Conceptual Aerodynamic Design of Delta-type Tailless Unmanned Aircraft

Transcription

1 IJUSEng 2014, Vol. 2, No. S2, Technical Note Conceptual Aerodynamic Design of Delta-type Tailless Unmanned Aircraft Alexander S. Goodman Marques Aviation Ltd, USA Abstract: Goodman AS. (2014). Conceptual aerodynamic design of delta-type tailless unmanned aircraft. International Journal of Unmanned Systems Engineering. 2(S2): This paper describes the conceptual design of a delta-like tailless unmanned aircraft for intelligence, surveillance and reconnaissance missions, with possible strike capabilities. The delta configuration yields greater performance at high angles of attack (α) and can produce lower drag than conventional aircraft. The lack of inherent flight stability allows the aircraft to perform combat manoeuvres and the absence of vertical control surfaces reduces radar signature. Aspects to take into consideration in the conceptual aerodynamic design of a delta-like tailless configuration include airfoil selection, aerodynamic modelling for steady state stability, wing planform shape, planform geometric alterations, control surfaces, and adaptive wing technology and aeroelastic concepts. This study proposes the use of the HS 522 airfoil for the inward part of the wing and the NACA airfoil for the outer wing. The HS 522 is an excellent fit for swept wings and low Reynolds numbers. The HS 522 produces only a small negative pitching moment and also performs well at high speeds. The NACA has reflex camber and helps promote longitudinal stability. When a fuselage is added to a wing, the aerodynamic centre (a.c.) of the wing-fuselage combination shifts forward. This is known as the Munk effect and must be considered. The dominant flow pattern over the proposed delta-like configuration will consist of leading edge vortex patterns at high α, containing a primary vortex and a secondary vortex. Wing sweep affects the a.c., lift curve slope, and zero-lift slope along with many other individual parameters, such as dihedral effect. Consequently, wing sweep angle is a critical parameter that should be carefully analyzed and tested in relation to aircraft desired performance. Several smaller elevons are proposed for small adjustments of flight attitude to achieve less drag, easily dampen aircraft oscillations, and lessen the wing decambering effect. Winglets help lower the strength of the tip vortices and can act as rudders for lateral/directional stability and control by taking advantage of a long moment arm. Multiple slotted reversed-flow flaps that mimic the natural flight of birds should be further investigated for low α flight attitudes to suppress the proliferation of detached flow, maintain high lift, and delay the stall. Marques Engineering Ltd. Keywords: Aerodynamics Aeroelasticity Conceptual design Delta planform Unmanned aircraft Stability 1 IJUSEng , Vol. 2, No. S2, 1-15

2 1. INTRODUCTION This paper describes the conceptual aerodynamic design of a variant of a delta blended wing-body tailless mid-range unmanned aerial vehicle (UAV) with intelligence, surveillance and reconnaissance (ISR) and possible strike capabilities. The tailless configuration is desirable for a number of reasons. With no vertical control surfaces, or at least no large vertical surfaces, the aircraft has minimal radar signature. [1] This configuration can produce lower drag than conventional aircraft and greater performance at high angles of attack (α). Also, with the lack of inherent flight stability, the aircraft can perform combat manoeuvres. [2,3] With the limitations in technology and materials in the past, the tailless design layout was not as efficient as the conventional layout and was also very unstable. With advancements in both technology and materials a tailless delta configuration can be designed to yield greater performance than conventional-style aircraft. [4] The performance of tailless aircraft is expected to improve with further experimentation and analyses. This paper addresses the following topics of aerodynamic design: airfoil selection, basic aerodynamic modelling for steady state stability, planform shape, planform geometric alterations, control surfaces, adaptive wing technology, and aeroelasticy. 2. AIRFOIL SELECTION Traditional cambered airfoils produce a negative pitching moment (C m ), nose-down effect, on the airfoil. This is counteracted through the empennage by the horizontal stabilators. In a tailless delta-wing type aircraft, careful selection of the airfoils is essential, since C m strongly contributes to the aerodynamic longitudinal stability of the aircraft. [5] The C m is measured around the aerodynamic centre (a.c.). Both C m and a.c. are discussed in further detail in the next section dealing with aerodynamic modelling. With no tail for longitudinal stability, the airfoils selected should have low or zero C m. Instead of using a symmetric airfoil, which has zero C m at zero α, a suitable solution is to choose a reflexed airfoil. [4] The following presents an analysis on reflex airfoils. The camber shape on an airfoil is closely related to C m. The aft part of the camber line has a great influence on C m. Because of this influence, the aft end of the camber line is reflexed. By increasing the degree of reflex, the C m vs. α curve shifts upward (positive). The drag polar is also affected and shifts down. This produces an undesired reduction in the maximum lift coefficient, but can be fixed by creating more camber. However, greater caber increases the negative nose down C m. In aerodynamics this is usually the case, improvement of one aspect negatively affects other aspects of the aerodynamic design. Another option is to change the location of the maximum camber. The position of the maximum camber has a small influence on the drag polar, but can greatly impact the pitching moment. [6] If the maximum camber position is shifted backwards, the C m increases in the negative direction (nose-down). The maximum camber position should, therefore, be towards the leading edge (LE) of the airfoil for a delta planform aircraft. This is illustrated in Figs. 1 and 2, where three different airfoils are compared. Fig. 1: Geometry of three airfoils (adapted from Jiangtao et al. [5] ) 2 IJUSEng , Vol. 2, No. S2, 1-15

