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Microsoft Word - Mini-Project_1_2023.docx 1 AE 4802 CON Mini-Project 1 Spring 2023 Complete the following problems based on the Boeing 777-like OpenVSP geometry posted with this assignment. Show your work, and describe your assumptions and steps logically and neatly. Include any needed plots and/or tables from computer analyses, along with titles, axis labels, and line types/colors as needed for clarity. You may discuss solution techniques with other students, but copying results or code is prohibited. Your assignment must be submitted electronically as a PDF on Canvas by Thursday, February 16th, at 11:59 PM. 1. Estimate the zero-lift parasite drag coefficient ? of the aircraft at an altitude of 36,000 ft and a Mach number of 0.83 using the OpenVSP parasite drag tool. Presume fully-turbulent flow (0% laminar flow) for all components. Set all interference factors (Q in OpenVSP) to 1.0. Presume a crud/excrescence drag of 20% (% of CD_GEOM in OpenVSP). Note that the length units of the model are in feet. In the parasite drag tool, set the “Group” for the “Join” component to “Fuselage” so that OpenVSP will add the wetted area of the wing join to the fuselage wetted area and treat the two as a single component. Use the default form factor and Cf equations, and use the model’s wing area as the reference area for normalizing ? . Export the .csv file from OpenVSP and create a nicely formatted table of the key drag buildup results for each airplane component. 2. Use VSPAERO to “trim” the airplane, estimate the wing span load distribution, and compute the induced drag. To do this, let’s first trim the airplane to an angle of attack and horizontal tailplane angle that produces the ? needed to “fly the airplane” at the flight conditions from Problem 1 and an airplane weight of 750,000 lbs while achieving ?? = 0 at this condition. Note that large commercial transport aircraft like the 777 typically trim with an all-moving tailplane, not elevators, leaving the elevators for pitch control. Here’s how we can solve the “trim” problem. We begin by recognizing that lift curves are linear to first order (except near stall). This means we can run two angles of attack and two horizontal tailplane angles and construct a linear system of equations to solve for the required angles such that we meet our required ? (such that L=W) and ?? = 0. First, let’s express the trimmed values of ? and ?? as linear functions of angle of attack, ?, and tailplane incidence, ? : ? = ?? ?? (? − ? ) + ?? ?? (? − ? ) + ? ? = ?? ?? (? − ? ) + ?? ?? (? − ? ) + ? Next, recognize that we can estimate all of the partial derivatives by finite difference approximations such as, 2 ?? ?? ≈ ? − ? ? − ? and similarly for the other partial derivatives, where the subscript 0 and 1 values correspond to points you run in VSPAERO. Finally, we can re-arrange the linear system above to solve for ? = ?trim and ? = ? ,trim such that ? = ? , trim meets L=W at the required flight condition and ? , trim = 0. To find the needed values to carry out this solution, open VSPAERO from the Analysis menu in OpenVSP. We will conduct the analysis only with the components in geometry Set_0, i.e., the wing, fuselage, and horizontal stabilizer, and note that the moment reference positions are set to 109 ft from the front of the fuselage. This is a “reasonable” c.g. location for the aircraft. Let’s run 2 angles of attack—0 deg and 2 deg—and 2 values of the horizontal tail incidence— -2 deg and 0 deg—which we can use as our subscript 0 and 1 values in the equations above. To change the horizontal tail incidence, adjust the Rotate value on the Motion menu for the Trim Hinge component. It’s easiest to run both angles of attack for each incidence setting in VSPAERO and then to change incidence. In VSPAERO, make sure to run in VLM mode. Also make sure that Mach Start in the Flow Condition input block is set to be consistent with the flight condition from Problem 1. After you click Launch Solver, the code will run. When it’s finished the Results Manager GUI window will pop up. If you ran the code with 2 angle of attack values, you will see 2 sets of load distribution curves (each a different color, and each with 2 curves—one for the wing and one for the horizontal tail) on the Load Dist tab, corresponding to each of the 2 angles of attack. You can inspect the different values of ? , ?? , etc. on the Sweep tab. Export the data to a .csv file. Repeat for the second value of tail incidence and then solve the linear system to determine the trim point. Answer the following questions: a. What are the values of ? , trim, ?trim, ? ,trim? Show your work to compute these values. b. Re-run VSPAERO with the angle of attack and horizontal incidence set to the trim point values. Produce a nice plot of the corresponding load distribution of the wing and the horizontal stabilizer at this trim point CL. Do not do a screenshot of the Results Manager window. Instead, export a .csv of the converged load distribution at the trimmed angle of attack and make a nice plot in Excel, MATLAB, or Python with axis labels, etc. Discuss the shape of the wing lift distribution. Co-plot an elliptical lift distribution and a triangular lift distribution each with the same total lift (? = ? , trim) for comparison. Is the resulting distribution more elliptical or more triangular? Qualitatively speaking, how might you change the wing twist to make the lift distribution more elliptical? More triangular? c. What is the ?? at this trim point? You can find this under the Sweep tab by plotting ? as the X-Data and E or ?? as the Y-Data. The .csv file for your converged trim point should also have the values. 3 3. Use Lock’s 4th Power Method and the Korn Equation to estimate the transonic wave drag coefficient, ? , of the wing at the flight conditions listed in Problem 1. Note that the airfoils are from the NASA supercritical SC(2) series. Use the method of strips with two strips, one inboard of the kink (between sections 0 and 1) and one outboard of the kink (between sections 1 and 2). Compute average values of the relevant airfoil characteristics at the midpoints of each of these strips to use in the Korn equation. Use the values of ? at the midpoint locations of each strip determined from the converged trimmed wing/body load distribution in Problem 2 in the Korn equation (you can find this on the Load Dist tab or in the .csv by manipulating the cl*c/cref data with knowledge of the wing chord at the strip midpoint locations). Show your work with Lock’s 4th Power Method, the Korn Equation, and the method of strips to compute the ? value for the full wing. Make a table with one column for each strip and rows that list your values of airfoil thickness-to-chord ratio, wing half-chord sweep, ? , airfoil technology factor, ? , ? , area, and ? of each strip. Hint: To make it easier to compute the half-chord sweep, go to the Sect tab on the wing component. Set Sec SW Loc to 0.5. Note the grayed-out value of Sec SW in the Section Planform data block; this is the 50% sweep value for the section. Repeat this process for both sections. This process should reduce some trigonometric tedium. 4. Compute the total drag coefficient, ? , of the airplane at the given flight condition by summing the zero-lift parasite drag, the trimmed induced drag, and the wave drag that you found in Problems 1-3. Also compute the ?/? of the airplane at the trimmed flight condition. Do these numbers seem reasonable? Can you substantiate them with any references you find online? Hi all, AE 4802 Mini-Project 1.pdf J 777 like 2023.vsp3 Please make sure you are using the Wing as your reference in your VSPAero calculations. Additionally, if you need help on computing the elliptical lift distribution, please use the attached file as a reference. Please make sure you are using the Wing as your reference in your VSPAero calculations. Additionally, if you need help on computing the elliptical lift distribution, please use the attached file as a reference.