Question 1 (Total: 15 marks) a) b) i) ii) iii) Sketch a typical Cm - a plot and discuss : the condition for trim the requirement for static stability, and the

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.

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.

project. Topic: *Technological Innovations in Aviation Promoting Aircraft Safety: The Invention of the Automatic Flight Control System and its impact on aviation safety (1912-2022)". General The final submission is a short research proposal. The suggested word count is 2,500-3,000 words (around ten pages, double spaced, font size 12). Abstract, list of references, tables with numerical results (if any), and figures (including their captions and titles) are not included into the word count. All submissions must be made via the dedicated Dropbox set up on Bright space platform. Report Structure and Key Points I suggest that the final report have the following structure: - Abstract-200 words maximum. Note that abstract does not count towards the word limit for the report. - Introduction, where the topic of the report is introduced and motivated. Suggested volume-up to 400 words. - Literature Review. Minimum number of references: 15. Suggested number of references: 25-30. At least a third of the references should be scholarly journal papers or working papers. Suggested volume- up to 800-1000 words. - Methodology. In this section, you need to identify at least one qualitative and at least one quantitative research questions pertaining to the topic of your report. Identify variables, making sure to specify the independent and key dependent variables. You are also to describe how you would set up and carry out your work to address the research questions you have identified. Suggested volume-up to 400 words. - Discussion. Discuss expected results of your study, based on theory, available evidence, your educated guesses. Make sure you link your discussion to the research questions you have identified in the previous section. Suggested volume-up to 400 words./n- Methodology. In this section, you need to identify at least one qualitative and at least one quantitative research questions pertaining to the topic of your report. Identify variables, making sure to specify the independent and key dependent variables. You are also to describe how you would set up and carry out your work to address the research questions you have identified. Suggested volume-up to 400 words. - Discussion. Discuss expected results of your study, based on theory, available evidence, your educated guesses. Make sure you link your discussion to the research questions you have identified in the previous section. Suggested volume-up to 400 words. - Concluding Comments. In this section, in addition to discussing the importance of your work, provide a discussion of weaknesses of your study, and also give some suggestions for follow-up work. Suggested volume-up to 300 words. - List of references, which are to be organized alphabetically by the lead author's last name. Only use those references that are in the text. For this assignment, there is no minimum or maximum number of references to be used this only related to the literature review. List of references is not included into the word count. - Appendices are not allowed. Plagiarism Plagiarism is the representation of another author's language, thoughts, ideas, or expressions as one's own original work. Plagiarism is considered a serious form of academic dishonesty, and attracts severe penalties, up to and including a failing grade for the course, with the possibility of additional administrative actions taken by the University. Please check with the instructor if you have any questions, concerns, or doubts.

Question 5 (Total 15 marks) Table Q1 gives the longitudinal stability coefficients for an F-104A fighter at Mach <0.3. All angles are measured in radians: CLO=0.833 CMD=0 CLa = 3.44 (b) (c) (d) (e) CLM = 0.68 CMn = -1.46 Table Q1: Longitudinal Coefficients of F104A Other relevant parameters includes: (f) Сма = -0.64 m = 7,390kg S=18.6 m² b= 6.1 m Aircraft elevator effectiveness can be expressed as follow: C₁=CL₂ + C₁ua + CLn 7= 3.05 m C.G.@ 22 % 7 (a) At an equilibrium flight, at standard atmosphere at sea level, where density is p = 1.225 kg/m³, a = 0 and n = 0, appraise the speed that aircraft is flying. Analyse the Longitudinal Static Stability of the aircraft. Appraise the longitudinal Stability Margin, and Evaluate the neutral point of the CG. When the airplane returns from a mission, it is 600 kg lighter. What will be the equilibrium value of a and n in degree, assume the same speed and altitude. CM = CM₂ + CM₂a + CM₂n For the return mission, if the aircraft CG is shifted afterward, what will be the aft limit of the CG movement.

Question 6 (Total 10 marks) (a) Consider a twin-engined jet aircraft with a conventional configuration, from which the aircraft data is summarised in Table Q2(a). (c) (d) m = 4,800 kg S = 31.8 m² b = 15.90 m V = 55 ms-1 P = 1.225 kg m-3 Ye=0 CL = 0.46 Yv=-0.90 Ly = -0.07 Ny = 0.13 (ii) L = -0.35 N=-0.11 Y₂=0.21 L = 0.1 Nz= -0.05 Table Q2(a) During a landing approach, the airplane suffered a bird strike, where the rudder is stuck at maximum deflection of 15° (all derivatives above are per degree), analyse the following: (1) Assuming the aircraft maintain a steady flight with no roll and yaw motion. Starting from the dimensionless equation for the lateral-directional motion, analyse the balance in side force, roll and yaw moment equations, to show the following equations: C₁ +Y₂v+Y + Yę < =0 L₂V + L + L =0 N₂v + N₂ + N₂ = 0 Hence, or otherwise, analyse the required aileron deflection to main the steady flight and the corresponding slide slip angle. (b) Use a top view of an aircraft sketch, appraise the difference between slide slip angle and yaw angle. (iii) Appraise also the bank angle of the aircraft. Use side view of an aircraft sketch, appraise the difference between angle of attack and pitch angle. Use another separate side view of an aircraft sketch, explain why the flight path angle of the aircraft in a steady climb, is mostly like less than the pitch-up angle.

