Problem 2. Aircraft turning radius (50 points) An object moving in a circular pa

Question

Problem 2. Aircraft turning radius (50 points) An object moving in a circular path at a constant tangential velocity is shown in figure 1. The radial acceleration required for the object to move in the circular path in given by 0 where a is the centripetal acceleration of the object in m/s2, v is the tangential velocity of the object in m/s, and r is the turning radius in meters. Suppose that the object is an aircraft, and write an MATLAB script to answer the following questions I. (5 points) Suppose that the aircraft is moving at Mach 0.85, or 85% of the speed of sound. If the centripetal acceleration is 2g, what is the turning radius of the aircraft? (Note: For this problem, you may assume that Mach 1 is equal to 340 rn/s, and that lg = 9.81 m/82) 2. (5 points) Suppose that the speed of the aircraft increases to Mach 1.5. Assuming the accel- eration remains 2g, what is the turning radius? 3. (15 points) Plot the turning radius as a function of the aircraft speed for speeds between Mach 0.5 and Mach 2.0, assuming the acceleration remains 2g Requirements on the plots: 1) Have labels on both axes (5 points); 2) Use proper font size, line width and marker size (5 points); and 3) In the PDF document, have a caption describing the figure (5 points) 4. (5 points) Suppose that the maximum acceleration that the pilot can stand is 7g. What is the minimum possible turning radius of the aircraft at Mach 1.5? 5. (15 points) Plot the turning radius as a function of centripetal acceleration for acceleration between 2g and 8g, assuming a constant speed of Mach 0.85. Requirements on the plots: 1) Have labels on both axes (5 points); 2) Use proper font size, line width and marker size (5 points); and 3) In the PDF document, have a caption describing the figure (5 points)

Explanation / Answer

1)

v = 0.85*340 = 289 m/s

a = 2*g = 19.6 m/s^2

a = v^2/r

=> r = v^2/a = 4261.3 m

2)

v = 1.5*340 = 510 m/s

a = 2*g = 19.6 m/s^2

a = v^2/r

=> r = v^2/a = 13270.4 m

4)

v = 1.5*340 = 510 m/s

a_total = 7*g

a_ total^2 = a_rad^2 + g^2

a_rad = sqrt(a_total^2-g^2)

a_rad = 6.93*g = 67.9 m/s^2

a = v^2/r

=> r = v^2/a = 3830 m

5)

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