# Aerodynamics

• Discuss the effects of the flaps on wing parameters such as: lift curve slope, angle of attack for zero lift coefficient, pitching moment coefficient, drag coefficient, maximum lift coefficient, angle of attack of maximum lift coefficient, etc. • Discuss how theory (XFOIL) compares (cant compare directly, Xfoil is 2D, your data is 3D - but can compare trends). • Perhaps also tabulate the results for easy comparison. Show me you understand the results. •Be focused and to the point. DISCUSS TRENDS.

V. Lift, Drag and Moment on a Wing 1. Objective a. To measure forces and moment on a model wing. To explore the effects of a trip strip and investigate wall effects. This laboratory has a lot of processing. Get started early and ask for help. It should however, prove very educational.

As "task1.m" script runs from "P2amain.m" script, it must output the following two plots (no user inputs required): (i) The "stagnation streamline" plot (the shape of the semi-Rankine body: r/R) in the range of: 09⁰, 179° (upper half surface) and = 181°, 191°, 201°,... 351° (lower half surface). 19°, 29°,. (ii) The "pressure coefficient" plot (the surface pressure distribution over the semi-Rankine body: C₂) in the range of: 0=9°, 19°, 29°,... 179° (upper half surface) and = 181°, 191°, 201°,... 351° (lower half surface). (Note) the C, plot in aerodynamics is "negative values in positive y coordinate direction" (rule of thumb). This will require you to modify the y axis data direction ("flip-flop" of the y coordinate) when you perform C, plot in MATLAB.

(task3.m) The flow over a circular cylinder (nonlifting flow): pressure coefficient (the surface pressure distribution) As "task3.m" script runs from "P2amain.m" script, it must output the following plot (no user inputs required): The "pressure coefficient" plot on the surface of the cylinder (the surface pressure distribution for both upper & lower surfaces in a single figure). Use a non-dimensional coordinate parameter x/R (in the range of -1 < x/R <1) for the x-coordinate of your plot. (Note) the Cp plot in aerodynamics is "negative values in positive y coordinate direction" (rule of thumb). This will require you to modify the y axis data direction ("flip-flop" of the y coordinate) when you perform Cp plot in MATLAB.

You have a CubeSat of 10×10×30 cm³ in size and 4 kg in mass. Estimate the size of a launch vehicle that is capable of inserting this CubeSat (4 kg payload) into a circular LEO of 200 km-altitude. The primary question is how small it could be when it is built using available technology today.< Conditions: 1) You are free to use any tools available for your design and/or analysis. Even a hand-calculation is fine.< You are free to choose any type of propellant available. You may use known values of any performance parameter without a detail calculation as long as you declare the source.< Consideration of launch site, launch angle, number of staging, drag loss, gravitational loss, and so on is up to your choice. Just make it clear what kind of assumption is made in your estimation.< You may choose any launch site with any launch angle, however, it might be suggested to select either of launch site of a) Naro Center in Southern Korean Peninsular or b) US Cape Canaveral, Florida with launch angle 180 degree or to the straight south direction.<

1. Suppose you purchase a 4x8 piece of plywood from Home Depot. You don't have a pickup truck (nor does your friend), but you do have a roof rack with cross bars on your car. So you will have to secure the plywood to the roof rack in order to get it home. Your friend (the one who does not have a pickup truck) suggests-that you tie the plywood on sideways (so that the short edge is front to back) and drive at about 13 mph.Use standard sea-level conditions p= 0.002369 slugs/ft3 and µ = 3.7372 x 10-7 slugs/ft-s. (a) Estimate the drag on the plywood for the case suggested by your friend. (b) Estimate the drag on the plywood if you turn the sheet so that the long edge is front to back. (c) Explain why your friend suggested the sideways configuration.

a) Develop a relation between local static pressure P and freestream static pressure P.. Assume the stagnation pressure remains unchanged (i.e.,isentropic flow). b) Write the local pressure coefficient C, in terms of free stream Mach number M, and the ratio P/P . c) Combining your results from a) and b), write an expression for the local pressure coefficient C, in terms of local and free stream Mach numbers. d) If the peak C, in incompressible flow is -0.43, estimate the critical Mach number. Hint: place all terms on one side of the equation and use a trial and error approach.