Question 8 (Total 15 marks) The approximate form of Dutch roll mode can be described in the state-space form as follow: Consider T-38 Talon aircraft, a fighter trainer, with the following flight condition: Flight Conditions Altitude Airspeed (a) (b) (c) mass Ixx Izz Ixz Air density Wing area Wing span [Y₂ Y₂ - Uo] M-K³H+K 25,000 ft 123.7 m/s 4,540 kg 5,965 kgm² 46,097 kgm² (1) (ii) (iii) 0 kgm² 0.549 kg/m³ 15.79 m² 7.69 Derivatives Yv Ny Yp N₂ Y₁ Nr Y₂ N₂ -1.260 0.240 0 0.0430 0 -0.170 0.160 -0.103 Appraise the characteristic equation of the Dutch Roll Mode Based on MIL-8785C, T-38 is a Class IV, CAT A aircraft, evaluate the flying quality of the open loop characteristic. (1) Which Level does the open loop T-38 meets? (ii) What is the requirement for meeting the highest requirement? A state feedback control system using rudder feedback is proposed to improve the damping ratio of the Dutch roll mode. So that it meets the MIL-8785C requirement as minimum o meets the requirement. Appraise the characteristic equation of the desired Dutch roll mode. Evaluate the system controllability Matrix. Design the Gain schedule (vector K) to achieve the improved flying quality that meets the MIL-8785C requirement.

Question 1 (Total: 15 marks) a) b) i) ii) iii) Sketch a typical Cm - a plot and discuss : the condition for trim the requirement for static stability, and the concept of stability margin The pitching moment coefficient vs Lift Coefficient plot (evaluated at a CG position of h = 0.25) for a jet liner is shown below in Figure 1(a) Pitching Moment Coefficient CM 0.25 0.2 0.15 0.1 0.05- 30.2 0.05 -0.1 -0.15 -0.2 0 0,2 0:4 CM VS CL 06 0.8 Lift Coefficient CL Figure 1(a): CM vs C₁ The aircraft and the level flight parameters are as follow: mass = 70,000 kg S = 185.8 m² CG @ 0.25 12 Alt = 10,000 m V = 237.4 m/s (i) Appraise the Stability Margin for the stated flight condition (ii) Appraise the Neutral Point of the aircraft (iii) What will be the elevator setting for the stated flight condition 14 77 --12⁰ 1=0⁰ 77= 20 n = 40/nIf the maximum elevator angle for this aircraft is -12°. The variation of CM VS CL plots at other CG location is presented in Figure 1(b) below SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) [Course code] Pitching Moment Coefficient CM 12 0.25 0.2, 0.15 0.1 0.05 o -0.05 --01 -0.15 -0.2 0 0,2 0,4 CM VS CL 0,6 0,8 Lift Coefficent 12 Tutor-Marked Assignment CG @ 0.25 14 1,6 CG @ 0.2 Page 3 of 11 CG @ 0.15 Figure 1(b) C vs C₁, at various CG Locations If the stall speed at sea level for the aircraft is Vstall = 80 m/s, based on the data presented at Figure 1(b), what will be the suitable design for the forward limit of the CG location.

