Rotorcraft Hover Ground Effect

Rotorcraft Hover in Ground Effect (flight-mechanics/performance/rotorcraft-hover-ground-effect)

Use when you must compute the hover-in-ground-effect performance of a rotorcraft rotor hovering over a flat ground plane: the induced-power reduction from the rotor height above the ground and the rotor radius, the IGE induced power, the IGE total hover power, the power margin against an available power, and the largest rotor height at which the rotorcraft can hover with that power. This leaf fills the rotorcraft gap in the library: the out-of-ground-effect hover sibling (flight-mechanics/performance/rotorcraft-hover-performance) explicitly defers hover in ground effect, and the ground-effect leaf in the aerodynamics family covers the fixed-wing wing-in-ground-effect configuration, a different physical problem with different outputs. The rotor model here applies the classic Cheeseman-style height correction to the induced power only; profile power is unchanged in ground effect. No recirculation, no partial ground contact, no vertical climb and no forward flight: those belong to sibling leaves.

Domain quick reference

All quantities are SI. Rotor thrust equals the rotorcraft weight in hover: T = m * g0, g0 = 9.80665 m/s^2.

• Disk area: A = PI * R^2.
• Ideal induced velocity (momentum theory, uniform inflow): v_h = sqrt(T / (2 * rho * A)).
• Ideal induced power: P_ideal = T * v_h.
• Profile power (average section drag model): P_profile = (1/8) * rho * sigma * Cd0 * A * Vtip^3, with sigma the rotor solidity, Cd0 the mean blade drag coefficient and Vtip the tip speed. The profile power does not change in ground effect.
• Ground-effect factor (Cheeseman-style height correction on the induced velocity, and therefore on the induced power at constant thrust): k_ige = 1 - (R / (4z))^2, with z the rotor height above the ground. Valid for z / R >= 0.5; below that the point model diverges. At z = R the factor is 0.9375; at z = 0.5R it is exactly 0.75; it increases toward 1 as the rotor climbs.
• IGE induced power: P_i_ige = P_ideal * k_ige.
• IGE total hover power: P_total_ige = k * P_ideal * k_ige + P_profile, with k the induced power factor (default 1.15, same convention as the hover sibling).
• OGE total hover power: P_total_oge = k * P_ideal + P_profile. If the available power covers P_total_oge the rotorcraft can hover at any height; otherwise ground effect sets a hover ceiling.
• Power margin: margin = P_available - P_total_ige.
• Maximum hover height: the largest z (z / R >= 0.5) where P_total_ige equals the available power. The IGE total power grows with z and asymptotes to the OGE value, so the root is unique; the logic bisects z over [0.5R, 50R].
• Default density rho = 1.225 kg/m^3 is sea level; pass the density at the chosen altitude to re-evaluate the check there.
• FAR 29 frames the rotorcraft certification context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the operating point: rotor radius R, rotorcraft mass m, height z above the ground, density rho, solidity sigma, mean blade drag coefficient Cd0, tip speed Vtip, induced power factor k and the available power.
2. Get the disk area with disk_area(radius) and the thrust T = m * G0 (hover thrust equals weight).
3. Compute the ideal induced velocity with hover_induced_velocity(thrust, area, rho) and the ideal induced power P_ideal = thrust * v_h.
4. Compute the ground-effect factor with ground_effect_factor(height, radius); it raises ValueError when z / R falls below the 0.5 floor.
5. Combine with ige_induced_power(P_ideal, factor) and ige_total_power(P_ideal, profile_power, factor, k) for the IGE power terms, and with oge_total_power(P_ideal, profile_power, k) for the OGE reference. The profile power input comes from the same section drag model used by the hover sibling.
6. Compare against the available power with power_margin(available, required).
7. If the available power is below the OGE total, find the IGE hover ceiling with max_hover_height(weight_kg, radius, available_power, ...); it returns None when OGE hover is possible and raises ValueError when the power is too low even in full ground effect.
8. For a one-call verdict run hover_ground_effect(weight_kg, radius, height, ...), which returns the full result dict and propagates every ValueError from the primitives.
9. Confirm the deterministic checks with the contract test scripts/test_rotorcraft_hover_ground_effect.py.

