The Boeing 747 has a wingspan of 65 meters and AR of 7.7. (a)Assuming take off weight of 910,000 pounds and a take off velocity 160 knots, calculate the lift coefficient at take off for standard sea-level conditions.(b) Compare the above result with the lift coefficient for cruise at Mach number of 92% of the speed of sound.
To calculate the lift coefficient at takeoff for the Boeing 747, you will need to use the following formula:
Lift Coefficient (Cl) = Lift (L) / (0.5 * air density * velocity^2 * Wing Area)
Where:
- Lift (L) is the lifting force generated by the wings
- Air density is the density of air at sea level (standard sea-level conditions)
- Velocity is the takeoff velocity
- Wing Area is the area of the wings
Let's break down the calculation step by step:
(a) Calculate the lift coefficient at takeoff for standard sea-level conditions:
1. Convert the wingspan from meters to feet:
Wingspan = 65 meters * 3.28084 = 213.2552 feet
2. Calculate the wing area:
Wing Area = Wingspan * Wing Span / Aspect Ratio
Wing Area = 213.2552 * 213.2552 / 7.7 = 5,858.2159 square feet
3. Convert the takeoff weight from pounds to Newtons:
Takeoff Weight = 910,000 pounds * 4.44822 N/pound = 4,050,218.2 Newtons
4. Convert the takeoff velocity from knots to meters per second:
Takeoff Velocity = 160 knots * 0.514444 m/s/knot = 82.31104 meters per second
5. Determine the air density at standard sea-level conditions:
The air density at sea level is approximately 1.225 kg/m^3
6. Calculate the lift coefficient using the formula:
Lift Coefficient (Cl) = Lift / (0.5 * air density * velocity^2 * Wing Area)
Cl = 4,050,218.2 / (0.5 * 1.225 * 82.31104^2 * 5,858.2159)
(b) To compare the lift coefficient for cruise at 92% of the speed of sound, you would need additional information such as the weight, velocity, and air density at cruise conditions. Please provide the necessary details, and I'll be happy to help you with the calculations.