Hw1_2011 - AE372 Flight Mechanics Spring 2011, Dr. Ilkay...

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Unformatted text preview: AE372 Flight Mechanics Spring 2011, Dr. Ilkay Yavrucuk HW#1 AE 372 Flight Mechanics Spring 2011 Due on: April 1st, 2011, 5pm. Note: You are allowed to talk and discuss the questions with each other. However, it is strongly recommended that anything written and submitted is your own work. It is very important that you go through the thought process to learn and be successful in this course. Q uestion1: Consider a car with a jet engine racing with an acrobatic airplane (Figure 1). Both the car driver and the pilot follow each other to check who is ahead in the race. YOU are of course observing the race standing still on the ground. The road points straight to North. xB V yB c.g. zB ω yE N xE oE zE S yI xI oI zI xC yC Vc zC Figure 1: A car with a jet engine racing with an airplane. 1 AE372 Flight Mechanics Spring 2011, Dr. Ilkay Yavrucuk The problem is set up such that one coordinate system is attached to the aircraft body at its center of gravity (body ­axis of the aircraft, O XBYBZB) , one coordinate system is attached to the car (body ­axis of the car, O XcYcZc), and another coordinate system is attached to the ground (earth fixed coordinate system, O XEYEZE) with its x ­axis pointing towards North. The inertial frame is O XIYIZI. The velocity of the car with respect to (w.r.t.) you (the earth fixed frame) is Vc and points directly towards North. The velocity, V , and the angular velocity, The following is known: 1. The atmosphere is still (no wind) 2. The airplane is in the following angular position (in Euler angles): θ=35deg, φ =  ­45deg, ψ=0deg. 3. The AOA at the position shown is α=10deg and the sideslip angle is β=5deg. 4. The magnitude of the velocity of the aircraft w.r.t you is 60m/s. 5. The angular velocity vector of the aircraft w.r.t you is ω B =[5  ­5 0]T deg/s at the moment shown in the picture. 6. The speed of the car is 220km/h. 7. The earth rotation and curvature can be ignored for these speeds (making the earth the equivalent to the inertial frame). I. Answer the following: a. What is the velocity of the aircraft w.r.t. the earth frame, written as components of the aircraft’s body axis system. b. Express the aircraft velocity (w.r.t. the earth frame) as components of the earth fixed coordinate system (NED coordinate system). First find a transformation matrix between the two coordinate systems. c. What is the velocity of the aircraft written as components of its vehicle carried frame? d. What is the time rate of change of the Euler Angles ( θ , φ ,ψ )? e. What is the velocity of the aircraft with respect to the car driver? f. What is the velocity of the car with respect to the pilot? g. What is the translational acceleration of the aircraft w.r.t. the earth fixed frame written in components of the aircraft body axis system? What is it when written as components of the earth fixed axis? h. What is the translational acceleration of the aircraft w.r.t. the car? II. Let’s remove the assumption that the earth is flat and non ­rotating. In this case, assume that the car is moving North in Ankara. Using geometric properties of planet earth find the following. Express your answer in SI units. a. What is the velocity of the center of mass of the car w.r.t. to an inertial frame in components of the body fixed axis of the car? b. What is the acceleration of the center of mass of the car with respect to the inertial frame? (You may assume that the intertial frame fixed coordinate system is aligned (parallel) with the body axis system of the car at the instant of measurement). ω , of the aircraft with respect to you (the earth fixed frame) is also shown in the Figure. 2 ...
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This note was uploaded on 03/19/2011 for the course AEE 300 taught by Professor Beşyüz during the Spring '11 term at Middle East Technical University.

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