3 Fig. 2: Aerodynamic coefficients for the three airfoils (adapted from Jiangtao et al. [5] ) 2.1. Analysis of the HS 522 and NACA Airfoils Two different airfoils are used throughout the wing planform of the proposed tailless aircraft. The inward portion of the wing is an airfoil with a close to zero C m. The outward portion of the wing is comprised of a reflexed airfoil to counteract the negative C m created by the UAV configuration. [1] The airfoils are also able to operate at lower Reynolds numbers (Re) because the aircraft s speed and chord length are small, which directly influences Re. The HS 522 airfoil was selected as the inward span airfoil (Fig. 3). This airfoil is an excellent fit for swept wings and low Re. This HS 522 airfoil can also perform well at high aircraft speed. [7] This airfoil does produce a nose down C m, however the C m is small compared to that of many other airfoils. Table A1 in the Appendix displays the results for three different low Res. [4] Fig. 3: HS 522 airfoil [7] A reflex camber airfoil is used for the outboard portion of the wing. The NACA 5 digit series airfoils are known to produce low C m. Specifically, the NACA airfoil was selected (Fig. 4). The NACA airfoil was then compared to a similar airfoil, NACA 23112, which differs from the NACA airfoil only by the farther aft position of the maximum camber location. [5] These airfoils were compared at the two Re of 0.5 x 10 6 and 1 x The results are shown in Table 1. Plots of airfoil aerodynamic coefficients vs. α can be found in Figs. A.1-A.4 in the Appendix. It can be seen from the Figures that as the maximum camber is pushed aft, the maximum lift decreases and the nose down C m increases. The combination 3 IJUSEng , Vol. 2, No. S2, 1-15

4 of these two airfoils may balance each other, depending on the spanwise distance distribution, and could create a slight washout. Fig. 4: NACA profile with camber line [8] Table 1: NACA 5-digit series airfoil analysis Airfoil and Re NACA 22112, Re = 5 x NACA 22112, Re = 1 x NACA 23112, Re = 5 x NACA 23112, Re = 1 x AERODYNAMIC MODELLING One of the most important parameters of an aircraft is the a.c. The a.c. is the point on the wing mean aerodynamic chord where the variation of C m with α is zero. Finding the a.c. on the wing planform is very important, however the influence of the fuselage must be considered. When a fuselage is added to a wing, the a.c. of the wing-fuselage combination shifts forward compared to that for a wing. This means that the fuselage will add a positive C m with each increase of α. This is called Munk effect. [9] The design of the proposed aircraft, however, resembles that of a blended wing-body similar to that of a flying wing. Thus, the addition of the fuselage will not play as big a role on the C m as a conventional aircraft, but still cannot be ignored. [4] In order to know how the aircraft will perform, modelling of the aerodynamic and thrust forces and moments must be determined for steady state and perturbed state. There are two ways to determine these forces and moments. These are experimental methods, such as flight or wind tunnel tests, and computational and/or empirical methods. The following presents basic mathematical models to show how to determine the aerodynamic forces, thrust forces, and moments. For the case of tailless aircraft conventional modelling is not appropriate, rather the wing-body effects need to be included. The steady state aerodynamic forces and moments are discussed below. They are broken down into longitudinal variables and lateral-directional variables. An in-depth analysis of these models is beyond the scope of this paper. Roskam [9] and Napolitano [10] discuss this topic in greater detail. Thrust and perturbated state forces and moments are not covered below. Perturbated state modelling is complex and it is a subject beyond the basic conceptual design presented in this paper. The following modelling data and equations were taken from Roskam [9] and Napolitano. [10] 4 IJUSEng , Vol. 2, No. S2, 1-15

