Airfoil Concept Development and Feasibility:
Airfoil selection is arguably the most important aspect of any aircraft design. The airfoil defines the performance envelope of the aircraft as well as lift, drag, moment, and stability characteristics. In an effort to determine the best airfoil 5 categories of airfoils were investigated. Utilizing preliminary research 1 category was ruled out and the remaining 4 underwent a feasibility assessment to determine which category would most likely produce the best airfoil. It is important to note that a detailed airfoil design is not the intended result of this study, the category that will most likely produce the best airfoil is the subject of this investigation.
The 5 airfoil categories are as follows, Traditional (NACA series), Low Reynolds number specific airfoils, Top surface airfoil, nth order polynomial airfoils, and Bezier airfoils. Traditional NACA airfoils have been around since the earliest years of aeronautics and have traditionally been a staple of airfoil development, but in our specific application of low Re number flow it has been well documented that they are often characterized by large LSB formation and poor Cl/Cd,max values10. With this information, NACA series airfoils are not addressed in feasibility because they have been proven poor performers in the past. Of the remaining 4 categories, low Re number specific airfoils have been utilized exclusively by previous RIT MAV teams. Information obtained from the University of Illinois at Urbana-Champagne (UIUC) Applied Aerodynamics group has been the biases for airfoils in this category. Information regarding lift, drag, and pitching moment is readily available from the Applied Aerodynamics group’s website under airfoils with the description of “Low Reynolds number airfoil” and provides a sound basis for airfoil choices. Top surface airfoils are airfoils generated from known airfoils, such as the one provided from UIUC data, as a thin surface defined by the top of an airfoil. This concept has been readily used to generate numerous airfoils that have produced good performing MAV concepts at previous international MAV competitions. nth order polynomial airfoils were pioneered by the University of Florida as a way of defining a thin cambered/reflexed airfoil with an nth order polynomial. This method provides freedom to quickly and easily vary parameters to study their effects. This method proved to be a winning strategy for University of Florida. The final method, Bezier airfoils, is very similar to nth order polynomial airfoils but the mathematical function that defines the airfoil is a Bezier curve. The method is currently being pioneered by a graduate student at RIT as a way of defining airfoils with out the instabilities that accompany an nth order polynomial.
Taking into account the extensive literature1,3,5,8 base that reports poor performance from thick airfoils (thickness/chord > 6%) and the improved performance of thin airfoils as Re number decreases identifies top surface, nth order, and Bezier, as advantageous airfoils. Knowing that past teams utilized foam airfoil construction thin airfoils were not an option, but with new composite construction methods thin airfoils development not only becomes a viable option, but a better option it terms of overall weight and strength. Figure 1 shows a low Re number airfoil, the S5010 from the UIUC airfoil database.
(Figure 1)
Comparing Bezier airfoils and nth order polynomial airfoils, only subtle differences are seen. Bezier airfoils were developed to play an almost identical roll as nth order polynomials without the disadvantage of increased boundary condition requirements and oscillatory effects with increased order. nth order airfoils often take undesirable shapes when attempting to form the necessary airfoil, where Bezier airfoils will always stay within the defining trapezoid. This property alone allows for quick and reliable airfoil definition.
Top surface airfoils became the desired choice of many MAV designers when the discovery of increased performance of thin airfoils was made. The concepts is that an airfoil that performs well at higher Re numbers will probably maintain some of that performance at low Re number if only its upper surface is used as a thin airfoil. This has been confirmed by Kellogg8, however only for one specific airfoil and only for 2 of the 4 camber values tested. This concept relies on the assumption that what is good at one Re number will be good at another Re number if the airfoils thickness is reduced. However, because of limited published data, this sort of airfoil must be tested to determine its actual performance but because of previous success with specific applications the possibility of a successful airfoil being derived from this category as high.
Based on these estimates of airfoil category performance the two most likely categories to produce good low Re number airfoils are the Bezier airfoils and the top surface airfoils. At the same time these categories are also the most feasible because they rely on thin airfoil geometry which allows for the use of a composite structure with a membrane skin, the preferred method of construction.
Planform Concept Development and Feasibility:
With an airfoil selected the next step is to decide on the wing shape, or planform, that would best fit the constraints at low speed and low Reynolds Number flight. With research done we started out with eight planform shapes. Next we analyzed which parameters were of primary, secondary, or less important, to flight performance concerning the wing shape. Finally using these tools we were able to conclude which planform best suited our requirements.
To begin we found eight different planforms to choose from. They are a Circular, Modified Circle, 3-Circle Design, Zimmerman, Inverse Zimmerman, Rectangular, Tapered, and elliptical. Primary requirements are the Aspect Ratio, Surface Area, and Maximum Linear Dimension (MLD). Secondary concerns were Control Surfaces, Control Integration, and Stability. Other requirements were Visibility, Ease of Manufacturing, and Winglets.
When looking a Circular surface the first major problem is the point at which the tip vortices commences, at the center, this means there will be a disruption of flow over the back end of the wing as well as an incurred induced drag. Furthermore, concerns over control integration suggested that a Circular planform should not be used. The Zimmerman planform was dismissed because the maximum span location is at the leading edge; this is where the shedding will take place, meaning disrupted flow across the whole body. Furthermore, from actual flying experience it was found that the Zimmerman wing had stability issues. The Tapered planform was dismissed because it would have to have the largest maximum linear dimension to generate the same amount of lift as the others. Finally, the Elliptical wing was dismissed because it lacked a large trailing edge, meaning control surfaces would be hard to develop, it is very hard to manufacture, and it would also have a very large max linear dimension.
