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2.a,b,c,d?
AERO 3230 Flight Dynamics, Spring 2019 EXAM 1, Feb 6, 2019 1. Consider a North-East-Down (NED) inertial axis system fixed on the ground. There is a wind blowing from North to South at a speed of V = 10 m/s. An aircraft is in level- flight (constant altitude, wings level) flying Eastward at an inertial velocity of Vac = 100 m/s and a pitch angle of 0 = 10°. a. Express the wind velocity in the NED axis system. [5 pts] b. Now express the wind velocity in the aircraft body-fixed axis system. (15 pts] C. Find the inertial velocity of the aircraft expressed in vector components in the aircraft's body-fixed axis system. [15 pts] d. Find the velocity of the aircraft relative to the wind, expressed in the body-fixed system (Recall: to find velocity of A relative to B, you subtract the velocity of B from the velocity of A, i.e., VA,rel,B = VA-VB) [5 pts] Lacrel,w= e. Based on the results of part (d), calculate the magnitude of the relative velocity (airspeed), the angle of attack a and angle of sideslip ß of the aircraft. (10 pts] 2. A satellite is spinning about an axis in space. At time t = 0, its angular speed is wo, and the moment of inertia about the spin axis is Io. The moment of inertia then begins to change with time due to panels being retracted, following I(t) = 10 -ct, where c > 0 is a constant. No external forces or moments act on the satellite. a. What conservation principle is applicable to the rotational motion under these circumstances? (5 pts] b. Find the equation of motion that governs the satellite's spin rate wſt) in fin da = ... (15 pts] dt

C. Integrate the equation of motion using the given initial conditions to determine the angular velocity at time t, i.e., find w(t) = ... (20 pts) d. Verify the answer you got in part (c) by finding the same angular velocity w(t) using the conservation principle and show that they are identical. [10 pts) 80 ft 50 ft NP M = 70,000 lb c = 20 ft A Xcgi 3. A cargo plane is ready to be loaded. Its mean chord is c = 20 ft. The neutral point (NP) and the main landing gear both happen to be 50 ft aft of the datum line. The top of the loading ramp (point A) is 80 ft aft of the datum line. Prior to loading, the aircraft has a mass of M = 70,000 lb. a. If the unloaded aircraft is to have a static margin of 15%, determine the location of the CG aft of the datum line. (10 pts] b. What is the maximum mass of a crate that can be loaded onto the airplane without causing it to tip-back when the crate reaches point A? (15 pts] (Hint: Tip-back is when the nose gear lifts off the ground. It occurs if the CG moves aft of the main landing gear location) c. Suppose a 7,000 lb crate is loaded and secured at a distance x ft aft of the datum line. Derive an expression for the static margin (expressed in percentage) of the loaded aircraft as a function of x. (15 pts] (Note: Your expression should involve only numbers and the variable x) d. Determine the aft-most location of the 7,000 lb crate that will allow the aircraft to take off with a 10% static margin. [10 pts)