5 3.1. Longitudinal Stability The longitudinal aerodynamic forces and moments that act on an aircraft in steady state conditions are 3.2. Drag Force The expression for is ; where, = drag coefficient, = is the dynamic pressure, and S = planform area. The steady state aerodynamic for the aircraft is dependent on α, airplane wetted area,, skin friction coefficient, Mach number, Re, and control surface deflections Lift Force The is calculated using ; where, = lift coefficient. The steady state airplane aerodynamic is also dependent on α,, Mach number, Re, and control surface deflections Pitching Moment The form for is ; where, = mean geometric chord. The steady state airplane aerodynamic C m is dependent on α,, Mach number, Re, centre of gravity, and control surface deflections Lateral-Directional Stability The lateral-directional aerodynamic forces and moments that act on an aircraft due to sideslipping are 3.6 Rolling Moment The expression for is ; where, = rolling moment coefficient and = span. The steady state airplane aerodynamic is dependent on the sideslip angle, α,, Mach number, Re, centre of gravity, and the deflection of lateral and directional control surfaces Yawing Moment The has the form ; where, = yawing moment coefficient. The steady state airplane aerodynamic is dependent on the sideslip angle, α, Mach number, Re, centre of gravity, and the deflection of directional and lateral control surfaces Side-Force The equation for is ; where, = side-force coefficient. The steady state airplane aerodynamic is dependent on the sideslip angle, α, Mach number, Re, and the deflection of lateral and directional control surfaces. For an in-depth analysis, four aerodynamic coefficients are considered important. According to Napolitano [10], these coefficients are referenced as the four pillars because they need to fit together in order for the aircraft to fly adequately. The four coefficients are: Plays a vital role in the longitudinal stability lift force. 5 IJUSEng , Vol. 2, No. S2, 1-15

6 Plays a vital role in the longitudinal stability pitching moment. Plays a vital role in lateral-directional stability rolling moment. Plays a vital role in lateral-directional stability yawing moment. 4. WING PLANFORM The wing planform for the proposed UAV is a variant of the delta configuration incorporating a blended wing-body without a tail. Examples of different delta shape planforms can be seen in Fig. 5. This planform shape was chosen to reduce radar signature for ISR and possible strike missions. The delta configuration is very common in high speed fighter jets because the shape allows the aircraft to cruise at very high subsonic speeds and achieve high α without stalling. This is accomplished due to the leading edge vortices that flow over the wing at high α. Fig. 5: Different delta wing planforms (based upon Anderson [6] ) In a tailless configuration, the wing span is extended farther back than the base of the aircraft. The airframe shape resembles that of a notched delta. Examples of similar wing planforms can be observed in the Northrop Grumman Bat and the Lockheed Martin RQ-170 Sentinel (Figs. 6 and 7). The notched delta planform balances out the centre of gravity along with the desired control surfaces to add greater manoeuvrability and control. [11] 6 IJUSEng , Vol. 2, No. S2, 1-15

7 Fig. 6: Northrop Bat (Image: Courtesy of Northrop Grumman Aerospace Systems) Fig. 7: RQ-170 Sentinel (Image: Truthdoser) There are two important vortex patterns that form over delta wings, a primary vortex and a secondary vortex. [6] The primary vortex is formed by the sharpness of the leading edge causing the flow shear to separate. The primary vortex consists of a pair of strong leading edge vortices characterised by low local pressure. [12] With the pressure drop caused by the primary vortices the lift is enhanced allowing the delta configuration to operate at higher α than conventional planforms. The formation of these primary vortices usually appears after a certain positive α is reached and becomes stronger with higher α, thus producing more lift. 7 IJUSEng , Vol. 2, No. S2, 1-15

