New Development of Classical Actuator Disk Model for Propellers at Incidence

The actuator disk model thrust formula was mathematically expanded in series and divided into two parts to show that propellers at incidence comprise an axial and a wing lift equivalent component. Both components share a common induced speed w. This is done by considering an enhanced disk area for momentum balance, to match Glauert’s hypothesis mass flowrate. To shed light on the theoretical developments, wind tunnel tests were conducted on a two-bladed propeller at angles of incidence ranging from 0 to 90 deg. The wing component is shown to increase with airflow velocity and angle of incidence. The axial component decreases with V, for all angles. The generally observed thrust increase with angle of incidence is explained, by the theory, to be mostly due to the wing component contribution. The theory also explains why at angles of incidence above 60 deg propellers inherently behave differently than at lower angles. While thrust decreases with V at lower angles, it grows with airspeed at an angle of incidence of approximately 60 deg or higher. This behavioral inversion happens as the wing component positive sensitivity to V overcomes the negative sensitivity of the axial component. A simplified formula is presented for predicting thrust at a given angle, based only on propellers data at an angle of incidence of 0, regardless of blade geometry.