Project for Extra Credit for Graduate Students
Due Friday Dec. 13 on line
Breaking the Sound Barrier with an Aircraft ?
Military aircraft routinely accelerate to speeds greater than the local sound speed. Historically, this was referred to as “breaking the sound barrier”.
Goal: Estimate the Mach number of the airplane.
Use the concept of critical Mach number and thermodynamics to analyze the situation and clarify the misunderstandings associate with the phenomenon.
Ambient condition: 100 kPa of ambient air and 20°C with 80% relative humidity.
Assuming an angle of the wave (~ 80°) and perform a thermodynamic analysis of the cause of condensation. You need to show the analysis procedure with appropriate equations used.
Page limit: 2-3 pages.
Make appropriate assumptions in the calculations. The following information is helpful
1) Attached is a static pic of FA-18 jet. You can use it as a 2D reference to measure pertinent angles on the airframe where the “white clouds” happen.
2) Karman-Tsien Rule (p. 472 in textbook) can be used to predict the stream Mach number (subsonic) at which the speed of sound is reached locally over the wing section. Use Karman-Tsien relation (developed for 2D) to proximate the 3D flow around the main body of the aircraft where the while clouds form. The Karman-Tsien relation is
is the pressure coefficient, with “i ” stands the incompressible case. The Karman-Tsien relation is plotted for a typical airfoil conveniently, knowing the typical pressure coefficient for incompressible flow of an airfoil.
Source: Theory of Wing Sections-Including A Summary of Airfoil Data, by Ira Abott and Albert E. Von Doenhoff, Dover Publications, Inc. New York 1959, pp. 258-260