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The propeller is modelled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. This disc creates a flow around the propeller. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the propeller, torque and induced velocity.
The Earth showing its axis and plane of rotation, both inclined relative to the plane and perpendicular of Earth's orbit. Another example is the Earth's rotation. The axis of rotation is the line joining the North Pole and South Pole and the plane of rotation is the plane through the equator between the Northern and Southern Hemispheres.
An actuator disk accelerating a fluid flow from right to left. In fluid dynamics, momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor, by W.J.M. Rankine (1865), [1] Alfred George Greenhill (1888) and Robert Edmund Froude (1889).
Consider the element at radius r, shown in Fig. 1, which has the infinitesimal length dr and the width b. The motion of the element in an aircraft propeller in flight is along a helical path determined by the forward velocity V of the aircraft and the tangential velocity 2πrn of the element in the plane of the propeller disc, where n represents the revolutions per unit time.
Feathered propeller on the outboard TP400 turboprop of an Airbus A400M. On most variable-pitch propellers, the blades can be rotated parallel to the airflow to stop rotation of the propeller and reduce drag when the engine fails or is deliberately shut down. This is called feathering, a term borrowed from rowing. On single-engined aircraft ...
Betz (1921) provided an approximate correction to momentum "Rankine–Froude actuator-disk" theory [4] to account for the sudden rotation imparted to the flow by the actuator disk (NACA TN 83, "The Theory of the Screw Propeller" and NACA TM 491, "Propeller Problems"). In blade element momentum theory, angular momentum is included in the model ...
A propeller with fixed speed would help. Heavy damping of the pitch rotation or a large rotational ... The yaw plane translational equation, as in the pitch plane ...
The propeller is modelled as an infinitely thin disc, inducing a constant velocity along the axis of rotation and creating a flow around the propeller. A screw turning through a solid will have zero "slip"; but as a propeller screw operates in a fluid (either air or water), there will be some losses.