Ground Effect

Ground Effect (aerodynamics/ground-effects/ground-effect)

Use when the task is wing aerodynamics in ground effect: induced drag reduction near the ground, the image vortex method, and the takeoff and landing consequences.

Domain quick reference

• Ground effect onset is roughly h / b < 1.5, where h is the height of the wing reference line above the ground and b the span; the effect strengthens as h / b shrinks.
• Image vortex method: the ground plane is replaced by a mirror image of the wing vortex system, reflected across the ground and with circulation reversed. The image system lies 2 * h below the real system and enforces zero normal flow at the ground. Its upwash at the real wing cancels part of the downwash.
• Induced drag reduction factor (image vortex result, elliptic loading): sigma = 1 / (1 + 16 * (h / b)^2). The induced drag in ground effect is C_Di,g = C_Di,inf * (1 - sigma), and the ratio to free-air value is 16 * (h / b)^2 / (1 + 16 * (h / b)^2). Example: h / b = 0.5 gives sigma = 0.2 (20 percent drag cut), h / b = 0.25 gives sigma = 0.5.
• The induced angle of attack falls by the same factor (1 - sigma), which raises the effective aspect ratio to AR / (1 - sigma) and the lift curve slope toward the 2D value a_inf.
• Lift at fixed angle of attack grows in ground effect; the lift-curve slope follows a_g = a_inf / (1 + a_inf * (1 - sigma) / (pi * AR)).
• Takeoff: reduced induced drag shortens the ground roll and eases initial climb; the wing lifts off at a lower angle of attack for a given speed. Landing: the ground cushion reduces sink rate and extends the flare, which pilots call float.
• The wing-in-ground-effect craft class exploits h / b below about 0.5 for cruise economy.

Workflow

1. Collect h, b, AR, C_L, and the flight condition.
2. Compute the height to span ratio h / b.
3. Compute sigma with ground_effect_factor and the drag ratio with induced_drag_ratio.
4. Apply the ratio to the free-air induced drag with induced_drag.
5. Correct the effective aspect ratio and the lift curve slope for the takeoff or landing estimate.
6. Flag the h / b band: below about 0.25 the reduction saturates, and the 2D limit applies.

Pitfalls

• Measuring h from the ground to the wrong wing reference; use the quarter-chord line or the wing aerodynamic center consistently.
• Using the span instead of the height to span ratio; the formulas are functions of h / b only in the image method.
• Forgetting the (1 - sigma) factor on the induced angle of attack when recomputing lift, which double counts the drag cut.
• Treating sigma as the drag ratio; sigma is the reduction, the ratio is 1 - sigma.
• Extrapolating the linear image method into h / b below about 0.1 where viscous and pressure effects dominate.
• Ignoring the float on landing: the reduced sink rate extends the flare and can push the touchdown point down the runway.
• Assuming the lift gain persists at the stall; ground effect does not raise C_L,max by the same factor as the linear lift.
• Applying ground effect corrections to the cruise condition; they are negligible above about 1.5 spans.

Behavior contract (gate 3)

The ground effect factor, drag ratio, image vortex offset, and lift curve slope logic is exercised by the gate 3 contract test: scripts/test_ground_effect.py against scripts/ground_effect_logic.py (stdlib unittest, offline). Run: python3 scripts/test_ground_effect.py

Compliance

• NACA Report 824 anchors the classic section data used for the free-air baseline; summary values only, per standards-map.yaml.
• The image vortex and ground effect formulas are common aerodynamic methodology, not reproduced text.
• compliance: STANDARDS-REF, gated: false.