Anatomy of the wing and its performance

• The mean geometrical chord (CMGC) can be used to compute the wing Reynolds number. • To compute the local Reynolds number, or the Reynolds number at a given cross-section, you need to use the local airfoil chord. • You can also use the mean aerodynamic chord (MAC) to compute the wing Reynolds number. • By the way, do not confuse the mean geometrical chord MGC with the MAC. 16 Anatomy of the wing • Main geometrical definitions of a trapezoidal wing planform. • The MAC is defined as follows, • In few words, the MAC is a two-dimensional representation of the whole wing. • The MAC is a very important quantity used for aircraft stability. • Aircraft center of gravity limitations and the actual center of gravity CG are often expressed in terms of percent of the MAC. • This is not strictly true, but the mean geometrical chord (CMGC) is approximately the same as the MAC. 17 Anatomy of the wing • A description of the geometric layout of an aircraft is fundamental to conduct an aircraft stability study. • It is convenient that the geometry of the aircraft can be adequately described by a small number of dimensional reference parameters, as shown in the figures below. • Many of the variables used in aircraft stability are common to wing aerodynamics. Photo credit: Flight dynamics principles, M. Cook, Butterworth-Heinemann, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. The MAC is projected into the fuselage to conduct the aircraft stability study. 18 • AR is used when determining the aerodynamic characteristics and structural weight of the wing. • For a constant-chord wing of chord c and span b, the aspect ratio is given by: Anatomy of the wing • Wing aspect ratio (AR). • Wing AR is a measure of how wide is the wing compared to its chord. • The wing aspect ratio can be computed as follows, • AR is related to induced drag as follows, 19 • The taper ratio affects the lift distribution and structural weight of the wing. • A rectangular wing has a taper ratio of 1 while a pointed tip delta wing has a taper ratio of 0 Anatomy of the wing • The wing taper ratio (TR or ). • The ratio of the tip chord to the root chord is the taper ratio. • The wing taper ratio can be computed as follows, 20 Anatomy of the wing • Different wing planforms – A selection of the most common ones. • Each one has different aerodynamic characteristics. Rectangular wing Trapezoidal wing Compound tapered wing Elliptical wing Slightly swept wing Moderately swept wing Highly swept wing Delta wing Double delta wing 21 Anatomy of the wing • And of course, the wing has a cross section, which can be different along the wingspan and can have different incidence angles. • From the 2D lectures, we know the aerodynamic properties of airfoil sections. • It is important to know that the wing will inherit most of the properties of the airfoil section. • However, due to three-dimensional effects, the performance of wings is different from that of airfoil sections. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 22 Anatomy of the wing • The wing planform area (including the continuation of the fuselage) is the wing gross area, • The exposed wing planform area is the net area (area excluding the continuation of the fuselage), • Note that the specifics of the method used to estimate the gross area or net area are irrelevant. • The wing area serves as the reference area for most aerodynamic coefficients. • When choosing the gross area or net area you must be consistent. • Consistency is as important as precision. 27 Anatomy of the wing • There is no accurate analytical method that can predict the lift of the wing-fuselage combination. • Either the configuration must be tested in a wind tunnel, or a computational fluid dynamic calculation must be made. • We cannot even say in advance whether the combined lift will be greater or smaller than the sum of the two parts. • For subsonic speeds, however, data obtained using different fuselage thicknesses, d, mounted on wings with different spans, b, show that the total lift for a wing-fuselage combination is essentially constant for d/b ranging from 0 (wing only) to 6 (fat fuselage with a short, stubby wing) [1]. • Hence, the lift of the wing-fuselage combination can be treated as simply the lift on the complete wing by itself, including that portion of the wing that is masked by the fuselage. • Therefore, we will consistently use the gross area . [1] Fundamentals of aerodynamics, J. Anderson, McGraw-Hill, 2016 28 Anatomy of the wing • A little note on how to estimate the gross area. • To estimate the gross area, the two most important methods are the Wimpress method (used by Boeing) and the Airbus method. • Either method is acceptable. • You must be consistent with the method used. • Remember, the wing area only serves as the reference area for most aerodynamic coefficients. • Obtained by connecting using straight lines the points where the leading and trailing edges meet the fuselage on both sides. • Obtained by extending the wing's leading and trailing edges forward into the fuselage. 29 Anatomy of the wing • Just to be loud on this. • When computing the aspect ratio, you use the wing area (gross area) and wingspan (tip to tip distance). Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 30 Other wing parameters Diheral angle and wing location 31 Anatomy of the wing • The dihedral angle is the angle between a horizontal plane containing the root chord and a plane midway between the upper and lower surfaces of the wing. • If the wing lies below the horizontal plane, it is termed as the anhedral angle. • The dihedral/anhedral angle affects the lateral stability characteristics of the airplane. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 32 Anatomy of the wing • Technical note. • The main purpose of the gull wing is to have more clearance. For example, propeller clearance. • They are also used to have a shorter and stronger landing gear strut. • From the aerodynamic point of view, when the angle between the root of the wing and the fuselage is the ideal, they reduce interference drag. 33 Beriev Be-12 seaplane with gull wing profile https://en.wikipedia.org/wiki/Gull_wing#/media/File:B eriev_Be-12_Gelenzhik_2Sept2004.jpg Vought F4U Corsair with gull wing https://www.beale.af.mil/News/Photos/igphoto/2000940168/ Vought F4U Corsair with folded wings https://commons.wikimedia.org/wiki/File:F4U- 4_Bu97388_folding_wings.jpg Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Anatomy of the wing • Vertical position of the wing. • When it comes to wing location, there is nothing written saying that one configuration is better than the other. • The vertical wing location may end up being based on a number of factors such as: • Accessibility, field of vision, length of landing gear, stability and control, aesthetics, amphibian or land operation, ground clearances, manufacturing and structural issues, designer preference, mission type, and so on. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 34 Anatomy of the wing • Same design concepts also applies for jet engines. 35 Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Bae 146 https://spottair.com/british-aerospace-bae-146-300qt-by-tnt/ Boeing 737-800 https://www.pinterest.com/pin/841117667895977414/ Anatomy of the wing • Same design concepts also applies for jet engines. • And the engines not necessarily need to be located under the wing. 36 Embraer ERJ-145XR https://www.flickr.com/photos/28042007@N07/4088339293 Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Honda Jet https://cutteraviation.com/aircraft-charter/charter-aircraft-fleet/hondajet-ha-420/ Cirrus SF50 Vision Jet G2+ https://flyer.co.uk/cirrus-reveals-g2-vision-jet-with-extra-takeoff-power/ Wing geometry parameters of some actual airplanes 38 Anatomy of the wing Data source: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. • Wing geometry parameters of some actual airplanes. 