Overview
This lecture explains how to estimate the drag polar of a military aircraft, specifically the F-16C, using geometric data and standard aerodynamic formulas. It covers calculating drag coefficients (including non-parabolic effects), wetted area estimation, and comparison to real aircraft data.
Drag Polar Estimation Procedure
- F-16C is the case study aircraft for drag polar estimation.
- The drag polar equation used is ( C_D = C_{D0} + K_1 C_L^2 + K_2 C_L ).
- ( C_D ) is total drag coefficient, ( C_{D0} ) is parasite (zero-lift) drag coefficient, ( C_L ) is lift coefficient.
- ( K_1 ) is related to aspect ratio (AR) and Oswald efficiency factor (( E_0 )), calculated via: ( K_1 = \frac{1}{\pi E_0 AR} ).
- ( K_2 ) models effects such as airfoil camber and is calculated as ( K_2 = -2 K_1 C_{L, \text{min drag}} ).
Determining Aircraft Geometry & Wetted Area
- F-16C key dimensions: wingspan 9.144 m, wing area 27.87 m², tail span 5.49 m, tail area 10.033 m².
- Wetted area (( S_{wet} )) can be estimated using CAD models (OpenVSP) or by decomposing the aircraft into standard geometric shapes.
- Total wetted area computed: 131.73 m² (after converting and correcting potential errors).
- Canopy, fuselage, and other parts approximated as a combination of cylinders, cones, and trapezoids for area calculation.
Skin Friction and Parasite Drag
- Equivalent skin friction coefficient (( C_{f_e} )) for fighter jets: 0.0035.
- Parasite drag coefficient calculated as ( C_{D0} = C_{f_e} \times \frac{S_{wet}}{S} ).
- For F-16C: ( C_{D, \text{min}} = 0.01654 ).
Non-Parabolic and Parabolic Drag Polars
- Minimum drag often occurs at nonzero lift (( C_{L, \text{min drag}} )), observed as 0.04 for the F-16C airfoil.
- Equivalent parabolic drag polar: shift ( C_{D0} ) by adding minimum drag and induced drag at ( C_{L, \text{min drag}} ).
- Final drag polar for F-16C: ( C_D = 0.01667 + 0.1167 C_L^2 - 0.009 C_L ).
Supersonic Drag Estimation
- Critical Mach number for the F-16C estimated at 0.85; maximum drag coefficient occurs at Mach 1.05.
- Wave drag coefficient at Mach 1.05 is approximately 0.0261.
- Supersonic drag due to lift calculated using adjusted ( K_1 ) formula based on Mach number.
Data Verification and Comparison
- Estimated drag polars and coefficients align closely with experimental and published data for F-16 and YF-16.
- ( K_1 ) and ( K_2 ) remain stable until critical Mach, then ( K_1 ) increases with Mach number.
Key Terms & Definitions
- Drag Polar — Relationship between drag coefficient (( C_D )) and lift coefficient (( C_L )) for an aircraft.
- Parasite Drag Coefficient (( C_{D0} )) — Drag not associated with lift; includes skin friction and form drag.
- Induced Drag — Drag due to production of lift.
- Aspect Ratio (AR) — Ratio of wingspan squared to wing area.
- Oswald Efficiency Factor (( E_0 )) — Measures wing efficiency in producing lift with minimum drag.
- Wetted Area (( S_{wet} )) — Total surface area exposed to airflow.
- Skin Friction Coefficient (( C_{f_e} )) — Average coefficient representing surface skin friction drag.
Action Items / Next Steps
- Practice calculating wetted area and drag coefficients for the F-16C using the outlined methods and given formulas.
- Refer to the textbook by Brandt et al. for detailed equations and step-by-step examples.
- Review airfoil data for minimum drag conditions and confirm calculations with provided values.