prandtl-Glauert rises shock stall recovers increasedrag divergence quarterhalf M crit thincambered swept sharp slender supercritical

18. Supersonic Flow  Wing sweep __________ M crit by decreasing the velocity component the airfoil “sees” by 1/cos __, although wing sweep increases induced drag by __________ aspect ratio and ___________ span efficiency factor  If we want to fly at supersonic speeds, we want to minimize _____ drag; strategies for doing so include the use of a _________ wing-body; an ____________ fuselage (Coke-bottle shape or “wasp waist”); offsetting the ___________ above or below the main wing; sharp, slender _________ (causing oblique shocks, which produce less wave drag than ______________ shocks); and ____________-geometry wings increases  decreasing reducing wave blendedarea-ruled tailplane wings bow wave variable

19. Next Lesson (T22)  Prior to class Read Study Homework problems EI  In class GR#2