39 Anatomy of the wing • Wing geometry parameters of some actual airplanes. Data source: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. 40 Anatomy of the wing • Wing geometry parameters of some actual airplanes. Data source: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. 41 Anatomy of the wing • Wing geometry parameters of some actual airplanes. Data source: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. 42 Wing performance in function of the main geometric parameters 43 Wing performance in function of the main geometric parameters • Comparison of finite-span wings (3D case) and infinite span wings (2D case – airfoils). Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 44 Wing performance in function of the main geometric parameters • Effect of aspect ratio on the drag coefficient of a hypothetical airplane. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 45 The optimum AR corresponds to the minimum CD value of the iso CL curve Wing performance in function of the main geometric parameters • Wing twist – Geometrical twist. • When we change the angle of incidence of the wing sections, we call it geometrical twist. • When the root airfoil AOA is larger than that of the tip airfoil, we call it wash-out. • The opposite scenario is called wash-in. • The angle between the root airfoil and the datum line is known as wing incidence angle or setting angle (datum-root airfoil decalage). Geometrical twist angle Geometrical twist angle Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 46 Wing setting angle HORIZONTAL DATUM LINE Wing performance in function of the main geometric parameters • Wing twist – Aerodynamic twist. • When we change the airfoil sections, we call it aerodynamic twist. • Geometrical twist and aerodynamic twist can be used together. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 47 Wing performance in function of the main geometric parameters • Effect of aerodynamic twist. • In the left image, the root airfoil stalls at a lower AOA than the tip. • In the right image, the root airfoil has a higher than the tip airfoil but stalls at the same AOA, the effective wash- out is zero. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 48 Wing performance in function of the main geometric parameters • Effect of taper ratio on the spanwise distribution of section lift coefficient (left image) and section lift force (right image) • Tapering a wing planform gives a number of significant aerodynamic and structural advantages, but it can also cause problems if overdone. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 49 • Note that the spanwise distributions are different depending on the quantity used. • If we use lift coefficient, the ideal case is a uniform distribution (straight line). • If we use lift force, the ideal distribution is of elliptical shape. Wing performance in function of the main geometric parameters • Sweep angle. • The main purpose of sweeping the wing backward (or forward) is to delay the onset of shock waves, reduce wave drag, and move the position of the MAC or CG. • In general, the maximum lift coefficient and lift curve slope are reduced with the sweep angle. • The swept wing is a mechanism for reducing the large drag increase encountered at high-speed subsonic flight and at supersonic speeds. • The flow over the wing (therefore the critical Mach number), depends on the velocity component perpendicular to the leading edge. • By adding sweep, higher critical Mach numbers can be reach because the velocity component normal to the leading edge is lower than the freestream velocity. • The velocity normal to the leading edge is equal to the freestream velocity multiplied by the cosine of the sweep angle (the local airfoil sees a lower velocity). 51 General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters • Sweep angle – Variation of minimum wing drag coefficient versus Mach number. Adapted from: Quest for Performance, NASA SP 468, 1985. 52 General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters • Influence of sweep angle on wing design. • Sweep angle reduces . • In the figure, we illustrate general trends showing the effect of aspect ratio on the lift coefficient slope of wings with different sweep angle at subsonic speeds. Theoretical variation of lift coefficient slope (or ) against aspect ratio for elliptical wings: 54 This relation represents the lift-curve slope for a wing with an elliptic lift distribution Airfoil lift curve slope General knowledge as our focus is low speed aerodynamics for the moment. Adapted from: Race Car Aerodynamics: Designing for Speed. J. Katz. Bentley Publishers. 1996. Wing performance in function of the main geometric parameters • Influence of sweep angle on wing design. • Disregarding the fact that the sweep angle decreases the lift curve slope, the sweep angle increases the AOA to reach maximum CL. • Wings designed for high speed are a good compromise of sweep angle, taper ratio, aspect ratio, and airfoil thickness. • Over the years, as better engines became available (clean, cheap and efficient) and in the quest for higher speeds, the trend has been to increase the sweep angle (the whole wing or only the leading edge as in delta wings) to reduce the wave drag. Adapted from: Aircraft design: a conceptual approach, D. Raymer, AIAA Educational Series, 2012 55 General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters • Experimental data – Influence of sweep angle on the aerodynamic performance of finite-span wings. Drag polars at Mach 0.7 and 0.9 for a straight wing (left) and swept (45°) wing (right), as reported by H. Ludwieg in 1939. Photo credit: Fundamentals of aerodynamics, J. Anderson, McGraw-Hill, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 56 General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. • Sweep angle – Delta wings. • Experimental data – Lift coefficients for delta wings of various aspect ratios; t = 0.12c,  57 General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters • In addition to reducing the lift, wing sweep changes the local section lift coefficient Cl. • The lift slope of infinite wings is , while the lift slope of a finite wing is zero at the tip and less than at the root and along the wingspan. This is due to the downwash of the trailing vortices. • Increasing the aspect can increase the lift slope, but the maximum value will never be that of infinite span wings (airfoils). • The figure below [1], illustrates the loss of lift near the wing tips of finite span wings. 58 [1] J, Katz. Calculation of the Aerodynamic Forces on Automotive Lifting Surfaces. ASME. J. Fluids Eng. December 1985; 107(4): 438–443. [2] Reference 10 in the figure: A. Donovan, H. Lawrence. Aerodynamic Components of Aircraft at High Speeds. Princeton Series Vol. VII, Princeton University Press, N.J., 1957. General knowledge as our focus is low speed aerodynamics for the moment. Wing performance in function of the main geometric parameters Photo credit: L. Prandtl. Applications of modern hydrodynamics to aeronautics. NACA Report 116, 1921. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. • Experimental data – Effect of aspect ratio on the aerodynamic performance of a rectangular wing. • Effect of the aspect ratio on the drag polar for rectangular wings (AR from 1 to 7): measured drag polars. • Effect of the aspect ratio on the lift curve for rectangular wings (AR from 1 to 7): measured lift curves. 59 Wing performance in function of the main geometric parameters • Optimal lift distribution. • The optimal lift distribution (we are talking about force) is the elliptical one, as it generates the less possible induced drag and lower wing root bending moments. • If you think in terms of section lift coefficient, the distribution should be uniform. • However, an elliptical lift distribution have the drawback that the whole wing will stall at the same time. • Due to safety requirements, it is recommended to have a wing that first stall inboard, so we do not loose roll control. This can be achieved by adding geometrical/aerodynamic twist. