Geometry Selection
Historical Data
More detailed research on various historical aircraft was performed including their airfoil sections and their power loading. These aircraft were picked by their similar operation purpose or conditions. Seen in Table 1 are the researched aircraft and their wing airfoils courtesy of David Lednicer [1]. Additional aircraft specifications were researched courtesy of 'Jane's All The World Aircraft' of various volumes [4].
Table 1, Airfoil and MTOW of the researched aircraft.
Further aircraft specifications can be seen in Table 2 where the wingspan, wing loading along other various parameters are recorded. These parameters are useful in order to perform performance matching. They are also useful to perform a sanity check of how the project aircraft fit with historical parameters of similar purpose aircraft.
Table 2, Further research on various aircraft parameters.
Research on Geometry and Initial Design
From the preliminary design, a trapezoidal wing design was utilized for this aircraft. The trapezoidal shape was chosen since it was more efficient than a rectangular wing design. Ideally, the wing shape follows an elliptical shape as proven by the Prandtl wing theory. This ideal shape would produce the least induced drag for any given wing airfoil. The elliptical wing design however has various downsides. The biggest one being the complexity of its construction especially due to its tip shape. Its design complexity further leads to a heavier wing design. Furthermore, the distributed lift nature of an elliptical wing can also prove to be a double-edged sword. Its ideal lift and drag profile, while reducing drag, induces an undesired stall characteristic. For most common geometric wing shapes, it is relatively easy to predict when and where the stall would begin and designs can be implemented to start the stall from the wing roots. In an elliptical wing design, however, the entire wing tends to stall simultaneously with little alert and tends to be unsafe [2].
The chosen wing geometric design initially utilizes an aspect ratio of 7.68 with a medium sweep angle of 12.4 degrees as seen in Figure 1. This design aspect ratio falls in line with most general aviation aircraft which has aspect ratios anywhere between 7.6 and 8 [3]. However, this design also utilized a low taper ratio which makes it less suitable for the slower flight the aircraft is designed for. For the low speed the aircraft is operating, it requires the wing to generate high lift at low speeds. An increase taper ratio, while allows for the wing to follow the ideal characteristic of an elliptical wing, generates less lift. Ontop of that, the sweep angle of the aircraft also further decreases the lift coefficient of the wing.
Figure 1, Original design of the aircraft wing.
This design requires to be modified as the design process progresses. Most likely, the wing design must be modified to fit a larger taper ratio to generate a higher lift. This, however, would reduce the wing's wing sweep angle which meant it would have a slight reduction in roll stability. This effect however can be negated with the addition of a twist and dihedral on the wings.
Geometry Selection
After an attempt at performance matching, it was clear that the aircraft possesses an extremely high wing loading for the performance target of the aircraft. The weight of the aircraft was noticeably heavy compared to the original wing design. The original wing design also utilizes a relatively high wing sweep angle which further reduces the lift coefficient of the wing. This leads to some wing geometry design changes by increasing the area of the wing which resulted in a higher taper ratio of 0.57 and shallower wing sweep angle. This design not only increased the wing area which reduces wing loading but also allows for higher lift potential. However, this change has also reduced the aspect ratio of the wing as the wingspan needed to stay constant. The new aspect ratio of the wing was found to be 6.1. In this adjustment, the locations of the mean aerodynamic chord and lift centers were kept the same as their locations are favorable as they are currently located. The new wing geometry profile can be seen below in Figure 2. The calculations will be discussed further in the next section.
Figure 2, New Wing geometries.
Geometric Calculation
Wing geometry parameters were initially acquired directly from the original concept sketch. This requires the calculation of Mean Aerodynamic Chord (MOC) along with the quarter chord lift centers graphically. This can be seen in Figure 3 where each of the steps is described. In practice, this was done utilizing sketch tools available in Fusion 360.
Figure 3, Steps taken to find the wing mean aerodynamic chord.
The wing's lift centers were then determined using the approximation that they are located on the 1/4 chord length of the MAC. These steps were repeated for the horizontal stabilizer(s) and vertical stabilizer(s). The distance between the lift centers of each component was then measured as seen in Figure 4 below.
Figure 4, Lengths between components.
The horizontal and vertical stabilizers were then calculated using Equations 1 and 2 below. In these equations, CVT and CHT were assumed to be 0.06 and 0.7 respectively.
Airfoil
From historical data of similar aircraft, multiple airfoils are found to be more common. One of them is the classical and common NACA 23012 and the second is NACA 23015. Both airfoil types are commonly found on general aircraft as well as home-built aircraft. However, the NACA 23015 can be found on many different amphibious aircraft and most notably some of the Grumman amphibious aircraft such as the HU-16 Albatross. A lot of research data is also available through various sources which made the analysis of this airfoil to be relatively less challenging. as seen in Figure 5, the airfoil has a reasonably flat drag coefficient with the regular operating coefficient of lift. It also has a small moment coefficient at the various attack angles which allows for the aircraft to be more stable and less lift center shift.
Figure 5, Shape and plots for the NACA 23015[4].
This airfoil has a maximum lift coefficient CL value of 1.63 and above Reynold's number of 3,000,000, the airfoil behavior does not change drastically until it approaches critical velocity and angle of attack.
Summary of Specifications
The summary of all the parameters determined in this section for the designed aircraft can be seen in Table 3. This design was then improvised and the parameters were re-calculated and seen in Table 4.
Table 3, Original wing parameters.
Geometry Discussion
Major dimensions for the control surfaces are yet to be determined. In this stage, the flap dimensions were roughly determined but they may still need to be further analyzed. This design process is an iterative process where changes and improvements are constantly performed. In this case, the wing geometry was revised twice and the tail sections have been revised twice as well. However, the tail section of the aircraft still needs to be refined to fit the calculation.
Furthermore, the general profile of the fuselage will stay relatively the same. However, modifications are required on the bottom of the aircraft hull to better accommodate the amphibious operation. Similarly, the nose of the aircraft must be raised and streamlined to be suitable for water landing.
Reference
[1] “UIUC Airfoil Data Site.” https://m-selig.ae.illinois.edu/ads/coord_database.html (accessed Apr. 09, 2021).
[2] A. I. of Aeronautics and Astronautics, “64. Design Implications of Elliptical Planform Wings,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, Florida, January 05-09, 2015. American Institute of Aeronautics and Astronautics (AIAA), 2015, [Online]. Available: https://app.knovel.com/hotlink/khtml/id:kt011KMH01/56th-aiaa-asce-ahs-asc/design-implications-elliptical.
[3] D. Raymer, Aircraft Design: A Conceptual Approach, Sixth Edition. Washington, DC: American Institute of Aeronautics and Astronautics, Inc., 2018.
[4] I. H. Abbott and A. E. von Doenhoff, Theory of Wing Sections Including a Summary of Airfoil Data. NEW YORK, 1959.