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 knots (kts), we need to take into account the altitude of the aircraft. Flight Level 280 refers to an altitude of 28,000 feet.
Step 1: Convert the indicated airspeed (IAS) from knots (kts) to meters per second (m/s).
1 knot (kt) is equal to 0.5144 meters per second (m/s).
Therefore, 290.0 kts is equal to 290.0 x 0.5144 m/s.
290.0 kts * 0.5144 m/s = 149.36 m/s
Step 2: Calculate the True Airspeed (TAS) using the formula:
TAS = IAS + (IAS x Altitude x 4)/1000
TAS = 149.36 m/s + (149.36 m/s x 28,000 ft x 4)/1000
Note: We need to convert the altitude from feet to meters by multiplying by 0.3048.
TAS = 149.36 m/s + (149.36 m/s x 8534.4 m)
TAS = 149.36 m/s + 1267805.984 m
TAS = 1267955.344 m/s
To convert the True Airspeed from meters per second (m/s) to knots (kts), we need to multiply by 1.9438.
TAS = 1267955.344 m/s * 1.9438
TAS = 2461897.3012 kts
Therefore, the True Airspeed (TAS) is approximately 2,461,897.3 kts.
To calculate the Lift Coefficient (CL), we need to know the weight of the aircraft. Since the weight is not provided in the question, it is not possible to calculate the Lift Coefficient.
For the final part of the question, we need the Lift Coefficient (CL) and the available power per engine in megawatts (MW). The aircraft is flying at a CL of 0.52 and a True Airspeed (TAS) of 250 m/s.
Step 1: Calculate the Lift force using the equation:
Lift = 0.5 x density x TAS^2 x wing area x CL
Step 2: Assume the wing area (S) of an Airbus A380 to be 845 square meters.
Step 3: Calculate the density (ρ) based on the given TAS and altitude:
ρ = p0 x (1 - (L x T^0.0065) / T0)^4.2561
where p0 is the air density at sea level (1.225 kg/m^3), L is the altitude in meters, and T0 is the standard temperature at sea level (288.15 K).
Step 4: Calculate the available power per engine using the equation:
Available Power = Lift x TAS / (η x wing area)
where η is the overall efficiency of the engine (assumed as 0.85).
By using these steps, we can calculate the available power per engine in megawatts (MW). However, since the weight of the aircraft is not provided, it is not possible to determine the Lift force or the available power.
To calculate the True Airspeed (TAS) in knots (kts), we need to correct the Indicated Airspeed (IAS) for the altitude. The equation used to find TAS is:
TAS = IAS * (√(Pressure Altitude/Tropical Standard Atmosphere))
Here's how you can calculate it:
1. Convert the Flight Level to Pressure Altitude:
- Flight Level is the height in hundreds of feet above a reference level (usually mean sea level).
- In this case, Flight Level 280 means the aircraft is flying at 28,000 feet.
- The standard conversion is 1 Flight Level = 100 feet.
- Therefore, Flight Level 280 = 28,000 feet.
2. Convert the Pressure Altitude to meters:
- 1 foot = 0.3048 meters.
- Therefore, 28,000 feet = 8,534.4 meters.
3. Calculate the True Airspeed (TAS):
- In this case, the IAS is given as 290 knots.
- Substitute the values into the formula:
TAS = 290 * (√(8,534.4/2,220)) knots
= 290 * (√3.846) knots
≈ 331.12 knots
So, the True Airspeed (TAS) is approximately 331.12 knots.
Now, let's move on to the next part of the question:
To calculate the Lift Coefficient, you need additional information such as the aircraft's weight, wing area, and air density. Please provide these details, and I'll be happy to assist you further.
Lastly, let's calculate the available power per engine in Megawatts (MW). To do this, we need to know the specific fuel consumption and the True Airspeed (TAS). Since the TAS provided in the question (250 m/s) is in meters per second, we need to convert it to knots.
1 meter/second = 1.94384 knots
Therefore, TAS = 250 * 1.94384 knots ≈ 485.96 knots.
Unfortunately, without the specific fuel consumption data, we cannot directly calculate the available power per engine. Specific fuel consumption is required to determine the fuel flow rate, which, in turn, can be used to calculate power per engine using the formula:
Power = Fuel flow rate * Specific fuel consumption
Please provide the specific fuel consumption value, and I'll guide you through the calculation.
To calculate the True Airspeed (TAS), we need to convert the indicated airspeed (IAS) to equivalent airspeed (EAS) and then to true airspeed (TAS). The formula for calculating TAS is:
TAS = EAS * √(ρ/ρ0)
Where:
EAS = IAS * √(ρ0/ρ)
ρ0 = standard air density at sea level = 1.225 kg/m³
ρ = actual air density at flight level 280
To calculate ρ, we can use the formula:
ρ = ρ0 * h/288.15
Where:
h = height above sea level = 28000 ft = 8534.4 m
Let's calculate ρ first:
ρ = 1.225 * (8534.4/288.15) = 2.849 kg/m³
Now let's calculate EAS:
EAS = 290.0 * √(1.225/2.849) = 249.32 kts
Finally, let's calculate TAS:
TAS = 249.32 * √(2.849/1.225) = 276.17 kts
The True Airspeed (TAS) is 276.17 kts.
Now, let's calculate the required lift coefficient:
Lift coefficient (CL) is given by the formula:
CL = 2 * weight / (ρ * TAS^2 * wing area)
Assuming the weight of the Airbus A380 is 1.2 million kg and the wing area is 845 m²:
CL = 2 * 1.2e6 / (2.849 * (276.17)^2 * 845) = 0.1204
The required lift coefficient (CL) is 0.1204.
Finally, let's calculate the available power per engine in MW:
Assuming the aircraft is flying at a CL of 0.52 and at a True Airspeed (TAS) of 250 m/s:
The available power per engine (P) can be calculated using the formula:
P = (CL * ρ * TAS^3 * wing area) / (2 * η)
Assuming the wing area is 845 m² and the engine efficiency (η) is 0.85:
P = (0.52 * 2.849 * (250)^3 * 845) / (2 * 0.85) = 18,875,983.52 W = 18.88 MW
The available power per engine is 18.88 MW.