The NP-2000 propeller is an 8 blade design used on the C-130 and E-2 aircraft,which has a radius of 2 m. Assume sea level conditions (p=1.2kg/m ) and a stationary aircraft such that velocity far upstream is zero. Assume actuator disk theory. a) Consider the blades rotating at 2000 RPM. If the velocity far downstream ofthe propeller is measured to be 40m/sec, find the resulting thrust coefficient. b) For the same RPM, the collective is now changed so that C, = 0.006 . What is the percent change in the velocity far downstream? c) What is the distribution of thrust on the disk? Explain your answer.

For a 2D airfoil with chord c the following characteristics are foundby wind tunnel experiments (where the angle of attack a is indegrees): C₁ = 0.121-a + 0.125 CmTE0=.0915 = + 0.075 Drag can be neglected. When answering problems b), c) and d), be sure to add a clear sketch of the situation. a.What can be concluded about the camber of the airfoil? Explain your answer. Calculate the location of the center of pressure XCP/Cfor alpha = 0°. Calculate the location of the center of pressure XCP/Cfor alpha = 5°. Calculate the location of the aerodynamic center XAC/C

Describe how finite difference and finite volume methods for solving transport equations are formulated. What are the relative advantages and disadvantages of these approaches versus influence coefficient methods?

A small wind turbine has three rotor blades, each comprised of a NACA 0009airfoil section with a constant chord of 0.5 m and zero twist. The blades are 4mlong, rotate at 20 RPM, and are pitched 8 above the disk plane. Freestream conditions are p, =1.2kg/m² , P. = 100kPa , and U, =1.0m/sec. a) Using the blade element method and 2 elements, estimate the power coefficient of the turbine. For the section coefficients, let C, = 2ra ,C, =0.005+0.004C’. b) Is your result consistent with the Betz limit? Why or why not?

3. A truck has a drag coefficient based on frontal area of Cp = 0.86. The truck has a mass of 12,750 kg anda frontal area of 10.5 m2. If the truck is traveling at constant speed on a level road, the forces retarding itsforward progress are the drag and the rolling friction. The force due to rolling friction can be written as F_{\mathrm{rf}}=W f_{r}\left(1+\frac{V}{V_{0}}\right) where V is the truck speed in m/s, Vo = 30 m/s and fr (the coefficient of rolling resistance) is approximately0.008 for a truck on concrete or asphalt. Plot the total power the engine must supply as a function of trucks peed, V. Comment on the relative importance of drag and rolling friction in the fuel consumption of the truck.

2. A sign is exposed to a 15 m/s wind on a standard day. Estimate the drag on the sign if (a) the sign is aligned lengthwise to the wind. (b) the sign is crosswise to the wind.

Discuss the factors that contribute to drag divergence as Mach 1 is approached from subsonic speeds. Describe the two discoveries that helped alleviate this problem in transonic aircraft design.

s)Explain, in terms of the geometric changes that occur, why a flap deflection alters the lift produced by an airfoil, positive or negative. Expand on this discussion fora multi-element airfoil with a deployed flap and slat, in terms of how the geometric changes augment the lift produced for a 3D wing.

