Induced velocity and sensor placement

Summary¶

When a propeller pushes air downward, it creates a recirculation zone around the drone — a toroidal vortex of disturbed, turbulent air that extends roughly one to 1.5 rotor radii above the propeller plane. Air inside this zone has already passed through the propellers. A sensor placed inside this zone does not measure the ambient environment — it measures air the drone itself disturbed. The sensor mast on libdrone is exactly as tall as it needs to be to position the sensor above this zone, and no taller.

Concept¶

The propeller's effect on surrounding air¶

A spinning propeller does not push a discrete parcel of air downward and leave everything else undisturbed. It induces a velocity field: air below the prop accelerates downward, air around the edges fans outward, and above the drone a pressure differential draws air inward and downward through the prop disk. The result is a continuous recirculation: air enters from above and the sides, passes through the prop disk, exits downward and outward below, then recirculates back up around the perimeter.

The recirculation region above the prop plane — where air is being drawn in toward the rotor — is turbulent and not representative of the ambient atmosphere. This is where instrument placement matters.

The toroidal vortex¶

The recirculation forms a toroid — a donut-shaped region centred on the drone, extending upward approximately one to 1.5 rotor radii (76–114 mm for a 6-inch prop) above the propeller plane. Inside this zone: - Air has already passed through the propellers - Air is turbulent and has elevated temperature from motor and ESC heat - Particulate matter, CO₂, and VOCs emitted by the motors are present - Humidity measured is influenced by prop wash, not ambient air

For a gas sensor, temperature sensor, or particulate matter sensor, measurement inside this zone produces data that is partly the ambient environment and partly an artefact of the drone itself. The fraction of drone artefact varies with throttle, wind speed, and flight manoeuvre.

Calculating sensor mast height¶

The minimum mast height to clear the recirculation zone is:

h_mast > 1.5 × R_rotor

Where R_rotor = rotor radius = prop diameter / 2.

For libdrone's 6-inch (152 mm diameter) props: R_rotor = 76 mm h_mast > 1.5 × 76 = 114 mm

The libdrone medium mast is 80 mm, the tall mast is 120 mm. For the SEN66 air quality payload, the tall mast (120 mm) clears the theoretical minimum. In practice, in hover conditions with the sensor above the prop arc, the Sensirion SEN66 on a 120 mm mast consistently produces readings consistent with ground-level reference measurements during field validation.

The induced velocity magnitude¶

The average induced velocity through the prop disk in hover:

v_induced = sqrt(T / (2 × ρ × A))

For libdrone at ~860 g AUW (8.44 N), 4 × 152mm props: A = 4 × π × (0.076)² ≈ 0.0727 m² v_induced = sqrt(8.44 / (2 × 1.225 × 0.0727)) ≈ 3.4 m/s downward

3.4 m/s downward flow through the prop disk. This flow is what recirculates upward around the perimeter. The recirculation velocity above the prop plane is lower than this — roughly 0.5–1.5 m/s — but sufficient to draw contaminated air into any sensor positioned below the toroidal vortex boundary.

Tradeoff: mast height vs CG and handling¶

A taller mast raises the payload mass higher, increasing the drone's CG. → See pendulum-stability for the quantitative effect.

At 40 g sensor payload on a 120 mm mast, the CG shift is approximately 5 mm upward. This shortens the effective pendulum arm, raises the natural oscillation frequency slightly, and requires marginal D-term reduction. For the SEN66 payload weight (approximately 20 g for the mast assembly), the effect is within noise. For heavier future payloads, the calculation should be repeated.

Reference¶

Mast heights and clearance¶

Note: the 1.5 × R threshold is theoretical. Real recirculation geometry depends on throttle level, wind, and flight manoeuvre. Field validation with a reference sensor at ground level is always the authoritative test for a new payload design.

Effect of forward flight¶

In forward flight, the drone moves through undisturbed air. The recirculation zone is swept behind the drone and the sensor is continuously encountering fresh ambient air. Sensor readings in forward flight are more representative of the ambient environment than in hover. For mapping missions, this means data quality improves when the drone maintains forward speed rather than hovering to take measurements.

Procedure¶

Rationale¶

Why the mast height is the minimum necessary and no more¶

Every additional millimetre of mast height: increases CG height (reduces pendulum stability), increases frontal area (increases drag), increases structural leverage on the GX12 connectors in a crash, and adds mass. The mast is sized to clear the recirculation zone — not to provide comfortable margin. If field validation shows the 120 mm mast still shows recirculation contamination at specific flight conditions, the next mast increment should be calibrated from measurement, not from an arbitrary safety factor.

Connections¶

requires: - lift-and-thrust related: - hover-and-forward-flight - vortex-ring-state - pendulum-stability leads_to: - vortex-ring-state