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Note: The solutions shown were obtained using a vortex lattice method (VLM) solver. 61 Wing performance in function of the main geometric parameters • Plots used to illustrate spanwise lift distribution. • Any of these plots can be used to illustrate spanwise lift distribution. • You can use the actual span value, or you can normalize it. • For minimum induced drag you should aim for: • If you use lift coefficient distribution (normalized or unnormalized), your goal is to obtain a uniform distribution (equivalent to that of an elliptical wing) • If you use the lift force distribution, you goal is to obtain an elliptical distribution. • The elliptical lift distribution (or uniform lift coefficient distribution) might not be optimal in terms of stall characteristics towards the tips. • Therefore, you will end up aiming for a little of aerodynamic or geometric twist towards the tips in order to delay stall. • Notice that in the spanwise lift distribution plot (bottom figure), there is a lost in lift towards the tips. This is characteristics of finite span wings and is due to 3D effects. • The high pressure in the bottom of the wing tends to move towards the top surface at the wing tips. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 64 Wing performance in function of the main geometric parameters • Plots used to illustrate spanwise lift distribution. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 65 • Any of these plots can be used to illustrate spanwise lift distribution. • You can use the actual span value, or you can normalize it. • You can use normalized or unnormalized lift coefficient distribution. • The normalized lift coefficient distribution (bottom image) can give an indication of the excess or surfeit of lift in the current section; therefore, it can be used to design the wing’s stall characteristics. Wing performance in function of the main geometric parameters • Spanwise distribution of section lift coefficient and stall progression of different wing planforms. Neither geometrical twist nor aerodynamics twist Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 66 Wing performance in function of the main geometric parameters • Spanwise distribution of section lift coefficient and stall progression of different wing planforms. Neither geometrical twist nor aerodynamics twist Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 67 Wing performance in function of the main geometric parameters • The effect of wash-out on stall progression and spanwise lift distribution. • The baseline wing is more tip-loaded than the ones with wash-out and this will cause it to stall closer to the wingtip, which may cause roll off problems. • Wash-out is used to control stall progression and can be improved by selecting a high-lift airfoil at the tip. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 69 • The baseline 2D curves are obtained by computing the cross-section Cl max. • For a wing with taper ratio, each section have a different Reynolds number. Therefore, a different Cl max. • Also, a wing with different cross-sections (aerodynamic twist) will have different Cl max. • The location where the spanwise lift distribution touch the baseline curve, is where the wing stalls first and where the stall progression begins. • This condition also corresponds to CL max. • This method to control stall progression is known as the critical section method. • The airfoil Cl max and spanwise lift distribution can be obtained from experimental measurements, linear methods (LLT, VLM, panel methods), or CFD simulations. Wing performance in function of the main geometric parameters • The effect of wash-out on stall progression and spanwise lift distribution. • Wash-out can also be used to achieve an optimal spanwise lift distribution. • By carefully tuning the angle of attack that each section sees, the induced drag can be reduced. • Remember, geometrical and aerodynamic twist can be used together. Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 70 • The baseline 2D curves are obtained by computing the cross-section Cl max. • For a wing with taper ratio, each section have a different Reynolds number. Therefore, a different Cl max. • Also, a wing with different cross-sections (aerodynamic twist) will have different Cl max. • The location where the spanwise lift distribution touch the baseline curve, is where the wing stalls first and where the stall progression begins. • This condition also corresponds to CL max. • This method to control stall progression is known as the critical section method. • The airfoil Cl max and spanwise lift distribution can be obtained from experimental measurements, linear methods (LLT, VLM, panel methods), or CFD simulations. Wing performance in function of the main geometric parameters • Most of the airfoil aerodynamic characteristics (2D) are inherited by wings (3D): • Airfoil shape – Curvature. • Reynolds number (sectional). • Mach number – Compressibility effects. • Stall mechanism and patterns. • Effect of early flow separation on lift and drag. • Effect of leading-edge separation bubbles on lift. • The effect of high lift devices (HLD) on lift and drag – Flaps and slats. • Effect of surface finish and leading-edge contamination on lift and drag. • Therefore, it is of paramount importance to choose a good airfoil. • As you might guess, designing/selecting wings is much more complex than two-dimensional cases (airfoils). • And this is chiefly to 3D effects (wing tip vortex and spanwise velocity components), and the interaction of the wing with other aircraft components (fuselage, nacelles, pylons, and so on). 71 Different wing planforms used in history 72 Different wing planforms used in history • Some of the different wing planforms used in history. • As you can see, there is no limitation regarding the shape of the wing. • Remember, when designing a wing your goal is to generate the required lift with the minimum drag. • You should also consider stability and structural issues. Airbus 380 Boeing 777 Embraer ERJ-145 ATR 72 Douglas DC3 Douglas DC6 Concorde L49 Constellation Boeing 747 Boeing 737-800 74 Different wing planforms used in history Antonov AN-225 B52 Hughes H-4 AC130 B-1B F-111 NASA AD-1 XB-70 F14 • Some of the different wing planforms used in history. • As you can see, there is no limitation regarding the shape of the wing. • Remember, when designing a wing your goal is to generate the required lift with the minimum drag. • You should also consider stability and structural issues. 75 Different wing planforms used in history Piaggio P180 Avanti Learjet 25 Cirrus SR22 Cessna C172 Rutan Boomerang Scaled Composites SpaceShipOne Scaled Composites Proteus Rutan Varieze • Some of the different wing planforms used in history. • As you can see, there is no limitation regarding the shape of the wing. • Remember, when designing a wing your goal is to generate the required lift with the minimum drag. • You should also consider stability and structural issues. 76 Different wing planforms used in history XF91 T-6G B2 XF5U X-24B A10 U2 Hawker Tempest P-51 Mustang Horten Ho 229 • Some of the different wing planforms used in history. • As you can see, there is no limitation regarding the shape of the wing. • Remember, when designing a wing your goal is to generate the required lift with the minimum drag. • You should also consider stability and structural issues. 77 Different wing planforms used in history F18 X29 F117 X36 SR71 Dassault Rafale Eurofighter Typhoon Sukhoi Su-30 Dassault Mirage Saab JAS 39 Gripen • Some of the different wing planforms used in history. • As you can see, there is no limitation regarding the shape of the wing. • Remember, when designing a wing your goal is to generate the required lift with the minimum drag. • You should also consider stability and structural issues. 