Worked example

A helicopter at 2200 kg mass with a 5.0 m radius rotor at sea level, hovering at z = 5.0 m (z / R = 1.0): rho = 1.225 kg/m^3, solidity 0.08, Cd0 = 0.012, tip speed 220 m/s, k = 1.15. Running hover_ground_effect(2200.0, 5.0, 5.0, available_power = 360000.0):

• Thrust: 2200 * 9.80665 = 21574.63 N.
• Disk area: PI * 5.0^2 = 78.54 m^2.
• Hover induced velocity: v_h = 10.589 m/s (hand estimate about 10.6 m/s, within the 9.5-11.5 m/s band).
• Ideal induced power: 228448 W (within 200000-260000 W).
• Profile power: 122935 W (within 100000-150000 W).
• Ground-effect factor: k_ige = 0.9375 at z / R = 1.0 (within 0.90-0.97); 0.9844 at z / R = 2.0 and exactly 0.75 at z / R = 0.5.
• IGE induced power: 214170 W, the ideal power times the factor.
• IGE total power: 1.15 * 228448 * 0.9375 + 122935 = 369230 W (within 350000-390000 W).
• OGE total power: 1.15 * 228448 + 122935 = 385650 W (within 350000-430000 W), the ceiling the IGE curve approaches as z grows.
• Power margin at 360000 W available: 360000 - 369230 = -9230 W, so the rotorcraft cannot hover at z = 5.0 m with 360 kW.
• Maximum hover height at 360000 W: max_hover_height returns 4.000 m (within 3.0-5.0 m): the rotorcraft can hover in ground effect only below about 4 m with that power.
• At 400000 W available (above the 385650 W OGE total) max_hover_height returns None: hover is possible at any height.

Verification

• Confirm ground_effect_factor(5.0, 5.0) equals 0.9375 exactly and ground_effect_factor(2.5, 5.0) equals 0.75 exactly (z / R = 0.5).
• Confirm ige_induced_power equals the ideal power times the factor and ige_total_power equals k * P_ideal * factor + P_profile for the same inputs.
• Confirm the factor increases toward 1 as the height grows, and that the IGE total power is always below the OGE total for a factor under 1, recovering it exactly at factor 1.
• Confirm max_hover_height returns about 4.0 m at 360 kW, returns None at and above the OGE total power, and rejects available powers below the IGE total at the lowest valid height.
• Confirm the bisected ceiling is a true root: the IGE total power at the returned height equals the available power to within 1 W.
• Confirm determinism: repeated runs return identical floats (no RNG, stdlib only, no external imports).
• Confirm every non-positive radius, thrust, density, solidity, drag coefficient, tip speed and induced power factor, every negative power, every factor outside (0, 1], and every z / R below 0.5 raises ValueError.
• Run the contract test offline: python3 scripts/test_rotorcraft_hover_ground_effect.py (32 tests, deterministic).

Pitfalls

• Calling the ground-effect factor below the validity floor: the Cheeseman-style point model diverges for z/R < 0.5 and ground_effect_factor raises ValueError there; z/R = 0.5 is exactly 0.75 and z/R = 1 is 0.9375.
• Reading max_hover_height None as an error: None means the available power covers the OGE total, so the rotorcraft can hover at any height; a ValueError (not None) is raised only when the power is too low even in full ground effect.
• Applying the factor to profile power: ground effect modifies the induced power only; P_profile is unchanged, and the IGE total is kP_idealfactor
  • P_profile.
• Treating the IGE ceiling as exact without the root check: the returned height is a bisection root where IGE total power equals the available power to within 1 W; verify that equality before quoting the hover ceiling.
• Factor outside (0, 1] or non-positive radius, thrust, density, solidity, drag coefficient, tip speed or induced power factor raises ValueError.

Related leaves

• flight-mechanics/performance/rotorcraft-hover-performance: the out-of-ground-effect hover sibling (momentum-theory induced velocity, ideal and profile power, total power with the induced power factor) that this leaf extends into ground effect. Its body defers hover in ground effect here.
• aerodynamics/ground-effects/ground-effect: the fixed-wing wing-in-ground-effect leaf (induced drag and lift change for a wing from height to span ratio and image vortices), a different physical configuration with different outputs. This leaf owns the rotor-disk hover-in-ground-effect induced-power reduction only.
• flight-mechanics/performance/rotorcraft-forward-flight-performance: the sibling rotor leaf for the speed-dependent power breakdown used after the hover check.
• flight-mechanics/performance/rotorcraft-vertical-climb-performance: the rotorcraft vertical climb sibling, adjacent to the hover power check in a rotorcraft performance pass.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_rotorcraft_hover_ground_effect.py

The test covers the worked example with the spec magnitude bounds (induced velocity 9.5-11.5 m/s, ideal power 200000-260000 W, profile power 100000-150000 W, IGE total 350000-390000 W, OGE total 350000-430000 W, ceiling 3.0-5.0 m), the exact factor anchors (0.9375 at z / R = 1, 0.75 at z / R = 0.5, 0.984375 at z / R = 2), the Cheeseman closed form and its monotonicity, the induced-power-factor model and its default constant, the OGE-IGE ordering and unit-factor recovery, the ceiling root consistency and None return above the OGE total, the convenience dict exact keys and primitive consistency, run-to-run determinism, absence of random or third-party imports, and ValueError rejection of every non-physical input in the validation list.

Compliance

• Standards referenced, not reproduced: FAR 29 (rotorcraft airworthiness, certification context only). The Cheeseman-style ground-effect relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.