Person A and Person B are trying to unlock the secrets of a tornado. They are trying to model the tornado using 2D vortex dynamics but need your help. They choose to model the tornado as a circular region, with a radius rc=25[m of uniform vorticity, w(0 ≤r≤re) = We Outside the radius of the tornado the vorticity is zero, (r>rc) = 0 They are at [Observation Station #1], 1= 100[m] from the center of the tornado, taking measurements.The vane-anemometer at the station is broken, but the manometer measure gauge pressure,P₁ = -300[Pa], They radio over to you over at [Observation Station #2], r2 = 2000[m] from the center of the tornado. You report back the measurements from your station, reporting the wind-speed, [₂] = 0[m/al, the gauge pressure reading from the manometer, P = 0[Pal, and temperature, T2 = 300[K]Gauge Pressure is with respect to 101.3[kPal. This is taking place on Earth with: a) Determine the expression for the velocity field, (r) = (ur, u), in terms of the parameters: Fe, Wo, and variable r. Do not plug number yet. (consider: 10 ≤rs rel, then re <rb. b) Determine the density and speed of sound at [Observation Station #2]. c) Determine the wind-speed, 1, at [Observation Station #1]. Assume density at P1 P2 (hint: Can incompressible Bernoulli's be used between the two stations?). d) Determine and the total circulation, Ta, of the Tornado. (hint: use results from c) and a)) e) Determine the wind-speed and the absolute pressure at the edge of the tornado, at r = re + €. (hint: e is a small length. Assume right outside the tornado's core).

For such a wing with varying chord, the mean aerodynamic chord (MAC) is defined as \mathrm{MAC}=\frac{2}{5} \int_{0}^{b / 2} c^{2} d y where y is the coordinate along the wing span and c is the chord at the coordinate y. Knowing tipchord length (C₂), root chord length (Cr), and the span (b) of a linearly tapered wing, show thatMAC will become: M A C=\frac{2}{3} c_{T}\left(\frac{1+\lambda+\lambda^{2}}{1+\lambda}\right) where λ=c/cr.Hint: You can start from a linearly tapered wing described below.

Consider the streamfunction: (a) [5] Determine the velocity field, u = (ur, ue). (b) [5] Is the flow divergence free? Calculate to show or explain why. (c) [5] Is the flow irrotational? Calculate to show or explain why. (d) [5] If possible, from u derive the expression for the potential function, (r, 0). (e) [5] Find the location of the stagnation point (s) in the flow field, if any exist. (f) [Bonus+2.5] Sketch the streamlines for r > 1. (g) [Bonus+2.5] Determine the area flux, [L²/T], between the streamlines that pass through the coordinates Pt₁ = (r,0) = (2, π/4) and Pt₂ = (4,π/4). Assume the dimensions of = [L²/T] and u= [L/T]

The lift-to-drag ratio is an indication of the effectiveness of an airfoil. \begin{array}{l} L=\frac{1}{2} \rho C_{L} S V^{2} \\ D=\frac{1}{2} \rho C_{D} S V^{2} \end{array} where, for a particular airfoil, the lift and drag coefficients versus angle ofattack a are given by \begin{array}{l} C_{L}=\left(4.47 \times 10^{-5}\right) \alpha^{3}+\left(1.15 \times 10^{-3}\right) \alpha^{2}+\left(6.66 \times 10^{-2}\right) \alpha+\left(1.0 \times 10^{-1}\right) \\ C_{D}=\left(5.75 \times 10^{-6}\right) \alpha^{3}+\left(5.09 \times 10^{-4}\right) \alpha^{2}+\left(1.81 \times 10^{-4}\right) \alpha+\left(1.0 \times 10^{-2}\right) \end{array} Using the first two equations, we see that the lift-to-drag ratio is givensimply by the ratio C₂/Cp. \frac{L}{D}=\frac{\frac{1}{2} \rho C_{L} S V^{2}}{\frac{1}{2} \rho C_{D} S V^{2}}=\frac{C_{L}}{C_{D}} a) Plot L/D versus a for -2≤ a ≤ 22⁰°.b) Determine the angle of attack that maximizes L/D.c) What is the value of maximum L/D?

For a particular airfoil section the pitching moment coefficient about an axis 1/3 chordbehind the leading edge varies with the lift coefficient in the following manner: a) Find the acrodynamic center and the value of Cmac ·b) Find the relation between the position of the center of pressure and the lift coefficient;plot a curve showing the variation of the position of center of pressure with liſtcoefficient.