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1. Consider the ASW design example in Chapter 3. (a) What would be the estimate of takeoff gross weight (using the method in Chapter 3) if the requirement of the cruise speed changes to: Mach 0.25, and Mach 0.85. Consider a turboprop engine for the first case. (b) What would be the estimate of takeoff gross weight (using the method in Chapter 3) if the requirement of the (one-way) cruise range speed changes to: 1000 miles and 2000miles. (c) What would be the estimate of takeoff gross weight (using the method in Chapter 3) if the requirement of the loitering period at the mission location changes to : 2 hrs and5 hrs. (d) The aspect ratio used in the textbook example was 7. What would be the takeoff gross weight, if this value changes to 5.5?

The jet engines of an aircraft produce amaximum thrust, Tmax that is proportional to density:9 Tmax= The wing surface area of the aircraft is 71 m².What zero lift coefficient of drag, CDO will the aircraft have if its absolute ceiling is atan altitude of 10 km and its maximum cruisespeed is 199 m s¹ at an altitude of 8 km?

5 6 7 8 9 The longitudinal equations of motion of an airplane may be approximated by the following differential equations: (a) Rewrite these equations in state-space form. (b) Fid the eigenvalues of the uncontrolled system. (c) Determine a state feedback control law so that the augmented system has a damping ratio of 0.5 and an undamped natural frequency of 20 rad/s. w = -2w + 1798 – 278e Ö = -0.25w - 150 - 458 An airplane is found to have poor lateral/directional handling qualities. Use state feedback to provide stability augmentation. The lateral/directional equations of motion are as follows: = [ABT Ap Ar Lag] The desired lateral eigenvalues are: -0.05 -0.003 -0.98 0.21 [AB] -1 -0.75 Ap 16 Ar 0.3 0 -0.3 1 1 -0.15 0 0 0 Aroll = -1.5 s-1 Aspiral = 0.05 s-1 0 = Aroll = -0.35±j1.5 rad/s Assume the relative authority of the ailerons and rudder are: 9₁ = Q= [ΔΦ] R= Assume the states in problem 4 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are three times as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =32[state feedback] C=[10] + Assume the states in problem 5 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are twice as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =22[state feedback], where 21,2 = -10 +j17.3. A0max=+10° = ±0.175 rad Ademax = ±15° = ±0.26 rad 0 1.7 0.3 0 Design an optimal control law for problem 4. Use the following constraints and weighting functions: 1 A0max 1 Δδ?, 0 -0.2 [Ada] -0.6A8] [As a ] 0 max. 1.0 and 92 = 8/8a = 0.33.

An aircraft climbs at an angle of 15°. The weight of the aircraft is 108 kN and its wing area is 75m². The aircraft's drag equation is given by Cp = 0.035 + 0.025 C2. If the engines of the aircraft produce 45 kN of thrust during the climb what is the fastest equivalent airspeed the aircraft could be climbing at? The answer should have units of ms ¹.

a) Develop a relation between local static pressure P and freestream static pressure P.. Assume the stagnation pressure remains unchanged (i.e.,isentropic flow). b) Write the local pressure coefficient C, in terms of free stream Mach number M, and the ratio P/P . c) Combining your results from a) and b), write an expression for the local pressure coefficient C, in terms of local and free stream Mach numbers. d) If the peak C, in incompressible flow is -0.43, estimate the critical Mach number. Hint: place all terms on one side of the equation and use a trial and error approach.

Evaluation and Discussion 8. Task A: A1: A2: A3: A4: A5: A4: A5: Why pressure distribution on the upper and lower surface are the same for NACA0015 airfoil at zero AOA? Why there is a difference in pressure distribution between the upper and lower surface for cases you simulated in this Task? Which sides (upper or lower surface) has higher pressure, and why? Do you see the difference in pressure (between upper and lower surface) changes with AOA? Why? Describe the pressure distribution on the upper surface by identifying the stagnation point, suction peak, and adverse pressure region. What is Cp? How do we compute the lift coefficient of the aerofoil from the Cp distribution? (15 marks)

A propeller-driven aircraft has a maximum endurance of 14.1 hours when flying according to cruise climb conditions. What is the range of the flight if the aircraft's speed is 68 m s™¹, the propeller efficiency is 0.85 and the specific fuel consumption is 10-7 kg W-¹ s-¹? The answer should have units of km.

Question 1. Calculate the temperature (in Kelvin) at an altitude of 9665 metres above sea level, assuming ISA atmosphere: O -47.82 O 0.0065 O 350.82 O 12 O 225.18 Not answered Question 2. Calculate the temperature (in Kelvin) at an altitude of 11471 metres above sea level, assuming ISA atmosphere: 0.0065 216.50 O 3 O 362.56 O-59.56 Not answered SESSMEN sity The Questions Question 3. Calculate the pressure (in Pascals) at an altitude of 5192 metres above sea level, assuming ISA atmosphere: O -19 O 52611 O 90423 O 53 101325 [a2-alkarbi] UFMFRU-15-1 DEWIS E-ASSE Not answered The Questions Question 4. Calculate the air density (in kg per cubic metre) at an altitude of 12504 metres above sea level, assuming ISA atmosphere: O 81.64 O 0.29 O 0.36 O 288.00 O-80.99 [a2-alk UFMFRU-15-1 DEWIS E-AS Not answered The Questions Question 5. An aircraft is flying at an altitude of 8364 m above sea level. Its airspeed with respect to the surrounding air is 137 m/s. Assuming ISA conditions, calculate the dynamic pressure (in Pascals). O 1965.1 O 288 -39.37 4716.52 O-928.7 OFMPRU-15-1 DEWIS E-ASSESSMEN Not answered

Project Part-1: 1. Implement and test (show execution of) the continuous-time component representing the dynamic model of a car given in the Textbook. Use the following values in the model: m= 1450 kg, k-63. Simulate the response for the case F-0, with initial conditions x(0)-0, v(0)=15 m/sec; and the case F-550 N with initial conditions x(0)=0, and v(0)=0. Use Trapezoidal discrete approximation of derivative with simulation step At-0.10 sec. Plot the component responses generated from your simulation. 2. Now add the effect of graded road to the above car model and regenerate the car responses to road grade of 0-5deg, and 0-10deg and the case F-550N with initial conditions x(0)=0, and v(0) 0 only. Plot the component responses generated by your simulation.

3. (30 points). You go on vacation and return to find a wind tunnel in your lab is filled with a mystery gas that is either nitrogen (k = 1.400) or helium (k = 1.667). Your colleague has left you a post-it note saying that she determined the temperature to be 293 K, the Mach number to be 1.2, and the wind speed to be 1208 m/s. (a) Which gas fills the wind tunnel? (b) What would the wind speed be if the wind tunnel was filled with the other gas?