Name: Assignment 2 GEOG336-CONTROL & GEODETIC SURVEYING Score: /120 For this portion of the assignment you will be performing some research/calculations dealing with a NGS Horizontal Control Station ‘AIRPORT RESET' 1. Use the NGS website to obtain Control Monument Datasheet. a. Go to the NGS website at www.ngs.noaa.gov i. Browse through the pull-down menus available to familiarize yourself with some of the tools and survey information available from NGS ii. Print Datasheet for monument ‘AIRPORT RESET' 1. Under DATA & IMAGERY menu select SURVEY MARK DATASHEETS. 2. On the lower right side of window that opens under Search By click on text, the left of the two icons to right of Station Name(s) a. Key in AIRPORT RESET as station name and change state to Minnesota, then click SUMBIT b. Highlight station ‘AIRPORT RESET' in the list that opens and click on Get Datasheets. Print the first two pages of the datasheet and provide a copy with assignment report. c. Go back to the SURVEY MARK DATASHEETS webpage and this time click on the Interactive Map and find 'AIRPORT RESET'. In NGS Map search tool (upper left) select NGS Datasheets: PID in pull down menu, and enter PID for ‘AIRPORT RESET' from datasheet and hit enter. The map should zoom in with monument at center of screen (triangle symbol). Print the map screen and provide a copy with assignment report. You could retrieve the datasheet here by clicking on the symbol and selecting Datasheet 'More info'. There are other search criteria such as property address, etc. that can be useful to find control in the area of a project. b. What is the PID (Identification #) for the station, which type of control monument is it (Horizontal, Vertical, both), what accuracy level is it (First, Second, etc.), and which reference ellipsoid are the geodetic coordinates based on? (12 pts.) 2. Using the geodetic latitude for station 'AIRPORT RESET' provided on the datasheet calculate the radii of curvature in the Meridian and Prime Vertical at this station (Use appropriate reference ellipsoid parameters from text on page 542). The Geodetic Azimuth from station 'AIRPORT RESET' to station ‘AIRPORT AZ MK' is listed on the datasheet as 232°46'48.2", verify this azimuth on your datasheet and calculate the radius of curvature of the 'Great Circle' in the direction between these two stations. Are the three of these calculated radii values the same? Why or why not? (28 pts.) 3. The LaPlace correction at station ‘AIRPORT RESET' is provided on the datasheet. Use DEFLEC18 to determine the components xi and eta which make up this deflection of vertical, and verify the LaPlace correction listed on datasheet. (DEFLEC18 calculation software can be found from the main NGS website in GEOID Models area (click to open in lower left), then click on GEOID18, click on DEFLEC18 in listing that loads on the left, then click on DEFLEC18 Interactive Computations in menus to the left) Key in Latitude and Longitude, Click on Perform... and printout the DEFLEC18 output and provide it in your report. Calculate the Astronomic Azimuth between station 'AIRPORT RESET' and station ‘AIRPORT AZ MK' from the Geodetic Azimuth given on datasheet, assuming Geodetic Azimuth = LaPlace Azimuth. (20 pts.) Perform the following calculations utilizing the formulas for Convergence of Meridians, Parallel of Latitude Offsets, and distances between control points. The radius of Earth of 20,906,000 feet will be used for calculations. The control points and associated geodetic coordinates (NAD83(1996)) utilized will be the following: Control Point AIRPORT RESET 3408 D Latitude 45°34'49.75247"N 45°21'24.19959"N Longitude 094°10'37.13349"W 094°45'46.78573"W 4. Calculate the Meridian Convergence between the control points utilizing both the rigorous and short line approximation methods. Show all intermediate value calculations (om, A, Aλ). What is the value of the difference between the calculated convergence using the two methods? (20pts.) 5. Solving one of the short line approximation equations for Aa from class (Aa=tan(0m)) we get that d = R R*Δα tan(Pm) Utilize this equation to calculate the East- West distance between the control points using both Meridian Convergence values calculated in #4 above and then calculate the difference between the distances. Is this difference significant? Explain. (20pts.) 6. Using the geodetic latitude of each control point individually calculate offsets for 1 mile, 5 miles, and 10 miles along the Great Circle to the parallel of latitude. Compare the differences between the calculated offsets at each distance for the two latitudes. Are these differences significant? Explain. (20pts.)

Question 2 (Total: 10 marks) a) b) i) ii) i) ii) iii) An aircraft has the longitudinal characteristic equation: s¹+5.08s³ + 13.2s² +0.72s +0.52 = 0 Apply Ruth's Criteria to evaluate the longitudinal stability of the aircraft Appraise number of root that has positive real part. Use a side view of aircraft, apply the concept of relative wind to explain the difference among, AOA, pitch angle and flight path angle The roll rate response to aileron input of an aircraft is given by the following transfer function: p(s) -1.62 {(s) (s + 1.232) = deg -/deg Appraise the flight behavior by sketching the time history plot of p vs time, when the aircraft is subjected to an impulse aileron input Sketch the corresponding time history plot of roll angle vs time. What is the time constant?

Question 7 (Total 10 marks) (a) The longitudinal dynamics of an aircraft at 15,000 ft at Mach 0.3 (U₁ = 335.00 ft/s) due to elevator input is considered. The equation of motion for the level flight in the state-space is given by : (b) (1) Additionally, the pitch response to the elevator is given by : (ii) -0.0353 0.0046 0 -0.2309 -0.545 309.00 0.00185 -0.00767 -0.395 0 1 Gen (ii) -31.34 -27 0 0.00132 9 -4.51576 W 0 0 5.63 -23.8 (1) (2) (3) 8(s) -4.516 (s-0.008) (s +0.506) n (s) (s²+0.033s +0.02) (s² +0.902s +2.666) Analyse the longitudinal stability of the aircraft by evaluating the frequency and damping factor of the phugoid and short period modes. Appraise the steady state pitch response due a unit step elevator input. (iii) Analyse the time response graph of u and w together on the same graph to analyse the short period. Do likewise for the phugoid mode. From the graphs evaluate the following parameters for phugoid mode. Period of oscillation Time to damp to ½ amplitude Cycle to damp to ½ amplitude Using the time responses drawn in Part (a)(iii) above, (1) describe the key characteristic and differences between phugoid and short period modes. Assume a step elevator input is applied. Explain why the aircraft response (after 10 seconds or more) is very much like phugoid