Propeller Static Thrust (Actuator Disk Theory)
Propeller Static Thrust (Actuator Disk Theory)
Actuator disk theory models a propeller (or rotor) as an infinitely thin disk that accelerates the air passing through it, and applying simple momentum and energy conservation across that disk yields a compact formula for static thrust — the thrust produced with no forward airspeed, exactly the condition at the start of a takeoff roll or for a hovering rotor. This idealized model neglects real losses from blade tip vortices, non-uniform inflow, and profile drag on the blades, so real propellers produce somewhat less thrust than actuator disk theory predicts for the same induced velocity — the theory is best used for quick sizing estimates rather than final performance predictions.
Static thrust from actuator disk theory is F = 2*rho*A*vi^2. where rho_a2 is air density, A_disk is the propeller disk area, and v_i is the induced velocity through the disk.
Inputs
rho_a2 := 1.225 kg/m^3=1.23 kg/m^3
A_disk := 3.14 m^2=3.14 m^2
v_i := 8 m/s=8 m/s
Thrust equals twice the mass flow rate through the disk (rho*A*vi) times the induced velocity, a direct result of applying momentum and energy conservation together across the actuator disk.
F_prop := 2·rho_a2·A_disk·v_i^2=492.35 N
Results
A static thrust of a few hundred newtons here is a reasonable order of magnitude for a small general-aviation-sized propeller at this disk area and induced velocity. Because thrust grows with disk area but only requires induced velocity squared, a larger-diameter propeller spinning more slowly can produce the same thrust more efficiently than a smaller, faster one — the fundamental reason large, slow-turning propellers are favored for efficient low-speed flight and drones.
Assumptions & limitations
- Actuator disk (ideal momentum) theory — neglects blade tip losses and non-uniform inflow.
- Static condition only (zero forward airspeed); in-flight thrust would differ with forward speed.
- Incompressible flow assumed at these induced velocities.
- Real propeller efficiency losses (profile drag, swirl) are not included.