Problem Statement
A jet plane which weighs 19620N has a wing area of 25m2. It is flying at a speed of 200km/hr. When the engine develops 588.6KW, 70% of this power is used to overcome the drag resistance of the wing. Calculate the coefficient of lift and coefficient of drag for the wing. Take density of air = 1.25 kg/m3.
Given Data
Solution Approach
To determine the coefficients of lift and drag, we’ll apply aerodynamic principles relating to lift and drag forces. We’ll use the power equation to find the drag force first, then apply the aerodynamic force equations to calculate both coefficients.
Calculations
Determination of Drag Force
Step 1: Calculate the drag force from the power equation.
The power used to overcome drag resistance is related to the drag force by:
Substituting the given values:
Step 2: Calculate the coefficient of drag using the aerodynamic drag equation.
Substituting the known values:
Step 3: Calculate the coefficient of lift using the aerodynamic lift equation.
During level flight, the lift force equals the weight of the aircraft:
The lift force is given by:
Substituting the known values:
Coefficient of Drag (CD) = 0.154
Coefficient of Lift (CL) = 0.407
Detailed Explanation
Physical Meaning of the Results
The calculated coefficients describe the aerodynamic performance of the aircraft’s wing:
- Coefficient of Lift (CL = 0.407): This value indicates the wing’s effectiveness in generating lift. A typical CL for an aircraft in cruising flight ranges from 0.2 to 0.5, so our result falls within the expected range for normal flight operations.
- Coefficient of Drag (CD = 0.154): This value represents the aerodynamic resistance experienced by the wing. Commercial aircraft typically have CD values between 0.01 and 0.2, with lower values indicating more aerodynamically efficient designs.
Lift-to-Drag Ratio
The lift-to-drag ratio (L/D) is a measure of aerodynamic efficiency:
This relatively low L/D ratio suggests that either:
- The aircraft is operating at low speed (which is confirmed by the 200 km/hr speed)
- The wing design prioritizes factors other than maximum aerodynamic efficiency (such as maneuverability or structural simplicity)
Aerodynamic Principles
The coefficients of lift and drag are dimensionless parameters that characterize how effectively a body generates lift and how much drag it experiences in a fluid flow. These coefficients are influenced by:
- Wing shape and airfoil profile
- Angle of attack
- Reynolds number (related to airspeed)
- Surface roughness
- Flow conditions (laminar vs. turbulent)
Power Requirements
The calculation showed that 70% of the engine power (412.02 kW) is used to overcome wing drag. The remaining 30% (176.58 kW) would be used for:
- Overcoming fuselage and empennage drag
- Powering aircraft systems
- Compensating for propulsion inefficiencies
- Providing reserve power for maneuvers and climbing
Engineering Considerations
For aircraft designers, these coefficients provide crucial information for:
- Optimizing fuel efficiency
- Determining required thrust
- Calculating takeoff and landing distances
- Ensuring stable flight characteristics
- Designing control surfaces for adequate maneuverability
Understanding the aerodynamic performance of aircraft wings is essential for engineers working in aerospace design, propulsion systems, and flight mechanics. The coefficients derived in this problem provide a quantitative basis for evaluating the wing’s performance and guiding potential design improvements.
