Airfoil Design:
Introduction:
For low Reynolds number airfoil design and analysis, XFOIL provides sufficient analytic lift and drag values as well as laminar separation bubble location. Utilizing XFOIL as a tool for low Reynolds number airfoil development allows for quick and easy assessment of airfoil performance trends. In addition thin airfoil theory can provide a very quick and easy way to establish possible airfoil candidates. Utilizing these tools aBezier (BEZ) series airfoil was designed that showed good lift and drag characteristics as well as positive pitch stability.
Approach:
The requirements state that theMAV shall be no greater that 25.4 cm (10”) while having the potential to be scaled to 20 cm (8”) or even 15 cm (6”). That approach was taken so that the inherent stability issues with smaller MAV’s can be eliminated as variables during the initial testing phase. However, it was important for the airfoil design to be able to adapt to various changes. A change in aircraft size directly affects the Reynolds number the airfoil experiences. With this in mind the aerodynamics group chose a Reynolds number, see equation 1, range of 60,000 to 100,000, representing the low end of the spectrum, knowing that as Reynolds number decreases performance usually decreases. This allows us to be sure that aircraft will be scalable to a smaller size will still performing the mission at a larger size.
(Equation 1: Reynolds number)
With an anticipated flight speed in the range of 4-6 m/s and a average chord of about 0.20m the anticipated Re number is about 80,000. The anticipated flight speed was generated from information gathered from the propulsion team and from the cruse Cl values presented in the next section. All the airfoils analyzed have the same amount of reflex, 1% at 85% chord, to address the issue of pitch stability. 1% reflex insures that the airfoil will have a Cm0sufficiently greater than 0 so that the completed MAV system will also have a Cm0 greater than 0, which is a requirement for static stability of the MAV. This value was determined by using an algorithm developed in MATALAB to solve thin airfoil theory14 for various selected BEZ airfoils. The position of max camber was not change in this study; it is thought that changing the position of max camber just translates the coefficient of pressure graph aft adding to additional pitch stability but reducing lift generation.
Cl/Cd is the primary measure of airfoil performance; it shows the airfoils’ efficiency by relating the amount of drag produced and the lift produced. The higher the Cl/Cd value the more efficient the airfoil is. This is an important measure for MAV performance given the power consumption requirements and high performance demands on the entire system. In addition to Cl/Cd, Cl,max is a measure of the maximum lifting performance of an airfoil. This parameter is considered secondary but plays an important role in determining airfoils for specific applications. These two parameters, as well as laminar separation bubble location are investigated when choosing a specific camber value for our MAV application. The results are presented in the next section.
Results:
Initially, a sequence of 4 camber values, 3, 6, 9, and 12% were tested in XFOIL over an angle of attack range from -5 to 10° to evaluate performance characteristics. Figure 1 shows an example of a 6% cambered Bezier airfoil. It was found that as camber increased from 3% to 6%, Cl/Cd,maxincreased as well as Cl,max however from 6% to 12%, Cl/Cd,max and Cl,max decreased.
Figure 1 (BEZ062518510)
It was determined from this analysis that the most favorable airfoil would most likely have a camber value in the range of 3 to 6%. In order to determine the best camber value for various applications a detailed analysis was conducted for airfoils with camber values of 3, 4, 5, and 6% at Re numbers of 60,000, 80,000 and 100,000. The Cl/Cd, max and Cl,max values found for the 4 camber values and 3 Re numbers are presented in Figures2 and 3respectively.
Figure2(Cl/Cd, max for various max camber values and Re numbers)
Figure 3(Cl,max for various camber values and Re numbers)
Figure 1 shows that the 5% camber has the highest average Cl/Cd,max value. The lower camber values show a low dependency to Reynolds number which is a great characteristic for an airfoil that needs to be scaled to various sizes and Reynolds numbers. Figure 1 also shows that 5% camber seems to be a cut-off value for increased performance; as camber increases to 6% there is a slight drop off in Cl/Cd,max value. This is consistent with the understanding that increased curvature, a bi-product of increased camber, caused laminar separation bubble formation with degrades performance. Figure 2 shows the almost linear increase of Cl,max with increase in camber. This tells us that lift generation is directly related to camber, and also hits at in increase in drag for higher cambers due to the lowered Cl/Cd,max value. In addition the angle of attack of maximum Cl/Cd,max was determined. This angle of attack is considered the best cruse angle of attack because it is the point where the airfoil is producing the most lift for the amount of drag produced. Cruse angle of attack for the various airfoils is presented in figure 4.
Figure 4 (Cruse angle of attack for various cambers and Re numbers)
This figure shows a linear relationship between cruse angle of attack and camber, which will be important in wing design which is discussed in a later section. The angle of attack values for the 5% cambered airfoil shows the reason for the drastic jump inCl/Cd,max for a Re number of 100,000. This facts does not change the assessment of the 5% airfoil because in general the values of Cl/Cd,max were still higher that for the other 3 camber values. In addition, this figure provides an order of measure check knowing that MAV’s traditionally cruse at an angle of attack of about 3-5 degrees. These results have highlighted the balance that must be struck between high lift airfoils and high efficiency airfoils and the angle of attack required for efficient flight.
