RCAIDE.Library.Methods.Aerodynamics.Common.Drag.induced_drag

induced_drag#

induced_drag(state, settings, geometry)[source]#

Determines induced drag coefficient for the full aircraft using multiple calculation methods.

Parameters:

  • state (Data) –

    Flight conditions and aerodynamic state containing:
    • conditions.aerodynamics.coefficients.lift.totalfloat

      Total lift coefficient [unitless]

    • conditions.aerodynamics.coefficients.drag.induced.inviscidfloat

      Inviscid induced drag coefficient [unitless]

    • conditions.aerodynamics.coefficients.drag.parasite.totalfloat

      Total parasite drag coefficient [unitless]

    • conditions.aerodynamics.coefficients.drag.parasitedict
      Dictionary of parasite drag coefficients by wing tag
      • wing_tagData
        Parasite drag data for each wing containing:
        • parasite_drag_coefficientfloat

          Parasite drag coefficient [unitless]

        • reference_areafloat

          Reference area [m²]

  • settings (dict) –

    Aerodynamic analysis settings containing:
    • oswald_efficiency_factorfloat, optional

      Vehicle-level Oswald efficiency factor [unitless]

    • viscous_lift_dependent_drag_factorfloat

      Viscous lift-dependent drag factor K [unitless]

    • span_efficiencyfloat, optional

      Span efficiency factor [unitless]

  • geometry (Data) –

    Aircraft geometry containing:
    • wingslist
      List of wing objects containing:
      • tagstr

        Unique identifier for the wing

      • aspect_ratiofloat

        Aspect ratio of the wing [unitless]

      • areas.referencefloat

        Reference area of the wing [m²]

Returns:

Results are stored in state.conditions.aerodynamics.coefficients.drag.induced

Return type:

None

Notes

This function calculates the induced drag coefficient using one of three methods depending on the available input data. The calculation accounts for both inviscid and viscous components of induced drag, with the viscous component related to parasite drag through a lift-dependent factor.

Major Assumptions

  • Three calculation methods available based on input data availability

  • Viscous induced drag is proportional to parasite drag and lift coefficient squared

  • Largest wing determines the effective aspect ratio when multiple wings are present

  • Fuselage-induced drag is not explicitly accounted for in span efficiency methods

Theory

Method 1: Oswald Efficiency Factor Provided The total induced drag is calculated directly:

\(C_{D,i} = \frac{C_L^2}{\pi AR \cdot e_{osw}}\)

where: - \(C_L\) is the total lift coefficient - \(AR\) is the aspect ratio of the largest wing - \(e_{osw}\) is the Oswald efficiency factor

Method 2: Span Efficiency Provided The inviscid induced drag is calculated from span efficiency (Note, this is not the same as the oswald efficiency factor):

\(C_{D,i,inviscid} = \frac{C_L^2}{\pi AR \cdot e_{span}}\)

The viscous induced drag is:

\(C_{D,i,viscous} = K \cdot C_{D,parasite} \cdot C_L^2\)

where \(K\) is the viscous lift-dependent drag factor.

Method 3: Inviscid Induced Drag from Analysis Uses pre-computed inviscid induced drag and calculates viscous component:

\(C_{D,i,viscous} = K \cdot C_{D,parasite} \cdot C_L^2\)

\(C_{D,i,total} = C_{D,i,inviscid} + C_{D,i,viscous}\)

The effective Oswald efficiency factor is back-calculated as:

\(e_{osw} = \frac{C_L^2}{\pi AR \cdot C_{D,i,total}}\)

Definitions

‘Induced Drag’

Drag component caused by the production of lift, including both inviscid and viscous effects.

‘Oswald Efficiency Factor’

Factor accounting for the efficiency of lift generation and its associated drag penalty of the entire aircraft.

‘Span Efficiency Factor’

Factor accounting for the efficiency of lift generation and its associated drag penalty of the wing.

‘Viscous Lift-Dependent Drag’

Additional drag caused by viscous effects that scale with lift coefficient squared.

References

[1] Stanford AA241 Course Notes. adg.stanford.edu http://aerodesign.stanford.edu/aircraftdesign/aircraftdesign.html