Froude's Propeller Theory

Propellers are a mechanism for the propulsion of an aeroplane. In its generic form a propeller is pair of rotating blades mounted on a shaft that houses the engine as well. As the engine operates the propeller turns sucking a large amount of air. As this air passes through the rotating blades, it gets energised, its speed increases. In the process the required Thrust to propel the aircraft is produced.

Figure 3.31: Froude analysis of a Propeller

 

The analysis we carry out follows William Froude (1810-1879). We consider the propeller as a thin disc rotating in air as shown in Fig.3.31. Let the pressure and velocity far away from the disc i.e., at section (1) be p₁ and V₁ respectively. The conditions just at (2) which is the front of the disc are p₂ and V₂. The disc imparts momentum and energy to the incoming air such that the pressure and velocity just behind the disc (3) are V₃ and p₃ respectively. At (4), far downstream the conditions are V₄ and p₄.

We assume that the air which is influenced by the disc is confined to a slipstream as shown.

Since the disc is thin and the area of cross section at (2) and (3) ar equal, we have

$$V_2~=~V_3$$ (3.100)

The pressures at (1) and (4) are equal to the freestream value.

We consider the control volume formed by slipstream and the ends (1) and (4) and write the momentum equation.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney