ashfordeOU Swept Wing Aerodynamics (aerodynamics/high-speed/swept-wing-aerodynamics)
Use when the task is wing sweep effects for high-speed flight: simple sweep theory, the cosine corrections on lift curve slope and section Mach, and the critical Mach number increase that sweep provides.
Domain quick reference
- Simple sweep theory: a yawed infinite wing behaves like an unswept wing at the velocity component normal to the leading edge. The sweep angle Lambda is the angle between the leading edge and the plane perpendicular to the freestream; all corrections below use cos(Lambda).
- Effective (section) Mach: M_eff = M * cos(Lambda). The section sees a reduced Mach number, which is the mechanism behind the critical Mach increase.
- Velocity components about the leading edge: normal M_n = M * cos(Lambda), tangential M_t = M * sin(Lambda).
- Lift curve slope (simple sweep theory): a_swept = a0 * cos(Lambda), a0 the unswept section slope (2 * pi for thin sections). The lift-curve-slope leaf applies this as one step of its correction chain; this leaf owns the sweep-specific analysis and design forms.
- Critical Mach: M_crit,swept = M_crit,0 / cos(Lambda), from the condition that the section reaches its critical Mach at the reduced effective Mach. A 35 degree sweep (cos = 0.819) raises a 0.7 section critical Mach to about 0.85.
- Design form: Lambda = acos(M_crit,0 / M_crit,target) gives the sweep angle needed to reach a target critical Mach.
- Range: the cosine corrections are subsonic small-disturbance results, valid for 0 <= Lambda < 90 degrees with the effective Mach kept subsonic; a swept critical Mach at or above 1 is out of domain.
- Validation anchor: NACA Report 824 (public domain) supplies the unswept section data that the cosine corrections act on.
Workflow
- Confirm the leading-edge sweep angle Lambda in degrees and the flight Mach number M.
- Compute cos(Lambda) with cos_sweep.
- Reduce the section Mach with effective_mach, or take both components with mach_components.
- Correct the section lift slope with swept_lift_slope.
- Estimate the critical Mach with critical_mach, or size the sweep for a target critical Mach with sweep_for_critical_mach.
- Report the swept values next to the unswept baseline so the change that sweep buys is visible.
Pitfalls
- Applying the cosine correction to dynamic pressure: simple sweep theory acts on Mach number and on slope, not on q.
- Using a sweep angle measured from the freestream instead of the leading edge: the corrections need the leading-edge sweep.
- Accepting sweep at or beyond 90 degrees, where cos(Lambda) <= 0.
- Using the swept critical Mach formula when the result would reach or exceed 1: the wing is transonic or supersonic there and simple sweep theory no longer applies.
- Reading a section polar at the free-stream Mach: the section behaves at M * cos(Lambda), not at M.
- Treating cos(Lambda) as exact for a finite wing: real wings need planform and leading-edge suction corrections; the cosine is the first-order estimate.
- Reusing the unswept critical Mach as the wing value: the / cos(Lambda) step is what quantifies the margin sweep buys.
- Assuming sweep cures all transonic problems: the root and tip regions still see three-dimensional flow and local supercritical conditions.
Behavior contract (gate 3)
The sweep logic is exercised by the gate 3 contract test: scripts/test_swept_wing_aerodynamics.py against scripts/swept_wing_aerodynamics_logic.py (stdlib unittest, offline). Run: python3 scripts/test_swept_wing_aerodynamics.py
Compliance
- Simple sweep theory and the cosine corrections are standard subsonic wing methodology (public-domain textbook content, e.g. Anderson, Fundamentals of Aerodynamics); NACA TR 824 is referenced as the pack's public-domain anchor for the section data, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.