123[10] Jones, R. T., “The <strong>Unsteady</strong> Lift of a Wing of Finite Aspect Ratio”, NACARep. 681, June 1939.[11] Jones, R. T., “The <strong>Unsteady</strong> Lift of a Finite Wing”, NACA TN 682,Washington, D.C., January 1939.[12] Jones, R. T., Fehlner, L. F., “Transient <strong>Effects</strong> of the Wing Wake on theHorizontal Tail”, NACA TN 771, 1940.[13] Tobak, M., “On the Use of the Indicial Function Concept in the <strong>Analysis</strong> of<strong>Unsteady</strong> Motions of Wings and Wing-Tail Combinations”, NACA Report1188, 1954.[14] Tobak, M., and Pearson, W. E., “A Study of Nonlinear LongitudinalDynamic <strong>Stability</strong>”, NASA TR R-209, September 1964.[15] Tobak, M., and Schiff, L. B., “On the Formulation of the <strong>Aerodynamic</strong>Characteristics in <strong>Aircraft</strong> Dynamics”, NASA TR-R-456, 1976.[16] Tobak, M., Chapman, G. T., Schiff, L. B., “Mathematical Modeling of the<strong>Aerodynamic</strong> Characteristics in Flight Dynamics”. NASA TM-85880, Jan.1984.[17] Tobak, M., Chapman, G. T., “Nonlinear Problems in Flight DynamicsInvolving <strong>Aerodynamic</strong> Bifurcations”, NASA-TM-86706, March 1985.[18] Klein, V., and Noderer, K. D., “Modeling of <strong>Aircraft</strong> <strong>Unsteady</strong> <strong>Aerodynamic</strong>Characteristics, Part 1 – Postulated Models”, NASA TM 109120, May 1994.
124[19] Klein, V., and Noderer, K. D., “Modeling of <strong>Aircraft</strong> <strong>Unsteady</strong> <strong>Aerodynamic</strong>Characteristics, Part 2 – Parameters Estimated From Wind Tunnel Data”,NASA TM 110161, April 1995.[20] Klein, V., and Noderer, K. D., “Modeling of <strong>Aircraft</strong> <strong>Unsteady</strong> <strong>Aerodynamic</strong>Characteristics, Part 3 – Parameters Estimated From Flight Data”, NASA TM110259, May 1996.[21] Klein, V., “Modeling of Longitudinal <strong>Unsteady</strong> <strong>Aerodynamic</strong>s of a Wing-Tail Combination”, NASA CR-1999-209547, September 1999.[22] Reisenthel, P. H., “Development of a Nonlinear Indicial Model forManeuvering Fighter <strong>Aircraft</strong>”, AIAA Paper 96-0896, 1996.[23] Reisenthel, P. H., Bettencourt, M. T., “Data-Based <strong>Aerodynamic</strong> Modelingusing Nonlinear Indicial Theory”, AIAA Paper 99-0763, 1999.[24] Reisenthel, P. H., Bettencourt, M. T., “Extraction of Nonlinear Indicial andCritical States Responses from Experimental Data”, AIAA Paper 99-0764,1999.[25] Levinsky, E. S., “Theory of the Wing Span Loading Instabilities Near Stall”,Paper No. 25, AGARD CP 204, Prediction of <strong>Aerodynamic</strong> Loading, 1976.[26] Hreha, M. A., “A Dynamic Model for <strong>Aircraft</strong> Post-stall Departure”, Ph. D.Dissertation in Aerospace Engineering, Virginia Polytechnic Institute andState University, Blacksburg, Virginia, May 1982.[27] Anderson, M. K., “<strong>Aerodynamic</strong> Modeling for Global <strong>Stability</strong> <strong>Analysis</strong>”,AIAA Paper 2002-4805, 2002.
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An Investigation of Unsteady Aerody
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iAcknowledgmentsAll that I struggle
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Figure 3-19 Roll angle time history
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0( α )x static dependence function
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11 IntroductionThe atmospheric flig
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3aerodynamic forces in terms of the
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5another state-space representation
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7a nonlinear indicial response theo
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9Figure 1-2 Internal state-space va
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11representation, we write it expli
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13C& α cV() t = C ( α ) + C C ()
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15(a)(b)*Figure 1-3 Influence of th
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17( α )1x0 U eff=1+exp(1-13)[ −
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19tˆ =c2V, (1-17)c being a charact
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21representing forward and aft fuse
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23In equation (1-19)∗αwdescribes
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25Ntiα2( x ) = a + b x c xC +tit1
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27The rolling moment of the aircraf
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29are the A-4 Skyhawk, F-4 Phantom,
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31Conventional wing rock is that oc
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33Figure 1-8 Crossflow streamlines
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35possible cases forC φ, where the
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37Figure 1-10 Roll angle time-histo
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39Figure 1-14 Rolling moment coeffi
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41Figure 1-15 C l vs. roll angle hi
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430.020-0.02C l-0.04-0.06-0.08φ =
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451.2.3 Analytical and Computationa
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47vertical fin inclusion, the oscil
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49Table 1-1 Geometrical and physica
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51Figure 1-22 Free to roll apparatu
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53Both of these problems make it di
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55experimental results the values o
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57► State equations:τdxi1,x+ xi=
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592.2 The Second Unsteady Aerodynam
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61With the help of the formulation
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63tunnel tests results shown in Fig
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65C2( ν ) = a + b ν c νN i 6 6 i
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67Figure 2-2 Static model responses
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69Figure 2-4 Variation of the norma
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71When the quasi-static sequences o
- Page 86 and 87: 73identification. The static data u
- Page 88 and 89: 752( x ) - 7.293 x - 5.427 xCN i= 0
- Page 90 and 91: 77Figure 3-1 Static normal force co
- Page 92 and 93: Figure 3-3 Identified static values
- Page 94 and 95: Figure 3-5 Rolling moment coefficie
- Page 96 and 97: Figure 3-7 Rolling moment coefficie
- Page 98 and 99: Figure 3-9 Rolling moment coefficie
- Page 100 and 101: 87with the roll angle, and attains
- Page 102 and 103: 890.060.04θ = 20 degModel response
- Page 104 and 105: 9140θ = 27 deg20φ, deg0-20-4015.6
- Page 106 and 107: 93C l0.150.1θ = 27 degModel respon
- Page 108 and 109: 95C l0.150.1θ = 38 degModel respon
- Page 110 and 111: 97100θ = 45 deg50φ, deg0-50-1000
- Page 112 and 113: 990.060.04θ = 45 degModel response
- Page 114 and 115: 101Table 3-1 Model parameters for t
- Page 116 and 117: 103Table 3-3 Continuation of Table
- Page 118 and 119: 105Table 3-6 Continuation of Table
- Page 120 and 121: 107Table 3-9 Continuation of Table
- Page 122 and 123: 109q, r, the Euler angles time rate
- Page 124 and 125: 1114.3 Results of the SimulationsTh
- Page 126 and 127: Figure 4-2 Phase-plane of the simul
- Page 128 and 129: Figure 4-4 Phase-plane of the simul
- Page 130 and 131: Figure 4-6 Phase-plane of the simul
- Page 132 and 133: Figure 4-8 Phase-plane of the simul
- Page 134 and 135: 121Considering these characteristic
- Page 138 and 139: 125[28] Goman, M. G., Stolyarov, G.
- Page 140 and 141: 127[45] Nguyen, L. T., Yip L., Cham
- Page 142 and 143: 129AppendicesAppendix AA.1 The Conv
- Page 144 and 145: 131u = V cosθ 0v = Vsinθ0sinφw =