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.
1. The pilot reads an Indicated Airspeed (IAS) of 290.0 kts. Calculate the True Airspeed (TAS) in kts?
2. Calculate the required Lift Coefficient?
3. 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 knots (kts), you can use the following formula:
TAS = IAS / √(ρ/ρ0)
where:
IAS = Indicated Airspeed in knots
ρ = Density of air at altitude in kg/m^3
ρ0 = Density of air at sea level at standard conditions (approximately 1.225 kg/m^3)
Given that the aircraft is flying at Flight Level 280, which is approximately 28,000 feet or 8,534.4 meters, you can estimate the density of air at that altitude using the International Standard Atmosphere (ISA) model:
ρ = ρ0 * (1 - (L * h / T0))^((g * M) / (R * L) - 1)
where:
L = Temperature lapse rate (approximated as -0.0065 K/m)
h = Altitude in meters
T0 = Temperature at sea level at standard conditions (approximately 288.15 K)
g = Acceleration due to gravity (approximately 9.81 m/s^2)
M = Molar mass of air (approximately 0.0289644 kg/mol)
R = Ideal gas constant (approximately 8.31432 J/(mol⋅K))
Plugging in the values, you can calculate the density of air at Flight Level 280:
ρ = 1.225 * (1 - (-0.0065 * 8534.4 / 288.15))^((9.81 * 0.0289644) / (8.31432 * -0.0065) - 1)
ρ ≈ 0.770 kg/m^3
Now you can calculate the True Airspeed (TAS):
TAS = 290 / √(0.770/1.225) ≈ 291.34 kts
1. The True Airspeed (TAS) is approximately 291.34 knots (kts).
To calculate the required Lift Coefficient, you can use the equation:
CL = Weight / (0.5 * ρ * V^2 * S)
where:
Weight = Mass of the aircraft (500,000 kg)
ρ = Density of air at altitude (0.770 kg/m^3)
V = True Airspeed (TAS) in meters per second (m/s)
S = Wing Area (845 m^2)
Plugging in the values, you can calculate the required Lift Coefficient:
CL = 500,000 / (0.5 * 0.770 * (250^2) * 845)
CL ≈ 0.512
2. The required Lift Coefficient is approximately 0.512.
To calculate the available power per engine in MW (megawatts), you can use the equation:
P = (D * V) / 1000
where:
D = Drag force in Newtons (N)
V = True Airspeed (TAS) in meters per second (m/s)
The drag force can be calculated using the equation:
D = 0.5 * ρ * V^2 * S * (CD0 + CL^2 / (π * AR * e))
where:
CD0 = Zero-lift drag coefficient (0.022)
CL = Lift Coefficient (0.52)
S = Wing Area (845 m^2)
AR = Aspect Ratio (Wingspan^2 / Wing Area)
e = Oswald Efficiency Factor (0.92)
Plugging in the values, you can calculate the drag force:
AR = (79.75^2) / 845 ≈ 7.51
D = 0.5 * 0.770 * (250^2) * 845 * (0.022 + (0.52^2) / (π * 7.51 * 0.92))
D ≈ 456,778 N
Now, you can calculate the available power per engine:
P = (456,778 * 250) / 1000 ≈ 114.20 MW
3. The available power per engine is approximately 114.20 megawatts (MW).