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Homework #1 Homework #2 Homework #3 Homework #4 Homework #5 Homework #6 Homework #7 Homework #8 Homework #9 Homework #1: Due January 15th, 2003 From Book: Chapter 2, Problems 2.3, 2.4, 2.7, 2.9 Chapter 3, Problems 3.1, 3.4, 3.8 (Note: The solutions manual solution for problem 3.8 is the hard way! A much easier method involves the hydrostatic equation.) Additional: 1) Write a program (C, FORTRAN, or Excel Spreadsheet) to calculate the variation of pressure and density with time for a rocket launched from sea level with a constant vertical acceleration of 5 m/sec2. Present your results as a plot of altitude, pressure and density versus time up to an maximum altitude of 100 km. Homework #2: Due January 24, 2003 From Book: Chapter 4, Problems 4.1, 4.3, 4.4, 4.10 and 4.12 (Note: Note that the book uses cp = 6000 ft-lb/slug, while more precisely, cp = gR/(g-1) = 6006 ft-lb/slug. This small difference may give you problems on problem 4.12. )
Additional: 1) Using the program you wrote for Homework #1, calculate the altitude for "max q", i.e. the altitude where the rocket experiences the maximum dynamic pressure. Also plot the variation of the speed of sound and the Mach number with altitude. Homework #3: Due February 3, 2003 From Book: Chapter 4, Problems 4.15, 4.17, 4.20, 4.21 and 4.24
Additional: 1) Show that the Mach relation po/p = [1+(g-1)/2 M2]g/(g-1) reduces to Bernoulli's equation for low Mach numbers. As a hint, use the approximation that (1+e)a ~ (1 + ae) for e<<1.
2) A turbofan on a jet flying at 12 km altitude and M=0.82 is show below. The fan blade diameter is 180 cm in diameter. If the Mach number just in front of the fan blades is 0.60, calculate, the pressure, temperature and density just in front at the fan. Also calculate the diameter of the captured stream tube far upstream of the engine.
3) A Venturi tube is another device used to measure airspeed. If the Venturi below measures a pressure difference of p1 – p2 = 70 lb/ft2 at sea level, calculate the airspeed assuming incompressible flow. For the more adventurous, repeat assuming compressible flow.
Homework #4: Due February 10, 2003 From Book: Chapter 4, Problems 4.34, 4.35, 4.36
Additional:
1) A small RC model airplane has a wing with 4 ft span and ½ ft in chord. Find the maximum velocity it could fly at and still have laminar flow over the entire wing surface. Also calculate the viscous drag at this speed. Assume sea level conditions and Rexcr = 500,000.
3) A pizza delivery sign on top of a car is effectively a sharp edged flat plate of dimensions 1m by 1m. If the air flow velocity across the plate is 7 m/sec, calculate the friction force on the plate and the boundary layer thickness at the trailing edge. Assume sea level standard conditions and remember to allow for two sides. Also, assume the boundary layer is tripped at the leading edge. Homework #5: Due February 21, 2003 From Book: Chapter 5, Problems 5.3, 5.4, 5.5, 5.7, 5.8
Additional: 1) Use the airfoil tool at http://mercury.pr.erau.edu/~gallyt/Naca4.html for the following comparisons:
a) For both the 0012 and 2412 airfoils, find the angles-of-attack for Cl=0 and 0.4 and compare to the wind tunnel results in the book appendix and in Abbot and Von Doenhoff's Theory of Wing Section (library).
b) Compare the pressure distribution for the 0012 and 2412 airfoils at Cl=0.2. Based upon what you know about how pressure gradients effect boundary layers, comment on the different pressure profiles in relation to transition and separation.
c) Calculate the pressure profiles for 2409 and 2415 airfoils at 4 degrees angle of attack. Again, comment on the relative effects of the pressure profiles on the boundary layer. Homework #6: Due March 3, 2003 From Book: Chapter 5, Problems 5.11, 5.16, 5.19
Additional:
1) An airfoil is tested in a low speed wind tunnel with the freestream conditions of M¥ =0.2, p¥= 2000 lb/ft2, and T¥= 530 R0. The lowest pressure measured on the airfoil upper surface is 1900 lb/ft2. (a) Calculate the pressure coefficient at that point. (b) Estimate the pressure coefficient at that same point if the flow speed was M¥= 0.7.
2) An airfoil with a 2 ft chord is tested in a supersonic wind tunnel with the freestream conditions of M¥=1.4, p¥=1400 lb/ft2, and T=430oR. A force per unit span of 820 lb/ft is measured. Estimate the airfoil angle of attack and the wave drag force per unit span.
3) Use the airfoil tool at http://mercury.pr.erau.edu/gallyt/Naca4.html for the following comparisons (You could also use it to solve Problem 5.16 above!):
a) Plot Mcr versus airfoil thickness for the symmetric airfoils 0006, 0009, 0012, 0015, and 0018 at zero degrees angle of attack.
b) Plot Mcr versus Cl for the NACA 0012 airfoil (just in the angle of attack range of 0 to 5 degrees.) On the same plot, do the same for the NACA 2412 airfoil. Comment on any differences. Homework #7: Due March 24, 2003 From Book: Chapter 5, Problems 5.21, 5.22, 5.23, 5.25, 5.26 Chapter 6, Problems 6.1, 6.3, and 6.4 Additional: a) A new airplane design will use an airfoil with a lift curve slope of 6.0 rad-1 on a wing with area of 200 ft2, span of 40ft, and efficiency factor of 0.75. Estimate the airplane lift curve slope and (L/D)max if CD0=0.045. b) The airplane in the previous problem weighs 2400 lbs and is powered by a piston-propeller power plant with a 200 shp sea level rating and hp=0.8. Calculate the airplane's maximum level speed at sea level and at 10,000 ft. Homework #8: Due April 7, 2003 From Book: Chapter 6, Problems 6.5, 6.6, 6.7, 6.8, and 6.9 Additional Problems: 1) Go to the web site of a general aviation aircraft manufacturer (Cessna, Piper, Mooney, Beach/Raytheon, Cirrus, etc) and collect geometry and performance information on a single engine airplane of your choice. Use this data to generate Thrust and Power versus Velocity plots and use these plots to determine: max. speed as sea level, max. speed at 10,000 ft, and equivalent airspeeds for L/D max and CL3/2/CD max. In addition to the web site data, you will need to make assumptions about the span efficiency factor (between 0.75 and 0.85), the propeller efficiency (use 0.80 for a fixed pitch prop, 0.85 for constant speed), and the zero lift drag coefficient. A good correlation for CDo is based upon the take off weight: CDo = 10^(a + 1.089 +0.515*log10(WTO))/S The factor, a , depends upon how aerodynamically "clean" the airplane is. Use a = -2.046 for fixed landing gear planes a = -2.222 for retractable landing gear with aluminum fuselage, or a = -2.301 for retractable landing gear with composite fuselage.
2) For the general aviation aircraft you picked, calculate the maximum R/C in 2,000 ft intervals up to the absolute ceiling of the aircraft. Determine the airplanes service ceiling. Integrate this data to get the time to climb to the servie ceiling (or just up to 12,000 ft if the cabin in not pressurized). How are your calculations comparing with the data the manufacturer supplies? Homework #9 (The last one!!): Due April 16, 2003 From Book: Chapter 6, Problems 6.12, 6.13, 6.16 through 6.20 (Use the following fuel weight conversions: kerosene (jet fuel) = 6.67 lb/gallon, and Av.Gas = 5.64 lb/gallon.)
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Copyright Tom Gally 2003
Contact: gallyt@erau.edu
