quiz1_v3

AE352: Aerospace Dynamical Systems (Fall 2023) Quiz 1 Duration: 30 mins Formulas • Bour’s Formula: d dt F −−→ OM = d dt G −−→ OM + −→ ω G/F × −−→ OM • Composition of velocity: ⃗v F ( M ) = ⃗v F ( O ′ ) + ⃗v G ( M ) + −→ ω G/F × −−−→ O ′ M • Sum of angular velocities: −→ ω A/B + −→ ω B/C = −→ ω A/C Question: Aircraft Carrier Landing. Consider an airplane which wants to land aboard an aircraft carrier (ship). To land, the airplane needs its arresting hook H (Figure 1b) to meet the arrester cable at L (Figure 1c). (a) Schematic indicating relative positions of the plane and the carrier. (b) Plane heading. (c) Carrier Heading. Figure 1: Final approach of a fighter plane at a carrier. For this problem, you may ignore yaw/roll and assume the pilot will bring the plane in line with the runway. Define airplane frame A = ( C, ⃗ p 1 , ⃗ p 2 , ⃗ p 3 ) and ship frame B = ( G, ⃗ b 1 , ⃗ b 2 , ⃗ b 3 ) as shown. The airplane frame has a distance l p ( t ) ⃗ f 2 + h p ( t ) ⃗ f 3 from point O, and the ship frame has a distance l s ( t ) ⃗ f 2 + h s ( t ) ⃗ f 3 from point O. The airplane pitches at rate ˙ ϕ and the ship pitches in the water at rate ˙ θ relative to F . Distances | −−→ CH | = d and | −→ GL | = r are constant. Also, −−→ CH = − d⃗ p 3 . 1