Figure Q3 shows the cross section of a wing of a supersonic aircraft, travelling at a...
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Figure Q3 shows the cross section of a wing of a supersonic aircraft, travelling at a velocity, V. Under the forces given, the wing has a torsional stiffness, K, resisting the moment produced by the lift, L and the aerofoil pitching moment, M. The flexural centre of the aerofoil is located a horizontal distance, ec, from the aerodynamic centre. This can be mathematically modelled as per equation 3.1. AC Flexural center Mo Spring Figure Q3-Wing Divergence of Aerofoil M+Lec=K9(EQ. 3.1) a) By making the necessary substitutions for the lift and pitching moment, derive an equation the elastic twist of the wing (e) in terms of the lift, pitching moment and spring stiffness. b) For the aerofoil, at what point will the divergence point occur? c) The aerofoil has a chord length of 1.6m producing an approximate area of 16m. The aerodynamic centre for the aerofoil is 0.25c ahead of the flexural centre. The lift curve slope has a value of 3.2 and the minimum torsional stiffness of the wing is 12x10N m. Assuming 2D flow at 3500km (p = 0.845kgm), determine the divergence speed for the aerofoil. d) Comment on the divergence speed calculated above highlighting the impact on the aircraft. [15 marks] Figure Q3 shows the cross section of a wing of a supersonic aircraft, travelling at a velocity, V. Under the forces given, the wing has a torsional stiffness, K, resisting the moment produced by the lift, L and the aerofoil pitching moment, M. The flexural centre of the aerofoil is located a horizontal distance, ec, from the aerodynamic centre. This can be mathematically modelled as per equation 3.1. AC Flexural center Mo Spring Figure Q3-Wing Divergence of Aerofoil M+Lec=K9(EQ. 3.1) a) By making the necessary substitutions for the lift and pitching moment, derive an equation the elastic twist of the wing (e) in terms of the lift, pitching moment and spring stiffness. b) For the aerofoil, at what point will the divergence point occur? c) The aerofoil has a chord length of 1.6m producing an approximate area of 16m. The aerodynamic centre for the aerofoil is 0.25c ahead of the flexural centre. The lift curve slope has a value of 3.2 and the minimum torsional stiffness of the wing is 12x10N m. Assuming 2D flow at 3500km (p = 0.845kgm), determine the divergence speed for the aerofoil. d) Comment on the divergence speed calculated above highlighting the impact on the aircraft. [15 marks]
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