[SOLVED] AER1216 Assignment # 1 

1. For a symmetrical airfoil, based on thin airfoil theory, calculate the lift and moment about the leading edge (per unit span) when the angle of attack is 3◦ and the freestream is at standard sea level conditions with a velocity of 40 m/s. The chord of the airfoil is 1 m. What is the Reynolds number? Use tables to find the density and the viscosity of air at sea level. [10 marks]
2. An airfoil has a mean camber line that has the shape of a circular arc. The maximum mean camber is kc, where k is a constant and c is the chord. Therefore, the camber line is described by

   􏰃 c􏰄2 􏰇 c kc􏰈2 􏰇c kc􏰈2 x−2+z+8k−2 =8k+2 (1)

   for 0 ≤ x ≤ c. Let the freestream velocity be V∞ and the angle of attack be α. Under the assumption that k << 1, express the γ distribution in terms of V∞, α, θ, and k. Find the angle of zero lift and the moment coefficient about the aerodynamic center. [20 marks]

3. An airplane weighing 60, 000 N has elliptically loaded wings 12 m in span. For a speed of 70 m/s in straight and level flight at low altitude, find the induced drag. (Hint: Note that you are asked to find the induced drag, not the induced drag coefficient.) [10 marks]
4. Consider an untwisted wing with an aspect ratio of 8. The chord at

   the tip is 0.4 times the chord at the root and varies linearly in between.

   The zero-lift angle of attack is −1.2◦ across the span. Using four sta-

   tions located at π , π , 3π and π , find the linear system of equations for 848 2

   A1, A3, A5, and A7. Find the lift coefficient and the induced drag coef- ficient as functions of the geometric angle of attack. Find their values when the geometric angle of attack is 3◦. [20 marks]

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AER1216 Fundamentals of UAS Fall 2021

5. Analyses such as thin airfoil theory or Prandtl’s lifting line theory are simple and straightforward compared to the advanced numerical analy- ses used to create the final product in modern aircraft design. However, that is not to say that these methods are never useful. How do you think these methods can be used in the aircraft design process? Provide the reasoning behind your answer. [10 marks]

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