Wing Spar Optimization of Radio Controlled Size Aircraft

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Wing Spar Optimization of Radio Controlled Size Aircraft
Schneider, Alexander Wolfgang
Place of Publication:
[Gainesville, Fla.]
University of Florida
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Subjects / Keywords:
Aircraft ( jstor )
Aircraft design ( jstor )
Aircraft wings ( jstor )
Carbon fibers ( jstor )
Cost functions ( jstor )
Design analysis ( jstor )
Design engineering ( jstor )
Design optimization ( jstor )
Moduli of elasticity ( jstor )
Structural deflection ( jstor )
Undergraduate Honors Thesis, Aerospace Engineering


This honors thesis shall provide a comprehensive optimization of wing spars for use in radio controlled aircraft. The model aircraft chosen for the experimentation is approximately 14 pounds with an approximate wingspan and length of 7 feet. The optimization will compare varying cross sectional spars at differing lengths utilizing several different materials defined by their moduli. The optimization utilizes a Latin hypercube with surrogate modeling. The optimization process has been altered to include a large array of design points for improved results. The results shall provide a basis for wing spar design and provide insight to specific material and geometrical design choices. ( en )

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University of Florida
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Schneider, Al exander, Honors Thesis, April 20 2016 1 Abstract This honors thesis shall provide a comprehensive optimization of wing spars for use in radio controlled aircraft. The model aircraft chosen for the experimentation is approximately 14 pounds wit h an approximate wingspan and length of 7 feet. The optimization will compare varying cross sectional spars at differing lengths utilizing several different materials defined by their moduli. The optimization utilizes a Latin hypercube with surrogate model ing. The optimization process has been altered to include a large array of design points for improved results. The results shall provide a basis for wing spar design and provide insight to specific material and geometrical design choices. I. I NTRODUCTION HE ability to cut weight without the expense of losing structural rigidity is of utmost importance in the design and fabrication of all aircraft. The recent advances in composites, unique alloys, and other complex materials has opened up a world of opportuni ty for aircraft structural engineers and radio controlled (RC) aircraft designers alike Available material choices are abundant and each have their own set of benefits and disadvantages. To add greater confusion, material strength is very dependent upon t he geometries and dimensions. Due to the large amount of alternatives it is helpful to perform a computer based optimization to aide in design and materi al selection for the structure of the aircraft. One of the most structurally intensive pa rt s of the a ircraft is that of the wing, its purpose, to provide lift for the aircraft [1] The wing structure is composed of spars, ribs, stringers and skin Spars are situated lengthwise in the wing carrying the majority of bending forces. Ribs lie tran sversely and provide airfoil shape and minor compression support. Stringers also lie lengthwise and provide support for the skin. The skin covers the internal components of the w ing, provides a smooth surface for passing airflow and handles shear loading Of all the components in the wing, t he spars provide the most significant support and are responsible for transferring the aerodyna mic loading, created by the wing, to the aircraft wing box and fuselage [2] See fig. 1 for an example of wing construction. Fig 1. RC Aircraft Wing Construction The most common geometrical shapes for aircraft wing spars are I beam, rectangular beam, Alexander W. Schneider ( ) Graduating May 2016, Spring Semester Term Summa Cum Laude Bachelor of Science in Aerospace Engineering Faculty Advisor: Dr. Richard Lind ( T