We are now left with the Modified Circle, the 3-Circle, and Inverse Zimmerman Planforms. Before we can progress we had to establish a rating system for our requirements, meaning; which was the most important and which was the least important. Taking into account our primary requirements we decided that the maximum linear dimension was our leading constraint because of airfoil design research and due to the fact that without this criterion our wing could be any size we wished. Lift is a direct function of Surface Area, the larger your wing is the more lift it generates, therefore, understanding that our main goal is to have our plane fly we chose surface are to be second. Furthermore, the aspect ratio is a function of span and surface area:
This means that as we increase our span, or decrease our surface area, we will increase Aspect Ratio. However, by increasing our span we are increasing MLD and by decreasing our Surface Area lift is decreased. Moving on too the plane’s secondary requirements we chose Stability to be the most important, if our plane is not inherently stable then we won’t be able to fly it. Furthermore, our airfoil design took into account stability, i.e. reflex, therefore, it is imperative to follow that design parameter throughout the wing design process. In order to steer the aircraft it would be necessary to have control surfaces that were functional and sized correctly so as not to disturb lift generation. Finally, Control Integration was not as prudent to the aero design as it will be to the manufacturing team.
Of the three planforms left we decided to look at which ones possessed certain characteristics more so then the other two. Because of the leading edge being flat Control integration would be fairly easy, just attach the prop to the front. Furthermore, the modified circle has an area similar to that of a circle therefore its MLD will be smaller then the others, while still achieving the same surface area. For the 3-Circle method and the Inverse Zimmerman we drew them up in solid works, each had the same MLD. However, the 3-Circle had a larger surface area while the Inverse Zimmerman had a larger Aspect Ratio. However, when looking at which would be more stable we decided on the 3-Circle planform. If the tip vortex strength is further aft (point of max span further back) the pressure distribution over the airfoil is less back so that if the tip vortices start to shed asymmetrically the instability will be less pronounced. Therefore, we found the following table:
Modified Circle / 3-Circle / Inverse ZimmermanPrimary Req. / MLD (1) / Surface Area (2) / Aspect Ratio (3)
Secondary Req. / Control Integration (3) / Stability (1) / Control Surfaces (2)
Point total / 4 / 3 / 5
It can be seen that the 3-Circle has the lowest score, corresponding to the best planform.
Vertical Tail Concept Development and Feasibility:
When designing the Vertical Tail it is important to implement certain requirements and constraints that will yield a stabilizing, light weight, addition.
Initially, we started with four possible designs for the fin. Described what our primary and secondary requirements were and why, rated each constraint, and then applied them to each design to find the optimum one.
The four concepts are:
A) A tail located below the wing with an airfoil cross section.
B) A tail located below the wing, one carbon sheet thick, with no air foiled cross section.
C) A tail above the wing, like you see on a Boeing 737, with an airfoil cross section
D) A tail above the wing with thin plate characteristics, like choice B.
Next we set out our primary criteria. Fist and foremost, it is important that the plan is stable in YAW, meaning that our tail contributes a moment large enough to counteract any moments due to the wing or fuselage, (CnB>0). The fin must be in a clear stream flow otherwise any stabilizing effect will be reduced or negated. An example is when the plane pitches up air over the top of the wing separates and if the fin were to be on top of the wing it would have no affect if the plane were to yaw. However, if the tail were below the wing in the same situation, it would still have stabilizing affects. Furthermore, the area-moment of inertia must be aft of the center of gravity, meaning our fin must have a large enough area so it can create a large enough force and moment to counteract any destabilizing forces or moments to. Secondary requirements were that the fin be light weight, easy to manufacture, and have low drag. The drag due to the Vertical Tail will be small in comparison to the rest of the plane. After selecting primary and secondary requirements we rated them in importance.
Primary Requirements:
1- CnB>0
2- Un-Separated Flow
3- Area-Moment of Inertia must be aft of the CG
Secondary Requirements:
1- Light Weight
2- Easy to manufacture
3- Low Drag
Having an airfoil cross section increases material, which increases weight and drag. Furthermore, manufacturing an airfoil that small accurately is very difficult. Therefore, we discarded Designs A and C. Our number one concern is met by both designs; the location of the wing will cause a restoring moment and bring the plane back to equilibrium. However, the fin on the top of the wing will not be in un-separated flow therefore rendering it less efficient when the plane pitches up as the fin on the bottom. Therefore, it was decided that a vertical tail, under the wing, with flat plate characteristics would be used.
Control Surface Concept Development and Feasibility:
Aircraft control is critical aspect for any aircraft designer to tackle. There are numerous different methods of controlling aircraft, so the underlying requirement that will drive the final choice will be the overall simplicity of the control system. The final aircraft will be very small and light which means the aerodynamic forces required to change the orientation of the aircraft will be minimal. With this in mind, limiting the number of moving surfaces will increase reliability, minimize weight and simplify construction. There are 3 primary degrees of freedom on and aircraft, Roll, Pitch, and Yaw. In a normal aircraft configuration roll in controlled by ailerons, which are flaps that act on the wings in a differential motion, simultaneously reducing lift on one wing and increasing lift on the other. Pitch is controlled by an elevator generally placed at a distance aft of the CG that either increases lift aft of the CG casing the aircraft to pitch down or decrease lift aft of the CG causing the aircraft to pitch up. Yaw is controlled through a movable portion of the vertical tail that acts identical to the elevator just opposed at 90°. See figure 2 for examples. For a flying wing configuration the control surfaces operate very similarly, they are usually are just located on the wing instead of at a distance away from the wing. Additional control surfaces that have multiple functionalities are possible for the flying wing configuration. Elevons, for instance, are control surfaces that act as an elevator and as ailerons simultaneously.