8 Eventually, the stall angle is reached caused by vortex break down. [12] An in-depth visual description is displayed in Fig. 8. Fig. 8: Flow over a delta wing planform (based upon Anderson [6] ) An important characteristic of delta wings is the leading edge radius. Depending on the mission, the radius needs to be tailored. For completely subsonic missions and hypersonic missions, such as in the Space Shuttle, a larger rounded edge should be used. The aerodynamics behind these two missions is different. The hypersonic re-entry of the Space Shuttle allows extreme high temperatures without damaging the wing. The large rounded edge is also used to create a large bow shock to slow the aircraft down. [6] The larger rounded edge for low subsonic flight missions is used to create higher lift to accompany the low speeds, as well as keeping the flow attached for longer. [5] 5. WING TWIST AND SWEEP 5.1. Twist There are two different types of twist, geometric and aerodynamic. Geometric twist involves varying the wing incidence angle along the span. Geometric washout is applied by decreasing α along the span from the root to the tip. Aerodynamic twist involves varying the zero-lift α along the span. Aerodynamic twist can be implemented by progressively changing the camber of the airfoil sections. Twist is used to reduce induced drag by changing the lift distribution seen by the wing. Another important characteristic of twist is the washout effect created, so that the wing root stalls before the wing tip. [2] This allows the control surfaces, such as the aileron, to function, allowing the aircraft to recover from the partial stall. Thus, aerodynamic washout is achieved by making the stall angle at the tip larger than at the root by either decreasing the camber from root to tip or by using different airfoil sections. [11] 5.2. Sweep The proposed tailles UAV is modeled after a delta wing. Therefore, wing sweep needs to be implemented. It has been discussed earlier that the delta type planform experiences additional lift through the vortical flow over the wing. The amount of wing sweep can greatly alter the aerodynamic characteristics of the aircraft and should be determined. The aircraft 8 IJUSEng , Vol. 2, No. S2, 1-15

9 can have varying leading edge and trailing edge sweeps. The α seen by each wing segment increases towards a swept wing tip. [1] This causes the wingtips to stall first, which needs to be avoided. The wing sweep affects the aerodynamic centre, lift curve slope, and zero-lift slope along with many other individual parameters, such as dihedral effect. [9] Since the sweep angle is such a critical parameter, it should be carefully analyzed and tested to determine which sweep angle best fits the desired performance of the UAV. 6. CONTROL SURFACES UAVs can have numerous types of devices for stability and control. With a lack of an empennage, the aircraft requires non-conventional control surfaces and/or have them placed in non-conventional positions in order to achieve stability and control. [1] The use of trailingedge high-lift devices should be avoided. These devices create large pitching moments causing longitudinal instability from which the aircraft may never recover. [13] With the location of the wingtips protruding behind the trailing edge of the aircraft, the elevons can function as elevators and ailerons for pitch control as well as roll control. [11] The wing can be equipped with either large elevons to compensate for the small moment arm or have numerous smaller elevons. [3] Using several smaller elevons could prove beneficial for small adjustments in flight attitude because such configuration creates less drag and more easily dampens the aircraft s oscillations. Using numerous smaller elevons instead of one large elevon can also lessen the effect of decambering along the span when the control surfaces are deflected. Many aircraft use wingtip devices such as winglets. Winglets drain the energy from the tip vortices and change the lift distribution over the wing (Fig. 9). [2] Fig. 9: Winglet vs. Whitcomb winglet (Image: Olivier Cleynen) Since the proposed UAV does not use a vertical tail, winglets could serve a dual purpose if designed properly. The winglets can help lower the strength of the tip vortices and act as rudders for lateral/directional stability and control. The rudders at the wingtips will also take 9 IJUSEng , Vol. 2, No. S2, 1-15