Schneider, Al exander, Honors Thesis, April 20 2016 2 and U beam (see fig 2) RC aircraft in particular most commonly use the rectangular beam for its ease to source, manufactu re, and incorporate in an in aspect ratio (ratio of height to width) altering its moment of inertia and its accompanying resistance to bending forces. Fig. 2. I beam, U beam, and Rectangular beam respectively. The most common spar materials found in RC aircraft vary from plastic and wood to carbon fiber and aluminum. The materials each have their own set of material properties, the most relevant being which measures the resistance of a material to deform. The deformation of the spar is important both in regards to wing tip deflection and yield/ failure of the spar. The other driving factor in wingtip deflection is the length of spar itself. The increas ed length of the wing and its accompanying spar create a longer moment arm contributing to higher stresses and a larger wingtip deflection. II. P ROBLEM S TATEMENT RC aircraft design is often a subjective process especially when determining the best material, size, and length for the main wing spar. Analysis may prove a certain material and size completely capable of performing the job but this is often not the optimal design to maximize strength minimize weight, and prevent defl ection. It can be difficult to choose the best combination of designs due to the expanse of design variables. The optimization performed here aims to determine the best combination of design points for a mid size 14 pound RC aircraft. For the sake of this optimization, several assumptions will be made. For one, the aircraft size is assumed to be 14 pounds with an approximate wingspan and length of 7 feet. The size matches several mid size RC aircraft and is well below the maximum 50 pound limit requirement for RC aircraft [3] The optimization thusly assumes this single aircraft design for simplicity in achieving results. It must be noted that a drastically different weight and size could alter th e results and may not apply to very large nor very small RC ai rcraft. The next assumption is in regards to the cross sectional area of the spar To maintain ease of comparison, width of the cross section will remain constant whereas the height will be altered to increase the cross section al area for differing designs in the optimization Furthermore, the elastic modulus for composite and fiber materials will be assumed to be E1. Finally, it is assumed that the original spar design is based off a previous analyzation ( which in fact it is) The initial/original design utilized in the optimization will be a unidirectional carbon fiber rod with a cross sectional area of 0 .200 in 2 and a length of 96 in. This was the selected spar for the Fly team and was chosen based off preliminary analysis and no optimization. III. A LGORITHM OF O PTIMIZATION The optimization employed for the experiment first begins w ith defining a function The function is known as the cost function, J. Each term in the cost function has a design parameter associated with it. These terms can have added multipliers to better categorize their importance in the design. The parameters utilized here are based of f the major importance in the design of the wing spars. They include weight, deflection, and factor of safety (FOS) The parameters are dependent upon the design variables. The design variables include cross sectional area, modulus of elasticity and the l ength of the spar. A range of values is required for each design variable and is chosen by selecting the most realistic maximum and minimum values for the design. Length, for example, is limited at the high end by the ability to transport the aircraft (for example must fit inside a transportation vehicle) and at the lower end due to the importance of increasing and maintain a sufficiently long wing). The ranges utilized are 0.15 to 0.40 in 2 for cross sect ional area, 435 to 23200 ksi for modulus of elasticity, and 80 to 120 in for length


Schneider, Al exander, Honors Thesis, April 20 2016 3 The resulting cost function includes each of the parameters mentioned and adds multipliers to relate the terms closer together. Even so, emphasis is highest with weight (e ven though it is scored with the same multiplier, the weight values had a greater difference between the design points and the original) followed by deflection and then FOS. The FOS term is unique due to the desire of meeting an FOS of 1.5 (the standard for most aircraft components) [4] Thus the resulting FOS is divided by the desired FOS and subtracted by 1. The absolute value of that result is utilized in case the FOS go es result in anything less than 1 will be aut omatically disqualified (the cost will be manually adjusted to a very large value). FOS is also multiplied by 50 due to its very small initial contribution to the cost function ( See eqn 1 ). (1) The optimization begins with inputting the minimum and maximum ran ges for each variable. A Matlab code created by Dr. Richard Lind is utilized for the optimization albeit in modified form [5] The initial code is set up to use a Latin hypercube to develop initial design points. The code is altered to utilize 50 points in the design space versus 5 and then handpick 5 points evenly spread out amongst the distribution. This allows for a greater r esolution of varying design points aimed at avoiding local minimums in the data (and helps to find the absolute minima). While using a greater amount of design points has the advantage of finding more accurate results, it has the disadvantage of increased cost (in the form of time). The amount of time to run the code more than doubles. For the sake of this experiment the 50 design points provide a good balance between computational time and accuracy. After the initial 5 design points are found, they are used to alter a Solidworks model [6] Each new model is placed into a fundamental element analysis (FEA) simulation study. A wingtip loading of 5 times the force of gravity is used to simulate an aggressive turn maneuver likely to be seen in flight (equiv alent to 70 lbs f ) The simulation provi des the parameters to input in the cost function. The cost function is evaluated at each of the original 5 points and the results are then input into a second code which performs surrogate modeling. This process is re peated two more times until there are 200 total points in the design field and 20 evaluated points. The FEA employs a tetrahedral mesh TET10 element with 4 Jacobian points. A mesh density of coarse was selected for improved speed during analyses. The results are tabulated and compared T he optimal design is the one that minimizes the cost function. IV. A NALYSIS OF R ESULTS An original optimization was performed outside of this thesis experiment utilizing only 20 total points and the results were not very refined. For this thesis, the optimization was retuned and improved vastly. This result can be proven by judging the differences in the costs in Table I. Table 1 Design Point Cost (Original) Cost (New) 1 7.835 30.29 2 16.58 14.38 3 17.21 93.76 4 250.4 93.87 5 48.79 57.49 6 25.34 35.61 7 25.24 84.85 8 26.27 11.22 9 26.31 12.96 10 70.10 81.44 11 718.9 122.0 12 697.8 25.67 13 659.8 33.77 14 613.2 131.2 15 575.6 58.10 16 20.72 44.77 17 20.17 92.25 18 21.39 45.21 19 20.70 42.59 20 20.20 12.87 Note the wildly varying (and high) costs of the first experiment compared with this current experiment. The 20 point optimization proved to be less than ideal compared to the 200 point optimization One similarity between the two optimizations (not shown) was that the original


