Rotor in Vertical Flight: Blade Element Theory

Rotor in Vertical Flight: Blade Element Theory

Basic method

Blade element theory is basically the application of the standard process of aerofoil theory to the rotating blade.A typical aerodynamic strip is shown in Fig. 3.1 and the appropriate notation for a typical strip is shown in Fig. 3.2. Although in reality flexible, the blade is assumed throughout to be rigid, justification for this lying in the fact that at normal rotation speeds the outward centrifugal force is the largest force acting on a blade and in effect is sufficient to hold the blade in rigid form. In vertical flight, including hover, the main complication is the need to integrate the elementary forces along the blade span. Offsetting this, useful simplification occurs because the blade incidence and induced flow angles are normally small enough to allow small-angle approximations to be made. Fig. 3.3 is a plan view of the rotor disc, viewed from above. Blade rotation is anticlockwise (the normal system in Western-world countries) with angular velocity W.The blade radius is R,the tip speed therefore being WR, alternatively written as Vt. An elementary blade section is taken at radius y, of chord length c and spanwise width dy. Forces on the blade section are shown in Fig. 3.4. The flow seen by the section has velocity components Wy in the disc plane and (vi + Vc) perpendicular to it. The resultant of these is The blade pitch angle, determined by the pilot’s collective control setting (see Chapter 4), is q. The angle between the flow direction and the plane of rotation, known as the inflow angle is f, given by