78 Finite-span wings features 3D world 80 Finite-span wings features – 3D world • Three-dimensional effects of finite-span wings – Wingtip and trailing edge vortices. Photo credit: An album of fluid motion. M. Van Dyke., 1988. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 81 Finite-span wings features – 3D world • Three-dimensional effects of finite-span wings – Visualization of the vortex sheet behind a rectangular wing. • Wake rolling up behind the wing at 9° AOA is visualized at different planes behind the wing. Photo credit: An album of fluid motion. M. Van Dyke., 1988. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 82 Finite-span wings features – 3D world • Three-dimensional effects of finite-span wings – Wingtip vortices. Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 83 Finite-span wings features – 3D world • Three-dimensional effects of finite-span wings – Visualization of vortical structures. Vortices on a 1/48-scale model of an F/A-18 aircraft inside a Water Tunnel Photo credit: NASA Dryden Flow Visualization Facility. http://www.nasa.gov/centers/armstrong/multimedia/imagegallery/FVF Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Doppler Global Velocimetry (DGV) of F/A-18 – Visualization of vortical structures Photo credit: NASA Langley Research Center. https://www.dvidshub.net/image/718184/doppler-global-velocimetry-f-18#.Uuj65GQ1jgo Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 84 Finite-span wings features – 3D world • Interference effects and surface flow patterns visualization using fluorescent oil. Photo credit: https://hiliftpw.larc.nasa.gov/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 86 Finite-span wings features – 3D world • Surface flow patterns visualization using fluorescent oil – Flow stall pattern on wing surface. Below stall – Flow attached Near stall – Highly three-dimensional flow, it detaches close to the wing root. Far beyond stall – The flow over the wing has separated. Photo credit: Introduction to flight. J. Anderson. McGraw-Hill, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 87 Finite-span wings features – 3D world • Surface flow patterns visualization using fluorescent oil – Wing/fuselage junction separation bubbles. Surface flow patterns visualization using fluorescent oil Photo credit: NASA Dryden Flow Visualization Facility. https://www.nasa.gov/aero/flow_patterns_image.html Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Photo credit: M. Gatlin, M. Rivers, S. Goodiff, R. Rudnik, M. Siltzmann. Experimental investigations of the DLR-F6 transport configuration in the national transonic facility. 26th AIAA conf, 2008. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 88 Lift-induced drag 89 Lift-induced drag • On the origin of the lift-induced drag, downwash, and induced angle. • Remember, lift-induced drag is a characteristic of finite- span wings. • The flow moving from the high-pressure region to the low-pressure region will generate trailing edge vortices and wingtip vortices. • This flow movement from the high-pressure region to the low-pressure region will also generate a downwash that will reduce the angle of attack that the airfoil effectively sees. • This effect is particularly strong towards the wingtips. • As a consequence of the downwash, every cross section of the wing will see a different angle of attack, the effective angle of attack. • The downwash (w in the figure), will also incline backwards the lift component, giving raise to the lift induced-drag. • The effective angle of attack is illustrated in the bottom figure. 90 Lift-induced drag • To reduce the lift-induced drag we can: • As demonstrated by Prandtl, we can simply increase wings’ aspect ratio AR. • Remember, AR is related to induced drag as follows, • The wing aspect ratio can be computed as follows, • By increasing the wingspan b we can increase the wing aspect ratio AR. • Increasing the wing aspect ratio AR is the simplest way to reduce the lift induced drag. • However, increasing the AR can have negative effects, such as, increased root bending moment, increased structural weight, poor handing qualities (low roll rate), airport operational problems, flutter, and so on. 91 Lift-induced drag • To reduce the lift-induced drag we can: • Add wingtip devices that artificially increase the wingspan by modifying the pressure distribution at the wingtips. • One of such wingtip devices are known as winglets, as illustrated in the figure. • Other options: • Planform design. • Use of geometrical and aerodynamic twist. • Nonplanar systems different from winglets (closed loop surfaces and box wings). • Wingtip modifications (hoerner wingtip, drooped wingtip, wingtip feathers). • Multiple lifting surfaces. • And of course, larger AR. 92 Lift-induced drag • Drag polar, lift-induced drag coefficient and induced drag factor. • The induced drag factor is zero only for elliptical wings. • For the rest of the wings is a number larger than zero and usually between 0.02 and 0.2. • Basically, it penalizes the wing. • The larger the number is, the more induced drag the wing will produce. • It can be used as indication to determine how far we are from the elliptical distribution. • The induced drag factor can also be used to compute the Oswald span efficiency e, which is another metric indicating how far we are from an elliptical lift distribution. • A value of e equal to 1 is an indication of a perfect elliptical lift distribution. (Oswald span efficiency) Induced drag factor. As you can see, the lift-induced drag depends on the aspect ratio. If we increase the aspect ratio, we will reduce the lift-induced drag. 93 (Oswald span efficiency) Lift-induced drag • Drag polar, lift-induced drag coefficient and induced drag factor. (Oswald span efficiency) • The induced drag factor is zero only for elliptical wings. • For the rest of the wings is a number larger than zero and usually between 0.02 and 0.2. • Basically, it penalizes the wing. • The larger the number is, the more induced drag the wing will produce. • It can be used as indication to determine how far we are from the elliptical distribution. • The induced drag factor can also be used to compute the Oswald span efficiency e, which is another metric indicating how far we are from an elliptical lift distribution. • A value of e equal to 1 is an indication of a perfect elliptical lift distribution. 94 Induced drag factor. (Oswald span efficiency) As you can see, the lift-induced drag depends on the aspect ratio. If we increase the aspect ratio, we will reduce the lift-induced drag. Lift-induced drag • There are different drag polar models that are typically used to represent the total drag of finite-span wings or aircrafts. This is the most common drag polar found in literature where • Sometimes, the following assumptions are taken in the polars, Wave drag and 95 Lift-induced drag • Illustration showing the effect of changing and on the drag polar. 96 Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. • The following quadratic model is widely found in literature, however, is not very accurate. • A more accurate quadratic model of the total drag is the following, • Have in mind that these quadratic models do not capture the drag bucket seen in airfoils. • You will rarely see the drag bucket when plotting the polars of finite span wing (3D wings). This is due to three-dimensional effects, wing surface roughness, or freestream disturbances, among many factors. Lift-induced drag • Curve fitting the true drag polar. • These models are important because they are used to predict the aircraft performance. • Therefore, we must be aware of their limitations. • For example, if the wing features a camber, the simplified drag polar model, 97 Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. is not longer a valid representation of the drag polar. • Also, in the presence of the drag bucket, these methods are not very accurate. • Therefore, they must be used with care or must be corrected. Lift-induced drag • Lift/drag polar for a large, subsonic transport – Contribution of different drag sources for a typical transport aircraft. Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Contributions of different drag sources for a typical transport aircraft. Lift/drag polar for a large, subsonic transport. 98 • From the drag polar flight data, notice that • In the drag polar flight data, is slightly lower than . Lift-induced drag • Flight data for different aircrafts. Drag components for an F-16C flying in steady, level, unaccelerated flight at 20,000 ft. Flight data for a drag polar for F-106A/B aircraft at a Mach number of 0.9. • The following equation correlates well the drag polar data in the left figure (the solid line in figure), Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 99 Lift-induced drag • L/D ratio for an F-16C as a function of Mach number at 20,000 ft. • Airplane performance is strongly related to L/D ratio. • Many metrics of airplane performance are obtained in flight at L/D maximum. • Performance conditions that occur at L/D max include: • Maximum range of propeller-driven airplanes. • Maximum climb angle for jet-powered airplanes. • Maximum power-off glide ratio (for jet-powered or for propeller- driven airplanes). • Maximum endurance for jet-powered airplanes. • Therefore, when designing a wing, it is extremely important to have the L/D max as close as possible to cruise conditions (AOA and cruise velocity). • You can take a look to Breguet equation (for range or endurance) to see the influence of L/D on aircraft performance. Performance Aerodynamics Propulsion Structures + Materials Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 100 Lift-induced drag • The total drag of an airplane or a wing, is the parasitic drag plus induced drag. • Recall that the parasitic drag is the drag not associated to lift production, • Form drag (or pressure drag) + skin friction drag • We can also add interference drag as another component. • Recall also that lift-induced drag is a byproduct of lift generation in finite span wings. • The drag breakdown of a typical transport aircraft shows that the lift-induced drag can amount to as much as 40% of the total drag at cruise conditions and 80–90% of the total drag in take-off configuration [1]. • Therefore, reducing lift-induced drag is of great interest in the aerospace industry. 101 Total drag in function of flight velocity Photo credit: https://commons.wikimedia.org/wiki/File:Drag_curves_for_aircraft_in_flight.svg. Apart from Fair Use, permission must be sought for any other purpose. [1] I. Kroo, Drag Due To Lift: Concepts for Prediction and Reduction. Annu. Rev. Fluid Mech. 2001. 33:587-617 Drag polar comparison – Wing data against airfoil data 102 Drag polar comparison – Wing data against airfoil data • Most of the airfoil aerodynamic characteristics (2D) are inherited by wings (3D): • Airfoil shape – Curvature effect on lift. • Reynolds number (sectional). • Mach number – Compressibility effects. • Stall mechanism and patterns. • Effect of early flow separation on lift and drag. • Effect of leading-edge separation bubbles on lift and drag. • The effect of high lift devices (HLD) on lift and drag – Flaps and slats. • Effect of surface finish and leading-edge contamination on lift and drag. • Therefore, it is of paramount importance to choose a good airfoil. • If you choose a not so good airfoil, the wing performance will be heavily affected. • So, what is a good airfoil? This was addressed in the previous lecture. 103 Drag polar comparison – Wing data against airfoil data • Due to three-dimensional effects, the behavior of wings is slightly different from that of airfoils. • The difference in the aerodynamic behavior is more evident when three-dimensional effects are larger. • Usually this is the case of low aspect ratio wings. • For very large aspect ratios, the behavior of wings is close to that of airfoils. • After all, airfoils can be seen as wings with infinity aspect ratio. • As you might guess, designing/selecting wings is much more complex than two-dimensional cases (airfoils). • In theory, we have infinite design variables. • Airfoils selection plus all wing’s geometric parameters. • Factors that affect the performance of wings: • Three-dimensional effects, such as wing tip vortex and spanwise velocity components. • Interaction of the wing with other aircraft components (fuselage, nacelles, pylons, and so on). • External disturbances, such as engine noise, vibrations, spanwise bending, boundary layer/wake interaction, shock waves, rain/ice, and so on. • Surface finish, interferences, discontinuities (such as control surfaces). 104 Drag polar comparison – Wing data against airfoil data • Comparison between predicted and measured drag polar for a wing having a finite aspect ratio and an airfoil. • The total drag of a wing is larger than that of an airfoil because of lift-induce drag and larger viscous drag. • Remember, lift-induced drag is a consequence of three-dimensional effects. • The equivalent drag polar model of an airfoil in a finite span wing can be expressed as follows, 105 Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. • Where m is a coefficient indicating the increment of the total drag of the airfoil. • Expanding equation E1, the drag polar increases by a small factor (which shift the polar upwards), E1 Drag polar comparison – Wing data against airfoil data • Comparison between predicted and measured drag polar for a wing having a finite aspect ratio and an airfoil. Photo credit: Aerodynamics, Aeronautics, and Flight Mechanics, B. McCormick, John Wiley & Sons, 1995. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 106 • Notice that the drag bucket is not present in the wing polars. • This is due to three-dimensional effects, wing surface roughness, or freestream disturbances, among many factors. • The wing will inherit most of the airfoil properties but mainly due to three-dimensional effects (lift induced drag), the two-dimensional behavior (viscous drag) is disguise or lost. Airfoil data (reference 1) Profile drag. Wing data (references 2, 3) Experimental total drag Theoretical fitting (reference 4) References: [1] Abbott, I., Von Doenhoff, A., Stivers, L. S., Summary of airfoil data. NACA Report 824. 1945. [2] J. Sivells, Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA-TN- 1422, August 1947. [3] J. Sivells, S. Spooner, Investigation in the Langley 19-foot Pressure Tunnel of Two Wings of NACA 65-210 and 64-210 Airfoil Sections with Various Type Flaps. NACA-TR-942, January 1949. [4] Aerodynamics, Aeronautics, and Flight Mechanics, B. McCormick, John Wiley & Sons, 1995. Effect of aspect ratio and taper ratio on induced drag 107 Effect of aspect ratio and taper ratio on induced drag • Effect of aspect ratio and taper ratio on induced drag and lift curve slope. Typical stall patterns Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 108 Correction factor for non-elliptical lift distribution Airfoil lift curve slope Correction factor for non-elliptical lift distribution Oswald span efficiency Effect of aspect ratio and taper ratio on induced drag • Effect of aspect ratio and taper ratio on induced drag and lift curve slope. Photo credit: Aerodynamics for Engineers (6th Edition). J. Bertin, R. Cummings. Pearson, 2013. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 109 Correction factor for non-elliptical lift distribution Oswald span efficiency • In reference to the figure, the best induced drag parameter for different AR, corresponds to a wing with a taper ratio anywhere between 0.3 and 0.5. • A trapezoidal wing with this taper ratio approximates an elliptic platform shape and gives the best results for lift and drag. • Recall that the induced drag parameter is zero only for elliptical wings. • For the rest of the wings is a number larger than zero and usually between 0.02 and 0.2. • The induced drag parameter penalizes the wing. It is an indication of how far we are from the elliptical lift distribution. • The larger the induced drag parameter is, the more induced drag the wing will produce. • A similar analysis can be conducted using the slope parameter showed in the previous slide. • The slope parameter influences the wing’s lift curve slope. Effect of aspect ratio and taper ratio on induced drag Photo credit: Peter Garrison. Air & Space Magazine, February 2019. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. • Comparison of elliptical wing and a taper wing. • By carefully designing the tapered wing, we can obtain the same lift distribution as the for the elliptical wing. 110 Effect of washout/washin on wing aerodynamic performance 111 Effect of washout/washin on wing aerodynamic performance • Spanwise variation of maximum section lift coefficient and section lift coefficient at maximum wing lift coefficient for wings of aspect ratio 9 and ratio of root chord to tip chord 2.5. Reynolds number approximately 4.4 millions [1]. • In the figure, by controlling the washout angle (left image), it is possible to change the lift distribution and the location where the wing first stalls. • The method used in reference [1] to determine CL max and the stall location is known as the critical section method [2, 3]. [1] J. Sivells. Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA Technical Note No. 1422. [2] S. Wakayama and I. Kroo. Subsonic Wing Planform Design Using Multidisciplinary Optimization. Journal of Aircraft, Vol. 32, No. 4, July-August 1995. [3] E. Olson. Semi-Empirical Prediction of Aircraft Low-Speed Aerodynamic Characteristics. AIAA 2015-1679, 2015. 112 Photo credit [1]. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Effect of washout/washin on wing aerodynamic performance • Spanwise variation of maximum section lift coefficient and section lift coefficient at maximum wing lift coefficient for wings of aspect ratio 9 and ratio of root chord to tip chord 2.5. Reynolds number approximately 4.4 millions [1]. • In the figure, by controlling the washout angle (left image), it is possible to change the lift distribution and the location where the wing first stalls. • The method used in reference [1] to determine CL max and the stall location is known as the critical section method [2, 3]. [1] J. Sivells. Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA Technical Note No. 1422. [2] S. Wakayama and I. Kroo. Subsonic Wing Planform Design Using Multidisciplinary Optimization. Journal of Aircraft, Vol. 32, No. 4, July-August 1995. [3] E. Olson. Semi-Empirical Prediction of Aircraft Low-Speed Aerodynamic Characteristics. AIAA 2015-1679, 2015. 113 Photo credit [1]. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Effect of washout/washin on wing aerodynamic performance • The critical section method [1,2,3], together with linear methods, such as the LLT, VLM, or panel methods, is a cheat way to determine the maximum lift coefficient and stall progression of aircraft and wings. • The maximum lift coefficient and stall progression of an aircraft or a wing is calculated using the critical section method as follows: • For increasing values of angle of attack, the lift coefficient at each location along the wing is compared to the maximum lift coefficient of that section, and a stall is declared when the maximum lift coefficient is first surpassed at any section. • The maximum lift coefficient for the aircraft or the wing is defined as the value achieved when the stalling condition is reached. [1] J. Sivells. Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA Technical Note No. 1422. [2] S. Wakayama and I. Kroo. Subsonic Wing Planform Design Using Multidisciplinary Optimization. Journal of Aircraft, Vol. 32, No. 4, July-August 1995. [3] E. Olson. Semi-Empirical Prediction of Aircraft Low-Speed Aerodynamic Characteristics. AIAA 2015-1679, 2015. 114 Photo credit: General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Effect of washout/washin on wing aerodynamic performance • The critical section method [1,2,3] is simple and computationally inexpensive, and gives surprisingly good results, probably because of the requirement to maintain good handling qualities at stall. • Stall should not begin at the wingtips since this could cause undesirable pitch-up or roll. • In the case of aft sweep, a conventional transport wing is prone to stall at the wingtips due to the effects of spanwise flow at higher angles of attack, so that aircraft designers modify airfoil sections on the inboard sections to degrade the CLmax of those sections and ensure stall beginning near the wing root. • Some margin is provided against stalling the tip sections, so that the wing is designed to stall just below the point where the critical outer section reaches its CLmax. • Studies have found that the critical section method can be too optimistic when studying sweep wings. • So, corrections can be applied based on previous experience. • For sweep wings and high-speed aerodynamics, a better alternative to the critical section method is the pressure difference rule [4]. • It is important to stress that both, the critical section method and the pressure difference rule need many solutions (different angles on attack, Reynolds number, and Mach number); and the only cost- and time-effective way to generate these solutions is by using surface panel methods and potential solvers. • Predicting the maximum lift of finite span wings is not easy. [1] J. Sivells. Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA Technical Note No. 1422. [2] S. Wakayama and I. Kroo. Subsonic Wing Planform Design Using Multidisciplinary Optimization. Journal of Aircraft, Vol. 32, No. 4, July-August 1995. [3] E. Olson. Semi-Empirical Prediction of Aircraft Low-Speed Aerodynamic Characteristics. AIAA 2015-1679, 2015. [4] W. O. Valerzo and V. D. Chin. Method for the prediction of wing maximum lift. Journal Aircraft, vol. 31,no. 1, 1994. 115 Effect of washout/washin on wing aerodynamic performance • Prediction of CLmax and stall progression/patterns using the critical section method [1]. [1] J. Sivells. Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA Technical Note No. 1422. 116 Effect of washout/washin on wing aerodynamic performance • Lift distribution near stall predicted by potential flow and critical section method [1]. • The waviness in places is due to the discontinuity in the segment of the wing, which features a leading-edge extension. 117 Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. [1] S. Gudmundsson. General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann, 2016. • Impact of washout and dihedral on the aerodynamics of a typical wing. High aerodynamic efficiency concepts The otto Celera 500L 118 High aerodynamic efficiency concepts – The otto Celera 500L case 119 • Prolate spheroid fuselage to reduce flow separation and promote laminar boundary layer. • The design of the Celera 500L fuselage takes advantage of an optimum length-to-width ratio to maximize laminar flow. • These benefits do not scale for large jet transports. Old vs. new: Piper PA-31 (left aircraft) next to the Otto Celera 500L (right aircraft). Extensive use of laminar flow surfaces in the Otto Celera 500L results in approximately 59% reduction un drag compared to a similar sized conventional aircraft. Photo credit: https://edition.cnn.com/travel/article/celera-500l-business-aircraft-future/index.html. Prolate spheroid fuselage to reduce flow separation and promote laminar boundary layer. Photo credit: https://www.ottoaviation.com/technology Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. High aerodynamic efficiency concepts – The otto Celera 500L case 120 • The Celera 500L makes extensive use of laminar flow surfaces which result in approximately 59% reduction of drag compared to a similar sized conventional aircraft. Photo credit: https://www.ottoaviation.com/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. High aerodynamic efficiency concepts – The otto Celera 500L case 121 • Other