Schneider, Al exander, Honors Thesis, April 20 2016 4 design still was the most optimal design (showing that the initial analysis to derive the original design was rather accurate). The reason for improvement for data also was du e to changes made to the cost function. The ranges for the variables were adjusted to improve the optimization. The time utilized to carry out the optimization could be seen as wasted time but the results show some rather interesting trends (in addition to proving the correct material/si ze spar was chosen). See Table 2 for the design points that were evaluated. See Table 3 for the evaluated costs. Table 2 Design Point Weight (Ounces) Deflection (in) FOS Cost (J) Original 17.6 6.7 1.51 6.44 1 35.0 7.5 2.13 30.29 2 23.6 13.6 1.37 14.39 3 30.0 5.3 0.41 93.77 4 7.0 100.1 0.07 93.88 5 57.1 4.2 0.12 57.49 6 24.2 1.8 3.62 35.61 7 30.2 1.1 5.08 84.85 8 22.6 2.4 2.89 11.23 9 15.1 8.3 1.37 12.96 10 25.6 1.3 4.54 81.45 11 24.8 1.1 6.22 122.04 12 59.2 1.4 1.05 25.68 13 34.4 1.8 3.51 33.77 14 24.8 0.67 6.5 131.22 15 28.7 1.5 4.27 58.10 16 18.3 12.1 0.41 44.77 17 5.4 99.3 0.095 92.25 18 93.2 10.4 0.75 45.21 19 20.1 50.6 1.23 42.59 20 44.2 5.5 1.40 12.87 Table 3 Design Point Area (in 2 ) Modulus (ksi ) Length (in) Original 0.197 19580 96.0 1 0.385 4152.4 105 2 0.206 23206 120 3 0.318 6941.5 93.1 4 0.267 1364.8 118 5 0.344 8799.4 98.8 6 0.288 23206 88.0 7 0.352 23206 90.0 8 0.263 23206 90.0 9 0.175 23206 90.0 10 0.312 23206 86.0 11 0.162 23206 98.0 12 0.387 23206 98.0 13 0.225 23206 86.0 14 0.162 23206 86.0 15 0.187 23206 96.0 16 0.213 12959 100 17 0.213 1573.6 100 18 0.213 14097 98.0 19 0.213 2712.2 98.0 20 0.213 15236 84.0 The major trend showed that materials with a modulus less than 100 (such as pine wood, spruce wood, hemp fiber, and fiberglass) were far and away too weak for the proposed size aircraft. On the other end, the materials with higher modulus (and an accompany ing increased weight) were simply too heavy and/ included a carbon fiber impregnated plastic, heavier and stronger than standard carbon fiber laminates). The only acceptable designs with the larger modulus were those wit h small cross sections and shorter wing spans (to alleviate the weight issue), and unfortunately had too much deflection. The optimal design ended up being the initial unidirectional carbon fiber rod measuring 96 inches in length. The resulting FEA is sh own in figures 3, 4, and 5. Fig 3. Wing tip loading showing stress Fig. 4. Zoom in of the area with the highest stress concentration


