HORIZONTAL FLIGHT: IMPROVED THEORETICAL ESTIMATES
When blade element theory was applied to axial flight, it proved useful in identifying the profile power required. Unfortunately, the theory failed to capture the complexities of the real situation requiring both theoretical and empirical adjustments. Likewise the relationships so far developed for horizontal flight can be modified to account for:
• Spanwise flow;
• Reversed flow;
• Non-uniform inflow;
• Blade stall and drag divergence.
2.9.1 Spanwise flow
The method of accounting for the hub force generated by the asymmetry of drag around the azimuth (introducing d. D sin ^) fails to consider the flow of air along the blade, the so-called spanwise flow. This omission becomes clear if one considers a blade aligned with the longitudinal axis of the helicopter and situated over its nose. Here the freestream flow is along the blade from tip to root. Although the drag associated with this flow will generate a hub force the sin ^ term fails to account for it since sin 180° = 0. The practice of replacing the factor 3 with a larger empirical value k in Equation (2.15) rectifies this omission. Studies have suggested that appropriate values lie between 4.5 and 4.7 [2.13 and 2.14].
Fig. 2.14 Variation of angle of attack across rotor disk.