In aerodynamics, force coefficients and the angle of attack are crucial for understanding how air flows around an object, such as an aircraft wing. Here’s a detailed look at their relationship and significance:
Angle of Attack (AoA)
Definition: The angle of attack is the angle between the oncoming airflow and the chord line of the wing or airfoil.
Generally, we can see the angle of attack as shown in Image 1 if we assume the flight path is perpendicular to the direction of gravity. But, for modeling such as Computational Fluid Dynamics, it is easier to change the angle of attack instead of rotating the geometry (as shown in Image 2), by converting the velocity components:
u = U*cos(AoA)
v = U*sin(AoA)
With the u and v are the velocity components in the x and y directions respectively, and U is the magnitude of the velocity.
so we must calculate the Lift and Drag based on the calculated forces (for example Fx and Fy) with the equations:
Lift = Fy*cos(AoA) – Fx*sin(AoA)
Drag = Fx.cos(A0A) + Fy*sin(A0A)
Image 1. AoA of an aircraft
Image 2. AoA by assuming relative flow direction
Lift and Drag Coefficients (CL & CD)
- Definition: The lift and drag coefficients are the dimensionless number that describes the lift and drag forces generated by an object relative to the dynamic pressure and the reference area.
- Formula:
Lift =1/2⋅CL⋅ρ⋅A⋅U²
Drag =1/2⋅CD⋅ρ⋅A⋅U²
Where:
L = Lift (N)
D = Drag (N)
CL = Lift coefficient
CD = Drag coefficient
ρ = density (kg/m³)
A = Reference Area (m²)
U = magnitude of velocity (m/s)
The value of the reference area depends on your own conversions, and must be consistent with previous works. For example, aircraft wings usually use span*chord, truck aerodyamics use frontal area, or submarine hydrodynamics use wetted surface.
Reference Values
Disclaimer: These reference values are just coarse estimations to help you quickly estimate the input. For more scientific projects, please use your own values!
| Fluid | Density (kg/m3) |
| Air | 1.293 |
| Water | 997 |
Some Unit conversions:
Density:
- 1 g/cm³ = 1,000 kg/m³
- 1 g/mL = 1,000 kg/m³
- 1 lb/ft³ ≈ 16.0185 kg/m³
- 1 lb/gal ≈ 8.3454 kg/m³
- 1 oz/in³ ≈ 27,679.9 kg/m³
- 1 kg/L = 1,000 kg/m³
Velocity:
- 1 mph≈0.44704 m/s
- 1 ft/s≈0.3048 m/s
- 1 in/s≈0.0254 m/s
- 1 knot (nautical miles/hr) ≈0.51444 m/s
- 1 Mach≈343 m/s
Length:
- 1 mm=0.001 m
- 1 cm=0.01 m
- 1 km=1,000 m
- 1 in≈0.0254 m
- 1 ft≈0.3048 m
- 1 yd≈0.9144 m
- 1 mi≈1,609.344 m
- 1 nmi≈1,852 m
Area:
- 1 mm² = 0.000001 m²
- 1 cm² = 0.0001 m²
- 1 km² = 1,000,000 m²
- 1 ft² ≈ 0.092903 m²
- 1 in² ≈ 0.00064516 m²