Final answer:
The calculation of induced drag on a Cessna 150 aircraft involves using the known values for lift, airspeed, aspect ratio, span efficiency factor, and wing chord along with the air density at 7,500 feet, which must be obtained from atmospheric data.
Step-by-step explanation:
To calculate the induced drag on the wings of a Cessna 150 aircraft, we must first understand the factors that influence this force.
Induced drag is a consequence of lift generation and can be computed using the following formula:
Di = (2 * L^2) / (ρ * V^2 * S * π * AR * e)
where Di is the induced drag, L is the lift force, ρ is the air density, V is the airspeed, S is the wing area, AR is the aspect ratio, and e is the span efficiency factor.
Given:
- Lift (L) = Weight of aircraft = 1600 lbs
- Airspeed (V) = 122 mph = 54.58 m/s
- Aspect ratio (AR) = 6.94
- Span efficiency factor (e) = 0.9
- Wing chord (c) = 4.75 ft = 1.448 m
- Span (b) = AR * c
- Wing area (S) = b * c
- Air density at 7,500 ft (ρ) can be calculated using standard atmosphere tables
After calculating the actual values such as wing area and air density at the given altitude, we substitute these values into the induced drag formula to obtain the aircraft's induced drag at cruising conditions.
Please note, the exact air density at 7,500 feet is not provided in the question and must be determined from standard atmosphere data based on altitude.