For the Airbus A380, the largest passenger aircraft ever built, you are given the following parameters:
Variable Value
Mass 500,000 kg
Wing Area 845 m2
Wingspan 79.75 m
Number of Engines 4
CLmax flaps retracted 1.9
CLmax flaps extended 2.6
Oswald Efficiency Factor 0.92
CD0 0.022
Flight Parameters
0.0/3.0 points (graded)
An Airbus A380 is flying in steady, horizontal flight at Flight Level 280.
The pilot reads an Indicated Airspeed (IAS) of 290.0 kts. Calculate the True Airspeed (TAS) in kts
Calculate the required Lift Coefficient
For this subquestion, assume the aircraft is flying at a CL of 0.52 and at a True Airspeed of 250 m/s (which are not the correct answers to the previous questions). Calculate the available power per engine in MW.
To calculate the True Airspeed (TAS) in kts, you need to apply the correction for altitude and temperature. Flight Level 280 corresponds to an altitude of approximately 28,000 feet.
First, calculate the equivalent airspeed (EAS) using the formula:
EAS = IAS * sqrt(rho0 / rho)
Where:
IAS = Indicated Airspeed = 290.0 kts
rho0 = density at sea level = 1.225 kg/m^3
rho = density at altitude = rho0 * exp(-altitude / H)
Assuming a standard atmosphere lapse rate of -0.0065 K/m and a standard temperature at sea level of 288.15 K, the temperature at Flight Level 280 can be calculated as:
altitude = 28000 * 0.3048 = 8534.4 meters
temperature = 288.15 - 0.0065 * altitude
Now, calculate the density at altitude:
rho = rho0 * (temperature / 288.15)^(1 + g0 / (R * lapse rate))
Where:
g0 = standard acceleration due to gravity = 9.81 m/s^2
R = specific gas constant for air = 287.1 J/(kg·K)
Finally, convert the equivalent airspeed from m/s to kts:
TAS = EAS * sqrt(rho / rho0) * (1 + 0.2 * (rho / rho0) * (Mach^2 - 1))
Where Mach is the ratio of TAS to the speed of sound, and assuming a speed of sound at sea level of 340.3 m/s.
As for the required Lift Coefficient, given that the aircraft is flying at a CL of 0.52 and at a True Airspeed of 250 m/s, you can use the Lift Equation to find the required lift force:
L = 0.5 * rho * V^2 * S * CL
Where:
L = Lift force
rho = air density
V = True Airspeed
S = Wing Area
CL = Lift Coefficient
Now, you can calculate the available power per engine in MW using the equation:
Power = Thrust * TAS
Where:
Thrust = Lift / (0.5 * rho * S)
Given that there are 4 engines, divide the total power by 4 to get the available power per engine in MW.