Rotor & Propeller — ForgeCalc

Hover Performance — Actuator Disk

Ideal momentum theory for a hovering rotor/propeller, corrected by figure of merit. Supports multi-rotor craft (e.g. quad/hex drones). Thrust set directly or from vehicle mass.

Thrust input mode

Total thrust required T (N)

Number of rotors N

Rotor radius r (m)

Air density ρ (kg/m³)

Figure of merit

Rotor speed (RPM)

Temperature T (K)

Formulas & rules of thumb

Per rotor (thrust T_r = T/N, disk area A = πr²): induced velocity v_i = √(T_r/2ρA); slipstream v_e = 2v_i.

Disk loading DL = T_r/A · ideal hover power P_ideal = T_r·v_i = T_r^{3/2}/√(2ρA) · actual P = P_ideal/FM.

Power loading PL = T/P (N/W) — higher is more efficient. Lower disk loading → lower induced power → more efficient hover.

Tip speed V_tip = (RPM·2π/60)·r; tip Mach = V_tip/a, a = √(γRT). Keep tip Mach below ≈0.7 to avoid compressibility losses. FM typically 0.6–0.75.

Built from the vault Aerodynamics deep dive (§8 Rotor Aerodynamics). Ideal momentum theory + figure of merit — see also the Aerodynamics page for wing lift/drag and the Compressible Flow & Nozzle page.