# Non-dimensionalization

In assessing rotor performance and the ability to compare calculations or different rotors, non­dimensional quantities are useful. The induced velocity is normalized using the rotor tip speed, VT. The velocity varies along the entire rotor blade but the tip speed is the defining value. In fixed-wing terms this problem does not arise, since the entire wing sees the same velocity. This defines the non-dimensional induced velocity thus: [3]

rotor blade tips (in hover) and the area is the total disc area. A fixed wing uses the planform area which in a helicopter rotor would be the planform area of the blades. While this will be used later, with momentum theory the blades are not considered, so the overall rotor disc area is appropriate. The thrust coefficient is then defined by:

The inclusion of the half in the denominator is consistent with the lift coefficient definition for a fixed-wing aircraft. However, the inclusion of the half is not universal. The reader is urged to always check the definition of the thrust coefficient if they are consulting any technical documentation. An error here is both annoying and potentially very serious. Combining (2.8), (2.10), (2.11) gives the following non-dimensional equation:

1 — 2 v/CT

Ct — 41?

The induced power coefficient is also normalized – noting the inclusion of an extra velocity (tip speed) in the denominator to balance the units:

Combining (2.9)-(2.13) gives:

CPi — Ct •1