Analysis of Design (Planform):
Introduction:
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.
Approach:
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.
Results:
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.
Analysis of Design(Vertical Tail):
Introduction:
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.
Approach:
The four concepts were:
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, (Cn>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-Cn>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
Results:
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.