Conclusions:
The outcome of the analysis showed that the 5% airfoil is the most efficient at an angle of attack of 5° with a Cl/Cd,max of about 35 and a Cl,max of 1. For the 6% camber airfoil the most efficient angle of attack varies from 5° to 6° because of Re number effects but showed a Cl/Cd,max of about 33 and a Cl,max of 1.15. These are considered the forerunners in performance and will be used in wing development and in cases where different MAV mission performance requirements are necessary. In general if a high lift airfoil is required a 6% camber airfoil or higher will be used, and in cases where efficient long duration flight is required the 4 or 5% camber airfoil will be used.
Control Surface Design:
Introduction:
Control surface sizing and design represents a very difficult challenge considering the unconventional shape of the flying wing and decision to use elevons as the primary control method. The foundation of controlling the aircraft motion with elevons is the different affects that deflecting the control surfaces up and down in unison and differential deflection. The details are explained in the following paragraphs.
In a traditional aircraft pitch is controlled by changing lift of an auxiliary surface, generally called the horizontal tail, aft of the main wing with creates a pitching moment. This method of control has the advantage of being able to impart large moments on the aircraft with small drag penalties in addition to being a linear relationship and easily determined analytically. For the flying win configuration there is no additional surface aft of the main wing, so the elevons are employed to move together to create a change in pitching moment. This, unlike the aft horizontal tail, does not provide large pitching moment changes without having large surface deflections and accompanying increased drag; in addition the effect is highly non-linear and is difficult to estimate analytically. The change in pitch due to symmetric elevon deflection relies on a change in the pressure distribution over the surface of the wing. As the elevon deflect downward (+de) the pressure distribution over the airfoil shifts aft generating a negative (nose down) pitching moment. In addition to a change in the pitching moment additional lift is also generated, however this does not affect pitch but must be considered as an effect. When the elevon if deflected upward (-) the opposite effect occurs; the pressure distribution shift forward on the airfoil causing the wing to pitch up, in addition lift in decreased. It is this coupling of pitching moment change and coefficient of lift change that prohibits high pitch rates and various maneuvers, like a pure pitching loop, for a flying wing MAV. However these maneuvers are not required for MAV missions so they are not of concern.
Roll control utilized a differential elevon deflection to create a rolling moment. A differential elevon input creates an increase of lift on one side of the wing and a reduction of lift on the other side which cause a rolling moment. The difficulty is that the drag increment that is produced is not symmetric so a coupled yawing moment is also produced in the direction away from the rolling moment; this phenomenon is called adverse yaw. The drag differential is because the side of the wing that produces more lift also produces more lift-induced drag, and conversely for the other side that produces less lift. To combat adverse yaw, an asymmetric elevon deflection is required where the elevon that deflects up is smaller that the one that deflect down. However the exact differential is generally obtained through flight testing.
The difficulty in determining the necessary control surface size, span location, deflection limits, and differential is due to the general inability to easily and accurately model the flow field around an MAV coupled with the unavailability of accurate wind tunnel facilities. In an effort to quickly test preliminary designs simplifying assumptions must be made and additional flight testing must be included for model validation. The following paragraphs will outline the work done in an effort to arrive at a preliminary control surface design.
In an effort to simplify the analysis the aircraft will assume to be flying at the trim condition. Also, the effects of the all component other than the wing will be neglected; this is not a great assumption because the other components will play a roll, but the wing will be a major contributor. In general control surfaces cover 10 to 30% a surface so for these tests we chose to use a 20% control surface, meaning the hinge line was at 80% of the chord. To gather data to check the assumptions and determine the effects of an elevon deflection the baseline airfoil, BEZ052518510, was analyzed using XFOIL at a Re number of 100,000 for an angle of attack from 0 to 10 degrees and elevon deflections from -8°(up) to 10°(down). Cl, Cd, and Cm, values were all collected. A MATLAB routine was developed to analyze Cl, Cd, and Cm at each angle of attack for all elevon deflections and determine δCl/δde, δCd/δde, and δCm/δde which are the control parameters for the elevon for roll, pitch, and yaw. Only the results for the trim angle of attack are presented in Figures 5, 6, and 7.
Figure 5 (Left-Cmde Right-δCm/δde)
Figure 6 (Left-Clde Right-δCl/δde)
Figure 7 (Left-Cdde Right-δCd/δde)
In general these results show the highly nonlinear trends associated with an elevon deflection. The right hand side plot of each figure is approximated by a constant value at its mean value. We can however learn a lot about how the control surfaces affect the various coefficients. The elevon effectiveness graph for pitching moment (δCm/δde) shows that for small elevon deflections the effect is high, as shown by the highly negative value, but the effect quickly drops off to a less negative value but stays constant. This means out plane with react quickly to small elevon movements initially but as the deflection increases the effect decreases. The same is true for changes in lift coefficient as shown by the high peak near 0 for the δCl/δde graph. Also the adverse yaw effect can be seen in the δCd/δde, if drag was symmetric the average value for an elevon effectiveness parameter, δCd/δde, should be close to 0, however in this case it is greater than 0 but not by much. For this simulation we know that we will have only a small amount of adverse yaw.
This analysis helped us to determine how control surfaces defections would affect the directional control of the aircraft, but exact forces were not found. The assumptions made to allow for this type of analysis also limit its use is determining useful force, and moment values, however the groundwork has been laid so that when the flight testing phase commences and control surface modeling that may be required to determine a specific flight phenomenon can be done quickly and effectively. For now, the 20% elevons with 10% asymmetric movement will be the primary design for initial flight testing.