10 advantage of the longer moment arm, thus needing less deflection for a desired attitude adjustment. [11] A Whitcomb winglet might prove to be more beneficial to this UAV than conventional winglet designs (Fig. 9). Whitcomb winglets decrease the strength of the tip vortices and turn that energy into forward propulsion. [3] The use of winglets causes less air disturbances produced by the wing and reduce Doppler radar detection, but at the same time the vertical structures will cause larger cross-sectional radar detection. As stronger, lighter and smarter materials are developed more effective control surfaces may be incorporated into the design of the delta aircraft. 7. ADAPTIVE WING TECHNOLOGY AND AEROELASTIC CONCEPTS This section discusses possible adaptive wing technology and aeroelastic concepts that improve the aircraft s performance by altering the flow over the wing. One of the advantages of the delta wing planform is that it is less affected by aeroelastic problems. [13] Aeroelasticity is the interaction between inertial, elastic, and aerodynamic forces when a body is immersed in a fluid flow. [14] Dynamic aeroelasticity is responsible for a critically unwanted effect called flutter. Flutter is dynamic instability caused by self-oscillation which decreases the aircraft s stability and can eventually lead to structural failure. Aircraft with high aspect ratios and less structurally sound wings tend to suffer from flutter effect. The delta planform has a low aspect ratio and is structurally strong, and it is therefore an excellent counter to flutter effect. [3] Since the delta planform is less affected by aeroelasticity, aeroelastic concepts such as self-twisting wings will not be as effective as they would on conventionally-shaped aircraft. Adaptive wing technology can greatly improve an aircraft s performance without the bulkiness and complexity of conventional devices. There are two types of control technology, active and passive control. Active control requires additional energy and/or the presence of feedback, while passive control is self-regulatory. Some methods used in adaptive flow control are: boundary layer suction, perturbation control, laminar control, shock control, turbulence control, separation control, load control, variable camber, and changes in the structure through aeroelasticity and damping. [15] These can further be broken down into geometric and pneumatic devices. A few of these devices are: vortex generators, Gurney flaps, reversed-flow flaps, ribblets, leading edge suction systems, divergent trailing edges, and zero-mass jets Reversed-Flow Flaps In terms of adaptive technologies, the best current low speed applications for lift enhancement and flow separation suppression are multiple slotted flaps. However, such flaps add weight penalties and complexity to the aircraft. [15] Both are problems to UAVs, especially smaller UAVs. Reversed-flow flaps can be used for lift enhancement and separation suppression and are less complex than multiple slotted flaps. These reverse flow flaps are a geometric control device. Observation of birds has shown that their feathers pop up during landing approaches. A solution is to create a self-adjusting movable flap close to the trailing edge of the aircraft wing. Through a passive approach, the flap will be a selfadjusting movable flap located near the trailing edge which hinges around the flap s leading edge. It has been observed that at low speeds, with no separation, the flap seems to rise up due to static pressure differences. [15] This causes the airfoil to de-camber, thus reducing the lift. Through perforations on the flap, this unwanted effect can be minimized. The reversedflow flap raises when separation begins, keeping the flow attached longer and raising the coefficient of lift. These reversed-flow flaps keep the boundary layer small and delay separation compared to a conventional airfoil, thus lowering the pressure drag associated with the growing boundary layer and flow separation. Also, reversed-flow flaps do not protrude into the inviscid flow outside of the boundary layer as in the case of spoilers. The placement of the reversed-flow flap is critical along with keeping the perforations clean in order for this flap to work effectively. It has also been observed that during transonic conditions the flap may experience severe resonance causing strong flow oscillations and 10 IJUSEng , Vol. 2, No. S2, 1-15

