Question

Q1) An aircraft waits for takeoff initially and starts to accelerate according to a = C1 + Gu where C1 is the constant acceleration resulting from engine thrust and C2v2 is the acceleration due to aerodynamic drag. C1 and C2 are constants, v is in meters per second a) Derive an expression for the length of takeoff runway required for the aircraft to reach the takeoff speed v. If C1 1.8 m/s2, C2 --0.00003 m1 and v -270 km/h, b) Find the length of takeoff runway when aerodynamic drag is excluded c) Find the length of takeoff runway when aerodynamic drag is included

Answer 1

When drag is considered: Write the equation for acceleration of the airplane when drag is included a C1C2 dv dv ds dv ds Here, constant is k and v is velocity Integrate on both sides. In(C,+Cv2 2C 2CLİn(G +Cy)-In(G)]

Substitute 1.8 m/s for C, -0.00003 m1 for k, and 270 km/hrx 1 forv 1 km/hr In(1.8-(0.00003 x 752))-In (1.8 2x(-0.00003) x (0.489346-0.69314718) 2x (-0.00003) - 1640.66 1641 m Answer to the subpart c is s-1641 m The answer to the subpart a when drag is not considered is s- al The answer to the subpart a when drag is considered is s- 2C