Schneider, Al exander, Honors Thesis, April 20 2016 5 Fig 5. Image of the deflection in the spar with distance Taking a closer look at figure 4 it can be seen that the majority of the stress is localized near the wing root. The root must deal with counter act ing the moment produced at the wing tip and the upward force seen through the body. The deflection seen in figure 5 is maximum at the tip as is completely exp ected. Although the wing will see a distributed load the single point load serves as an accurate approximation. Wing tip tests are very common in industry and utilized by the large aircraft manufacturers, Airbus and Boeing [7] Inferring the r esults and viewing the simulation data provides some serious insight into available improvements both in the design and optimization process For the design there are several opportunities be to utilize a tapered spar (increasing from the tip to the wing box) to allow sufficient resistance to the higher loads at the root and decrease mass at the tips For the sake of this exp eriment all spars were uniform (since they are easier to source and manufacture), but for the sake of the best design this is one valid design change In addition, instead of using a single material or one type of laminate, a sandwich construction could be utilized. Sandwich construction consists of utilizing a lightweight/soft material like balsa wood sandwiched between two thin layers of very strong material like carbon fiber. The advantage is decreased weight without the severe penalty of a drastically r educed modulus of elasticity. Finally, the spar could be made hollow ( like a box). While pricier to source the design would cut down weight and maintain sufficient strength. For the optimization there are also areas of weakness. For one, the length range should be shortened. The reason for the larger range (80 to 120) was to satisfy mainly satisfy aerodynamic wants A larger wing and shorter chord is most favored by the aerodynamicist as it decreases drag and increases lift. Unfortunately, a structure ha s to make it all the way to the wingtips and there are limits to the possible overall length. The longer the wing, the stronger the structure needs to be (especially if the aircraft is carrying a payload) and the heavier the resulting aircraft If the ran ge were brought down lower it would allow greater optimization to instead occur with the cross section and the material choices. In addition, the optimization could still use a greater amount of design points. The more numerous the design points the greate r the chance there is to find a minimum in the data. Finally, the optimization could also be improved by altering the FOS term in the cost function. For many design points a large FOS was harming their overall cost when in fact the large FOS was n ot actual ly a negative aspect of the design ( so long as the weight was not too great ) The FOS is mainly utilized to ensure the wing spar would not were times when by too great of a margin V. C ONCLUSIO N RC aircraft are a unique take on aircraft design. While smaller than real aircraft (and not as expensive/sensitive to accidents) they still require time to design, analyze, and fabricate. While RC planes can be designed, built, and flown by hand, they ma y not achieve much more than a nosedive or structural failure. During the design of larger RC aircraft this realization becomes even more important. D eeper analysis and optimization can improve designs, provide successful builds, and offer enjoyable flight time. This thesis attacked the problem of selecting an optimal wing spar for a small to mid size payload carrying RC aircraft. The experiment began with a previously analyzed spar and sought to improve upon the design (or at least provide insight into pos sible design changes). What resulted was a large amount of useful information for both the physical design and the optimization process. Surprisingly, the best wing spar ended up being


Schneider, Al exander, Honors Thesis, April 20 2016 6 the original spar design. This begged the question: was all that time for optimization worth it? The time taken to optimize was quite less than the time taken to conceptualize and analyze the original design and provided quite a large amount of data to consider. The optimization process provided helpful alternatives and aide d in ensu ring the best design was chose. It more than proved its usefulness in the aircraft design process. As has been very evident throughout engineering curriculum, sometimes the results are not as desired and often not as expected. It is important to localize the reasons for these results, infer the data, and apply, alter, or expand the next round of testing to resolve any issues discovered. An engineer does not merely perform a test and call it a day, rather they appl y and implement the principles and les sons learned to improve designs. Application is king. R EFERENCES [1] "Pilot's Handbook of Aeronautical Knowledge", 2016. [Online]. Available: nuals/aviation/pi lot_handbook/. [Accessed: 21 Apr 2016]. [2] "Aeronautics Parts of an Airplane (WINGS) Level 2", 2016. [Online]. Available: [Accessed: 21 Apr 2016]. [3] "Academy of Model Aeronautics", Modelairc 2016. [Online]. Available: [Accessed: 21 Apr 2016]. [4] "Factors of Safety", 2016. [Online]. Available: safety fos d_1624.html. [Accessed: 11 Apr 2016]. [5] "MATLAB MathWorks", 2016. [Online]. Available: [Accessed: 21 Apr 2016]. [6] "Products",, 2016. [Online]. Available: cad design software.htm. [A ccessed: 11 Apr 2016]. [7] B. WIRED and B. Test, "Boeing 787 Passes Incredible Wing Flex Test", WIRED 2016. [Online]. Available: 787 passes incredible wing flex test/. [Accessed: 21 Apr 2016]. [8] "Mechanical Properties of Carbon Fibre Composite Materials", Performance 2016. [Online]. Available: http://www.performance 2.asp. [Accessed: 11 Apr 2016]. [9] "Modulus of Elasticity or Young's Modulus and Tensile Modulus for some common Materials", 2016. [Online]. Available: http: // modulus d_417.html. [Accessed: 11 Apr 2016].

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