Lift and thrust

Summary¶

A multirotor stays airborne by throwing air downward. Newton's third law requires an equal and opposite reaction force — upward thrust on the drone. The efficiency with which a propeller generates thrust depends on how much air it moves and how fast: it is always more efficient to accelerate a large mass of air slowly than a small mass quickly. This explains why larger propellers are more efficient for hover, and directly determines the choice of prop size for any given mission.

Concept¶

Newton's third law as the real explanation of lift¶

The common answer — "propellers generate lift" — is not wrong but skips the interesting part. The complete answer starts with Newton's third law: for every action there is an equal and opposite reaction. A spinning propeller accelerates a column of air downward. The reaction force — equal in magnitude, opposite in direction — acts on the propeller and on everything attached to it. That reaction force is thrust.

This reframe matters immediately. Thrust is not a mysterious aerodynamic property. It is a direct consequence of throwing mass in one direction and being pushed in the other. To produce more thrust: move more air, or move the same air faster.

Momentum theory and disk loading¶

The power required to produce a given thrust T from a propeller of disk area A in air of density ρ is:

P = T × sqrt(T / (2 × ρ × A))

The key relationship: for the same thrust T, doubling the disk area (which means approximately 1.41× the propeller diameter) reduces required power by approximately 30%. A large, slow propeller is always more efficient than a small, fast one at producing the same thrust — because the large propeller moves more air per unit time and imparts less kinetic energy to each parcel of air.

This single equation explains why: - Helicopters with large rotors are more efficient at hovering than jets - A 6-inch prop at 28,000 RPM outperforms a 3-inch prop at 60,000 RPM for any hover-dominant mission - Increasing propeller size improves flight time more than increasing battery capacity by an equivalent mass

Drones fall continuously — and continuously correct¶

A multirotor without motor power is aerodynamically inert. It falls. There are no wings, no glide path, no natural stability. Every moment of level flight is the result of active, continuous correction by the flight controller. What looks like hovering is a computer solving a control problem thousands of times per second, continuously adjusting motor speed to push the drone back toward the commanded attitude.

This reframe changes what "flying" means for a multirotor. You are not harnessing a natural force to maintain equilibrium, as in a glider or a sailboat. You are running an active correction loop against gravity, inertia, and wind simultaneously.

Reference¶

Induced velocity formula¶

v_induced = sqrt(T / (2 × ρ × A))

Where: - T = total thrust (N) - ρ = air density (1.225 kg/m³ at sea level, 15°C) - A = total rotor disk area (m²) = π × (D/2)² × number of rotors

For libdrone at 860 g AUW (8.44 N thrust), 4 × (152 mm / 2)² × π rotor area: v_induced ≈ 3.4 m/s downward — relevant for sensor mast height calculation. → See induced-velocity.

libdrone V2.4.6 thrust figures¶

Config	AUW	Peak thrust (4 motors)	Hover throttle	TWR
No payload	~807 g	~10,000 g	~28%	~12.4:1
+80g payload	~887 g	~10,000 g	~30%	~11.3:1

Motor: BrotherHobby Avenger V2 2507 1750KV on 6S, HQ 6×3×3 props. Peak thrust per motor: 2400–2600 g at 40–55A.

Procedure¶

Rationale¶

Why 6-inch props on a 330 mm wheelbase frame¶

The 6-inch prop diameter (152 mm) at 330 mm wheelbase gives a minimum 15 mm tip clearance. The momentum theory calculation shows that 6-inch props require significantly less power for hover than 4-inch or 5-inch props at the same AUW. The efficiency gain directly translates to longer flight time per battery charge. For a payload platform where hover-dominant missions are the norm, this efficiency benefit outweighs the mass and size penalty of the larger prop.