Chapter 2

Rotor in Vertical Flight: Momentum Theory and Wake Analysis

We begin examining rotor aerodynamics by building models based on momentum transfer – see Glauert [1]. This allows the essential performance of the rotor to be assessed. The most straightforward flight condition is hover, which provides the first part.

2.1 Momentum Theory for Hover

The simplest method that describes the lifting rotor is actuator disc theory. It is based on achieving a lifting force by generating a change of momentum. It assumes the existence of a streamtube which is an axially symmetric surface passing through the rotor disc perimeter which isolates the flow though the rotor. The air is assumed to be incompressible and therefore the flow past any cross-section of the streamtube is constant (Figure 2.1). This also means that because the flow is one dimensional, the flow must remain in the same direction, which for most flight conditions is appropriate. However, this does give rise to a failing of the theoretical model under certain flight conditions.

Figure 2.1 Inflow through rotor in hover


The flow enters the streamtube, is accelerated through the rotor disc and then is exhausted from the bottom of the streamtube. Far upstream of the disc, the vertical flow velocity must tend to zero making the streamtube cross-section infinite in size. However, the streamtube establishes itself and passes through ...

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