advanced aerodynamic concepts used in the Celera 500L: • Winglets, high aspect ratio wings, wing planform optimized for elliptical lift distribution, NLF airfoils, ventral fins, elliptical planform horizontal stabilizers, laminar flow control, pusher propeller, boundary layer ingestion, reduced excrescence and interference drag, among many. Photo credit: https://www.ottoaviation.com/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. High aerodynamic efficiency concepts – The otto Celera 500L case 122 • A 3D model can be found at the following link, • https://sketchfab.com/3d-models/celera-500l-306092a41d174e719e83bd143a5ad042 Photo credit: https://www.ottoaviation.com/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. High aerodynamic efficiency concepts The Honda HA-420 HondaJet 123 High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 124 • The Honda HA-420 HondaJet is a light business jet produced by the Honda Aircraft Company. • The HondaJet is an advanced, lightweight, business jet featuring an extra-large cabin, high fuel efficiency, and high cruise speed compared to existing small business jets. • To achieve the high-performance goals, an over-the-wing engine-mount configuration, a natural-laminar-flow (NLF) wing, and a natural-laminar-flow fuselage nose were developed through extensive analyses and wind-tunnel tests. • The wing is metal, having an integral, machined skin to achieve the smooth upper surface required for natural laminar flow. • The fuselage is constructed entirely of composites; the stiffened panels and the sandwich panels are co-cured integrally in an autoclave to reduce weight and cost. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 125 • The aircraft is a low-wing configuration with the engines mounted over the wing. • The aircraft is 41.14 ft long, has a wingspan of 39.87 ft, and is 13.21 ft high at the top of the T-tail. • Design maximum takeoff weight is about 9200 lb. • The estimated maximum speed is about 420 knots at 30000 ft and the maximum range is about 1100 nm. • The cabin is pressurized up to 8.7 psi to maintain an 8000 ft cabin altitude up to 44000 ft. • The aircraft provides a very large cabin volume compared to those of other four-passenger seat arrangements and it is also possible to add two more passenger seats without sacrificing comfort. • The aircraft is powered by two Honda HF-118 fuel-efficient turbofan engines, each rated at 1670 lb thrust at takeoff power. • The engine is controlled by the Full Authority Digital Engine Control (FADEC) system. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 126 • Over-the-wing Engine-Mount Configuration • Engine location was the major design decision in the development of the HondaJet configuration. • In general, locating the engine nacelles over the wing causes unfavorable aerodynamic interference and induces a strong shock wave that results in a lower drag-divergence Mach number. • Computational studies were conducted using a three-dimensional Euler solver. • Experimental studies were conducted in the Boeing Transonic Wind Tunnel (BTWT) to validate the computational predictions. • It was found that the shock wave is minimized and drag divergence occurs at a Mach number higher than that for the clean-wing configuration when the nacelle is located at the optimum position relative to the wing • The over-the-wing engine mount configuration exhibits lower drag than does the conventional rear-fuselage engine mount configuration. • By employing this optimum over-the-wing engine mount configuration, the cruise efficiency is higher than that of a conventional rear-fuselage engine-nacelle configuration and, in addition, the cabin volume is maximized. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 127 • Wing design • Detail design studies were performed to minimize the induced drag with minimum wing weight. • The study showed that the takeoff weight is minimized for a 1100 nm range aircraft when the wing geometric aspect ratio is 8.5 and a winglet having a height of 9% of the wingspan is installed. • Because of the over-the-wing engine-mount configuration, the stall characteristics were carefully studied by computational analysis and low-speed wind-tunnel tests. • From the computational analysis using a vortex-lattice method, and a three-dimensional panel method, a taper ratio of 0.38 and a washout of 5.1 degrees were chosen to provide good stall characteristics with minimum induced drag penalty. • The zero-lift angle of the over-the-wing engine-mount configuration is about 1.2 degrees higher than that of the clean-wing configuration. • The maximum lift coefficient of the over-the-wing engine-mount configuration is about 0.07 higher than that of the clean-wing configuration. Thus, there is no disadvantage with respect to the lift characteristics due to the nacelle installation over the wing. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 128 • Natural-laminar-flow (NLF) airfoil • To satisfy the requirements of the HondaJet, a new natural-laminar-flow airfoil, the SHM-1, was designed using a panel code and inverse design using a conformal-mapping method. • The pressure gradient on the upper surface is favorable to about 42- percent chord, followed by a concave pressure recovery, which represents a compromise between maximum lift, pitching moment, and drag divergence. • The pressure gradient along the lower surface is favorable to about 63- percent chord to reduce drag. • The leading-edge geometry was designed to cause transition near the leading edge at high angles of attack to minimize the loss in maximum lift coefficient due to roughness. • The upper-surface trailing-edge geometry was designed to produce a steep pressure gradient and, thereby, induce a small separation. By the incorporation of this new trailing-edge design, the magnitude of the pitching moment at high speeds is greatly reduced. • The airfoil exhibits a high maximum lift coefficient with docile stall characteristics and low profile-drag coefficients in cruise and climb. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 129 • Natural-Laminar-Flow Fuselage Nose • A natural-laminar-flow, fuselage-nose shape was developed through extensive analysis and experiments to reduce the fuselage drag. • Using a three-dimensional, panel code with an integral boundary-layer method the fuselage-nose contours were designed to maximize laminar-flow length by maintaining a favorable pressure gradient and minimizing crossflow. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 130 • High lift system • A 30-percent-chord, double-slotted flap, which is deployed by a mechanical linkage, is employed to satisfy the stall-speed requirement as well as the high-speed requirement. • The position of the vane with respect to the flap is fixed. The shapes of the vane and the flap as well as the gap and overlap were designed using a two-dimensional, multielement, panel code. • The flap and vane shapes and positions were tested on a 1/3-scale, half-span model in the Honda Low-Speed Wind Tunnel and the results were compared with those from computational studies using a panel code. • A test was also conducted using a 1/6-scale model in the Honda Low- Speed Wind Tunnel. • The results for two Reynolds numbers allowed the full-scale maximum lift coefficient to be estimated more accurately using an analytical method that incorporated the pressure-difference rule. • The maximum lift coefficient for the full-scale Reynolds number is estimated to be higher than 2.5, which satisfies the stall-speed requirement. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 131 • This paper is beautiful example of aerodynamic design and multidisciplinary design optimization in industry. • We just reviewed the aerodynamic design aspects, but in the paper, the author also address the following topics: • Performance. • Flight Simulator. • Stability. • Aeroelasticity. • Structure. • Systems integration. • Ground tests. • Flight tests. • Wind tunnel testing. • Avionics. • You are highly encouraged to read the paper. References: M. Fujino. Development of the Honda Jet. 24th Congress of International Council of the Aeronautical Sciences, 29 August-3 September 2004, Yokohama, Japan High aerodynamic efficiency concepts – The Honda HA-420 HondaJet 132 • A 3D model can be found at the following link, • https://sketchfab.com/3d-models/honda-private-jet-396a2651bf2b4409b34a6cf786b09ea9 Photo credit: https://www.ottoaviation.com/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Design for speed The evolution of the B-52 134 Design for speed – The evolution of the B-52 135 • Evolution of the B-52 according to the design speed requirements. • Apart from the design speed requirements, there were also requirements on the ceiling, range, payload and engine type (among many other requirements). • The final wings have a large aspect ratio, very large span, and 35-degree swept wing. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. 1945 Cruise speed requirement 260 knots 480 km/h 1946 Cruise speed requirement 345 knots 645 km/h 1947 Cruise speed requirement 440 knots 800 km/h 1948 Cruise speed requirement 440 knots 800 km/h Jet engines required 1950 Cruise speed requirement 440 knots 800 km/h Jet engines required 1951 Cruise speed requirement 440 knots 800 km/h Jet engines required Side-by-side cockpit Design for speed – The evolution of the B-52 136 • The B-52 in service today can reach cruise speeds as high as 650 mph (Mach 0.86). • With a range of 7652 nautical miles (14160 km). • A service ceiling of 50000 ft (15150 m). • And a very large payload. • It is expected to flight until 2040 and beyond. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. https://en.wikipedia.org/wiki/Boeing_B-52_Stratofortress#/media/File:B- 52_Stratofortress_assigned_to_the_307th_Bomb_Wing_(cropped).jpg https://commons.wikimedia.org/wiki/File:B-52s_arrive_at_Al_Udeid_Air_Base_3.jpg Design for speed – The evolution of the B-52 137 • Do you notice something estrange of wings? Or better, something missing? Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. https://www.boeing.com/resources/boeingdotcom/defense/b52_bomber/images/b_52_gallery_l rg_03_960.jpg https://www.boeing.com/resources/boeingdotcom/defense/b- 52_bomber/images/b_52_gallery_lrg_05_960.jpg Design for speed – The evolution of the B-52 138 • The B-52 does not rely on ailerons for roll control (as many other large airplanes). • Aileron activation would cause the wing to twist, undermining roll control with ailerons. • Therefore, spoilers (or spoilerons) on each wing are responsible for roll control. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. https://www.boeing.com/resources/boeingdotcom/defense/b- 52_bomber/images/b_52_gallery_lrg_04_960.jpg https://theaviationgeekclub.com/wp-content/uploads/2018/05/B-52-Low-Level.jpg Design for speed – The evolution of the B-52 139 • A 3D model can be found at the following link, • https://sketchfab.com/3d-models/boeing-b-52h-stratofortress-5497331214854040bd7de1e024b135af Photo credit: https://www.ottoaviation.com/. Copyright on the images is held by the contributors. Apart from Fair Use, permission must be sought for any other purpose. Wing design principles How to compute/estimate the aerodynamic charateristics of wings? 140 Wing design principles • When designing your wing always have in mind the following: • You need to design the wing in such a way that it generates the required lift. • We want a wing with low induced drag from the aerodynamic point of view. • This means a spanwise lift distribution as close as possible to the elliptical lift distribution. • We also want low viscous drag. • This strongly depends on the airfoil selection. • Satisfying the previous two requirements is not an easy task. If your wing generates the required lift, this is not a problem. • You can generate the required lift by changing any of the geometrical parameters of the wing, namely, aspect ratio, taper, span, sweep angle, geometrical/aerodynamic twist, and so on. • The wing first stalls inboard. • This can be verified by plotting the spanwise lift coefficient distribution. • The wing has gentle stall characteristics. • The wing does not generate large bending moments. 141 Wing design principles • Things such as, • Dihedral/anhedral angle. • High lift devices. • Wingtip devices. • And other operational requirements, such as, volume for fuel storage, roll rate, and so on, will come at a later stage. • As you can see, to design a wing you have many possibilities. • In fact, there are infinite combinations of the wing geometrical parameters. • Therefore, the use of a fast and reliable tool is highly advisable. 142 How to compute/estimate the aerodynamic charateristics of wings? • At this point, the question is, how do we compute the aerodynamic properties of wings? • To do so, we can resort to the following methods: • To design the wing, we can also use: • Semi-empirical methods (e.g., DATCOM). • Previous experience. • Experiments in wind tunnel. • Trail-and-error (worst approach). • To estimate CLmax and stall progression, we can use the critical section method. • Mathematical and computational complexity. • Physics involved. • Computational resources. • Simulation time. • User experience. • Accuracy. Less More 143 • Prandtl lifting-line theory (LLT). • Vortex lattice methods (VLM). • 3D panel methods. • Computational fluid dynamics (CFD). How to compute/estimate the aerodynamic charateristics of wings? • When doing the initial design of your wing, you will be tempted to use CFD. • However, CFD is too expensive to be used during the preliminary design phase. • CFD can be used to fine tune your design at a later stage. • But if there is no other choice, or if you have enough time and resources, feel free to use CFD. • Mathematical and computational complexity. • Physics involved. • Computational resources. • Simulation time. • User experience. • Accuracy. Less More • Semi-empirical methods. • Prandtl lifting-line theory (LLT). • Vortex lattice methods (VLM). • 3D panel methods. • Computational fluid dynamics (CFD). 144 References 145 References • J. Sivells, Experimental and calculated characteristics of three wings of NACA 64-210 and 65-210 airfoil sections with and without 2 degree washout. NACA-TN-1422, August 1947. • J. Sivells, R. Neely, Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data. NACA-TN- 1269, April 1947. • J. Sivells, R. Neely, Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data. NACA-TR- 865, January 1947. • J. Sivells, S. Spooner, Investigation in the Langley 19-foot Pressure Tunnel of Two Wings of NACA 65-210 and 64-210 Airfoil Sections with Various Type Flaps. NACA-TN-1579, May 1948. • J. Sivells, S. Spooner, Investigation in the Langley 19-foot Pressure Tunnel of Two Wings of NACA 65-210 and 64-210 Airfoil Sections with Various Type Flaps. NACA-TR-942, January 1949. • J. Sivells, An improved approximate method for calculating lift distributions due to twist. NACA-TN-2282, January 1951. • J. Sivells, G. Westrick, Method for calculating lift distributions for unswept wings with flaps or ailerons by use of nonlinear section lift data. NACA-TR-1090, January 1952. 146 References • J. Anderson, S. Corda, D. Van Wie, Numerical lifting line theory applied to drooped leading-edge wings below and above stall. J. Aircraft, Vol. 17, No. 12, 1981. • C. Cone, The theory of induced lift and minimum induced drag of nonplanar lifting systems. NASA-TR-R-129, January 1962. • H. Multhopp, Methods for calculating the lift distribution of wings (subsonic lifting-surface theory). Aeronautical research council R&M No. 2884, January 1950. • R. Neely, T. Bollech, G. Westrick, R. Graham, Experimental and Calculated Characteristics of Several NACA 44-series Wings with Aspect Ratios of 8, 10, and 12 and Taper Ratios of 2.5 and 3.5. NACA-TN-1270, May 1947. • L. Prandtl, Applications of Modern Hydrodynamics to Aeronautics. NACA-TR-116, January 1923. 147