Hover and forward flight

Summary¶

Hovering requires total thrust to equal weight. Forward flight requires the drone to pitch forward, redirecting part of the thrust vector horizontally — which simultaneously reduces the vertical component and requires more throttle to maintain altitude. There is a counterintuitive consequence: a heavier drone requires less pitch angle than a lighter drone to achieve the same horizontal speed, because its larger thrust magnitude provides more horizontal force per degree of tilt. Maximum speed is limited by the geometry of how much vertical thrust remains after tilting far enough to produce the required horizontal force.

Concept¶

Hover: equilibrium of forces¶

For level hover, the sum of all forces acting on the drone must be zero. Vertically: total motor thrust upward = weight downward. Horizontally: in still air, no net horizontal force, so motors need no horizontal component. Each motor runs at equal speed, producing equal thrust, and the frame is perfectly level.

Hover throttle — the percentage of total throttle required to maintain altitude — directly reveals the thrust-to-weight ratio:

hover_throttle ≈ 1 / TWR

For libdrone at TWR ≈ 12.4:1 bare: hover_throttle ≈ 1 / 12.4 ≈ 8% of maximum thrust → This equals approximately 28% of throttle input (since throttle is not linearly mapped to thrust at low values in Betaflight's thrust linearisation).

High TWR means more throttle headroom above hover — more authority for rapid altitude changes and wind gusts.

Forward flight: the tilted thrust vector¶

To accelerate forward, the flight controller pitches the drone nose-down. The total thrust vector, previously pointing straight up, now tilts forward. The thrust has two components: - Vertical component: T × cos(θ) — supports weight - Horizontal component: T × sin(θ) — accelerates the drone forward

As pitch angle θ increases, the vertical component decreases. To maintain altitude, total thrust T must increase to compensate — the motors must work harder just to stay at the same height while also producing forward force.

At constant forward speed, horizontal thrust equals aerodynamic drag:

T × sin(θ) = Drag

Maximum forward speed¶

There is a maximum pitch angle beyond which the vertical component of thrust can no longer support the drone's weight even at full throttle:

T_max × cos(θ_max) = Weight θ_max = arccos(Weight / T_max)

For libdrone bare (807 g, T_max ≈ 10,000 g): θ_max = arccos(807/10000) ≈ 85° — nearly horizontal, not the limiting factor.

The practical speed limit is reached earlier: the aerodynamic drag grows with the square of speed, requiring greater pitch angle to overcome it. At some speed, the pitch angle needed to overcome drag also requires throttle above 100%. That is the actual maximum speed.

The pitch paradox¶

Counterintuitive conclusion: a heavier drone requires less pitch angle than a lighter drone to achieve the same forward speed.

The reason: a heavier drone must generate more total thrust T to support its weight in hover. In forward flight at angle θ, its horizontal force component is T × sin(θ) — larger for the same angle θ because T is larger. To generate enough horizontal force to overcome drag at a given speed, the heavier drone needs a shallower angle.

The lighter drone, with its smaller T, must pitch more steeply to generate the same horizontal force component. At extreme pitch angles, the lighter drone is actually less efficient in forward flight despite its lower AUW.

Note: this does not mean heavier drones are faster overall. Their higher drag at the same speed ultimately limits them. But the relationship between weight and pitch angle is not the simple inverse that intuition suggests.

Reference¶

Force balance equations¶

Hover: T = mg

Forward flight at constant speed and altitude: T_vertical = T × cos(θ) = mg (altitude maintained) T_horizontal = T × sin(θ) = Drag (constant speed)

Required total thrust in forward flight: T = mg / cos(θ)

For θ = 30°: T = mg / cos(30°) = mg / 0.866 = 1.155 × mg → 15.5% more thrust required than hover to maintain altitude at 30° pitch.

libdrone V2.4.6 hover figures¶

Hover throttle changes with battery voltage — higher at the end of a flight as voltage drops. Monitor voltage in OSD.

Procedure¶

Rationale¶

Why hover throttle is a useful build quality indicator¶

After maiden flight, hover throttle should match the calculated value from the TWR estimate. If hover throttle is significantly higher than expected, either the AUW is higher than estimated (check with scale) or the motors are not producing their rated thrust (check for mechanical damage, incorrect motor direction, wrong prop). If lower, the AUW estimate was pessimistic. Hover throttle is the first post-maiden sanity check.

Connections¶

requires: - lift-and-thrust - six-degrees-of-freedom related: - pendulum-stability - angular-momentum-multirotors - induced-velocity leads_to: - induced-velocity - vortex-ring-state - inertia-and-stopping