Inertia and stopping distance

Summary¶

A moving drone does not stop when the stick is released. It continues moving because of inertia — Newton's first law. To stop, the flight controller must pitch the drone backward, redirecting thrust against the direction of motion. This takes distance and time, and first-time pilots dramatically underestimate both. At 5 m/s, stopping takes approximately 2–3 metres at comfortable deceleration. GPS position hold manages inertia automatically but does not eliminate it — the drone still overshoots and settles. Flying smoothly means anticipating where the drone will be, not where it is.

Concept¶

Newton's first law in practice¶

An object in motion stays in motion unless acted upon by an external force. For a drone moving forward at 5 m/s, the kinetic energy is:

KE = ½ × m × v² = ½ × 0.86 × 5² = 10.75 J

That energy must be removed by doing work against something. Aerodynamic drag does some work — but at 5 m/s, drag on a drone-sized object is small. The primary braking force is the thrust vector reversed: pitch the nose up to redirect thrust backward.

Stopping distance calculation¶

To decelerate from 5 m/s at 0.5g (comfortable, ~5 m/s²):

stopping_distance = v² / (2 × a) = 25 / (2 × 5) = 2.5 m stopping_time = v / a = 5 / 5 = 1 s

At 1g deceleration (aggressive, ~10 m/s²): stopping_distance = 25 / (2 × 10) = 1.25 m stopping_time = 0.5 s

At 10 m/s (fast forward flight): stopping_distance (0.5g) = 100 / 10 = 10 m

These distances apply in still air. In a headwind, deceleration is faster (drag assists). In a tailwind, it is slower (drag and thrust both needed).

The overshoot problem¶

When the flight controller pitches the drone back to decelerate, the drone tilts. The pendulum effect then creates a restoring torque trying to return the drone to level. The flight controller is commanding nose-up while the pendulum is pulling toward level. If the PID D-term is insufficient, the drone overshoots the commanded position, corrects, overshoots again — oscillation at the pendulum frequency.

In GPS position hold, the flight controller manages this automatically: it detects the drone moving past the commanded position and applies braking pitch in advance. But the drone still overshoots slightly, decelerates, and settles. The physics cannot be eliminated by software — it can only be managed.

Smooth flying technique¶

A smooth pilot anticipates where the drone will be, not where it is. Key habits:

• Apply corrections early. A correction applied 1 second before the drone reaches a position requires less extreme pitch and produces less overshoot than a correction applied at the position.
• Reduce speed before obstacles. The stopping distance at 5 m/s is 2.5 m. At 10 m/s it is 10 m. Do not approach obstacles at speed unless there is 10+ m of stopping room.
• Use position-hold mode to stop. In GPS-assisted modes, releasing the stick commands the drone to hold its current position. The flight controller handles the braking. In acro mode, there is no automatic braking.
• Read the OSD speed readout. Knowing the actual ground speed numerically calibrates the pilot's sense of stopping distance.

Reference¶

Stopping distances at common speeds¶

Libdrone V2.4.6 AUW: ~860–900 g. Aerodynamic drag at these speeds is 1–5 N (small relative to thrust). The stopping forces are dominated by the thrust vector reversal, not drag.

Inertia in wind¶

In a 5 m/s headwind, the drone moving forward at 5 m/s ground speed has 0 m/s airspeed. Drag is zero. Stopping from ground motion relies entirely on thrust reversal — wind provides no assistance. In a tailwind, the drone moving at 5 m/s ground speed has 10 m/s airspeed. Drag now helps braking. In cross- winds, stopping in one direction while drifting in another requires the pilot to manage two axes simultaneously.

Procedure¶

Rationale¶

Why this article focuses on physics, not technique¶

The operational flying technique (how to approach a landing zone, how to stop for a survey waypoint) belongs in piloting-operations. This article exists to give the numbers behind those techniques — so that a pilot following the technique knows why it specifies the distances it does, and can adapt intelligently when conditions change. A pilot who memorises "stop 3 metres before the obstacle" is fragile; a pilot who knows stopping distance scales with v² can adapt to any speed.

Connections¶

requires: - lift-and-thrust - hover-and-forward-flight related: - pendulum-stability - vortex-ring-state - moment-of-inertia leads_to: - piloting-operations