11 eventually damaging the flap. [15] A possible fix is to use an active reverse flow flap instead of the previously discussed passive, freely movable, flap Zero-Mass Air Jets The other promising adaptive control method is the implementation of zero-mass air jets. [15] Zero-mass air jets are pneumatic active devices used to delay boundary layer separation at high lift conditions. This is done by periodic pulsating the flow, which in turn energizes the flow. Zero-mass air jets act similar to how slotted flaps work and can be used in conjunction with them. As the flow begins to separate, the air jets inject disturbances into the flow which energizes the flow by enhancing the mixture of the shear layer and the outer flow, thus achieving flow reattachment. These zero-mass air jets have been found to work at high subsonic Mach conditions. When the flow is supersonic, the effectiveness of the air jets decreases and may not be acceptable for the purposes of trying to inhibit shock-induced separation. [15] 8. CONCLUSION The design of an aircraft is a very difficult and complex process. It does not matter if the aircraft is manned, unmanned, small or large; each have their own difficulties. Tailless delta aircraft have been around for decades, but have recently seen a rise in production. This can be attributed to the emergence of more advanced materials and technologies that enhance aircraft performance. It was shown that there are many trade-offs when designing the wing planform. When one aspect of the design is increased or optimized then at least one, most likely multiple, aspects or parameters will be decreased. This paper helps create an outline of a conceptual design of a tailless delta-like UAV, but the analysis presented is not sufficient for a complete wing design. Many important factors were left out such as materials, structures, and the propulsion unit. The aerodynamic modelling section was briefly described, however a detailed analysis of the aerodynamics and thrust forces and moments need to be conducted in order to create the needed complex flight control system. The flight control system is the brains of the aircraft and with a subpar system a tailless delta aircraft will not be stable and possibly not be capable to complete the desired mission. As more aircraft of this design are developed, the aerodynamic performance will become greater and a detailed design layout will become just as generalized as a conventional tube and wing aircraft. Acknowledgements The author wishes to thank Marques Aviation Ltd for their support during this project. 9. REFERENCES 1. Friedl J. (2001). Aerodynamic design of a tailless aeroplane. ACTA Polytechnica. Journal of Advanced Engineering. 41(4/5): Loth JL. (2007). Engineering approach to aerodynamics and aircraft performance. (2 nd ed.). McGraw-Hill. New York. 3. Marqués P. (2013). Flight stability and control of tailless lambda unmanned aircraft. International Journal of Unmanned Systems Engineering. 1(S-2): Prisacariu V, Boscoianu M and Cîrciu I. (2013). Design and construction a flying wing unmanned aerial vehicles. Proceedings of the International Conference on Military Technologies. 22 nd 23 th May. Brno. Czech Republic. 5. Jiangtao S, Hao Z and Junqiang B. (2006). Airfoil design of tailless unmanned air vehicle (UAV). Proceedings of the 25 th International Congress of the Aeronautical Sciences. 3 th - 8 th September. Hamburg. Germany. Pp Anderson JD. (2010). Fundamentals of aerodynamics. (5 th ed.). McGraw-Hill. New- York. 7. Aerodesign. (2001). Airfoil database for tailless and flying wings. ( 8. Airfoil Tools. (2014). ( IJUSEng , Vol. 2, No. S2, 1-15

12 9. Roskam J. (2007). Airplane flight dynamics and automatic flight controls. Design, Analysis and Research Corporation. Lawrence. USA. 10. Napolitano M. (2011). Aircraft dynamics: From modeling to simulation. John Wiley & Sons, Inc. United States. 11. Donlan CJ. (1944). An interim report on the stability and control of tailless airplanes. National Advisory Committee for Aeronautics. 796: McLain BK. (2009). Steady and unsteady aerodynamic flow studies over a 1303 UCAV configuration. PhD thesis. Navy Post Graduate School. Monterey. United States. 13. Loftin LK. (1985). Technology of the jet airplane. Wings and configurations for highspeed. In Loftin LK. (Ed.). Flight. Question for performance: The evolution of modern aircraft. NASA Scientific and Technical Information Branch. Washington. D.C. Pp Weisshaar TA. (2010). Static and classical dynamic aeroelasticity. Vol. 3 Structural Mechanics. Section Encyclopedia of Aerospace Engineering. John Wiley. London. 15. Stanewsky E. (2001). Adaptive wing and flow control technology. Progress in Aerospace Sciences. 37(7): NOTATION a.c. Aerodynamic centre Span Mean geometric chord Drag coefficient Rolling moment coefficient Dihedral effect ISR Re S Lift coefficient Change in aircraft lift coefficient with α Pitching moment coefficient Change in aircraft pitching moment coefficient with α Yawing moment coefficient Weathercock effect Side-force coefficient Drag force Side/lateral force Drag force Lift force Intelligence, surveillance and reconnaissance Lift force Rolling moment Pitching moment Yawing moment Dynamic pressure Reynolds number Planform area α Angle of attack 12 IJUSEng , Vol. 2, No. S2, 1-15

13 11. APPENDIX Table A.1: Results for the HS 522 airfoil at different Re (adapted from Prisacariu et al. [4] ) 13 IJUSEng , Vol. 2, No. S2, 1-15

14 Fig. A.1: NACA airfoil performance at Re = 5 x 10 5 (Airfoil Tools [8] ) Fig. A.2: NACA airfoil performance at Re = 1 x 10 6 (Airfoil Tools [8] ) 14 IJUSEng , Vol. 2, No. S2, 1-15

15 Fig. A.3: NACA airfoil performance at Re = 5 x 10 5 (Airfoil Tools [8] ) Fig. A.4: NACA airfoil performance at Re = 1 x 10 6 (Airfoil Tools [8] ) Copyright of IJUSEng is the property of Marques Engineering Ltd and its content may not be copied or ed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or articles for individual use IJUSEng , Vol. 2, No. S2, 1-15