(Solved): For this discussion, imagine that the Boeing 747-100, as illustrated in the figure, is at cruise whe ...

For this discussion, imagine that the Boeing 747-100, as illustrated in the figure, is at cruise when the outer right engine shuts down. This generates a moment that must be counteracted to avoid spinning the aircraft. The pilot could generate an opposite moment by turning the rudder. They could also increase the remaining engines to max thrust. For a detailed description of this figure, refer to 4.4 Figure Transcript(DOCX). \( \downarrow \) It's important to note that the aircraft would not be in equilibrium in the forward direction ( \( \sum F_{a} \neq 0 \) ). Ignore the extra drag of the shutdown engine. In your post, discuss how much side force the rudder must produce and what other actions the pilot should take to keep the plane in equilibrium. Use the following information: - Drag (assume it is at the CG) \( =35,000 \mathrm{lbs} \). - Each engine's thrust before shutdown \( =8,750 \mathrm{lbs} \). - Max cruise engine thrust \( =10,000 \mathrm{lbs} \). - Total lift (assume it is at the CG) \( =500,000 \mathrm{lbs} \). (Note: At cruise, the lift equals the weight.) Make sure you understand the issues with an engine-out emergency related to the equilibrium of a rigid body. You will also complete the following in your discussion: - Post a free-body diagram of the airplane. Calculate the rudder side force necessary to keep the plane in rotational equilibrium. Solve for the sum of the forces in each direction with the rudder side force set to maintain rotational equilibrium. Assume the extra rudder drag is \( 10 \% \) of the rudder side force. - Investigate the impact of each engine's thrust percentage setting. - Discuss various possible actions the pilot may take to extend the flight range. You are encouraged to use a MATLAB script for your calculations. Fully describe your calculations, assumptions, and results. A top view of a Boeing 747 with some dimensions. The plane fuselage is 231 ft. 10.2 in long with a wingspan of 195 ft. 8 in. The center of gravity, CG, is on the fuselage centerline near the center of the wing area. The sideways distance from the CG to the inner engine's centerline is 28 ft. 5 in. The sideways distance from the CG to the outer engine’s centerline is 67 ft. 6 in. The distance of the rudder aft of the CG is 119 ft. 8 in.