The helicopter rotor produces an upward thrust by driving a column of air downwards through the rotor plane. A relationship between the thrust produced and the velocity communicated to the air can be obtained by the application of Newtonian mechanics – the laws of conservation of mass,
momentum and energy – to the overall process. This approach is commonly referred to as the momentum theory for helicopters.It corresponds essentially to the theory set out by Glauert1 for aircraft propellers, based on earlier work by Rankine and Froude for marine propellers. The rotor is conceived as an ‘actuator disc’, across which there is a sudden increase of pressure, uniformly spread. In hover the column of air passing through the disc is a clearly defined streamtube above and below the disc: outside this streamtube the air is undisturbed. No rotation is imparted to the flow.
The situation is illustrated in Figs 2.1a–2.1c. As air is sucked into the disc from above, the pressure falls. An increase of pressure Dp occurs at the disc, after which the pressure falls again in the outflow, eventually arriving back at the initial or atmospheric level p•. Velocity in the streamtube increases from zero at ‘upstream infinity’ to a value vi at the disc and continues to increase as pressure falls in the outflow, reaching a value v• at ‘downstream infinity’. Continuity of mass flow in the streamtube requires that the velocity is continuous through the disc. Energy conservation, in the form of Bernoulli’s equation, can be applied separately to the flows before and after the disc. Using the assumption of incompressible flow, we have in the inflow:
momentum and energy – to the overall process. This approach is commonly referred to as the momentum theory for helicopters.It corresponds essentially to the theory set out by Glauert1 for aircraft propellers, based on earlier work by Rankine and Froude for marine propellers. The rotor is conceived as an ‘actuator disc’, across which there is a sudden increase of pressure, uniformly spread. In hover the column of air passing through the disc is a clearly defined streamtube above and below the disc: outside this streamtube the air is undisturbed. No rotation is imparted to the flow.
The situation is illustrated in Figs 2.1a–2.1c. As air is sucked into the disc from above, the pressure falls. An increase of pressure Dp occurs at the disc, after which the pressure falls again in the outflow, eventually arriving back at the initial or atmospheric level p•. Velocity in the streamtube increases from zero at ‘upstream infinity’ to a value vi at the disc and continues to increase as pressure falls in the outflow, reaching a value v• at ‘downstream infinity’. Continuity of mass flow in the streamtube requires that the velocity is continuous through the disc. Energy conservation, in the form of Bernoulli’s equation, can be applied separately to the flows before and after the disc. Using the assumption of incompressible flow, we have in the inflow:
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